Notes for Reading Geochemical Fingerprints

Notes for Reading Geochemical Fingerprints Notes for Reading Geochemical Fingerprints Go over syllabus structure of class introduction of some applications so have road map of how geochemistry used, P[.]

Notes for Reading Geochemical Fingerprints

puzzle solving homework assignments and some labs

These to be done mostly outside of class Will set up times for lab to be open in evening

2 exams, First will cover processes and analytical techniques, 2nd will cover applications.Report to class on a published paper using geochemistry to address some problem about

20 minutes each (for 10 students)

Mostly Archaeological examples….some environmental or geological

feel free to correct my pronunciation!

Deemphasize details of chemical processes, chemical equilibrium

But cover it some There is not single or simple procedure for applying geochemical methods to archaeological finds Have to be creative and innovative If you don’t

understand how geochemical differentiation works, then can’t be creative or innovative inapplying it

Colossi of Memnon: (use computer graphic or overhead, showing N and S Colossi)(goal: start thinking about uncertainty in data and what it means, how a graph helps understand that uncertainty and whether data distinguish two materials as being different

Built fires to try to crack stone But stone made of Quartzite…Monomineralic, and simple compositional structure (Quartz=SiO2) Also the structure of quartz is isometric, meaning its structure is the same in all directions It expands more evenly when gets hot Does not crack Also, coefficient of expansion not real high to begin with Efforts failed.Earthquake succeeded in 27BC, Northern of the 2 Colossi lost upper half of body

Repaired by Roman emperor Septimius Severus about 200 years later (according to Greek Historian Strabo)

Did repair use Quartzite from same area, or had area of active quarrying changed? Where was the quarry?

Show computer graphic or overhead of map from Bowman et al 1984

Major quarries north and south of area of Colossi (Gebel el Ahmar, Silsila, Aswan)But quartzite made mainly of quartz Can’t always tell apart Sometimes trace

constituents show up as color differences, or may be differences in minor minerals But Trace chemistry a good way to tell (explain trace chemistry)

Data table 1 (major elements) (hand out) Quarries at Silsila and Silwa strikingly

different even in major element chemistry (show with CaCO3, and SiO2)

Rear block looks like Aswan by SiO2 analysis But the problem is that SiO2 could not bemeasured by their analytical technique! It was calculated by subtracting everything else from 100% Not very credible

Have them look at other elements and try to decide which quarry each came from (Rear block added by Romans, Main block part of original) explain “<” symbol and

significance

(prompt to compare rear and main…are they the same? how can we tell? go through consideration of +/- uncertainty Ask specific elements, MnO, TiO2?

Data table 2 (trace elements) (hand out)

Can look at other elements Decreases the chance that there is a chance correlation

between rocks that weren’t from the same site! All elements need to match up…

otherwise might be fluke correlation

Have them look at Th Could you identify the source on the basis of Th? Why or why not?

No: Th varies too much within sources and both parts of pedestals are within range of each source

Show graph of Eu vs Fe Useful to show with two elements that distinguish More reliable to use all elements of course But human brains can’t deal with it as easily and hard to illustrate on a flat piece of paper by any means other than statistical reports Nice

to have a graph Randy Korotev, if you can’t see it in a graph, all the statistical tests in the world aren’t going to help you

graph gives view of scatter important in assessing variation and whether one can really tell which group something belongs to

Eu probably in feldspar-so mineralogical analysis could have yielded similar results But,less data: 1 variable, mineral proportions, less reliable than many compositional

variables

bowman et al, 1984, archaeometry v26, 218-229

Review: Geochemistry as a tool,

1) look at processes because need to understand them in order to know how to use 2) Look at statistics (mostly conceptual) because otherwise don’t know what

geochemistry is telling you (Consider how data acquired, # samples, uncertainty)

3) Examine processes and technologies used in past (glass, ceramics, metals, etc),

because can’t understand how to use geochemistry unless understand what it’s being applied to

4) Look at examples of application as practice in using tool and to show some of ways it can be used

Summary of ideas from Colossi of Memnon example:

