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GEOL6379-Applied Biostratigraphy - Friday 03/01/2024video1153812717
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00:00 Basic theory of very good. Uh basic theory of, of uh
00:09 And then some, some secondary theory the importance of this thing called a
00:15 temperature, which I'll get into in and in the middle of it
00:19 But the main thing to say about temperature, we're gonna talk about this
00:23 lot. So it's important that you a sense of what we're talking about
00:26 that because when we, when, you, when you date something,
00:30 you say this rock is a million old or 100 million years old,
00:35 you're doing is really telling what you , which when you date it,
00:39 matter what system you're dating, you're determining the last time that system say
00:46 in a Fels bar or lead in Zircon, whatever your system is you're
00:51 about, when were the last time system was at its closure temperature,
00:56 temperature at which the system becomes closed the clock starts ticking. It's important
01:02 recognize that sometimes the closure temperature can really, really low as low as
01:08 70 °C, which means that if rock is buried to say you got
01:14 sandstone, you bury that sandstone to kilometers. It's gonna start resetting some
01:23 these isotopic clocks uh which can be useful for learning about how deep this
01:28 was buried. Uh On the other , if you're not interested in how
01:32 it was buried, but when it deposited, you're gonna need a different
01:35 . You're gonna need one that's insensitive being buried down to 100 degrees.
01:40 So we'll start now with some, basics of radioactivity, we'll move into
01:47 some description of closure temperature and from , we'll move in and start talking
01:54 individual isotopic systems and their best geologic when we do and don't want to
02:01 them next week. No, I'm the end of this. Yeah,
02:06 did. You did don's part first you'll have a test not next
02:10 but the week after. Right. . OK. So today and tomorrow
02:15 gonna be going through the techniques depending how we do, depending on
02:18 what kind of interactions we have. will uh probably have next Friday.
02:24 be largely um discussing sort of case and examples and getting you guys to
02:30 of interact. And I'll give you now that we've done this, which
02:33 the best way to go. Um that'll be really a practice for the
02:38 . I will ask you questions about this situation. Uh What system is
02:43 appropriate for the answering this geologic OK. So we can start with
02:52 , right? We know that the age of rocks starts with the principle
02:56 superposition. That's nice. Um We even be able to go up to
03:01 rock like this and figure out that got the trilobites in it, which
03:05 it's paleozoic or dinosaurs in it, means it's mesozoic. Um But,
03:11 that was done, you know, time ago. But after a
03:14 somebody figured out that, you when the dinosaurs went extinct,
03:18 when did the dinosaurs go extinct? me later, after that, the
03:28 of the Cretaceous. But how many ago was that? 65?
03:33 it's now, now folks think is 66 how do we figure, where
03:38 that? 66 number come from? we had dinosaurs in this rock and
03:45 dinosaurs here. Somebody wants to say is 66 million years. How do
03:48 figure that out? Where does, does this notion? I mean,
03:52 got, you know, that you've the geologic column here. It
03:56 right? The geologic column has all names on here. What, how
04:02 we define Jurassic rocks? What makes rock? A Jurassic rock?
04:16 that actually can, I mean, me. Well, no, I
04:22 , a rock is the, I , the original definition of Jurassic rocks
04:25 rocks that have Jurassic fossils and that may sound circular, but it
04:31 isn't we've, we've de, we've that these are the fossils that are
04:35 and Don talked with you LA for last times about different bio stratigraphic uh
04:41 of various fossils. This one's useful this and this one's useful for
04:44 So, Jurassic fossils, Jurassic rocks the rocks that have Jurassic fossils in
04:49 . And we pretty much agreed what Jurassic fossils are and that ain't gonna
04:54 . That's a Jurassic fossil that But, but these numbers are actually
04:59 to change and we'll talk about let's, uh, I don't
05:03 we'll get to that in a Well, actually, we can go
05:06 so we can, we can you know, I said Jurassic,
05:11 do, let's do Cambrian and pre again, Cambrian rocks are rocks with
05:14 fossils in it and that's gonna be . We're not gonna, we're not
05:18 later on say that's not, that's Cambrian. No, we're never gonna
05:21 that because Cambrian fossils have been agreed . They are, they look
05:25 There's something that we're gonna draw a there, that's not the same
05:29 Um So that's a paleontological definition. not gonna mess with that, but
05:36 want to know and that's gonna be same, whatever, whatever Strat interval
05:40 choose the legacy needs to also paleontological determined and that's not gonna change.
05:47 But how many years ago is That's a concern, right? Because
05:53 , I mean, it's, it's that fossils help us this way.
05:56 if we're gonna answer some geologic we have to know how fast things
05:59 happen. Um A mentor of mine I learned a lot about geo chronology
06:04 was, was famous for saying, dates, there are no rates you
06:08 to figure out what rate of geologic you're talking about. You got how
06:12 years are involved? The fact that in this particular Ammonite zone doesn't really
06:17 you that it tells you that it's below the next Amoy zone. But
06:20 we know how many years ago, one of those were, we're not
06:23 about rates will not be able to , well, you know, anthropogenic
06:27 change is faster than any time in , in the past. Well,
06:30 you have numbers, you can't say like that. When did, how
06:34 did something, how, how fast this extinction event happen? Well,
06:38 this Ammonite zone and that Amy zone tell you at the time. So
06:42 are we gonna figure out the Well, this, this just shows
06:46 that the, the nature of of these time of these, of
06:50 answers has changed over time. here's just the last, the ESC
06:56 are, you know, we've, shown ECL my, just the last
07:01 million years on this diver and what have along the, the,
07:05 the way here is different publications and about when these uh periods were
07:13 And remember these numbers haven't changed because changes in our understanding of the
07:18 But back in 1937 somebody said that boundary between the EFC and the legacy
07:24 down here at 50 48 million Well, in 1961 somebody said what
07:29 is more like 36 and then it around until now it's at about 3033
07:36 something. All of these have moved . Um Some, a lot more
07:40 that when I was an undergraduate many years ago, I was told
07:45 the precambrian Cambrian boundary was 570 million ago. And that was the best
07:50 could do at the time. now we have a pretty good idea
07:52 it's about 542 plus divis one. why do these things change? Two
07:59 happen? Is that well, we're gonna, these numbers, all
08:03 these numbers, all of, you , where, where we put these
08:07 is based on some sort of isotopic of ages. Um And so we're
08:13 do that and, and let's uh , so let's go through some
08:19 How help me help me out what are ways in which we could
08:24 isotopic methods to these sedimentary rocks to their age and, and be give
08:33 as much latitude as possible. Imagine outcrop, imagine a technique, imagine
08:37 rock. What would be helpful to the age of this thing beyond
08:42 it's got Cambrian fossils in it. . The co, the content,
08:56 fossil fossil that, that fossils don't us how many years ago it
09:01 Fossils will tell us that it's we already know that. Go to
09:06 boundary and use an isotopic measurement to what the age of the boundaries are
09:12 boundary. Um, that's, you're on the right track there.
09:16 come I can't see? Oh, don't have your thing on? Uh
09:20 . Yeah, there you are. . Hello Taylor. Um You're absolutely
09:25 . So, but, but but saying going to the boundary is
09:28 little bit complicated because these are sedimentary . It's difficult to date a sedimentary
09:33 . Let me just let me just ahead here and say, here's one
09:36 we could use by going to the . As Taylor suggests, we could
09:40 a cross cutting relationship if we had rock that cross cut this, this
09:46 paling to logical boundary. And I say it's an IOUs, an igneous
09:51 . We can date that igneous rock some precision and suppose we dated that
09:56 . What would it tell us about , uh about the age of the
10:02 significant transition? We've got an age that red rock there. What does
10:07 tell us about what we're really interested ? Yeah, the, the,
10:14 paleontological interesting transition has to be older whatever we dated in this exam.
10:21 that's great. It's older than now it came, if it came to
10:24 that we were looking at the Cambrian boundary and we looked at a dike
10:28 they gave us 50 million years. , then we're stuck with saying the
10:32 is older than 50 million. Uh , you know, maybe somebody else
10:37 gonna find another one and another one another one and you get better.
10:41 That's a good way. But, as I say, you know,
10:43 might have a dike that's way much and doesn't tell you all that
10:47 Um What about dating individual minerals say, a sandstone, we could
10:54 a bunch of these minerals. What that tell us? And this is
11:00 we'll talk a lot about tomorrow is dating of detrital minerals and how
11:04 tells us something about provenance, but tells us about, about uh uh
11:09 histories of basins. It's a very deal and, and you can also
11:12 us, you can also use this to tell us about the age of
11:15 sediment, but it has a, has a similar limitation as the one
11:19 just described. What's the limitation here I date some of these grains?
11:24 , what does that tell us about age of the sedimentary rock in which
11:27 are obtained? Yes. Mhm. , yeah, of course, of
11:42 . But just, just as we only know the context in this
11:46 But what, what did you say time? We, we, we
11:50 us again what the, what this us? Thank you. The dike
11:55 younger. So the, the, , the Cambrian rocks have to be
11:58 than the, the rock we What about in this case?
12:05 you can't deposit something until it So we date these grains and we
12:11 that the sedimentary deposit must be younger that. If we were to date
12:16 whole bunch of them, say 100 500 grains out of a sandstone.
12:21 that, that can be done relatively these days. With the technology we
12:25 popping off a couple 100 grains is a big deal. Let's say we
12:29 200 grains in this context to determine age of this sediment, which one
12:35 those 200 grains is gonna be the important to us. The youngest.
12:47 . The, the youngest one, all those older ones, we're gonna
12:52 repeat the same information we learned. we look at 200 grains and we
12:57 attention to the youngest one. The must be younger than that still.
13:01 right. So that's so, so we had a, a detrital date
13:05 then a cross cutting dike. We're in, we're narrowing in, we
13:08 do both at the same time, ? Um The third way, the
13:13 way is to do this is to lucky and find some volcanic rocks that
13:19 like that. And I, I to say that the best way to
13:24 a sedimentary rock is to date an rock that's easier said than done.
13:30 course, because you have to find outcrop of this sort where you have
13:34 , a volcanic rock above and The thing you're interested in if you
13:39 find. And, and the reason , is this is so much,
13:42 best way is because the, the , the dating and the interpretation of
13:48 date you get from a volcanic rock usually very straightforward. If you're trying
13:53 date, if you're trying to, date other rocks that are plutonic rocks
13:56 may have slow cooling involved, that things. And we'll talk a lot
14:00 why the rate of cooling will complicate issue depending on which system we
14:05 But no matter what isotopic system we're , um a volcanic rock should basically
14:11 the same answer doesn't really matter because rocks go from very hot to very
14:15 , very fast. We understand the this volcanic rock was erupted in a
14:22 or in a week or something like , right? Whereas sedimentary rocks could
14:25 thousands of years to accumulate a similarly uh deposit. So we can interpret
14:31 , we understand what it is. so that's the best way an even
14:35 way would be this, right, you find our, our interbedded volcanic
14:40 are right smack at top and And this is why we know that
14:44 Cambrian precambrian boundary is 542 plus or one because they really found one of
14:49 places in Namibia. There's the precambrian boundary. There's a rite under
14:54 There's a rite up here. yeah, we got it. That's
14:58 best way because ry lights can be , they can be dated unambiguously.
15:03 what we wanna do. That's my . That's why the boundaries keep
15:08 Well, there's two reasons these boundaries changing is that people keep finding better
15:13 . And there's also is that, know, this, this,
15:16 this, this history goes back to when the technology wasn't as good.
15:21 know, when you couldn't carry a in your pocket that also made c
15:26 telephone calls. Um The advancement of machines that make these measurements has allowed
15:32 to uh to look at different kinds samples, smaller samples, greater
15:37 all the, all the machines are so that this is involved. This
15:40 a measurement. Um And so the gets better all the time every 10
15:45 , somebody comes out with an even mass spectrometer that's gonna do even better
15:49 smaller samples and finer and older and . Um But none of that's any
15:54 unless you have one of these. ? And so over the years
15:58 and this is, this is kind tricky too because imagine what do you
16:02 to find this outcrop? You need understand that this is the palely interesting
16:06 and you further need to recognize that a real life that we can do
16:11 sometime and, and this place in that I'm familiar with was actually the
16:16 thought they had some, some volcanic . So they got the geologist to
16:20 into the field with them and find rock. You know, they,
16:22 have 11 group of people who understands fossils, one group of people who's
16:26 so much with the fossils, but the other stuff. So that eventually
16:32 . And so that's how we can numbers to the Strat democratic column,
16:36 was originally based on fossils. We're gonna change uh when the Jurassic
16:41 but all the time we might be the numbers. Although it's gonna probably
16:45 , if we're doing it well, , the, the, the changes
16:49 , as we progress are gonna get and smaller, we're gonna eventually start
16:53 that that's the time I remember it have been 1010 or 12 years
16:57 Now I went to a GS A and there was a symposium that was
17:02 about the, um, all about , the age of the, where
17:08 it? It was the age of , yeah, the Jurassic Triassic boundary
17:14 they were, you know, they fiddling around whether it was 2,
17:17 or 2, 13 and that sort thing. Um, and so now
17:22 , it's some number that's getting smaller smaller used to be. It was
17:25 210 plus or minus 20 now it's to 212 plus or minus a
17:30 I should say that in general um, when we date rocks,
17:37 is something you should keep in mind we're, as we're thinking about
17:41 um, for simple dating for like a rite. Um The, the
17:48 is such that we ought to be to date that rock to within half
17:52 percent. The uncertainty should be half percent or better. That means if
17:56 100 million years old should be 100 or minus 0.5 that's entirely normal.
18:02 special anymore. Used to be, know, 40 years ago. If
18:06 told somebody you dated something to plus minus a half, they would,
18:09 know. Oh, yeah, you do that. But nowadays, if
18:12 , you know, if you say plus or minus one, you
18:15 the geologists in the crowd are gonna why so bad? What went
18:21 Uh That's how good things are Half a million, half a percent
18:25 , is not special at all. some cases, it can get down
18:28 1/10 of a percent. Uh And , you know, and that's part
18:32 the, the, the, the improvement of the technology as this
18:35 better and better as we can The difference between signal and noise better
18:40 our machines. We can start resolving and smaller things. And so now
18:44 can start talking about, you what was, what was the rate
18:47 evolution of something that only took six 7 million years? If you
18:51 if you can't, if you uh, if you can't,
18:55 date something to within plus or minus , you're never gonna resolve something that
18:59 took a million years. But if can resolve it to plus or minus
19:03 you can start talking about million year that occurred 300 million years ago.
19:11 All right. So of course, of this is based on the regular
19:14 decay of some chemical elements. And we'll mention, as I've, as
19:19 hinted to, and as we'll mention geo chronology, as we'll discuss quite
19:24 bit in these lectures is also capable providing information about the thermal history of
19:30 samples, not just when they were , but what was their thermal
19:34 When were they at certain temperatures? that's because as I mentioned, many
19:38 these systems are sensitive to heating you heat them up a little bit
19:43 the, the clock that we are will be reset, we start over
19:47 that's a function of temperature. And good news is is that we have
19:51 different clocks that have many different So we can understand whether or not
19:56 rock was heated to only 70 degrees maybe it was 100 and 50
20:00 maybe it was 400 degrees, we tell the difference by looking at these
20:04 systems. Um And so this can be applied to all sorts of
20:10 These are the two things that, I've applied it mostly to.
20:15 is, you can understand, the age and uplift of, of
20:19 of mountain belts because as rocks are uplifted, they're being cooled off.
20:23 so as they hit certain certain you can sort that out. Um
20:28 you can understand the history of basins well or just the Strat democratic uh
20:33 of basins. So we'll return to soon. But I'm gonna talk a
20:38 bit of physics now to remind us of some stuff that we probably already
20:42 . Um when we're gonna talk about radioactivity, we gotta remember that uh
20:47 are made up of electrons, protons neutrons. Um We talk about the
20:53 characteristics of an, of an atom largely determined by the number of
21:00 Carbon. Is that thing with six . Uranium is that thing with 92
21:06 , but they have neutrons coming along the ride. Um And so we
21:11 talk about the total number of neutrons protons as the atomic weight. And
21:15 what it means when we talk about 12 or carbon 14 or uranium
21:20 That's the total. And it's important , because we keep track of the
21:27 because some isotopes are radioactive and some are not radioactive even in the same
21:32 . For example, carbon 14 and 12, carbon 12 is six protons
21:37 six neutrons. Not radioactive. Carbon is six protons, eight neutrons.
21:42 is radioactive. Um Other examples on slide include um uranium 238 and uranium
21:50 . Both radioactive, different different rates decay, but they're both radioactive
21:56 We'll talk a little bit about that a little in a little while two
22:00 of strontium. There are four isotopes strontium that we'll talk about. 42
22:04 them are just mentioned here. All of the isotopes of strontium are
22:09 They're not, they're not changing just carbon 12 is not changed.
22:13 one difference is is that strontium 87 the daughter product. It is the
22:19 by the decay of rubidium 87. , whereas carbon eight or carbon 12
22:24 Stron 86 are not changing the amount strontium 87 in the world or in
22:30 sample is increasing if you have some in that sample. So we say
22:35 say that such an element, we that an element like uranium 2388 is
22:40 . An element like Stron 87 is , it is produced by the decay
22:44 something else. So I use some these terms already, we talk about
22:50 radioactive elements. We say they are parents and they decay to something we
22:55 the daughters. The daughters may themselves unstable. Sometimes you decay to something
23:01 is unstable, which decays to something decays to something and eventually that decays
23:06 something that is stable. Um, the case of uranium and uh and
23:11 heavier than lead, uh, we to decay down to lead, lead
23:15 the last thing on the periodic table always stable, everything higher than that
23:20 gonna be radioactive. And so all uranium atoms, all they uranium and
23:25 , which we use as chronometers, decay down to lead, but over
23:31 or seven or eight steps. the key thing is that the rate
23:36 which this decay occurs is constant and . And this is actually a bit
23:41 a strictly speaking, I shouldn't say rate is constant, but I'll get
23:45 that in a minute. But if know how it decays and we can
23:49 the amount P present of the parent the daughter, then we can calculate
23:54 age. That's all there is to . So I'll go into the mathematics
23:58 that in a minute. Uh But that, let's just talk about the
24:03 that we have actually uh uh that happened, there are several kinds
24:08 decay and the type of decay does relate to the rate of decay.