Define uncertainty, precision, accuracy

Each quarry has a unique geochemical signature, even if rock type is the same

To use geochemistry, you have to consider not only the measured concentration of

an element, but how much natural variation and analytical uncertainty there

is in the measurements

More measurements increases confidence

Considering more elements yields a more believable result because it decreases the likelihood of a chance correlation More measurements also increases

confidence

Graphing the geochemical data can make it easier for the human mind to visualize whether the two compositions are the same or different within the chemical variation

Mineralogy affects material behavior as well as chemistry

Another note: authenticity of an artifact can be tested through geochemistry The repairs to the N Colossus were readily distinguishable from the original on the basis of geochemistry

Activity: Write down, as though trying to convince someone else, where the blocks

of the northern Colossus came from and why you believe it Trade your

paragraph with someone else who will critique it

Pre-industrial Pb pollution:

Introduce idea that one needs to know background level before human pollution

contribution can be determined

background: that which would exist without human input

historical: that concentration which has existed historically

Lake stratigraphy, provides a means to establish historical pollution, background

pollution, and the effects of human activity over an extended period of time

When might you expect Pb levels in lake sediments to increase and why?

How is Pb getting into the lake sediments (source: direct deposit from air, washed into lake from air deposit on land, washed into lake from human caused land sources)?

Computer image or overhead of Europe showing Sweden: look at lake sediments in Sweden from ~Bronze Age to Present

Influenced by any local mining, but more significantly by any air borne material

generated by the developing metal industry

Show Computer graphic or overhead of Graphical representation of sediment core Pb deposition data from 3 lakes and fly ash data from one

Analysis: industrial revolution…where is it? Blip at very right, last 150 years or so shows up in SCP (spheroidal carbonaceous particles… fly ash characteristic of oil and coal burning)

But increase in Pb before this Draw on board, showing start of rise around 500BC, peak around 0 BC, dip, then increase into present age

Renberg et al., 1994 Nature 368, 323-326

Show computer graphic or overhead of onset of metallurgical techniques (cupellation is a process where metal is purified by oxidation at high temperature with oxidizable metals dissolving into a containing cupel), coinage, Roman Pb mines, etc

Can establish the present human contribution of Pb to lake sediment

This reflects Pb in atmosphere

Can establish past human contribution of Pb to lake sediment

This can be correlated to coin manufacture and mining of Pb by Roman Empire

Other factors to consider: weather patterns, where Pb brought from

might look for effect of going to unleaded gasoline

Summary of ideas from Pre-industrial Pb input into lake sediments:

Stratigraphic variations in chemistry, such as in lake sediments, can reveal past

changes in pollutants in the atmosphere

This can help establish the present human input of pollutants to the atmosphere

It can identify or confirm past mining and industrial activity

Key idea is often the correlation of chemical trends with time with known activities.

Greek Attic Red-on-black pottery:

530BC a new pottery technique was invented in Athens Involved a striking red-on-blackcolor

Even into the 1940’s it was not obvious how it was done

Problem was, chemical analysis revealed that there was no difference, chemically,

between the red and black areas Not simply painted on No pigments Not a glaze (a material of different composition, melts at a lower temperature producing a glassy coating)

How was it done?

Understanding the progress of technological development, and how technological skills were maintained, applied, and spread to other areas of interest Aided by understanding what was done….relationships with other, similar processes help us understand the development of the society and its technologies

Various metal oxides can act as pigments MnO = black

(Show overhead of black on red, ca 560 BC)

Black on red Easier technique But also no difference in composition

But the black areas were finer-grained, smaller particles, under a microscope.

Before the pot was fired, a finer-grained slurry was painted onto the pot as a slip

(slip is a wetter,thinner slurry added to a ceramic before firing, often to provide a

The fine grained slip prevents oxygen from getting to the slip-painted areas The rest of the pot turns red, voila! Black on red!