24:13 can have some things that decay really by alpha decay and some things really
24:17 . So that's, that's not a . Um One way in which something
24:23 decay, there are two different kinds beta decay, one called beta minus
24:27 which we basically transform a neutron into proton and an electron. And so
24:35 changing one of the things in the to another thing in the nucleus,
24:40 total number doesn't change. So in case, we have potassium 40 it's
24:45 into calcium, 40. Kept the didn't change. But, but we
24:50 it calcium now because it has uh protons. And by the way,
24:55 me, I guess I didn't talk , I didn't talk about this nomenclature
24:59 shown here. This is how we write um isotopes fully. You write
25:04 K for potassium, right? And 40 up here tells us how many
25:10 neutrons and protons. This 19 down is actually superfluous because potassium is already
25:17 thing we have defined as the thing 19 protons. So you don't have
25:21 put that in there. But it's because you don't have to remember which
25:24 is. Potassium is at 19, at 17. Um It also helps
25:28 you're doing a diagram like this where can see look what happened. The
25:31 became 20 but the 40 say So what happened? We took a
25:36 turned it into a proton and now call it calcium. So it is
25:40 new element. It's chemically different now it's got more protons. It also
25:45 off some energy and an electron and other stuff. The energy here is
25:50 . We'll get to the Q means . Um uh It's just a silly
25:55 . It doesn't really help. Um decay or beta positive decay is the
26:01 . We transform a proton into a . And so here we've gone from
26:05 , 18 to oxygen, 18, is nine, oxygen is eight.
26:10 same concept uh that last one is geo geo geologically useful one. This
26:16 not so much. Um There's also uh a thing called electron capture and
26:24 can decrease um the to the, number of protons without changing the mass
26:32 taking an electron from one of the shells and creating a neutron from a
26:39 , you take an electron or they fuse together, they become a
26:43 . So that's a, that's a that happens uh in potassium argon,
26:48 talk about that later. And then , alpha decay. And this is
26:53 example where we do change the total of, of uh the uh
26:57 the, the, the atomic number the thing uranium 238 will decay to
27:04 234. And then what's given off is what's called an alpha particle or
27:09 helium nucleus. Four pro it's got massive four, it's got a protons
27:15 two. So that means two protons two neutrons are tossed out. Um
27:20 here's where we actually lose mass. the other case, it all goes
27:24 inside the probe in the nucleus. here we're tossing things out.
27:28 it turns out, as I thorium 234 is itself unstable. It'll
27:32 to something else. But this is , the first decay on the
27:36 something else. When we say uranium decays, we sometimes skip this stuff
27:41 the middle and say uranium 238 decays lead 206 because usually because all the
27:47 in the middle here happens pretty We can kind of ignore it,
27:51 strictly speaking, there are, there steps along the way. Uh but
27:56 not gonna worry about all those steps it just to define ALPH, here's
28:01 example of alpha decay in which we have to worry about steps because it
28:04 finishes after one. So 147 decays Nemi 143 plus uh helium. So
28:14 are different ways in which we can . Um We're gonna discuss examples of
28:19 of these uh but how it decays not hugely important for what we're going
28:23 worry about. Um one other uh that's uh gonna be important um because
28:32 ha it happens in nature, but gonna have, we're gonna pay more
28:35 to when it happens artificially. And is something called the NP reaction.
28:40 NP reaction is when you take energetic and throw them into a nucleus and
28:45 knock out a proton NP means N in P goes out. And this
28:50 to this is how carbon 14 is . Carbon 14 is produced from the
28:56 in the air nitrogen's up here And, and a cosmic ray just
29:00 and hit one of those nitrogen atoms that, that cosmic ray had a
29:04 going fast enough, hit that nucleus out a proton. It's not nitrogen
29:10 . It's carbon now. And because carbon with eight protons and 686 protons
29:16 eight neutrons, it's unstable. It decay. Uh It actually decays right
29:21 to nitrogen, but that's another Um But that nt reaction is another
29:26 in which we can make something This will come into play because we
29:31 going to do this in the lab on to produce something argon 39 which
29:37 important for um improving the potassium argon system. But we'll, we'll probably
29:43 about that tomorrow morning. Um OK. One more way that that
29:49 can decay is by something called spontaneous in which a large nuclide like uranium
29:58 will on occasion not just toss off uh a helium atom but will actually
30:04 into two pieces that are about the size. Here. We've got an
30:08 here is uranium 238 decays to me give me 143 inch at night.
30:14 not always the same two things. this is just an example of things
30:18 can happen and this is important and we'll talk about this tomorrow and
30:25 is one of the most, one the thermal history methods that has the
30:31 uh history of application in the oil is fishing track dating. It's called
30:36 fishing track. When you make, , when this fishing in occurs,
30:40 got some uranium in your crystal and fishing occurs. And these two guys
30:44 really big, right? They toss , they, they're actually shot out
30:47 this place with some energy and they so big that they shoot through the
30:51 of the crystal and create a damage in that crystal. Why is that
30:56 ? Because if you heat that crystal a little bit that damage zone goes
31:01 and the heating, the temperature at that damaged gun goes away is about
31:06 °C, which if you're interested in oil business is an excellent temperature to
31:10 worried about. That's the temperature at we start making oil, right?
31:14 , um we'll talk more about that but fish and fish and track
31:19 You've ever heard of fishing trap Good? No, that's fine.
31:23 it's a big deal, especially for thermal histories of basins because it has
31:28 a low closure temperature. This damage in a crystal and you can look
31:34 it in a microscope. See that's , that thing there was produced when
31:37 fission broke down, when the fission and, and, and, and
31:41 this crystal and you can look at , you can measure it. It's
31:43 tiny little thing about 14 for about microns long, this this thing.
31:48 you're looking at it at a high but you can, you can find
31:52 . And uh what's very cool about is from the geological perspective is if
31:57 crystal say that was, say that was in a ry light, it's
32:02 forms and it starts occasionally efficient if were to erode that rhyolite on
32:08 Uh oh the, the, let just say the, the crystal
32:11 this is most commonly associated with is mineral appetite. Appetite has a lot
32:16 uranium and it's very susceptible to this . Appetite gets eroded from your uh
32:21 your rhyolite or your granite and gets into your sandstone. If that,
32:27 you're interested in knowing has that sandstone been buried deep enough to make
32:33 Well, one thing you can do look at those, look at those
32:37 in your sandstone and have they been ? You, you might pay,
32:41 might have a good idea of when sandstone was deposited. This is a
32:45 sandstone. If that is an oil , then some of those appetites are
32:52 have ages when we did them in lab, they're gonna be younger than
32:56 . They're in a Miocene rock. know that's a Miocene rock from
32:59 from the, from the uh But if that, if that's been
33:04 into the oil window, the appetites gonna start over, they're gonna have
33:08 younger than the deficit. Um, said that already. Ok.
33:18 oh, and this is another important . This is great news for
33:21 Geologists, radioactive decay is independent of or pressure. We don't have to
33:26 about things being uh uh decaying faster slower as they are buried down deep
33:32 the earth. That's not a That's great news because otherwise that would
33:36 a huge complication. Um Now, I said, we know the,
33:41 rate of decay is constant and that's a mistake. But because, because
33:47 in fact, impossible to predict when given nucleus will decay. If we
33:52 a uh that the uranium atom sitting on the table, there's nothing about
33:58 atom that says it sticks into However, we know that if we
34:03 to line up a million of we would, we'd have, we'd
34:07 that what percentage of them would decay the next time period, next
34:12 they all have this same probability. over time people behave like that,
34:17 it's a bit like it's a bit if we had, I used to
34:20 this experiment or demonstration in physical I do this demonstration when I'd have
34:27 big 100 person class. But you 100 person class and you also need
34:31 with coins in their pocket, which happen anymore. But if you
34:34 we all had, if we all coins in our pocket, we could
34:38 a coin. Right? And if in this room here, there's only
34:42 of us here. We flipped the . We'd expect to get four
34:45 right? What if we went um, what if we went to
34:50 Cougars basketball game on Saturday? And asked everybody to flip a coin.
34:55 many heads are we expecting to There was about 7000 people at the
35:00 game. So there'll be about 3500 . So there's, but there's
35:05 there's that the, the fact that got so many more heads in that
35:08 example, doesn't say anything about The quarters are different just that there
35:12 more of them. But so in the example of flipping a
35:18 we know that the probability is one . In the case of a,
35:22 uranium item, the probability is one of 10 billion in the next
35:27 OK. So that's what doesn't Um And so we can, we
35:32 , we can uh describe that mathematically the probability of decay in some small
35:37 interval. DT is gonna be DT where LAMBDA is this uh proportionality
35:44 for different things, you know, use a different lambda for,
35:48 for different, for uranium or potassium whatever. Um, and so the
35:54 at which these things happen, whether the eight of us here flipping the
35:58 or 7000 people in, in the stadium or maybe we wait a few
36:03 , we go to an Astros There'll be 40,000 people, you flip
36:07 coin, there'll be 20,000 heads the and, and then we're gonna call
36:11 a decay. So the rate of is proportional to the amount of parent
36:16 right here. We only got the Astros game, we're gonna get
36:21 . It's all the same stuff. just get more when we have
36:23 So we can write that mathematically as rate of change, the NDT is
36:30 to N right number. We have to time. It's gonna be some
36:36 next to N. And we can that poor proportionality as an equation.
36:40 we toss in this decay constant, lambda, which is going to be
36:44 us something about the probability of a event. If that was a,
36:49 was a, a quarter being this lander would be 0.5. If
36:53 was, you know, for it's gonna be a number of like
36:55 to the minus 10. But it's some number that is uh specific to
37:00 system we're interested in whether it's uranium or flipping quarters or whatever.
37:06 this equation then is something that this the beginning of our ability to tell
37:10 is knowing that the rate of decay proportional to the number we have.
37:15 can rearrange and integrate that equation. we can, we can see that
37:19 can just write that as the natural , the, the, the negative
37:23 the natural log of the number we is is is equal to the,
37:29 proportionality content. Uh the decay constant time. This is what we're
37:34 right? Plus some, some, constant of integration. Um However,
37:42 we take, if we make an here and we take the amount of
37:46 present at the beginning at times if we say that's N zero,
37:52 we can evaluate the constant of, integration and that equals minus log of
37:58 zero. So we can substitute that in. And now we've got the
38:02 a log of N equals N the T times minus log of N
38:07 You can rearrange all that. Do , all the rules of logs do
38:14 and put these, put, put side of the equation race to the
38:17 , you get the ratio of what have today. And the number you
38:22 with N zero is equal from E the minus lambda T. So that's
38:29 . We can measure, we measure in the lab and that's something we
38:34 in the lab. Lambda. We know this already because we've done other
38:38 to tell us what that is. so, gosh, all we need
38:41 know is how many we started That's not something we could measure the
38:46 . So what's the, you that, that, that, that
38:49 , that seems great in theory. how are we gonna use this?
38:53 , we can carry on a little further, we can substitute and we
38:56 , we can, we can uh that equation for either N or N
39:02 . And, and if we do , if we, if we then
39:05 say that now we're gonna involve the , we know that the number of
39:11 , the number of daughters star means . The number of daughters that were
39:16 by radioactive K, it's gonna be to the number of parents that we
39:21 with. Subtracting away from the number parents that we have right.
39:26 This is assuming that this is a system and all we do is we
39:30 a parent, it transforms into a . So, and, and plus
39:34 is always gonna equal and not. now we've got an expression in which
39:40 , which we can get rid of not and not. It's not something
39:43 can know, but we can know is the daughters. We can measure
39:48 in the lab. So we substitute back in here. And now we
39:51 an equation and substitute all this And now this is it this is
39:55 thing at the bottom here is called age equation in which we say that
39:59 number of daughters is equal to the of daughter we started with.
40:05 excuse me, I, I skipped . I'm gonna go down here.
40:09 , the number of the number of JIC daughters is equal to the number
40:14 parents. We have times Z and minus one. However, um,
40:21 we assume there were no daughters at beginning, then, um, we
40:29 , uh, get rid of T here and do it this way,
40:34 get D equals D, not plus either and the t much one.
40:38 you look at that and you still got a problem there,
40:41 Because we're still being asked, we measure this, we measure the number
40:46 , of parents, we have that is something we measure in the
40:49 D, the number of daughters, can measure that in the lab.
40:52 again, we've just substituted N not DNO. How's that? How's that
40:56 ? Well, we're actually, gonna find a way but this is
41:00 equation D equals D not plus nd lada T. Before we, before
41:06 fix this problem, we will fix problem straight away. I wanna make
41:11 we understand this concept of half And so we've talked about this
41:17 The half life is something that's The rate of decay is something that's
41:22 because the half life is defined as , the time required for half of
41:29 we have to decay away. And at team one half a after we've
41:37 through one half life, the number daughters and the number of parents should
41:41 exactly, exactly the same because that's have these now, please.
41:49 I'll do it this way. Ok. Thank you. Thank
41:52 Um, so the number of daughters parents should be equal when you um
41:59 you've been through one half life. if we plug in one half life
42:03 T, we can say that D N are the same. So we'll
42:07 put in N here twice and we then rearrange that and we can say
42:11 the half life is then gonna be natural log of two divided by the
42:17 the decay constant or 0.63 0.69 divided the decay constant. We can graphically
42:24 this uh this here. We have uh on the y axis. We
42:28 the proportion of atoms left if you with one. And then we just
42:33 this over time. After one half , we're gonna have half of what
42:36 had. After two, half we're gonna be down to a
42:39 three, half lifes, down to eighth and so forth. And so
42:41 see that this is why I said the rate of decay isn't constant.
42:47 the, what is constant is how it takes to drop by half.
42:50 the half life that doesn't change, is related to this probability,
42:55 in, in whether you're flipping a or you're, you know what's,
43:00 , another physical? Oh, excuse , I'm gonna sneeze. Or maybe
43:04 won't, let's find out. Um, you can flip a quarter
43:09 you can roll one of those, know, Dungeon and dragons 20 sided
43:12 . Right. It's the same idea that in one case, you,
43:15 get, you get the thing half time. In the other case,
43:19 get 1/20 of a time. Uh the case of uranium, it's like
43:24 a billion sided die. You it doesn't happen very often. But
43:27 you have a, if you have trillion of these things in your,
43:29 your, in your zircon, you're them all the time you're having decay
43:34 . Uh This described this, this also describes why it's not a good
43:40 to try and date something after it experienced more than about five half
43:47 Did you see what's happening to this ? The slope of this curve is
43:51 nice and flat here. The and we're gonna have to measure
43:56 this, this, this value here then bring it over to this thing
44:00 read down the, the age and see that as, as we get
44:04 to these really small numbers, any of uncertainty in that number is gonna
44:09 into a huge uncertainty in where it this purple curve. So it's not
44:13 useful to try and date something that's through more than about five half
44:17 Because when you make a measurement in lab, it's very hard to tell
44:21 it's gone through five half lives or half lives. It's just the,
44:24 slope is just so flat that this why we can date. This is
44:28 that carbon 14 dating is probably the system. You're most familiar with carbon
44:34 dating is you read about it in newspaper when they're trying to date
44:37 you know, some archaeological site, good for things that are hundreds to
44:41 few 1000 years old because it has half life of 5700 years. It's
44:48 for dating something more than about 20,000 . If you wanna date something that's
44:53 of years old, you have to something that have half lives that are
44:56 of years old. Um We can this graph as the decay of the
45:02 atoms in the same way as we draw the growth of the daughter
45:05 One is rising, the other is . The, the, the total
45:08 change. Um I said this already I'll skip that. Um So as
45:16 said, the uh some daughter products themselves radioactive, although everything eventually comes
45:22 something stable. So sometimes we can the stuff in the middle and just
45:26 straight to the final daughter product. an example of uranium 238 bunch of
45:31 decays, but it decays down to to a six. Ok. And
45:36 talk more in detail about this when get to uranium dating. OK.
45:43 , um one real big deal here that when it comes to radioactive
45:50 we have to be really strict uniform . Um you know, uniform.
45:57 is this idea that the president is key to the past. If we
46:00 know about today, we know about past, but we know that that's
46:03 strictly true because, you know, we, if we try to apply
46:07 is to all geologic events in the , we'd never say that the dinosaurs
46:11 killed by a meteor because a meteorite falling out of the sky this
46:16 The presence is now, but the experience is, is broader than
46:22 That can't be true for radioactivity. can't say that well, in the
46:26 , uh radioactivity was different. We to uh we have to say that
46:29 is some natural law like water always downhill and uranium always had this proportion
46:35 , of, of, of radioactive . And that's important. And so
46:40 are, you could say it's an that the half lives of the ra
46:43 isotopes are the same as today as were billions of years ago. It's
46:46 an assumption that's been borne out by . Uh One of the ways they
46:50 observe this is go to rocks from moon. The moon is an excellent
46:56 for this thing because the, the and the moon are old and they
47:02 also had this very simple history. What are, what's something that happens
47:08 earth that doesn't happen on the Excuse me, gravity happens on the
47:17 . There's, it's not as, know, but I mean, there's
47:20 gravity, thermal reset of the Well, that's, you're, you're
47:29 the right track there. But why there no thermal reset? I think
47:33 had something, plate tectonics, there's plate tectonics on the moon which would
47:37 to no tectonic burial and getting the reset. I mean, strictly
47:41 if you could drop something down into interior of the moon, it get
47:45 enough, but it doesn't happen because no plate tectonics. Stuff that sitting
47:48 the surface of the moon has been there for a very long time because
47:52 tectonics is over. Now, there's thing that's problematic for us here on
47:57 that doesn't happen on the moon, , it never rains on the
48:09 And this is a wonderful thing for samples, right? Because we don't
48:13 to worry if they've been altered in way. Um First thing you wanna
48:16 when you're doing a lot of geo is get a thin section. Look
48:19 your rock, see if it's you know, if it's been
48:22 then you have to worry about your been screwed up somehow. It's never
48:26 on any of these rocks in the . So we've got these basalts from
48:30 moon. They are old and they , they've never been buried, they've
48:34 been rained on, couldn't ask for better sample. And so these samples
48:38 been brought back and taken to places JSC down the road here and they've
48:42 dated by many different isotopic systems. if the, I if we,
48:49 we had gotten our estimates of the constant wrong or if we had gotten
48:54 right for today, but they had over time, we shouldn't get the
48:58 answer by, by, by doing these different systems, they should be
49:02 . But we, we can date of these rocks by sometimes up to
49:05 different independent systems. And these are that we would predict if we know
49:10 if we know the decay constant, of these answers should be the
49:14 They are the same. Um you know, maybe we'll find some
49:18 to doubt this sometime, but we that there's no major problem. And
49:23 these are the half lives of the we're gonna talk about. Mostly.
49:26 fact, there's only, well, are, these are some geologically interesting
49:30 lives and they vary by a factor 100. You see that the uh
49:34 235 decays to lead to a seven a half life of 700 million years
49:40 suma 147 decays to su to Excuse me, that's a mistake.
49:44 should be neodymium. 143. Uh change that later. Um This
49:52 um That's actually a mistake that should 143 that has a half life of
49:57 billion years. These are still useful us. Um However, most of
50:03 things we're gonna talk about involve the of potassium and uranium. These are
50:08 of illustrative but not used of But most geology can be understood by
50:13 decay of potassium and uranium. Potassium uranium are abundant enough in rocks and
50:19 to be useful. And they have half lives that range from 0.7 to
50:23 billion years, which means that they've around about the right amount of time
50:29 in excuse me, thorium um has half life of a 12 billion years
50:38 we'll talk about that yet. It didn't have room for thorium on this
50:41 . But it's a, it's a . It's got a 12,
50:43 it's 12 billion. So what we happens is the, and that should
50:49 that that shouldn't say rate of It should say probability of decay,
50:53 probability of decay over time hasn't changed it's isotope A B or AC just
51:00 a graph, whatever the probability is . Flip A coin, 50%.
51:04 , that coin was a 50% coin billion years ago. Um We know
51:09 didn't happen that if that, if been any sort of variation in the
51:13 of things, they didn't vary independently that these things are, are changing
51:17 again, this would show up in uh rocks from the moon or even
51:24 rocks here on earth rol lights from, you know, 20 million
51:28 ago, we date them by different to get the same answer. So
51:35 lots of ways then have been, been sorted out to try and understand
51:39 rocks in the age of the One of the, one of
51:43 one of the uh famous ways um um Lord Kelvin or William Thompson in
51:51 1870 published an an estimate for the of the earth. He said that
51:57 we know how big the earth We know how uh uh we know
52:02 big it is and we can estimate original temperature. He estimated the temperature
52:08 molten iron and, and by he went down into AAA coal mine
52:15 Wales and measured the temperature down one below the surface. And with that
52:20 , he was able to come up some stuff and say, well,
52:22 earth is this big, it started this hot, it's this thermal uh
52:27 geothermal gradient today. That means the is somewhere between 30 100 million years
52:33 . But the problem was is that didn't know about radioactivity. Um And
52:40 he didn't know about radio activity is you've noticed in all of these equations
52:43 I showed you this decays to this Q on the end there's energy.
52:48 And so Kelvin got the edge of earth way, way underdone because he
52:52 appreciate that the earth was cooling slower he imagined because it was making its
52:56 heat. Well, that's, you , you can redo his equations and
53:01 it out how the earth, how the earth is now by that
53:04 But the better way is to go and date rock straight away. And
53:09 the discovery of radioactivity about 100 and years ago by, you know,
53:14 folks you've probably heard of in physics Beal Kri Rutherford, it provided a
53:20 of heat to override this mistake that made in his calculations. But then
53:24 also provides the basis for any of quantitative estimates for ages and rocks.
53:29 is how we could say the dinosaurs extinct 66 million years ago or this
53:35 in Trinidad is, you know, million years old. Um I'm gonna
53:42 that, skip that. So, well, anyway, we know we
53:50 from looking at some rocks at the is the edge of the earth is
53:53 billion years. Um All right, questions about that little derivation should be
54:02 straightforward. We've got an age Um And with that, we
54:06 if we measure things in the we can figure out an age of
54:11 . And as I said, we this, this diagram here before
54:15 uh we know that, you we've, we've made changes in the
54:18 of important geologic boundaries over time because gotten better outcrops and better technology I
54:27 um I just know that you, I didn't say it, but it's
54:35 excellent question. Um In some we can me, it has been
54:41 directly. Um And, and, , and there was actually an experiment
54:45 was done to, to understand the of rubidium 87. They actually uh
54:52 refined a bottle of rubidium, you , this, they just got it
54:57 that this rubidium had, was just pure bottle of rubidium. And they
55:01 how much strontium was in there. little. But they, it's a
55:04 , big pile of rubidium and a , little bitty bit of contaminants of
55:08 . But they measured that and then put it on the shelf for 40
55:14 and then they measure it again and got more staunch in it than it
55:18 40 years ago. And that sounds of crude, but it worked.
55:23 the reason and they figure, and , they knew that the half
55:26 excuse me. And with this, can calculate the half life.
55:29 it turns out the half life was billion years. So you might
55:34 well, how are you gonna be to measure that tiny little change if
55:37 half life is 47 billion years? did we get anything in just 40
55:42 ? And the answer is because we a pound of rubidium here.
55:46 the number of decays is dependent on many we have. If you actually
55:51 a huge hunk of rubidium, a or a kilogram, I don't know
55:54 much they had, they had a that then even if the half life
55:59 billions of years, if you have kilogram of that stuff, that means
56:05 of these things are sitting there ready decay and in 40 years, a
56:10 million of them will decay and that's measurable thing. And so with
56:17 they got the half life of rubidium there. They start looking at geologic
56:23 that, that have every expectation that should get the same answer no matter
56:27 system we use. Usually volcanic If you know the half life of
56:32 system, you can date that rock that system and then you date the
56:35 , you date you, you do chemical analysis for another system and then
56:40 take the age as given from the one, you know, and calculate
56:43 half life that way. Did you that Taylor? OK. So that's
56:48 or less how it's done. A of them have been, have been
56:51 from first principles and then the rest them are basically relative to those
56:57 So that's a good question. That's . Um, you guys wanna take
57:05 brief break in an hour. we usually go till how late on
57:10 day? Five, right? And tomorrow we start at 830. Is
57:13 correct? All right. Let's uh, let's give my, my
57:18 to 10 minutes because we're at we're at a good stopping point
57:24 So we'll come back in 10 Ok. So we got an age
57:36 and, but to really have this , make any sense. We need
57:40 three things to be true. We've talked about the decayed constant thing.
57:45 that's already been sorted out. And we talk about rubidium strontium in the
57:51 section, we will address this question how many daughter products, how many
57:57 there are to begin with. In cases, we can geo chemically,
58:00 can say there aren't any daughters to with. Like potassium argon, the
58:05 potassium decay to argon. But because is a noble gas, it doesn't
58:10 parts of minerals. So we can pretty much sure that when we measure
58:15 , it was because of radioactive it wasn't that begin with. In
58:18 cases, it's more complicated than We'll get to that in a minute
58:22 in an hour. Uh But what gonna talk about. Next is this
58:27 of a closed system? Um, we mean by a closed system is
58:34 we have no loss or gain of or daughters except for in situ radioactive
58:41 right here in our rock or our , the parent decays to a
58:45 That's the only thing that happens and does. So, within the context
58:49 this system, we're talking about, , the system would be the mineral
58:55 gonna look at minerals. So this F bar or zircon or whatever it
59:02 . So when we talk about open behavior, the chief concern in these
59:07 is going to be the loss of daughters. Um Generally, don't worry
59:12 loss of parents. Um And that's because daughters were, were created an
59:19 , they were not a part of original mineral. And so when they
59:22 formed in there, um they may be happy in there. You
59:26 the like potassium decays to argon, is now in this mineral, but
59:30 not a part of the lattice, not there in any strong way.
59:37 now, of course, you can an open system in which you add
59:40 uranium. Uh But we're really, just gonna ignore that for the
59:44 we're gonna talk about open system as loss of daughter products. Um And
59:50 the loss of data products due to particular phenomenon called diffusion within the
59:56 Um And we'll talk about that in minute. But what this then means
60:01 that when we have a geo chronological , this spelt bar is 10 million
60:06 old. What that means then is was the last time the beds bar
60:12 at the temperature at which this system a closed system. Um Sometimes that's
60:21 . Sometimes there are geologic complications that have to keep in mind. But
60:25 we get into the geology, we'll about more of the physics. So
60:31 is defined as a thermally activated which means that it, the rate
60:36 as you increase the temperature. Um indeed, as we'll show in a
60:40 , it's not, it doesn't just a little bit, it increases exponentially
60:44 , the rate of something it has in the exponents, the,
60:48 the, the rate equals something times to the T. So, um
60:53 change temperature a little bit, the can change a whole lot. The
60:57 thing about diffusion is it's just totally . If, if, if uh
61:01 move jiggling around, it will jiggle a particular way, but that's,
61:06 randomly directed. Uh And so it look like, I mean,
61:11 it is the case that generally what have a system in which we
61:14 we, we have a diffusion situation which we move from high concentration to
61:19 concentration. That's not because the you know, the things that are
61:22 high concentration we're seeking out that area there. I mean, basically when
61:27 put, you know, you put in your iced tea, you
61:30 your sugar becomes after if you, you stir that sugar up, pretty
61:34 that tea that sh that tea is , the same sweet because random diffusion
61:40 made it. So uh what we in our situation is we have,
61:46 have an the iced tea. If take that analogy, the the sugar
61:50 get out of the glass. You , the, the thing that we're
61:53 at this thing that's diffusing it, only diffusions randomly within our system,
61:58 under the right conditions, it can right out. And I'm gonna illustrate
62:03 with a silly example. It's a , very uh crude example, but
62:08 hope it works out. Ok. And we're gonna imagine a hotel,
62:14 odd hotel that has 36 rooms, no hallways and on the, each
62:19 of these rooms has a door on four walls. Um And what we're
62:26 do is start in this ho this with one person in each room.
62:29 that's color coded here. Yellow means . And then we're gonna have each
62:34 of these people pick a random number they'll move north, south, east
62:38 west, depending on what they which is totally random. And the
62:43 are, if you move into another , you stay. But if you
62:46 to the outside of the hotel, gone and you can't come back
62:49 And this is, this is analogous what we think happens in diffusion and
62:53 . Once a daughter product diffuses it's now diffusing out there and it's
62:57 different story and it's not coming back . So we start this by,
63:02 know, just picking these random And now we have a situation here
63:06 we have several of the rooms on outside, have nobody in them because
63:11 all, all of these, all these rooms, you know, had
63:15 , the, the the random walk to walk outside. Uh Whereas in
63:20 ones in the middle actually got more in them because the, the random
63:23 pushed two people in the same But if we do this long
63:27 we will see that eventually we get situation in which we have a high
63:33 in the center and very little on outside. And of course, this
63:38 a ridiculously a coarse example with only rooms and five time steps. But
63:43 did this in Excel many years If you wanna do it fancier,
63:46 could figure out some sort of Python to make it beautiful, but it's
63:50 same concept. Um And we can look at this in terms of its
63:56 , but also in terms of its amount, you see, we started
63:59 with 36 then we move to 26 25 we get down to 21 and
64:04 is all because of just moving things randomly about. So that's diffusion,
64:11 thermally activated diffusion would just go faster it was hotter. So we
64:15 we could move from step zero to five, very fast if we were
64:19 a high temperature, very slowly, we were at low temperature. And
64:24 at, at high temperatures, things , you know, if, if
64:27 let this go a little bit further you know, to basically simulate at
64:31 temperature, we go through more time . We do this a few more
64:35 . You'll see that the hotel will empty out. And it's not hard
64:38 imagine. We do this a few times. It's just it, it
64:41 away. Um And that's the concept closure temperature. If you, if
64:46 turn the temperature up high enough, things are going out all the
64:50 Uh But if the temperature is very , you may, you know,
64:54 may the, the the the rate which you change rooms becomes essentially
64:59 And this is why, for we can hold a metamorphic rock in
65:02 hand, metamorphic rocks are formed down , right? They're not formed at
65:06 surface. You take a shale and put it down, it becomes a
65:10 , it's more it's stable down These minerals form, it's a
65:13 Why is it that a shift doesn't it shift comes back to the
65:16 it doesn't turn back into a It's because the, it's, it's
65:21 shifts are not stable here at the surface, they don't form at the
65:24 surface, but they can sit here the earth surface because the, the
65:28 at which they are transforming back to stable stuff is exponentially dependent on
65:34 And when you drop that temperature down surface temperature, you drop the rate
65:38 reaction literally trillions of times. So it's unhappy. And if you let
65:44 sit here for another 10 trillion it might turn back into a
65:48 So temperature is very important. So gonna put some formality to this so
65:55 we can really think about the con , the the things which govern uh
66:00 temperature, we wanna do that. so that we can, we need
66:04 have this formality so that when we talking about choosing samples and interpreting data
66:10 our geologic context, we know what some of the pitfalls and concerns.
66:15 so we're gonna start, we're gonna this thing called the diffusion equation.
66:19 from that, we will get the temperature equation. And we're gonna start
66:24 imagining this simple thing in which we a one dimensional rod which I've sort
66:29 shown a two dimensional rod, but this one dimensional rod in which energy
66:33 only travel in one direction. And is thermal energy is throwing flowing past
66:38 points A and B, we can that the total heat energy in the
66:44 between A and B is some integration this energy function between, you
66:49 integrate from A to B this function which is a function of distance and
66:55 . OK. Now, because we're gonna describe conservation of energy,
67:02 gonna say that the rate of change heat energy is equal to the heat
67:09 flowing across the boundaries per unit time whatever is generated inside this rod.
67:16 we can write that mathematically to say . Now we're talking about the rate
67:20 change. So that's this DTD over business, the rate of change of
67:25 thing. And this just be described the heat flowing across the boundaries.
67:30 the, the flux at A as function of time minus the flux at
67:36 as a function of time plus this Q which is our internal heat
67:42 Um So that's just taken that first and written it as this thing.
67:50 , if we, if we just a little simple fundamental theorem of calculus
67:56 , we can uh know that this is equal to the derivative of these
68:04 . And by, and we can that to say that now we have
68:07 the interval from A to B is to the, the change in energy
68:11 respect to distance plus the change in with respect to distance minus whatever is
68:19 generated inside relative to distance. the good news is, is that
68:25 up in there that that equation is possible if the integrand is itself
68:31 So we can get rid of all integration. And just say that
68:34 the change in energy with respect to is equal to the change in flux
68:38 respect to distance plus Q, there's minus sign in there just because of
68:43 , the way in which we're defining and B. Now we usually describe
68:50 by their temperature, not their thermal , which is what we were really
68:55 back there. So to convert into , we have to come up with
68:59 things called specific heat and density. that's pretty straightforward. Um We know
69:05 the ma the, the, the mass, excuse me,
69:08 the thermal diffusivity is then gonna be to the, the specific heat,
69:13 is a function of X times the , which is a function of X
69:16 the temperature, which is a function X and time. And so we
69:21 that back in there. Now, got this equation in which all we
69:24 all we have now is the specific and the density which we're just gonna
69:29 are actually constants. And we, we see that we've got an expression
69:34 has temperature time and the flux of energy. So we're getting, we're
69:38 somewhere. So now we get, we carry on, let's just consider
69:43 of these questions, how does heat flow? And by the way,
69:48 talking about heat energy. Now, of this stuff that we're talking
69:53 the mathematics and the philosophy of all this applies, whether we're talking
69:57 temperature or sugar in your iced tea argon in your F bar or lead
70:03 your zircon. It's all about Heat heat is just an easier thing
70:07 think of. You know, we can, we know heat radiating
70:10 a fire or an oven or a stove. But the same concept,
70:15 same ideas will be transported. When talk, we stop talking about heat
70:18 start talking about daughter products. This is easier to think about in terms
70:23 heat, but it's no different, concept. So let's just, you
70:27 , if some things we can say heat energy, we know for
70:32 that if the temperature is constant, no transfer of energy, we know
70:37 if there are temperature differences, the energy is gonna go from the hot
70:40 the cold. You pick up a , a hot pan, your hand
70:43 burned. Not the other way around greater the delta t, the greater
70:48 heat flow. That's why it's a hot pan. You'll notice immediately and
70:54 flow of heat energy will vary for materials. You pick up a hot
70:58 of wood or a hot piece of , the iron will scald, you
71:01 because it transfers heat better. So are things we can just easily say
71:06 the world. And we can transfer into a mathematical equation in which we
71:12 that the flux of something is gonna equal to the, the thermal,
71:19 flux of thermal energy. Uh excuse , the flux is the of thermal
71:24 and ka is the thermal conductivity and is the change of temperature with respect
71:30 distance. So, um now we've an equation that describes this stuff,
71:36 energy passing through our material. And we have to all, all we
71:40 basically say that this is all dependent this characteristic K dot Which is just
71:45 material property. Um So we that we, that, that we've
71:51 this to get F we can So we've got this equation up
71:57 That's not something we like to deal . Flux is flux is a thing
72:00 changing. But so we can substitute thing. We, we,
72:04 we, uh we, we drive F into here and if we
72:09 now, as I said, we're gonna assume that the, we're gonna
72:12 that we're dealing with one thing, iron or it's feldspar. So we're
72:16 gonna say that the specific heat and density are a function of distance.