In the 1940’s realized that the Red on Black was a similar, but more complex process.Observed under microscope that Red areas were rough and porous,……black areas were fine grained, smooth, not porous

Process:

1) select finer particle slip, add wood ash for alkali (flux = lowers melting T slightly), paint areas that will be black (areas in between the figures)

2) fire in oxidizing atm at 850C entire pot red

3) Add green and wet wood to fire, produces CO, reducing atmosphere Increase Temperature…….pot turns black as Fe is reduced to magnetite… slip melts and seals ceramic

4) Temperature decreased slightly, dry wood replaces wet and the conditions are

returned to oxidizing non-slip portions of the pot oxidize to red, but the vitreous slip hassealed other parts of the pot and oxygen cannot reach the Fe to oxidize it….stays black

Pottery in the Attic style (like these) in the Metropolitan Museum of Art were examined once this technique was understood The colors in these pots were found to be a result of different pigments used in the pots Thus, they were shown to be forgeries

Summary of Greek Attic Red-on-Black Pottery:

Texture as well as chemistry can yield information about what manufacturing process was used (pottery, also metals)

Understanding chemistry of color and be valuable in trying to understand how something was made

Understanding how something was made provides insight into cultural and technological change

Geochemistry Puzzle Assignment #1:

Atmospheric Mercury deposition in Minnesota Lakes in modern times.

Be careful, complete, and neat in your answers I don't want un-interpretable scribbles with numbers strewn all over the place, nor do I want hand-drawn graphs on notebook paper Be professional!

This assignment is intended to exercise your ability to graph and analyze data A large part of applying geochemical data is the creative ability to conceive of ways to graph or manipulate chemical numbers to help you understand what it really tells you about the problem you are addressing

This problem is not intended to be a simple calculation, but rather it is intended to be a puzzle where the real goal is to figure out what calculation to do, what graph to draw, or how to interpret either calculations or graphs Key things to remember are that mercury

is added both directly to the lake surface (surface area on the table below) from the air, and also runs into the lake from the associated drainage basin (catchment area in the tablebelow)

This problem is adapted from the research of Swain et al., 1992 Increasing rates of Atmospheric Mercury deposition in midcontinental North America, Science v257, 784- 787

1) Considering the data provided, how has Hg deposition in Minnesota lakes changed with time? (hint: look at time vs Hg accumulation graphs)

2) How does the accumulation rate change with lake surface area and catchment area (catchment area is the area of land that drains into the lake)?

(hint: look at the data table and consider accumulation rates, lake areas, and catchment areas…are simple relationships seen between accumulation rate and either lake area or catchment area?)

3) Consider Thrush lake and Kjostad lake Why doesn’t the deposition rate increase by 25x when the lake size increases by 25x? (hint: consider the units in which deposition rate is reported)

4) How much Hg is being deposited directly into the water from the atmosphere today? (report in micrograms per square meter per year- units is an important hint in figuring outhow to figure out the answer) hint: the way to think of this problem is to imagine a lake

that has no catchment area at all (catchment area excludes the lake area), or catchment

area/lake area = 0 You can make a graph showing accumulation rate (flux) vs

catchment/lake area and project to 0

5) How much Hg was being deposited directly into the water from the atmosphere in preindustrial times? hint: use the same hint as question 4

6) Assuming that this same amount of Hg is being deposited on each square meter of land in the catchment areas (as is being deposited on water in question 4), how much of the Hg deposited on land washes off into the lake? hint: pick a lake, say Meander Subtract the amount of Hg deposited directly into the lake from the total accumulation The remainder must be the amount washed in from the catchment How much is this per square meter compared to the deposition per square meter? Does most Hg that deposited

in soil areas (non-lake) stay in the soil or does it wash off into surrounding lakes?

7) Hg accumulation rate is actually calculated by measuring concentration as a function

of time of accumulation Time is determined by 210Pb dating (a radiodating technique) Suppose that for a particular layer of sediment, the sediment accumulation rate as

measured from the Pb-isotope ages of the sediments, is 4 grams per square meter per year(4gm-2year-1) If the concentration of Hg in the sediment of that layer is 5parts per million(5ppm), what is the Hg flux into the sediment (in micrograms of Hg per square meter per year)?