72:20 are just a, a material Feldspar has this density. And so
72:25 we can rearrange those things and get of those guys. And and then
72:30 it finally to say that the, change in temperature with respect to time
72:37 equal to the second derivative temperature with to distance uh mediated by this deep
72:44 , which is the diffusivity, which just our, our thermal conductivity divided
72:49 our density and our, our uh specific heat. This is known as
72:57 second law, the diffusion equation. it's, it's fundamental and you can
73:02 that it's, it's, it's, pretty straightforward to go from just imagining
73:05 one dimensional rod and, and just a few things about heat. And
73:09 we've got this, this, this thing. So what's that good
73:13 ? 00 I should say that this assumes that the diffusivity is the
73:19 in all directions. Um But in meteorology, as well as
73:25 we don't have to assume that these are the same in one direction.
73:28 we can generalize this three dimensions. we can have a diffusivity in the
73:32 direction and Y direction we might wanna that. And as I said,
73:37 equation can, is just as valid the diffusion of mass or the concentration
73:43 mass as thermal energy. So that's nice about this is we derived it
73:47 thermal energy, but we're now we're apply it to things in our
73:55 Now, one more thing that's interesting helpful is that although d the diffusivity
74:01 expressed as a constant in this, this uh equation, it is itself
74:07 on temperature. And this is something pretty straightforward. We talked about earlier
74:11 the, that this these processes move if it's hotter. So, so
74:19 got a, we've got an expression that says the diffusivity is actually
74:23 I should do that. The diffusivity actually related to this D not,
74:28 is just basically the diffusivity at infinite . And then mediated by these things
74:33 the natural, natural ee is E big E is something called an activation
74:40 . R is the gas constant and is temperature. So this activation energy
74:45 a, again a, a function the material. It might be harder
74:49 diffuse through zircon than it is through , for example. Um And so
74:58 substitute this. So also what is and activation energy is the energy barrier
75:06 the reactants must overcome for a reaction proceed. Um If you have
75:12 if you had a car that was in gear, but on a flat
75:17 , you could get it going, could get it rolling. But the
75:20 , the more people in the the higher the activation energy you gotta
75:23 , you gotta really push it to it going. Once it rolls,
75:26 can roll. But the activation energy , of a big car is much
75:31 than the activation energy of sit of guy sitting on a bicycle, you
75:34 move that easier. So that's, the concept of activation energy. And
75:41 to show you the uh how, , how sensitive this is to,
75:45 temperature. I just gave you some that are not, they're good
75:51 It's not too important that we look a lot of the details. But
75:53 we just put in some numbers here diffusion of argon in feldspar, which
75:58 talk more about tomorrow. But just an example, if we pick a
76:01 of 29 kilocalories per mole and ad of five, those are just perfectly
76:06 numbers. But, and we just , let's start with a temperature of
76:10 and 50 degrees. We go through calculation, this calculation here and we
76:16 a, we get a value of at that temperature D is then a
76:19 of temperature D at 100 and 50 is five times seven minus 15 centimeters
76:24 per second. That's, but look happens when we change the temperature to
76:31 degrees, 100 degree change. Look happened to the te, the
76:36 It went from five times 10 to minus 15 to 4 times 10 to
76:40 12. That's a factor of 1000 ? We've made it go 1000 times
76:48 by increasing the temperature by 100 If we decrease it, if we
76:52 it another 100 degrees, it'll be 1000 another 1000 another 1000. So
76:57 explains why there'll be some, there'll some temperatures at which is going super
77:02 or super slow. Um Oh, a factor of 713 fine. All
77:08 . Uh I'm gonna, I'm, , I'm also, I'm gonna zip
77:11 these other examples. Um All So we're almost through with some of
77:19 equation stuff. Um But now that got this, this, this,
77:24 uh relationship between temperature distance and time can, uh we can refine a
77:32 bit. Um any of you, all taken calculus, right? If
77:39 take differential equations, any of no, not important. But this
77:44 what's called a differential equation. And of the ways you deal around this
77:52 that you can make certain assumptions about geometries or initial conditions and things get
77:58 lot easier. And so what we're do here is make a few assumptions
78:04 the shape of the thing we're diffusing , it can be a sphere,
78:08 can be a cue, it can whatever. Uh And when we make
78:13 assumptions, this happens and let me well, let me just go back
78:20 here. We have an equation that t temperature time, diffusivity and
78:27 We make some assumptions about the geometry things. We can get equations that
78:31 like this. I know you can't this. I know you don't need
78:34 remember this, but I just want show you that there are examples for
78:37 sphere, the infinite cylinder, the sheet and the cube. And what
78:40 can do is we, we can , so we can, we can
78:44 this equation two ways one in which can solve for this parameter D on
78:49 squared or I should go back and the A, we're gonna, we're
78:54 introduce a couple new terms. A is gonna be a, a
78:58 characteristic A will be the radius of sphere or the side of the cube
79:03 the radius of the cylinder or the of the slab. So by,
79:07 introducing a geometry, we can then relative to those things, we can
79:12 assumptions. The other, the the other variable we're gonna introduce is
79:17 variable F and F is if we , if we d if we start
79:23 diffusion action F is the fraction of stuff we started with that we still
79:30 . So we start with one and you were diffusing and diffusing and diffusing
79:34 if F, if you got rid all of your diffusion F would go
79:37 to zero. So I'm just gonna in, in here on the equations
79:42 uh the sphere. The simplest example just say that these are, these
79:47 the results of some mathematicians working these out. And the thing is is
79:51 what we can do is write equations F which include now things that we
79:57 measure the diffusivity. The temperature and , the, the, the
80:06 And so, um, let me , we're gonna pay attention to this
80:13 . Oh, well, wait a . Uh, yeah, we'll pay
80:18 to this equation in a minute. with that information, we're gonna be
80:23 to hone in on this thing that trying to figure out, gonna,
80:28 formally define this thing called closure So let's just define it. In
80:33 words, closure temperature of a system defined as the temperature at which the
80:39 and loss of a particular species is . We've got both retention and loss
80:44 on here because we're talking about something growing. This is a radioactive
80:49 We, we've got parents which are to daughters. If we were well
80:54 the closure temperature, the daughter would stay there. If we were well
80:59 the closer temperature, the daughter would leave, but we're always gonna be
81:02 a new one. Eventually, this is gonna decay away. So the
81:07 temperature is that temperature in which the of new ones by the radioactivity of
81:12 thing of the dog of the parent balanced by the loss of things.
81:17 it's by the time we make a one that, that, that,
81:19 one we made in the, in previous step has diffused out of the
81:23 , it's hot enough that it diffuses the same time that it takes to
81:27 a new one. That's the closure . In practice, this closure temperature
81:33 the temperature of the system at the represented by its parent age. We
81:40 parents and daughters in a thing and get an age of 100 million
81:46 100 million years ago. This this belts bar, this zircon was
81:52 , that temperature. That's what it . So that's that, that,
81:57 means that when we interpret our geo age, we really need to talk
82:03 all of these ages as apparent This is what it appears to
82:07 but we have to understand it in of it being that it was 100
82:10 years ago, it was at the temperature. Well, that's fine.
82:16 the next thing we're gonna have to is figure out what that temperature
82:19 And if we just say at the doesn't help like saying, it's like
82:24 I was born in my hometown. , and yeah, everybody was,
82:28 if you wanna sort of track your , you have to define what that
82:32 is. Uh So we're gonna, gonna go through some formal formal uh
82:39 in which we can figure out what closure temperature is for different systems.
82:47 By the way, this temperatures, thing is not restricted to geo
82:52 other disciplines have it in particular uh mats, you know, when we
82:57 about dating something or figuring out the magnetic pole or something. Uh You
83:03 heat up AAA thing and it'll lose magnetism magnetism, but it doesn't just
83:09 its magnetism like that. It has , it has the same concept that
83:13 see here. OK. So we can describe closure temperature this
83:18 We, we've described it in let's describe it in, in uh
83:23 . We've got two graphs here in we've got time going across the bottom
83:28 on the top one here, we've temperature rising up as we go
83:31 And in this graph here, we're have the ratio of daughters to parents
83:35 will be rising. So if we it, you know, if we
83:40 a cooling history, that is like this monotonically cooling, just always
83:45 cooler at some point, we will hot enough so that the daughter to
83:51 ratio is essentially zero hot, you . So the diffusivity is so high
83:56 make a new parent. Yep, goes out. So, although
84:00 you know, and, and this be zero for a for a very
84:03 time if the thing stays hotter than closure temperature, if the closure temperature
84:07 very low. For example, the temperature is 100 degrees like it is
84:12 fishing tracks. If you've got a that has been buried to below 100
84:18 or hotter than 100 degrees, that crystal will stay at apparent zero degrees
84:25 long as you're above 100 degrees. another example, would be a granite
84:31 below the surface and it stays down for a long time. If you
84:36 a closure temperature, that's only 100 . If you were to, if
84:39 were to drill down to a granite five kilometers below the surface and,
84:43 sample that granite, you bring it up, you date some of those
84:46 , they would give you a date zero because they were very recently too
84:51 to retain their, their daughters. eventually it starts to cool down whether
84:56 a, you know, granite that's uplifted or a basin that's being
84:59 Somehow, you're cooling your sample. you'll get to a situation in which
85:05 rate of the, the daughter the, the, the, the
85:08 to parent ratio begins to rise a bit. It rise slowly here because
85:12 still pretty hot. It's still hot that we're losing pretty fast, but
85:16 not losing them at the same rate we were before. And when we
85:20 to this temperature here, that's the at which we're losing them as fast
85:26 we're making them. But as we down a little bit colder, we
85:32 to increase the rate of retention until get to some temperature. Well,
85:36 below this temperature here and at that , the daughter to parent ratio will
85:42 increase at essentially a straight line, will be a line proportional to
85:47 the K constant of the system we're in. And if we were to
85:53 measure that system millions of years we'll get a number. And you
86:00 see that this curve kind of is, is uh is flat and
86:05 deepens up. If we measure millions years later, this curve essentially points
86:12 down to this time. That's the we will get by measuring the
86:17 And excuse me, that's the time get by measuring the daughters and
86:22 And we can read that up and the closure temperature. So graphically,
86:26 what closure temperature means. The time which the time the temperature where you
86:31 at, when we get the time calculate by measuring backwards this way.
86:40 . Now, to uh to, , to add this bit of calculation
86:46 figuring out what each individual closure temperature . We're gonna imagine uh cooling in
86:51 situation in which we're gonna start by on either side of the closure
86:57 we're gonna say consider cooling over intervals at closure temperature where the definity drops
87:04 a factor of heat. And of , we, we picked e because
87:08 gonna be able to cancel it out on. And to put it another
87:12 , we know that the diff the at our high temperature or our low
87:18 divided by our diffusivity at our high , the ratio of those two things
87:22 equal to e we can expand those out because we know that the diffusivity
87:27 , is dependent on temperature from that we saw before. So we've got
87:31 of this. He's equal to But what good is that?
87:37 we can uh oh What am I ? Oh, we just simplify this
87:50 by, by the, you simple algebra, we can simple that
87:53 , they get that out and we that e equals all of that raised
87:58 the exile And then we take the of both sides and we've got one
88:04 all of that there, right? . What good is that?
88:06 We're getting someplace we, this, business, right? In here,
88:13 over T one minus one over T . We can approximate that this way
88:19 two minus T one divided by T , you know, we, we
88:22 do that. Why are we gonna that? Well, because with the
88:26 we've defined this, we know that one plus T 2/2, that's the
88:32 of this thing. And we've already that average to be the closure
88:36 So we've introduced, we, we've our closure temperature here. We also
88:41 that T two minus T one is another way of saying delta T
88:46 and this seems like an odd but it's gonna help, we're gonna
88:49 delta temperature into delta time multiplied by rate of time rate of change of
88:57 with respect to time. And so that's the case, all of
89:04 it's gonna be substituted with this. so we're gonna get that equation.
89:08 here, now we have an equation has the activation energy, the cooling
89:14 , the change in time, the constant and our closure temperature, we've
89:22 our closure temperature in our equation. , this is good news. Um
89:29 gonna use those equations I showed you and we're gonna assume from the moment
89:34 we're gonna talk about a, a geometry because that's nice and simple.
89:38 indeed, we're gonna ignore this second of this thing because it really doesn't
89:42 , add much to the uh to situation. And we're furthermore gonna notice
89:49 at, we've, we've defined this at the closure temperature at the closure
89:54 , we know that F equals zero is the place where we balance
89:58 we're gonna be equal loss. And the definition of F, we've lost
90:02 . So at this point, we plug in the half and then
90:06 so that's just a bunch of numbers . And we can, uh we
90:10 , we can say that delta T one over F, all of
90:14 the 0.5 and the six and the to the three halves, all
90:18 And there's another pi squared in there becomes delta T equals 1/55 divided by
90:25 divided by the A member A is distance. So substitute that in there
90:34 we get that equation. And then finally that our diffusivity is dependent on
90:41 , we can substitute that back in . And all of that gets us
90:45 , this equation. And I hope wasn't too painful, but we can
90:49 see where that came from and, in it, we will interpret this
90:53 . Now, one thing I should is that 55 turned into an A
90:57 , the 55 was AAA number we . When we assumed spherical, we
91:02 another number. If we assume another so that A has to be put
91:07 there for the geometry for sphere, would be 55. Um So I
91:13 said that the term is 55 for , 27 for cylinder. Now,
91:20 thing about this equation, which is bit odd note that the closure temperature
91:26 on both sides of this equation. we must not be done yet we
91:30 to solve for closure temperature, So you see a problem in solving
91:35 temperature on that equation. Uh What , what would we do next to
91:41 and solve that? Here's closure temperature this side. Super great. Here's
91:47 temperature in here problem though, Where's the problem? What?
91:59 we have to get on that But how are we gonna do
92:01 We have to, we got to it here. So we can,
92:04 we, we can get rid of log by putting it raised to the
92:07 , right? But then we have raise this to the power and we're
92:10 to the same problem. So what do you do? This is
92:14 example of where we can figure out easily, we solve this equation
92:19 So it's a very simple, what do is you, you have all
92:23 I'll explain in a minute where where we, we get all the
92:27 other terms, we get all the terms uh by uh experiment. But
92:30 we were to, if we imagine had all these other terms, the
92:33 and the R and the, and , the cooling rates and the
92:36 the D and the A, we all those things, we could substitute
92:40 some value for TT C here. it doesn't matter what you put in
92:45 . Let's just say, I always to pick 600 0 And by the
92:49 , I should point out these calculations to be done in Kelvin. You
92:52 substitute back and change it into but you put in a number 600
92:59 say, and you do all your and then you get some number
93:03 It's probably not gonna be 600 to , let's say it's now 275 you
93:09 that 275 and now you do that you do the calculation and what you'll
93:13 is 270 put the 270 you get you put the 269 and you get
93:22 and you're done. So that's what's solving iteratively. When you have this
93:25 both sides, you just put it there until you get the same answer
93:29 both sides. You know, this an equation. Uh So long as
93:32 , it's that way. So we , that's not a problem. So
93:40 dealt with that little arithmetic issue, now consider the effects of these individual
93:47 on this closure temperature. We're getting trying to understand what closure temperature means
93:51 geo chronologic systems. Um activation energy this push, you have to get
94:03 get this thing going. What happens we increase activation energy? What is
94:10 ? Does the closure temperature get bigger smaller? Look at that equation and
94:14 me it gets bigger although it's Well, actually it's not what I
94:21 , explain why. OK. well, it's also, it's also
94:29 here though, but the good news it's in the numerator here. It's
94:33 the denominator of this denominator, which when that as that gets bigger,
94:38 gets bigger, which means this gets , which means it, it
94:42 I'm sorry, I'm not supposed to that. Um So when he gets
94:48 , um the whole thing gets what about what about cooling rate as
94:53 rate of cooling increases? What happens the closure temperature if this gets
95:05 Well, yeah, if this but it's even, it's, it's
95:07 complicated because if this gets bigger, this whole thing gets smaller, which
95:14 the whole thing, it's bigger. ? So the faster the cooling
95:18 the higher the closing temperature, um more important consideration might be dimension.
95:25 is something we've got a better feel . We don't have a good feel
95:28 cooling rage or activation energy. We a pretty good sense for the size
95:33 the crystal. That's little a here the crystal gets bigger or, or
95:39 I should, I should say, the diffusion domain gets bigger for the
95:43 , let's assume that the diffusion domain the same as the crystal as the
95:49 domain gets bigger as a gets What happens to the closure temperature?
96:01 . Don't look at the equation. do you think should happen as the
96:05 as the size of the crystal gets ? Is the closure temperature of the
96:09 gonna get bigger or smaller? What's smaller? Why close your temperature is
96:17 temperature at which you have to? is. OK. Suppose we had
96:29 tiny little crystal, you know, talking about having to diffuse outside of
96:34 . If, if, if, we don't have to, if we
96:36 have to go very far, then don't have to turn the heat very
96:39 to eventually get to the edge, . But if it's this big and
96:44 at the same temperature, it's gonna a lot longer to eventually find our
96:48 out. But if we turn the up, you know, it'll go
96:52 just as fast. So, as , as the crust, as the
96:54 gets bigger, I mean, the size gets bigger, we should
96:58 it to be more difficult to get at the same temperature. Excuse
97:05 a little bit like that. the bigger your house is, the
97:08 , the more it is to stay and warm. Um And so that
97:12 works out the same as, as gets bigger. This is the,
97:16 is a part of this quotient, ? So as this gets bigger,
97:20 gets smaller, but that's a part this quotient which goes into here.
97:23 the whole thing gets bigger. So I think the most intuitive bit of
97:28 is the bigger crystals should be easier retain their daughter products. Mhm Which
97:43 ? Oh, well, we, can treat each one of these separately
97:48 sometimes we'll group them together and D I and I squared, as I'll
97:52 just coming up, sometimes it's hard tell the difference between see D not
97:56 not is the intrinsic diffusivity of the . But when we do an
98:02 we can measure how far, how diffusion was moved. But the problem
98:09 is that was that because we moved short distance very slowly or excuse
98:15 short distance quickly, I get this , a short distance slowly or a
98:20 distance fast, we can get the result. So, so a short
98:28 slowly will give you one way or long distance quickly can, can give
98:34 the same. So, so many we don't break out DNA because they're
98:39 to answer your question. OK. So we, so we need to
98:44 determine the diffusion parameters of E and not on A squared for each
98:51 Um So I'm gonna describe how we these experiments and then we'll be done
98:55 this business. If you want to the data to, to figure this
99:01 out, you're gonna do an experiment the laboratory. Um Couple things we'd
99:06 to do. We'd like to make that our phase remains stable throughout the
99:15 . We're gonna be heating this thing to have diffusion happen, but we
99:19 want to heat it up so far it melts. For example, that
99:23 be, we would be measuring diffusion some other thing. Uh We,
99:28 even have to be more careful about than that. Suppose we're heating up
99:31 biotite, say biotite has water in . If you heat it enough,
99:35 water will go away and it's not anymore. So you gotta worry about
99:40 . Um You have to have some of how big your things are.
99:44 can start by measuring the size of crystals and assume that's the thing it'd
99:48 nice if the shape of the particles with one of our, our met
99:52 , our things, our diffusion But that's a small thing. Um
99:59 we'd like to heat simple heat it hot and keep it that way for
100:03 long time. So if we were do that, we can apply this
100:09 . Remember we have this equation where can measure diffusivity uh as a function
100:14 temperature. Well, this equation, we take the log of everything,
100:19 get log of Dion A squared equals of DNA squared plus this. And
100:24 ? That's why did we do that take the log? Because now we
100:27 an equation of a straight line where is Y, this is the
100:33 this is the slope and this is . So that's nice. Why is
100:38 nice? Because what we're gonna do we're gonna make, we're gonna do
100:42 experiment. And when we're done doing experiment, we can calculate by,
100:47 these approximations which came from those, long lists of equations I showed you
100:53 , we can calculate what the diffusivity or at least the diffusivity relative to
101:01 for a particular thing. And so everything is nice and straightforward, we
101:05 get a straight line on this And the slope of that diagram is
101:12 be the E over R. Remember , that's this, that's the
101:20 And the uh intercept up here is to be going to be this,
101:26 log of D on A squared. if we have, if, if
101:30 gives us E over R, the gives us D not on A
101:36 Now, we've got everything we need calculate the closure temperature. And here's
101:41 real data um from my lab a years ago where we measured diffusivity of
101:47 in calcite, drew a line there the E got the, we got
101:51 the stuff and we were able to a closer temperature of 60 degrees.
101:56 that's you could do an, you do an experiment, everything works out
102:01 . You get a straight line and we can say the closure temperature of
102:04 system helium in calcite is a number we can do that for all of
102:09 systems. And I won't go through anymore right now. Um Let's
102:18 we'll talk about that when we get South bars. Um Yes, like
102:24 missing a slide, but I'll just so we can do this, we
102:27 do this appro we can do this this, this calculation for all of
102:31 systems. And then we can, , and then we know which of
102:35 ones are sensitive to temperature and which more robust. Uh And I've got
102:39 , I've got a list of them on which I'll show you later.
102:42 some of them are very sensitive to . Some like this one have a
102:46 temperature of only 70 degrees, which that once we get up a little
102:51 above 70 degrees, we're gonna start our diffusion. It's gonna reset the
102:56 . Others might have a closure temperature 800 degrees. This is very important
103:02 know because when we date a you know, one is gonna tell
103:07 when it was crystallized that moment, crystallized at 800 degrees. The other
103:11 is gonna tell us when it would at some very low temperature. As
103:16 as we know what, what it . This is great news because one
103:20 us something about, you know, and something tells the other thing,
103:24 we have to be able to work out and it, it would be
103:27 if, if you had a pile your personal papers and one of them
103:31 , you know, this is when were born and this is when you
103:33 from high school and this is when got married and this is when you
103:36 that car and somebody might look and , well, well, these,
103:40 are, these are these pieces of all have different ages on how
103:44 how can we interpret that? you just know that, you
103:47 we don't, we don't, we born and we don't graduate high school
103:51 we don't buy a car all on same day. We have to appreciate
103:55 these documents mean. And that's the thing. We have to do is
103:58 have to appreciate when we date a by uranium, we get one thing
104:03 we date the same zircon by helium , we get a very different
104:07 So that's the concept that, that need to have in mind. I'll
104:10 you the actual numbers of each system a little bit. But this is
104:14 we go about figuring that out. been figured out for each system
104:19 So that's where that goes. People me, 000 That remember that our
104:31 temperature has a cooling rate in That's something we have to.
104:37 that, that's I'm glad you pointed out. Yeah. So when we
104:41 that, we, we can we can, we can get this
104:44 . This is just a constant, is a constant, this is the
104:48 . Again, this is what we're this. We measure experimentally, this
104:52 we measure experimentally this, we have assume we have to say,
104:56 given a particular cooling rate. And speaking, when we measure, when
105:01 want to calculate closure temperature, we say, let's assume a cooling rate
105:05 10 degrees C per million years. As we saw, if you,
105:10 you choose a higher rate of you'll get a higher closure temperature.
105:14 when somebody says the closure temperature of and Y, they're usually assuming AAA
105:20 rate of 10 degrees C per But that's a ne no, you
105:24 , you can pop, you can , if, if you're in a
105:26 situation in which that's inappropriate you can in another cooling. But without,
105:32 specifying the particular geologic situation, people to calculate a number. So they
105:37 in 10 degrees C per million. All right, that was another hour
105:43 talking, maybe worth trouble. Um , um, so we're gonna now
105:57 , hey, we're gonna, we're go into our, our next,
106:01 first actual example of a system how works and what we can use it
106:07 . Um But why don't we take 10 minute break and we'll start again
106:14 with rubidium strontium dating, which is one of the uh uh things that
106:19 posted to uh canvas. All So first system we're gonna talk about
106:30 detail is the radium strontium dating In this, in this case,
106:36 have Verdi 87 is radioactive and decays strontium 87 by beta minus decay.
106:43 , we're transforming uh a neutron into proton, which is why we move
106:48 37 to 38 on that equation. was one of the earliest methods used
106:55 geo chronology. It's not used as as it used to. It's superseded
107:00 some other methods, but it's an method to start with because it illustrates
107:04 well. Uh an important concept called Isac method which were, which is
107:10 of the way in which many systems around this problem of not knowing how
107:15 daughters we had to begin with. it's similar to other systems that
107:20 we'll talk about in the future. talk about potassium argon and some of
107:24 others. Um So learning about this , whatever everything we learn about ISOS
107:29 be carried over. So we're gonna this with every system we talk
107:34 We'll talk about the, uh, geochemistry of the parents and daughters.
107:40 Rubidium is a group one, a with an ionic charge of one and
107:44 ionic radius of 1.5. Um Strontium a charge of uh plus two and
107:53 very much smaller radius. Um so they're different from each other.
108:02 rubidium is a lot like potassium and is a lot like calcium. See
108:08 , these numbers here. And so you can find a mineral that has
108:15 in it or should I say potassium it and no calcium in it,
108:23 gonna start out with something that has rabid bearing mineral. Um A rabi
108:28 mineral will unlikely to crystallize strontium It's just not, it's not in
108:34 cards. So that's a problem because we don't know how many do we
108:40 with, then it's gonna make it to measure the age. Excuse
108:50 So I'll get to that question in minute, but let's just get a
108:52 more details about the system involved There's the equation for decay again,
108:58 uh the decay constant for bum 87 1.42 times 10 minus 11 per
109:04 Which if we flip that around and the closure temperature, we get this
109:08 temperature of 49 billion years. It like a very long time. But
109:16 that if we can find minerals that a large amount of rubidium in
109:22 then geologic time scales are appropriate to up enough stuff that we can measure
109:29 all of our cases. What we have to worry about is can we
109:34 enough data product to the mass spectrometer measure? And we can get around
109:41 problem in one of three ways, can make the sample have uh be
109:47 old. That's what we did with samples from the moon. If the
109:51 is very old, then we just long enough. We can, we
109:54 build up some of this daughter Even if decays very slowly, we
109:59 also have the sample um have a of parent in it. If you
110:04 , if you have like a potassium bar, then the decay of potassium
110:08 be easy to measure because potassium is the name, right. A third
110:13 you can fix this problem is even you don't have a lot of parent
110:18 even if the sample isn't super, old, we can get around this
110:22 . If we just have a really sample because we just shovel the sample
110:27 the mass spectrometer and then we can whatever got product is there. So
110:32 long as we can fix one of things, we'll be OK. And
110:35 why generally we, we find minerals have a reasonable concentration of radium.
110:41 , and the good news is Concentration doesn't have to be lots,
110:45 can have like 200 parts per 304 100 parts per million is uh
110:52 enough to date most geologic minerals because , because of our equipment is so
110:59 , we can measure teeny weeny little . So there are two isotopes of
111:06 , rubidium 85 and rubidium 87 rubidium is the one we're worried about because
111:10 radioactive. The ratio of the two today has a constant value. Uh
111:17 are four isotopes of stature, they're stable isotopes. They don't have a
111:23 life, they're all stable. Um the one in italics, there is
111:29 , as I mentioned before, that's one that is decaying that has been
111:34 is the product of the decay of 87. So we can say that
111:39 ratio of 86 to 88 is a number or the ratio of 84 to
111:43 is the constant number. But any that we use 87 will be always
111:49 . And that's why we say the of these minerals of these of isotopes
111:54 only approximate because it depends on what of material you're looking at. All
112:00 . So we can take our age and substitute in the actual parents and
112:04 this time. But, and so this case, we're using the,
112:12 , the, the subscript I for earlier, we used zero, but
112:16 the same idea. So the, amount of strontium we have is equal
112:20 the amount of strontium. 87. started with times the, the,
112:24 product of the amount of rubidium we 87 we have times ZT I
112:30 But here's our problem. It's very for the branch of 87 initial value
112:37 be equal to zero. So we a way to sort that out and
112:43 way we're gonna do this might seem bit odd at first, but
112:45 it works. First thing we're gonna is choose a non radiogenic isotope of
112:51 daughter as some normalizing factor. And going to pick in this case strong
112:58 86 we're gonna divide both sides of equation by staunch of 86. So
113:05 we have a ratio of 87 to equals the ratio of 87 to
113:10 We started with times the ratio of rubidium distraction 86 times the ent and
113:18 looking at this and you're thinking, , how does that help us at
113:21 ? Because we've just moved from needing know the amount of staunch in 87
113:25 we started with to the ratio of to 86. We started with,
113:29 still a thing we started with. the thing that was existing millions of
113:33 ago. How does this help? me? All right. The reason
113:39 helps is that we can take advantage the fact that when minerals are formed
113:46 an igneous rock. Anyway, we that these minerals have a different affinity
113:54 radium and strontium. So, so a natural segregation of rubidium strontium with
113:58 going into sub minerals a lot and others. And strontium going into some
114:03 a lot but not in some And so what that means is there's
114:08 be in a, in a rock simple same history. We're gonna have
114:13 dispersion of rubidium strontium ratios in those . Um And because no process fractionates
114:22 isotopes, the minerals that form with rubidium strontium ratios will form with exactly
114:30 same strontium isotopic values just after So if that doesn't make any
114:38 let's look at it graphically. Let's a granite site that has these minerals
114:43 it, appetite, pla glaze Kellar and muscular. At the moment
114:49 crystallization. These things would plot on graph like this in which the X
114:55 is is the parent divided by the daughter 87 rabid and divided by 86
115:04 . And on the y axis, have the isotopic value abstraction. These
115:12 care about whether we're, they're incorporating Restrain. Some like Robin better,
115:19 like straum better. And that's why flock along the line here, but
115:23 don't care about that extra neutron in rabbin 87 versus shoot me the strontium
115:30 versus Stron 86. That's not a that is made. So the isotopic
115:37 of strontium in these minerals will start to be exactly the same because that's
115:41 was in the magma they crystallize into thing. That's the same, this
115:45 different. So now we know that 87 is radioactive, right? And
115:54 gonna decay, we know Rania makes . So over time, how are
116:03 point's going to evolve? What's gonna to this muscovite point? Say after
116:13 time, what is the radium 87 strontium? 86 ratio gonna do?
116:18 gonna go up, go down or the same. Excuse me?
116:31 that's too. I mean, half over time will it go up,
116:34 down or be the same? It go down? This ratio will go
116:39 , right? Why? Because this decaying and this is excuse me on
116:47 to do that because this is decaying this isn't right. So at,
116:54 some time equals zero, they're all same. But, but, but
116:58 on there, this is gonna be and this isn't. So the the
117:03 of these things of, of the axis is gonna go down for all
117:06 these things. What is the value the Y axis gonna do? What
117:12 Rubidium str what is Rabii 87 decaying 87? Right? So what's
117:23 what's the value of the Y ax gonna do gonna go up?
117:28 So we can excuse me over the medium 87 decays to strong
117:36 And so these things are gonna move way. Why have I drawn some
117:40 those arrows long and some of them , they're all moving in the same
117:46 . They're moving that way because they're down in the x axis, they're
117:49 up in the Y axis. They'll this sort of northwest trajectory on this
117:54 . But why have I shown that of these lines are longer than the
118:03 ? Not the rate the amount has this things, things out here
118:10 have a greater amount of rein. remember we said we go back to
118:15 flipping of the coins, we flip flip in this room. We only
118:19 four heads, we flip at the game, we get 3000 heads,
118:23 flip at the baseball game, we 20,000 heads. This is the baseball
118:29 , right? We're gonna have more in this situation because we started with
118:34 stuff this decay over here hardly even in the diagram because we had
118:39 we have, we start with We'll get zero. If we start
118:42 a GOB, we'll end up well, less than that because each
118:46 of these goes smaller and we go this way. So the proportion is
118:51 amount of decay is proportional to how we started out on this, on
118:55 edge. And so at some time , one, these values should have
119:00 , should have all migrated to that . And so then we can slap
119:05 line on there. And that line gonna be for the slope of that
119:11 is gonna be proportional to the We started out zero age, we're
119:16 , right? And over time, rotate up here, just rotate
119:21 the steeper. That line gets the the system is. And notice that
119:27 we do this way we get the , the intercept of this, of
119:31 line is the initial value that problem had to begin with. Well,
119:34 are we gonna do this if we know the initial value, this tells
119:38 the initial value, although we can of skip over the initial value if
119:42 want because we're really doing this just figure out the age. But now
119:46 got the age. This is called Isochron. This line, this blue
119:51 here, it is called an ISO it's line of equal age. And
119:56 is how we get around. The of not knowing how much daughters
120:03 Now. Clearly it works fine. . It's great. The problem is
120:07 got to have, you gotta make line, you gotta have three
120:11 let's say, from the same rock you can assume started out at the
120:15 and now have rotated up. So can't just do an iso on a
120:19 point. But if you've got some that has a suite of minerals that
120:24 happy saying have this, this, history, then the is Aron
120:30 The ISO method gets us around this of, oh my gosh, how
120:34 did we start with? Well, we go. We got it.
120:39 Here's an actual example of some rocks Texas. Um These are central
120:46 We'll, we'll use this, this central Texas rocks as an example because
120:49 why not? Um And we'll show for some other systems later on.
120:56 so here's, here's a uh uh real data from a, a rock
121:00 central Texas. This is, excuse , this uh this down here looks
121:05 one point, but it's actually the K Fels bar and wr means
121:10 rock. And because this is a granite with a lot of K
121:15 in it, the whole rock and K feldspar aren't very far apart from
121:18 other. So you got two points there. Then you got the Muscovite
121:22 and the bis head here, you a line through those points. This
121:25 , you know, these are the you measured the lab draw a line
121:28 that point. The slope of that is proportional to an age of
121:34 This granite from central Texas has got , you know, it's got a
121:38 Protozoic gauge of 1081 plus or minus . Based on the uncertainty of that
121:43 , it also tells us the intercept 0.8. That's interesting sometimes. But
121:48 the, from the point of view the age, it's not essential to
121:52 . So there you have it Central 1081. Um Here's an example uh
122:01 the moon and we get the same of story. Let me, let
122:05 point out that this rocks a billion old and notice the dispersion on the
122:10 of strong ratios go from essentially 0 900 huge range here. And that's
122:17 because we get a nice line. and we get, we get
122:21 a leverage on that line. We , we can do it fine.