Hint: this is not a hard math problem The challenge is to conceptualize what you are doing and why, then do the simple calculation

Data determined from Swain et al., 1992 Flux is in micrograms per square meter per year (µgm-2year-1) Area is in millions of square meters.

flux

preindustrial flux

For this class, mainly need to have a conceptual understanding of the fact that different

elements partition into materials differently For example, Alcohol partitions into a gas

phase more than into a liquid water phase Thus, when heat water, alcohol evaporates preferentially But some remains in water

Rock-magma

hydrothermal system-ore deposit

sediments-groundwater

water-air

liquid water- ice

two different crystals in a rock or magma

The degree to which any element partitions between any two materials can be measured

as a function of T, P, X, fO2, pH That is what I want to get to primarily in this lecture

However, it is good to have an understanding of the chemistry associated with this partitioning It is good for you to grapple with it So I’m going to at least mention the roots of this relationship mathematically

Components of Energy:

Work = w

w =

note: negative sign indicates work is positive when volume decreases

Changes in volume and pressure affect work Compressing something increases energy, expanding lessens (or uses) energy (transfers it to the surroundings)

Heat = q

q =

This defines a relationship between temperature and heat As add heat to something, its temperature increases The equation shows how increasing T results in an increase in heat (energy) to the system.

∆E (change in internal energy) = q + w

This expression is equivalent to the 1rst Law of Thermodynamics in that it shows a balance of energy between what is added to a system and what that system contains.(Energy can be converted from one form to another, but it cannot be created or destroyed)

We’re going to skip the mathematical derivation, but there are important terms that we simply define because they are useful in describing what makes a reaction “go” These arise from transformations of E

Enthalpy = H ≡ E + PV

Entropy = dS =

notes: the ratio of dq/T is found in experiments to be a state function, meaning that it is only dependent on its present state, not the pathway it took to get there This ratio then is

a fundamental property of a material as T changes The result is that T affects the ability

of heat to do work, low-temp heat can’t do as much work as high-T heat

We have come to associate entropy with the degree of randomness of a system, with higher temperature favoring greater randomness and the universe trending toward either equal or greater entropy (2nd law of thermo.)

Gibbs Free Energy = a value that tells us whether a reaction will proceed or not, and to what degree Therefore a key in understanding partitioning, a reaction of an element between two materials

Gibbs Free Energy = G ≡ H – TS

∆G = 0 at equilibrium

∆G > 0 reaction proceeds towards reactants

∆G < 0 reaction proceeds toward products

at equilibrium,

Can be modified to account for other changing variables of the system For example, at constant P but changing volume, the term +P∆V can be added (where ∆H is taken at STP) More pressure makes reaction favor the lower volume reactant or product go through example of graphite-diamond transition considering effect of P (delta V), and melt-solid transition considering the effect of T (Delta S)

RTln [products]/[reactants] = RTlnK

Examples of what K (equilibrium constant) is:

Ca++ + CO3 ⇔ CaCO3 (note: living things can alter result from equilibrium)

K = [CaCO3]/([Ca++][CO3 ]) note: [ ] designates chemical activity often

approximated by concentration, or concentration times a fudge factor

Ways of thinking of equilibrium (all equivalent):

1) [CaCO3]/([Ca++][CO3 ]) must stay constant at equilibrium If we increase Ca++, CaCO3 must increase to compensate

2) If we increase Ca++ (reactant), G will decrease and reaction will proceed toward products (CaCO3)

3) key idea: if increase the activity (concentration) on one side of a reaction, the reactionwill proceed in the opposite direction

Every balance of compositions is a function of T, P, X Living things, and kinetics (rates of reactions, may not be equilibrium), also affect.

The result is that everything has a unique compositional fingerprint But tracking that fingerprint can be complex because so many things can cause differences

Focus on partitioning:

We can imagine reactions between any two things for each element:

Yb in seawater ⇔ Yb in a clam shell

∆H – T∆S = -RT ln([Ybshell]/[Ybsea]) [rest of K]

Zn in seawater ⇔ Zn in flint

Zn in groundwater ⇔ Zn in flint (can modify original composition)

Ti in mineral ⇔ Ti in magma

weathering can modify compositions (T, P, fO2, pH)

e.g Clays reflect source rock and weathering conditions

Partition Coefficient: A simple ratio, simplifies chemistry

What is the concentration in the solid before melting? (0.1%)

What is the concentration in the solid after some melting? (~0%)

What is the concentration in the liquid when completely m elted? (0.1%)

What is the concentration in the liquid when half the rock is melted? (0.2%)

What is the concentration in the liquid when the rock is 10% melted? (1%)

For each prompt: how much E is in the solid (or liquid) and how much solid or liquid is there?