122:25 we're gonna look at a rock from moon and of course, um this
122:29 from a, a rock called a . Anybody remember what a dunite is
122:33 your igneous class. Dunite is a that's 90% olive. So this is
122:40 olives and, and you might well how much rubidium or potassium is
122:46 an olive? Not very much, look at because you, and you
122:50 see that because look at the look how look how, how much
122:54 spread is that previous diagram went from to 900 0 to 900. This
123:00 from zero to 0.2. So there's little variation in the rubidium here.
123:06 if you let it sit around for billion years, you get a nice
123:10 that's defined here and we could still the same thing. And so here
123:13 get a bunch of a very low material but because it's on the
123:18 it sit around for a long They, they plotted it up,
123:22 got an age, the moon is billion years old. We knew
123:27 So, I mean, that, how we know we got, we
123:29 ages from the moon. Um So basically the Isochron method, couple of
123:38 we have to make here is of , that um we've had a closed
123:42 that, that nothing's been moving around the rock hasn't been altered and hasn't
123:46 reheated. Um What if we get uh a situation where the things
123:53 don't uh line up on a Um Here's an example um from a
123:59 in Nepal or those, those are data that were measured, not a
124:05 good line. Uh You can draw line on there sort of and say
124:11 about, that's about 20 million but it's a, it's a rotten
124:16 . The way this granite has been is that this was a, a
124:21 that was melting, it was formed the melting of previous sedimentary rocks.
124:26 those previous sedimentary rocks had a wide of material in them and they were
124:32 and they came to be found in granite, but this granite didn't mix
124:36 . And so this assumption we had the beginning that all of the strontium
124:40 in a crystal would crystallized with the value. Go back to remember
124:47 If we, as we can assume everything is fine. But what if
124:51 didn't start? What if this didn't out as a nice flat line?
124:54 if these were all over the place they didn't really come from, we
124:58 it the man is Lou granite. you could walk through it and it's
125:00 granite, but the, the rock was melted to produce that granite was
125:05 homogeneous. And so we ended up data that look like that crummy
125:13 So just because you can do, doesn't mean it works every time.
125:18 Then there's the second problem of how , what happens if we heat the
125:22 up? Um If you're, if are, for example, trying to
125:29 remember that first example, we showed how are we going to figure out
125:32 age of this paleontological interesting boundary? , we've got a granite that intrudes
125:38 . What's dated by the Rubidium Stron ? OK. That's a thought
125:42 then we'd have, we'd have an limit. On the age of that
125:47 thing. However, we have to and, and, and we'll go
125:51 this in all of our techniques. could go wrong? Well, what
125:57 go wrong here is a metamorphism. the heating of a rock is sufficiently
126:01 or high temperature, the strontium isotopes homogenize in the minerals in the
126:06 What does that mean? So, we said that we could take a
126:12 , let it sit for a T one would be the age of
126:15 rock. Let's take this rock and it. And in that case,
126:20 happens is all of the strontium isotopes equal as they recrystallize. And so
126:28 metamorphic times would be now re re uh establish a flat slope here.
126:36 we then let that evolve over time sets it to zero. We let
126:41 go over time and we could get thing here. But that wouldn't be
126:45 original age of the rock. That be the metamorphic age of the
126:49 which is fine if you're trying to out metamorphism. But if you were
126:53 in the original age of this rock out this wasn't the way to
126:57 Now, you may have been able figure that out already. If this
127:00 was metamorphosed enough to do this, could tell by the texture of the
127:04 . But if you're interested in this would tell you that if you're
127:08 in the age of the original rock you're interested in the cross cutting
127:12 blah, blah, blah. We've another technique, the uranium lead
127:16 which we'll talk about next, which do this. But this is just
127:21 show you what can go wrong with with that. And so to put
127:27 another way you could think of Iraq strontium, 8786 space versus time a
127:34 starts out, all of these minerals out with the same value that they
127:38 dispersing because they have different uh amounts them metamorphism brings them back all together
127:44 they go oxygen on their happy Second time. So we can measure
127:49 if we wanted to just some examples . Um There's a AAA nice
127:55 from Canada, got a nice bunch information in there. You see,
127:59 don't have a very big spread in things, but we still get a
128:02 age. Uh It's kind of kind uncertain value, but this was from
128:06 . We can do better than that . But that's that you would interpret
128:10 as the time in which these re of that grant of the nice took
128:17 . Um And here's just one more of metamorphism. I know that's not
128:22 your thing. But uh an interesting here of, of the scale of
128:26 re homogenization here are some examples from bunch of these uh metamorphic rocks in
128:35 . And if you plot the whole whole rocks uh from from this
128:46 just you take the whole rock and it up and measure the stranch in
128:49 that defines a line with an age about 548. But if you take
128:57 , the minerals from this one rock and you plot them glad you clays
129:03 biotite, it gives a different It gives a, a slope of
129:07 million here. So what we can here is that by looking at the
129:12 of, you know, tens of , the, the whole rocks define
129:17 original age of 540. But on scale of one rock, it has
129:21 re homogenized such that, that tells that they were metamorphosed 403 million years
129:27 . So when we re when we , it occurs on the scale of
129:33 , not kilometers. Um Let's Do I wanna talk about this?
129:41 period? Um OK, I will about maybe I have to talk about
129:53 . Yeah, I do have So the next thing I want to
129:55 about is um how we can use isotopic values of shales to tell us
130:05 about the provenance if you were interested , in uh an ancient shale.
130:10 just what's what's this broad information about what's being brought to us. You
130:16 measure this astron isotope value of the and tell you whether that, whether
130:21 a provenance was continental or more oce be, but to set that
130:27 I'm gonna talk a little bit about . Um, here's an example of
130:35 of the oldest bits of material we on the earth of, of
130:39 We've got a 4.4 billion year And what's interesting about this value is
130:43 gives this intercept, which is about lowest intercept that's ever been measured.
130:50 . It's, it's called Baby, stands for basaltic Achon. Best initial
130:56 a chondrites is a kind of And best initial says that this is
131:00 as low as anybody's ever measured. is how low the the the solar
131:04 started rocks that have a higher initial . Like let's go back to our
131:11 our granite from uh our, our granite from Texas that has a
131:17 of 0.8. Whereas we think the system started at a 0.69. So
131:24 is a lot bigger than that. that means is that the material that
131:28 melted to produce this granite was already part of the continent because in order
131:36 get a high value like that, have to have decayed. Rubidium.
131:42 is more likely to be in the than in the ocean. If
131:45 if you make a continent and let sit around for a while, the
131:48 value will go up. And so we measure uh values that are significantly
131:55 than these, these meteorites. We say that that's uh uh an expression
132:01 continent continent building. So, for , here's a granite from uh from
132:08 radium strontium value. It's got a of 0.71 that's modest. That's a
132:15 big value. And so again, means that a continent was, was
132:20 to produce that. Whereas if we to this grant, this uh basalt
132:24 Endy in Argentina, and we get same value. It's got an age
132:29 472. That's interesting. But it's a value of 0.70 very low
132:36 That means that, that the uh mantle was involved when this was being
132:41 . So you were probably looking at rift zone that was bringing up mantle
132:45 than just recycling cotton. So you use that information to tell you a
132:48 bit about what was going on. so this leads to this business because
132:54 is more incompatible element than strontium in systems. When we look at the
133:01 , the rubidium strontium value of the is greater than the source it came
133:06 . So when we make, when , when we fractionate crust, we
133:09 continents rabid and moves from the mantle the crust. And so since rubidium
133:17 over time, this crust is gonna a higher 87 to 86 ratio as
133:23 rule values greater than 706 indicate extraction a crust. And this then has
133:35 used to try and figure out the the history of a continent like North
133:40 . See that green line there. , all these pink value, these
133:45 places here are granites that were formed the Mesozoic. And a bunch of
133:51 have done isotopic values of these things get their initial value. And to
133:57 west of that green line, we've values less than 706 to the
134:02 to the east of that line, have values higher than 706. And
134:06 that tells us that all of this here was added. It's not a
134:10 of sort of the ancient continent, was added in the Mesozoic, which
134:13 , which is the same thing that jobs tell me. So we've got
134:18 , a notion that continents have this value. Well, that then can
134:23 used for this provenance business that I that we're getting into because continents because
134:29 high 8786 value reflects old granitic We can look at the composition of
134:37 ocean and see how it changes the of the ocean is gonna be a
134:43 of what's being eroded into it. when we look at modern ocean,
134:48 can go select a piece of the Ocean water and the Atlantic Ocean water
134:52 so forth. It's very well The 8076 ratio in modern oceans doesn't
134:59 to change very much. And organisms take on this staunch of value
135:05 the water they live in. So can figure out what the strong and
135:09 6 ratio of the ocean was in past by looking at shelves. And
135:19 can then use that variation to tell in some rocks. It's called strontium
135:26 stratigraphy. And it works when the 80 seventies situation of the ocean is
135:31 rapidly. And of course, that wasn't di meta modified by diogenes or
135:39 . And so here's how that works , here's a graph showing the 8786
135:45 value of the ocean over time. And this is obtained by just
135:53 you know, getting, getting raky pods, anything you want,
135:58 measure them and you'll get the 8786 of the ocean in which those organisms
136:05 . And you can see it goes and down, up and down.
136:08 since about, let me just so just zoom on the, in on
136:12 last 100 million years since about 60 years old, since about 50 million
136:20 . It's a fairly monotonically increasing history . And so if you had some
136:28 that you didn't have good fossils and didn't have any other way, if
136:33 marine rocks, you might be able date them. This way. If
136:36 just pick a, you know, , measure the isotopic composition of,
136:41 your rock or a fossil in that ? Say it was 0.7085.
136:47 that means it's 15 million years Ok. Now, let's go back
136:53 this one. Why do you suppose goes up and down so much?
136:58 goes back and forth, back and . What, what is the,
137:02 is the reason for that change? could happen in the oceans or
137:09 You know, we say that the isotopic composition is a reflection of what's
137:14 added to the ocean. Why would , why would the uh staunch remember
137:21 ? 87 when, when that value high, when 8786 is high,
137:26 indicates continent and when it's low, indicates not continent or ocean. Why
137:33 it change like that so much glaciers you're, where you're holding the water
137:40 it's in ice or in the Well, that's a good place to
137:44 water. But I mean, it's , he said glaciers, um you're
137:50 the right track. We're trying to moderate the material that's going to the
137:54 , but really by not adding something the ocean by, by having glaciers
138:01 back water. We're not really worried the water, we're worried about
138:05 the, the, the sediment that's transferred to the water. So,
138:09 mean, you're on the right How are we gonna change things as
138:12 move into the ocean? You've, , you've been concentrating on the water
138:16 . But how can we can we as the water is delivered,
138:21 can we change its isotopic composition? isotopic composition of the ocean is reflected
138:32 what's dumped into it. And I mean the water but the stuff in
138:37 water. So why would the, like, for example, well,
138:43 just go to this one, for , here in the last 40 million
138:46 , we've increased a whole bunch What does that suggest has happened?
138:54 that we've had more continents being eroded in the past for the last 40
138:58 years. The amount of old continent into the ocean seems to be going
139:02 and up. Can anybody think of , of a place since 40 million
139:10 ago? That's been eroding like Excuse me? What, what?
139:24 , I mean, not. I'm about really eroding where um I'm thinking
139:34 a mountain range not since for I mean, that's a good
139:41 That's old stuff, but there's a , there's a bigger mountain range that's
139:44 active than the Appalachians. Now, , we're talking, see, this
139:47 the thing that the app have. Appalachians really been evolving very much in
139:51 last 40 million years. Where's a ? That's where's in it? The
139:57 . That's, yeah, it's exactly . The Himalayas are the biggest mountain
140:02 . They happen to have a lot old trust in them. And the
140:06 between Indonesia really started going about 50 years ago. So here we see
140:11 the oceans, the presence of the , the Himalayas are an old and
140:16 range. They're gonna be dumping. know what, what river delivers more
140:20 to the oceans than any other Just to pass what river delivers more
140:29 . The Amazon. Yes. What delivers more sediment? Not number
140:38 Mississippi is a good one. But , the one in India, the
140:44 . Yeah, because you've got this mountain range right next to the
140:49 You know, the amount of sediment really a reflection of the relief of
140:53 mountain range. You got this huge mountain range right next to the
140:56 That's where more sediment is delivered. that's the, that is, that
141:00 uh reflected here we see in the of the oceans. The the the
141:06 of, of uh the structure, is a global figure. These
141:14 it doesn't matter. No. As said, if we said that earlier
141:17 , the uh the, the the 8786 ratio of is invariant in modern
141:23 go get us. And that's you know, they've, they've done
141:25 by scooping out some water from Hawaii some water from Calcutta and some water
141:30 the Aleutian Islands and they get the answer. So the, the the
141:34 oceans seem to be very well So when we see uh a graph
141:40 this, we can call on a source changing it all. And the
141:44 are a great example of how to that. They're the, they're the
141:47 active mountain range. They're really they're eroding like Tracy and they're dumping
141:51 bunch of sediment into the ocean that then reflected in the geochemistry of the
141:56 . And because, and so that this shows us is that if you
142:00 a sequence of rocks for which the aren't very good, you don't have
142:03 volcanic rocks, but it's a it's a marine sequence. You could
142:08 to, to measure strontium isotopes in sequence. Because from about 50 million
142:14 to the present, we have a uh correlation between the strontium isotopes of
142:20 water and the time obviously, if go back in time, it goes
142:24 and down because things like the Himalayas and start and go back and
142:29 What? So the Himalayas are an of how we're gonna make this ratio
142:33 up, right? We get a mountain range with some old continent,
142:36 it in there. Strontium isotope goes in the ocean. What would cause
142:40 to go down? And I don't just stop eroding if the 8786 ratio
142:53 really low. He said that that from the mantle, right? How
142:58 we more introduce more mantle into the ? Yes, you increase the,
143:06 increase the uh the rate of spreading the mid ocean ridges. We put
143:10 brand new basalt down there in the of the oceans. So when
143:13 when this ratio is going down, breaking up continents, we're making new
143:18 crust. So continents, continents make this value, go up,
143:26 , breaking open, make this value down. And that's why it goes
143:30 and down and up and down. are currently in a going up
143:33 And so we could use that for dating since about 40 million years.
143:40 would be a potential way to do . Um And it makes sense because
143:44 our understanding that continents have a high , oceans have a low value.
143:57 So, um from a, from practical point of view, I'd try
144:02 add this for most of our, systems. Um Modern mass spectrometer can
144:09 determine these values with a very small of material, very much less than
144:14 mg. So, in terms of practicality of dating these things, you
144:20 need a big sample. Uh If gonna do an iso you'd like to
144:25 a spread of veridian Stron values. But for rocks that are sort of
144:31 rocks, you know, it's, no problem dating rocks that are older
144:36 20 I would say. Now I this slide many years ago, I'd
144:40 maybe you can even go down to 5 million years if you had the
144:45 conditions. So again, we've got three ways in which we can figure
144:53 out if the sample has a lot parent, if the sample is old
144:56 if the sample is big. if the sample is young, like
145:00 million years, you better hope you know, you've got a nice
145:03 hunk of sample. You're not gonna this by some little pebble or
145:07 Uh OK. Let's see. What is it? It's almost four.
145:14 me just take a moment. And I think you guys don't need to
145:28 that. So what I'm gonna do is move on to another topic unless
145:35 guys have any more questions about rum . Come here. Stop that.
145:43 you go. So we been as I said, is not a
145:49 commonly used technique these days because it, it does require three or
145:54 minerals from the same rock. it's good for an igneous rock.
145:58 can't date detrital minerals by bum strain you can't assume they have any sort
146:03 similar history. Uh But I introduce because it's the best way to describe
146:09 concept of an ISO which will be in other examples. So gonna close
146:18 we're gonna move on to the last of stuff that we've posted for you
146:26 . That's the Rubidium. Uh excuse , the uranium Thorium uh lead system
146:34 we'll start this now and we'll finish uh tomorrow morning. Ok.
146:59 System number two. 000, I , I didn't mention one thing.
147:03 just, I won't go back but say that. No, I'm not
147:08 bother them. Ok. System number , we're gonna talk about the decay
147:13 uranium to lead and thorium to Um This is OK in many
147:21 the gold standard of figuring out how things are if all you want to
147:26 is when this rock crystallized or when grain of sand crystallized, this is
147:32 number one, especially when we talk the minerals Zira uranium L Zircon dating
147:40 what a lot of people think geo , there's gobs of other geo chronology
147:45 . But if you had to, you had to pick one, this
147:48 what it is. And the reason because of the characteristic of lead and
147:54 , um the closure temperature of lead Zircon is a super high number.
148:00 when we date a Zircon, we're when it crystallized and what happened to
148:05 afterwards, if we cooled off slowly rapidly, if it was metamorphose doesn't
148:11 . And so that's why it's one the best ways to determine the crystallization
148:14 rocks. It's generally focused on accessory , minerals such as these Zircon monoxide
148:22 rio xeno spen. Because remember our ways we could have the,
148:29 the way that we're gonna work this is we're gonna pick minerals that have
148:33 rather high concentration of the rain. Zircon is one of those of those
148:37 . So we can't just pick nice . We've all heard of, you
148:41 , c spars and stuff like that there's no uranium in a F
148:47 but there's quite a bit of uranium a Zerka. Um So the geochemistry
148:53 these things, um uranium is a four charge and it has an ionic
149:00 of 1.08. Uh It's very similar thorium as it happens, it's also
149:07 similar to zirconium. Notice that zirconium plus four and has an ionic radius
149:13 . So when we're making a uh and zircon is the chemical formula
149:19 zircon is Z RSI +04. So we're making a zira and the magnets
149:26 , you know, we're picking stuff of the magma and zircon is
149:30 I mean zirconium is there. But a uranium comes along uranium will fit
149:35 into this spot, that was gonna for the zirconium. So substitution for
149:39 into the zirconium, easy peasy However, for the lead, the
149:45 has a charge of plus two and ionic radius of 1.4. It's different
149:50 both size and charge. And and, and remember when we're
149:54 remember back to your mineralogy or even geology, when we have an ionic
150:00 , we can worry about its the of things and the charge of
150:04 But what's the rule we have for when we're thinking about building a mineral
150:08 we, we, we tally up the charges, what all the charges
150:11 to add up to? Not at gotta add up to zero.
150:18 you gotta balance out to zero, ? You gotta have the negative charges
150:21 the positive, the negative charges come the oxygen and then you just gotta
150:26 that up to zero. And that's rule, there's no break in that
150:29 when you make something, it has be electrically neutral. So if you
150:33 gonna substitute a lead in for for a zirconium, you'd have a
150:37 problem and you, you might be to figure it out by substituting something
150:41 that, that balances it, but really difficult. Furthermore, this thing
150:45 really big, this, this thing really big compared to where it's going
150:51 . So this was what another reason uranium lead in zircon is so prized
150:56 because we have a very good feeling when we crystallize zircon, it will
151:03 uranium in it and it will not led. So that when we go
151:09 on to measure the uranium lead we can say that lead is from
151:13 situ decay. We don't really worry much about well, what, how
151:17 lead was there to begin with? just say not because of this,
151:23 of this geochemistry lead is very different zirconium. Uranium is very similar to
151:29 . So we can start with minerals have a lot of uranium in
151:33 which means that we don't have to forever for the game to came because
151:36 started out with relatively high values. and even out of crystal that the
151:40 , you know, zircon is a if it's a big guy, but
151:46 would be enough. Uh Because, know, because this substitution allows the
151:50 , excuse me, the uranium content be in a zircon might be half
151:55 percent, sometimes up to 1% uranium a mineral like that. And that
152:00 easy peasy to date it. Um , we've got another interesting situation because
152:08 got two isotopes of uranium. but we've got five isotopes uranium,
152:12 two of them have relatively long half . These other ones have really short
152:17 lives. But uranium 235 as we've , has a half life of 703
152:23 years and uranium 238 has a half of about 4.5 billion years because uranium
152:31 has such a short, shorter uh constant um, or half life.
152:40 all the uranium 235 that ever existed earth is gone of the,
152:44 the abundance of, of uranium. of, of all the uranium left
152:48 the in earth is less than The ratio of uranium 238 to 235
152:53 100 and 37.88. And that's just reflection of the one decays faster than
153:00 other, but there's still some left not much, but that's, that's
153:04 big deal. Um So we can an equation for the decay of each
153:10 these uranium 238 decays to lead 206 eight helium particles plus six beta particles
153:21 some energy. I'll just, I'll this graphically in a minute. Uh
153:26 decay constant is there. If you that over and to calculate the half
153:30 there, it is again, 4.47 uranium 235 we can draw the same
153:38 . I mean, put it out again. In this case, we
153:43 uh lead 207 is our ultimate decay uh product. In this case,
153:47 get seven alpha particles and four beta . Now, oh and then there's
153:55 is another thing that, that decays lead. Thorium 232 is the only
154:00 lived isotope of thorium. So we have to worry about the other guy
154:05 we write the equation for thorium Dom decays to lead 208. And here
154:13 is, it has a half life 14 billion years. Now, we've
154:22 these isotopes. There's a bunch of of lead. The only ones we
154:26 to worry worry about are the ones red. You'll note that 206207 and
154:33 are in italics because they are They're the ones that decayed to
154:38 that, that, that decayed that produced by the decay of Uranium
154:44 It's, uh, it's kind it's easy to remember which decays,
154:49 if you just remember that uranium 238 the even one, there's 238 and
154:56 the even one decays to the even . So uranium 238 decays to lead
155:01 . The odd one decays to the one. Uranium 235 decays to lead
155:07 . And then you just gotta remember lead 208 is the bigger one that's
155:12 . Right. Now. You'll note this, this, this uh nomenclature
155:18 that those three are stable. There's isotope of lead which actually listed as
155:24 of half life, but notice how that half life is led to a
155:29 , has a half life of one 10 to the 17th years. That's
155:34 quite a long time. So it's is picking, you know, what's
155:39 difference between having a half life what is that? A billion,
155:47 ? That's 100 million billion years is half life. What's the difference between
155:53 and being stable? I know it's wanted to say, so somebody's measured
155:58 and says, well, if you 100 million billion years, you'd lose
156:04 of your le lead to a So from our perspective, we're gonna
156:08 that stable, which is nice because good to have one of your isotopes
156:12 be stable. So, here's an of the decay of uranium 238.
156:18 see uranium, the, the the red arrows are alpha decays.
156:22 blue arrows are beta decays and you out decaying and this goes on and
156:30 , no matter what you do, , you'll, you'll get down to
156:33 206. Now you'll notice that some these things have two options. You
156:38 , like when you get to whatever is polonium, uh 100 whatever it
156:45 , 200 whatever it is, you see that some of them decay
156:50 this way and some of them decay this way and that's really just a
156:53 of ones that go one way or other. And that's the case for
156:55 lot of these, there's a, branch decay, it can go this
156:58 or that way. But the good is, is that you see all
157:01 branches that come back together to be to a six. So, uh
157:07 all we have to worry about So, uh and, and so
157:11 let's look at the individual decays a bit closer because we can, we
157:15 show that why it is. We make very much ignore these guys in
157:19 middle. Basically. Uranium 238 has half life of 4.5 billion years.
157:24 decays to thorium 234. Thor M has a half life of 24
157:31 So we're moving right out of there quick indicates to proact tum 230 it
157:36 a half six hours. Then we back up to uranium. Uranium.
157:41 has a medium kind of half life 248,000 years for some things. That's
157:47 long half life. But for most what we're worried about, it's not
157:50 long. It decays down to thorium which has a half life of 75,000
157:56 , which we will find there'll be situations where we're gonna worry about
158:01 but generally not. And then those decay radon 226 half life of six
158:09 years and then three days, three , 51 2nd, 35 milliseconds.
158:16 rest of these are all just teeny minutes and seconds, days, a
158:20 of days here and then all of comes eventually down. So there's only
158:23 couple of that long list that are than a few 1000 years. Um
158:30 basically we're gonna fit, we're gonna it down to lead 206 in about
158:36 times the age of the, of longest half life. So it takes
158:42 300,000 years for this system be to completely in equilibrium. So if you
158:51 date uh a sample by uranium if it's less than 200,000 million
158:56 200,000 years. Not really a good , but once you get above
159:00 this whole thing is in equilibrium and gonna ignore rocks that are less than
159:04 half a million years old. For , for this approach, we can
159:09 the same thing about the decay of 235 except it's a little less
159:15 Again, we have some, some decays and some beta decays and a
159:20 of branch decays that go one way another. Um But just as in
159:25 first case, uh it doesn't matter we'll all branch and it'll all end
159:30 in the same bucket down here. look at the uh half lives of
159:35 guys. Um, half life uranium 35 700 million years. But then
159:45 one's in our, this one's 3000, 2000 years, a couple
159:51 years, couple of days, minutes, seconds, seconds, uh
159:58 very short. And then we get here. So in this one,
160:02 even, what's the longest one in thing we got 32,000 years is the
160:07 one. Excuse me? Yeah. that's gonna, that's gonna obtain its
160:14 in 100,000 years easy. And then , we can look at the decay
160:19 thorium 232. It's even simpler. aren't as many possibilities. Only a
160:27 of branches and we get down there let 208. Uh Again, the
160:33 the decay rates and, and the things are pretty short. Here's a
160:37 of years and hours, days, , seconds, minutes, microseconds,
160:43 hours, microseconds. Ok. So just nothing. So that, that
160:48 is established really fast. And for our purposes, we can,
160:53 can just know that there are things the middle. Uh, but we're
160:56 gonna worry about how fast it but one thing we are gonna worry
161:00 in a minute later on, we to go back to or something later
161:09 like here. Yeah, we're gonna attention to the helium because strictly
161:16 that is a, that's a decay too. We can say uranium decays
161:20 lead, but just as well, decays to helium. And,
161:26 indeed, I'll tell this story more , I guess. Yeah, I
161:33 . But the very first rock that ever dated was dated by the uranium
161:38 method, uh, because they looked this equation and they said we got
161:42 helium. It's probably gonna be easier measure the helium, we'll measure the
161:47 . And uh they got, they an answer they weren't prepared for and
161:51 they measured the lead and they got different answer. So when we talk
161:54 uranium helium dating tomorrow in the it, well, just a bit
161:58 a spoiler. Let me, let , let me, let me ask
162:02 this consider cause your temperature, if were to measure in a mineral,
162:10 uranium lead age and the uranium helium . Both of these, the helium
162:17 helium uranium ratio should be proportional to right because this is all happening according
162:24 this half life business. So as goes on, you're gonna get more
162:29 more healing for every uranium that you get eight helium and that's just
162:35 build up over time just in just as in the case of when
162:41 have one uranium, it decays to leg and that's gonna build up over
162:45 . Now, if we were to at a single mineral and measure that
162:52 and look at the uranium lead ratio the uranium helium ratio in the same
162:59 might we expect those values to, give the same age or not?
163:09 the difference between lead and helium can you? Well, that's true.
163:19 , but then when, when they're of a, of a crystal
163:22 that gas versus solid thing is not important. There's this and there's
163:37 it's hugely 100 times bigger, 50 bigger. That means it's gonna be
163:44 to diffuse lead out of a crystal helium, the same crystal, whatever
163:47 that is, if you turn the up a little bit, you
163:50 we talked about how, you diffusion will start acting, it'll act
163:54 on something small, then something So when they date, when they
164:01 dated something they got, they well, let's do the helium because
164:05 get eight of them. That sounded a great, you know, that'd
164:08 easier. But it turns out there very many helium's in there. They
164:13 an answer that was much younger than were expecting because they didn't understand the
164:18 of closure, temperature. When you the rock up, the healing can
164:22 away. But we'll talk more about tomorrow. Um, ok.
164:36 all right. Um Here's just another way to consider the evolution of these
164:42 over time. Here is if we . Um let's see, let's
164:50 here's the proportion. So the solid represent the evolution of the parents starting
165:00 billion years ago. And the dotted represent the evolution of the daughters over
165:06 same period. So two ol uranium 235 is in lead is,
165:11 here in red. So you can that uranium 235 is dropping really fast
165:18 now has flattened out. We're almost of uranium 235 because we've gone through
165:24 six half lives of uranium 235 in space of the age of the
165:31 it's almost all gone. And that's we're gonna have all the uranium 27
165:35 gonna get. But during that same period, uranium 238 in blue has
165:41 decaying and notice that it's, if started out at one, whatever that
165:45 , notice where we are now, basically at 0.5 because we've gone through
165:51 one half life of the, of 238 over the age of the
165:57 And if we look at this last here, uh the green,
166:04 the green one is an even flatter . We've gone at the age of
166:09 earth. We've gone down about 20% what we started with because it has
166:14 even longer half life. Ok. , well, th th this
166:20 this just shows us that we we can date really old rocks and
166:25 young rocks with these techniques because the lives are about right for our
166:31 And again, the favorite mineral for by this system and, and really
166:39 all systems. But like I when, when, when a lot
166:44 people think of geo chronology, this what they think, what they're talking
166:47 . If they don't have a more notion is dating zircon by the uranium
166:53 method. It's the most commonly dated . Uh because it, it starts
166:58 as I mentioned earlier with a high of uranium and a low concentration of
167:03 with lead. It's also very favored the closure temperature of lead is very
167:10 . It's so high that we don't a very good notion of what exactly
167:13 . It's above 750 degrees. It be 1000 degrees. Nobody really
167:18 It's just super, super hot, so high that it it withstands
167:24 you can metamorphose the rock and the lead will not leave the
167:29 which is great. If you want know the original age of some metamorphic
167:33 . Indeed, I skipped over The business we talked about what's,
167:38 do we know the age of the ? The oldest rock that we know
167:42 is this 4.1 billion year old rock Canada that's had its crystallization age 4
167:50 , 4.1. It's a metamorphic but we're not talking about the age
167:55 metamorphism. We're talking about when it crystallized because Zircon has this high closure
168:01 . The other thing we like about is in the sedimentary environment. It's
168:05 tough, it's just as tough as corps. So when you're rolling around
168:09 and sandstone, they're staying there. as we'll talk about tomorrow, uh
168:15 dating is a very big deal these and zircons stay throughout the history.
168:21 so we can use dating of Zircons a provenance indicator because it stays
168:27 Uh Zircons come all the way down Mississippi River, you can date them
168:32 in uh you know, in New . Um they're still fine because even
168:37 they've traveled all the way from so they're, they're robust in the
168:43 environment, they're robust in the metamorphic , they're robust in the sedimentary
168:48 Um That's why they're great. And they have low uranium, uh high
168:53 and low lead. Ok. So could go about dating um uranium lead
169:02 by ISOS in the same way as described ISOS before we can do a
169:08 Aron for uranium 238 decaying just like we're going to normalize with a stable
169:16 of the daughter. So we're gonna by lead 204. We could do
169:20 and, and, and you can that and this technique is not used
169:25 lot and you might use it in to date some carbonate rocks. If
169:29 don't have a fossil in your, your limestone, some people have dated
169:33 uh limestones by this ISO method. same concept, these rocks, these
169:39 formed in an ocean, they had same um lead ratio to begin
169:43 They have a variation in uranium We get an iso can be
169:48 You could also do it with That's 238. You could do the
169:51 thing with uranium 235. Uh The is that the uh the decay.
169:58 you don't get the, the, abundance of your aim 235 is gonna
170:01 really low. Uh which makes it . You could do a nice
170:06 the thorium 232 as well. we are gonna take advantage of the
170:14 that in uranium lead tech uh we got two isotopes of one element
170:20 decay to two isotopes of another Both of the parents are uranium,
170:25 of the daughters are lead and this us. And, but, but
170:34 addition to there being two isotopes of , they have a different decay rate
170:38 different decay constant. So, we've that helps. So we're gonna use
170:43 fact that we've got 22 decay systems the same system, in the same
170:49 to check them against one another. , we could write the equations like
170:58 way, uh to uh to um their different uh decay constants here.
171:05 , I've written lambda eight to represent decay constant of 238 and Lambda five
171:13 the decay constant of 235. So are equations, we could write that
171:18 , that references the ratio of parents daughters to time. Um I
171:26 I think I briefly mentioned this before I think I didn't do it enough
171:29 we, when we see a star that on the, on the lead
171:34 , that means radiogenic lead. That we are, we are assuming that
171:38 have subtracted away whatever lead was there begin with. And in the
171:42 we can say that that was probably . So these two systems, although
171:48 have different uh decay constants might yet give you the same answer. So
171:55 you were to measure the lead 206 238 ratio in a in a sample
172:00 measure the 2072 35 ratio in the sample when you calculate an age from
172:06 , based on these equations, when get the same age, those that's
172:11 to have be a condition of they are concordant, these two
172:17 And so we could draw a graph these isotopic ratios. As described in
172:24 equations. We could draw a graph a line in which all of the
172:28 on that red line have the same in the two systems. So that
172:36 is called the Concordia line. Because , every point on there and you
172:40 see how some of them have have been annotated, there's the 500
172:43 point, there's the 1000 million, the 1500 million and so forth.
172:48 some anything that lies on at that here, if you were to,
172:53 you were to fall down here to value and then calculate an age based
172:57 this 3.1 something that would give you age of 1500 million. If you
173:03 over here, it's a very different . It's not 3.1 it's 0.26.
173:09 because it's got a different decay you calculate in age, it would
173:12 give you 1500 million. So you've Concordia, all of this red line
173:19 called the Concordia line. That's good . Well, um see where we
173:30 , we'll get back to the Concordia in a minute. Um Going back
173:37 our two equations. Um we could divide these two equations by each other
173:47 rearrange them so that we could get relationship of the two isotopes of the
173:56 radiogenic isotopes L 207 and L That's uniquely dependent on just this thing
174:04 . The, the ratio of uranium to 238 which is a constant.
174:10 , that's just a constant. We what that value is. That's 100
174:12 37. And then there's this the, the, the,
174:18 the e, the land T for two different systems. Now, the
174:22 here is that although we can measure or excuse me, we can measure
174:27 lead isotopes in the lab. That's thing, we can go measure,
174:32 We can't solve this equation for T once again, T is in the
174:37 in two different places. So we solve for T. But what you
174:42 do is just plug in tea a of times and make a day to
174:47 . You could make a table like and say for various, I
174:51 and this is a very coarse table I've made up. It, it
174:55 every 400 million years. But you , you could make this table around
175:01 value you wanted to suppose. you measure the value in the lab
175:05 then you could just increment it very to figure out what it was.
175:10 what I'm saying is if you measure in the laboratory, you can then
175:15 , that's, that corresponds to 1.6 years. So this is one way
175:19 go. If you could just measure two isotopes that are the daughter
175:25 you didn't even have to measure the situation. Measure the lead because they
175:30 at different rates. The they, grow at different rates. The lead
175:36 to lead 206 ratio is a unique of the age. Uh So that's
175:42 way to go, but there's still power in this Concordia diagram. Um
175:50 let's just say, for example, have a point that we measured on
175:53 , on our graph. It's that dot We've got three different possibilities for
176:00 the age here. If we measure down, we get the uh the
176:05 207 age. If we measure across the Y axis, we can get
176:10 lead 206 age or if we measure the in from the origin up to
176:18 , that's the lead 207206. um it is the case now that
176:30 is what, what's shown here in blue dot would be called a discordant
176:34 where the lead 207 age and the 206 age are not the same because
176:39 doesn't plot on that on that red . Nowadays, we can be very
176:50 about which zircons we look at and know just by visually inspecting them which
176:55 look nice and which ones don't. we can really try and avoid discordant
177:03 . But I'm gonna tell you about points because you may have to read
177:07 of something. You know, if go into some region where the geology
177:10 not been well done and some of geo chronology might be old, there'll
177:15 discordant data. And so what's what has done now and was done
177:21 the past is that we will get rock, whether it's a granite or
177:26 rite. These would be the most rots. Zircons are more common
177:32 in uh Fels pye rocks. So are mostly found in rites and
177:42 And so the, the, the from a Strat democratic point of
177:46 , a rite is best because it granites, it has zircons in
177:51 But even if you find a nice , you're gonna want to support the
177:56 segregate them. Here's a picture of zircons from a particular rock and you
178:00 they're, they're not all the they've got different sizes and shapes and
178:05 got pollutions and stuff in them. what will be done is after you've
178:11 the, after you've obtained these zircons , and by the way, so
178:16 would get a bunch of zirconi, gotta crush up the rock and then
178:20 got to separate the heavy minerals from light minerals using this this heavy
178:25 these liquids that have really high And so you can pour your powdered
178:29 in there and all your quarts in Fels bar will actually float on top
178:33 this liquid and your zircons will sink to the bar. And so eventually
178:37 get a nice concentrate of zircons and like that. But even then you
178:42 sort these zircons by these characteristics like size, their color, their shape
178:47 their magnetic susceptibility. The magnetic susceptibility nice because that's a machine you can
178:53 to do that to sort them by . You have to get a piece
178:56 , you get tweezers and actually move blue ones over here and white ones
179:00 here. It's very tedious, but it will show up a show a
179:05 on the diagram. But however, do it, you can separate these
179:10 out and then you will see the on this diagram. So this diagram
179:19 called the Uranium L Concordia diagram or called the weatherill diagram named after George
179:24 who thought it up. And if uh had discordant data and,
179:35 and this was very common in the times of doing this, let's say
179:39 19 eighties, you'd see this sort data a lot, not so much
179:43 . But if you have uh discordant such as this, they, they
179:48 plot in a fashion such as And so the red line as I
179:53 is called the Concordia line. The line is called the Discord line.
179:58 it's, if, if you get nice straight line like that,
180:01 it's potentially interpretable. You've got an intercept and a lower intercept. Now
180:10 to interpret these things. There's two going on here. Um We've got
180:18 situation in which these, these points started up here and have been drawn
180:23 on this line based on, on unknown, some, some difficult to
180:27 sort out issues, but maybe because , of, of alteration, maybe
180:34 of diffusion, maybe because of, don't know but some, but it's
180:38 that sometimes these things will start up and be drawn down towards the
180:43 In which case, we interpret the intercept to represent the beginning where this
180:47 started. And these things have been away. And if you have a
180:50 line like that, OK, that's . Unfortunately, there's another way to
180:56 that is that maybe, uh and me go back to this picture of
181:01 . Uh And we see, we have a really good example here,
181:07 show you some others in a minute tomorrow, but like, all right
181:14 , see right there, there might a little bit inside that Zircon,
181:17 a little bitty round spot in Maybe there's one there, maybe.
181:23 I told you that Zircons are they'll stick through the igneous metamorphic or
181:28 environment. They are so robust that can take an old rock like an
181:33 granite or an old sandstone and you it under the right tectonic conditions,
181:37 could melt it. Ok. When melt that rock, you melt all
181:42 quarts, you melt all the F , you melt all the bow
181:45 easy peasy. The zircons still hang there. You can't even melt some
181:51 . And so that zircon will be called um xeno christic. It's from
181:57 older crystals, it's foreign to this magma and that little bit of old
182:04 can hang in there. And then new zircon as this magma then crystallizes
182:09 new zircon will form around that old . So you have a core of
182:14 and a younger bit. And so you were to analyze that entire zircon
182:18 some group of zircons, the age would get would be some combination of
182:24 age of the old bit and the of the younger stuff that grew around
182:28 . And so that's how one way you might interpret an an orientation like
182:32 is that we're mixing between a population old zircons and a population of young
182:39 . And that's, it's a mixing in here. In which case,
182:42 crystallization age of your rite would be here. OK. Um So Accordia
182:52 Cordia upper intercept. So here we the, the, the,
182:56 the conundrum, the upper intercept can interpreted as the age of crystallization or
183:04 age of the inherited component stuff that there and didn't melt. Alternatively,
183:11 lower intercept can be interpreted as the of crystallization or the time in which
183:16 lead loss event has occurred. How we gonna be able to tell the
183:20 between the two? Oh Well, we, uh uh let's, let's
183:28 about this l loss idea a little before we go on. Um So
183:35 is um some of these weather diagrams the top here, we'll ignore this
183:41 down to the bottom. Um Imagine rock that is say 1700 million years
183:48 . It gets to this point where red dot is, but then something
183:52 to it and it, it, zircons that had this condition are,
183:59 pulled down towards the, the, growth of new zircon or the loss
184:05 , of uh lead you need, pulled down this way and then
184:13 this disturbance event is over and they to evolve, moving from, from
184:19 place to these to this new place . So this, this, this
184:26 of data now looks like this. go from here through here, through
184:31 . And so what we would say that, well, this looks like
184:35 rock is this old, but it disturbed at this time. And so
184:41 would interpret this to be the real and this is just a reflection of
184:45 that happened to it. Um what happen to it? Variety of
184:52 Actually, I don't think I want trouble you with that. Um But
184:56 just take some more good examples of data. Here's, we're going back
185:02 central Texas again. Here's a similar and the one we looked at for
185:07 Stron. And here we have a of zircons. These are all zircons
185:12 we have a bunch of points which , and, and notice that we're
185:16 in here, we're not showing the the, the, the uh origin
185:20 this diagram. We've zoomed in to look at the ages from 800 to
185:26 . And we've got one point here plots pretty close to Concordia and then
185:30 other points that fall off here like and what these points will have,
185:35 points will have been segregated by, I said, by color or by
185:40 susceptibility or by whatever they chose. , but this is, there's a
185:45 from 1992 and back then, the spectrometer were usually not sensitive enough.
185:54 , I should say it depends on kind of mass spectrometer you have.
185:58 back then often you would be looking each one of these points represents more
186:07 one zircon. They had to push sample in there to measure the sensitivity
186:12 the machine. Usually couldn't handle just grain because they couldn't tell the signal
186:17 the noise. So they would use few grams, 10 or 20 or
186:24 . Um And so that's what each of these things would be and they
186:28 vary again by color or magnetic susceptibility size or shape. Somehow. They
186:35 wanted to segregate them and, and a spread on this diagram. Of
186:40 , if all the, if all points land on the red line that
186:44 all concordant, it doesn't matter how segregate them. But the point was
186:47 that they, they would expect this distribution of data. So if you
186:55 a nice line, then you can that up and see where it intercepts
186:59 . And that's what they're after. were expecting a line that was
187:05 But once you got data like you would draw a line 1082.
187:09 right, there's your answer. That's age of the rock. Notice that
187:12 the same age we got for the strontium age, which was what,
187:16 81 or something. I can't It's the same. Um So I'm
187:24 skip that. Oh no, I'm . Well, I'm just gonna tell
187:27 that when we talk about zircons and melting, there's a, there's a
187:34 we can figure out whether a zircon gonna melt or not. It depends
187:37 the temperature and the composition, but zircons they don't melt. So we
187:41 have to worry about that. But is an example of where we could
187:45 a rock that uh has an inherited . This is a, this is
187:51 , a sand uh a granite from Arizona, from Arizona, excuse
187:56 near Tucson. And we see that a bunch of points here. There's
188:01 of them there, there's one of there and they, they define a
188:04 line that goes up here to 1400 and goes down here to 66
188:12 So if we go back to that slide, we can interpret the upper
188:19 as the crystallization age or the lower as the crystallization. What are we
188:26 use to figure out what to Well, you, you might want
188:34 have a geologic map of the This is a granite, let's
188:39 right? This granite is intruding some older, younger rock or older
188:43 right? So you go to the and, and in this case,
188:49 granite is intruding uh Jurassic rocks. does that tell you about the age
188:58 the granite? It has to be than Jurassic, right? So the
189:01 crystallization age of this granite can't be . It could be this. It's
189:07 66. So how do we interpret ? That this is a rock that
189:13 the older mesozoic rocks. It's a rock itself, it intruded 66 million
189:18 ago. Why does it have this behavior is because the rocks that melted
189:26 million years ago had some zircon in those zircons did not completely go away
189:33 that magma was formed. And so that magma is formed, and then
189:37 magma crystallizes new zircons start to grow on top of the old zircon.
189:43 this one, either this one has particularly well represented old bit. This
189:48 has a poorly represented old bit and just a mixing between the two.
189:54 so you have to combine your understanding how these zircons might be distributed on
190:00 diagram with your understanding of the local . So not hard to say this
190:05 was crystallized 66 million years ago because can't have crystallized 1400 million years ago
190:12 it's intruding rocks that are only 300 years old. OK. OK.
190:22 Yeah, that's what this, that's this says here. It's intersect
190:25 this no, this value because remember red line curves down, right?
190:30 so this will intersect at 1413. what that means. Yeah, I
190:38 , it may intersect at a really number. But I mean, because
190:41 , well, if we, if are modeling this as a straight
190:45 it will have to inter it, will have to intersect because the red
190:49 curves and curves only in that So yeah, um let me show
190:57 another example of inherited components of this from even older data. But the
191:05 idea is still the same. This from the Idaho Baffle. And here
191:09 have another pretty clear example of Here, we have four points which
191:15 cluster is really close to the, the uh Concordia line. And then
191:19 all zip off towards 1700. Um should point out, let me go
191:25 to this one. Not only do look at the geologic map to say
191:30 this rock intruded mesozoic rocks, but we look at the whole other region
191:35 what's the sort of, what's what's the basement rocks in this region
191:39 might have been melted to produce There's a bunch of rocks in Southern
191:44 that have an age of about So it's not surprising that the age
191:50 the inherited component is the same as we expect to find in the lower
191:55 in this region. And we see same thing happening here in uh in
192:02 , the broad age of the crust the deep, the pre the precambrian
192:08 . If you go and look at the precambrian rocks in Idaho S 1700
192:12 a real common thing to find. so the fact that this thing seems
192:16 be mixing between 47 and 1700 is normal. That's the age of the
192:25 that melted. But the, all zircons didn't know. And so we
192:32 this as a mixing line more once , moreover, this, this Eocene
192:39 granite is clearly an Eocene granite because intruding rocks that are olden. This
192:45 not a precambrian rock because it's intruding stratum. Um It's hard to
192:59 I'll give you another example from something I published uh from my phd
193:04 many years ago. Uh And this a little bit of a complication of
193:09 . This is Zircons from a granite Mount Everest. And here we show
193:16 single zircon and by the way, , these, this, this,
193:20 example here from 1981 all of these are multiple zircons because again, the
193:26 spectrometer was not sensitive enough to be to measure a single grain. Uh
193:31 the best they could do. But this paper, which is just a
193:35 years later, but it was had more modern uh uh mass spectrometer.
193:41 of these points are singles or Now as we move it up in
193:48 , we'll be talking about measuring little of zircon. But here we've moved
193:51 the point where we can measure one . This was 25 sir.
193:57 but as we start measuring smaller and bits, we can start seeing more
194:04 . And here we have a granite we are interested in figuring out the
194:07 of. And so a bunch of were collected and they were all analyzed
194:12 you see that they spread out all the place here. Um But one
194:16 them plotted pretty much right here at million, but all of these other
194:22 plot all over the place. And you draw two lines between these four
194:28 that goes up to 500 million, one with a different slope still intersects
194:34 you, you know, because of curve there, but it intersects at
194:38 billion. And if you look at geology of the region, we know
194:43 this was a Miocene granite, that's a problem. But we also could
194:49 and see what kind of rocks are there that could have been melted.
194:52 are quite a lot of four division in this region. 500 million,
194:57 also precambrian rocks that are about 2 . So what we have is not
195:02 single source of mixing, but we the, the juvenile material down there
195:07 20 then a range of, of zircons that might be between 502,000.
195:12 that we're just seeing the, the of that here. Um So this
195:18 the same idea we're looking at but now it's a more complicated inheritance
195:23 multiple sources. If you went back tried to do this sort of
195:28 say in the 19 seventies, they have done single grains, they would
195:32 done 10 or 15 grains at the . And they would have probably defined
195:35 sort of raggedy line that was somewhere the middle here, that would have
195:39 a state, they would have they would have probably said,
195:42 you know, that's a mixing line 21.6. And that probably that these
195:50 don't suggest a single mixing line because data are more sophisticated because now we're
195:56 at one grain at a time, I say nowadays, one grain at
196:01 time is sometimes too coarse. Uh we'll say, the next, the
196:05 step up in technology is shooting these with lasers. Um No, and
196:14 we are the uh what these data produced by a technique. Let me
196:27 . Where am I am I going this? Uh Oh I gotta do
196:44 at the end. Um OK, do that later. Uh These data
196:57 produced by a technique called thermal ionization spectrometer. Well, I'll, we'll
197:03 , we'll talk more about that But what's required of this technique is
197:08 the Zircon, putting it in some and dissolving it entirely and then measuring
197:13 bulk isotopes on that whole crystal and it shows up like that. But
197:22 since about this time, I mean , yeah, since about this
197:30 there have been other machines available. And uh as time goes on,
197:37 machines have gotten a lot cheaper. what they can do as shown
197:42 these little white circles, you can take a single zircon like this one
197:49 shoot it with a laser beam or ion beam and, and liberate material
197:54 that teeny little portion of the And then that that material is then
197:59 and then sucked up into a different of mass spectrometer, but measured,
198:03 the isotopes, same sort of And you can understand what the age
198:07 that part of the crystal is. me, that part of the
198:11 as opposed to that part of the . And you can see this,
198:14 grain seems to have a core so , that crack there and then there's
198:19 other bit around it. And nowadays can go in there and grab that
198:25 , that's 1991 and that bit there 203. So suppose this came,
198:32 , this is from a nice, this could just as easily have come
198:35 a, from a, a And if you were to date this
198:41 by the old method in which you the whole thing, you're not gonna
198:45 1900 you're not gonna get 200 you're get what uh 1700 you know,
198:50 , some, some, some uh value. And if you're interested in
199:00 old history of this rock, you , you wanna know about the
199:03 if you're interested in the young history this rock, you wanna know about
199:06 200 but doing the old way, get a 1700 which doesn't mean nothing
199:11 1700 million years ago to this rock the, the interesting times are 219
199:17 . But you wouldn't see that in old ways. Um And this just
199:22 another example of a, of a core in there. That's a little
199:26 bit, that might be quite a older. Uh And so we have
199:31 pay attention to that kind of Now, um Let's see. Um
199:48 , however, the Zircon's plot kind nice. Here's a bunch of Zircons
199:52 are all concordant. They're, they're all on top of one another,
199:55 they go, if you take the of all these guys, you can
199:58 a nice age for this volcanic rock 377. Um But sometimes you can
200:07 that there's clearly a history going on these zircons that are complicated. There's
200:11 metamorphic outside which is unzoned, an inside that is zoned. Uh And
200:20 need to be able to sort that . Here's another example. This is
200:26 a rite. This is another one my rocks that I dated to.
200:29 this was a, a rite that involved in a fold. We were
200:33 in the structural history of this So we wanted to figure out how
200:36 the fold was. We dated, youngest rock that was folded and this
200:40 how this was done in, I know, 2000 and when was this
200:47 2010 maybe. And it was done at uh um and we have a
200:53 here that can take these zircons and little, you can see the little
200:57 in them. These little holes is what the zircon looked like.
201:01 these holes were added as we zapped zircon and then liberated the material from
201:07 and analyzed that bit. And you see that the ages are given in
201:11 here. And you can see the of these zircons, 100 microns.
201:14 these are pretty big zircons and these were pretty clean zircons. We
201:19 see any really serious cores in but we went ahead and zapped them
201:23 over the place because we didn't know weren't gonna be cores. The ages
201:26 all about the same. We plot on a histogram and we get an
201:30 here. So these ages are calculated with just the uranium 238 approach because
201:39 , they're often discordant when they're this . And so we take it,
201:43 , we assume that if we put a bunch of uranium 238 ages,
201:51 will cluster around the true age. But we have to continue to worry
201:57 this problem of uh if we see like that and we're interested in the
202:01 of crystallization, we're gonna zap it the corner here. If we're interested
202:05 the old part, we go for . Um got a few minutes and
202:14 so, oh we got a That's a whole another thing.
202:17 no, no. So we got , I'm gonna stop here because my
202:20 is going and this mono is another story that we're gonna have to talk
202:24 . So tomorrow morning, we will here and we'll finish the uranium lead
202:31 and then we'll go on to the argon stuff, which is already loaded
202:36 . I'll have to, I'm gonna on these slides. I've still,
202:39 basically don't have to do much, I'm gonna, I'll load up some
202:42 slides tomorrow that or I'll send them we'll get them loaded up. So
202:46 can download those tomorrow morning. any questions? All right, we
202:56 carry on with more dating of uranium , uh, in the
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