Concentration of an element in one material

Concentration of an element in another material

Obsidian compositional variations:

Igneous rocks involve melting and crystallization Variations in the degree of melting or crystallization have a big effect on composition

Suppose, underground, the magma

that the obsidian flow is derived

from is slowly crystallizing

Consider an element excluded

from the solid (often Th, or REE

are excluded)

Will the concentration of this

element be higher or lower in flow 3 from flow 1?

It is possible to figure out not only which region an obsidian point came from, but which

flow, even if they are compositionally similar If quarrying occurs top down, this can

yield temporal information

Geochemistry Puzzle Assignment #2:

Geochemistry of volcanic glass in archaeological sites.

Suppose that you have three archaeological digs near a single active volcano It is knownfrom geological work that the magma-chamber-source for this volcano contains

crystallizing feldspar Eruptions often contain phenocrysts of feldspar Experimental studies show that the partition coefficient for Ni between feldspar and melt is very low (say <0.01 for Conc Ni in feldspar divided by conc Ni in residual melt) Analysis of small glass beads found in the artifact horizon at each site, associated with an eruption of this volcano, yield the following results:

Glass beads at site 1 contain 6ppm Ni

Glass beads at site 2 contain 10ppm Ni

Glass beads at site 3 contain 5ppm Ni

1) Which of these 3 sites is the oldest and which is the youngest? Explain your

reasoning (hint: how will the concentration of Ni in the remaining melt change as some

of the melt crystallizes into feldspar which contains almost no Ni?)

2) What fraction of the melt present at the eruption seen at the oldest site has crystallized

at the time of the 2nd oldest site? (Hint: consider all the Ni to remain with the melt Howmuch does the amount of melt need to change to yield the observed change in Ni

concentration?)

3) What fraction of the melt present at the eruption seen at the 2nd oldest site has

crystallized at the time of the youngest site?

4) In a separate study, a researcher estimated the relative ages of these three sites based

on relative changes in pottery style, assuming that pottery styles change at a regular and predictable rate The model for the rate at which pottery changes suggests that more timehas passed between the oldest and 2nd oldest sites than between the 2nd oldest and

youngest sites Does the geochemistry data support this claim or not? Explain

Soil chemistry:

Review Soil horizons (see Phys Geol notes)

See physical geology notes for pedalfers and pedacals and USDA soil classification system

Sequence of elemental solubilities: Na and K, Ca, Si, Fe, Al

Soil Maturity

Sequence of stabilities of inherited minerals in clay fraction of soil:

soluble salts (gypsum and halite)

Calcite,

Dolomite, apatite

Olivine, feldspathoids,

Amphiboles, pyroxenes

Biotite, glauconite, mg-chlorite

Feldspars (K and Na feldspars more stable than Ca, more Ca= faster weathering)

More resistant inherited minerals include

Vermiculite, slightly weathered micas

Formation of gibbsite and dissolution of silica

Al2Si2O5 (OH)4 + 5H2O = 2Al(OH)3 + 2Si(OH)4

reaction direction if increase acidity? Have increased (OH)- in water Consider

H2O = H+ + OH- Adding OH- on right side is like decreasing H+, thus increasing acidity moves reaction to right

Phase Diagrams:

Because chemical reactions depend on T, P, and X (as seen from chemical reactions and Gibbs Free Energy expression), we can make plots of T, P, and Composition showing

where reactions occur These are called phase diagrams, or for soil or water reactions,

fence diagrams Very helpful in understanding visually how reactions depend on T, P, X

In Archaeology, soil composition depends on climate (T, fO2, pH)

CaCO3 + H+⇔ Ca++ + HCO3

-Talk through what happens if more acidic (lower pH, higher H+)

relative to reaction stuff we learned before

(consider both lnK, and the idea that reation always goes other way)

Show on an Eh, pH plot with a simple vertical line On which side will CaCO3 occur? This is one of most common soil minerals that reflects climate

Show Fe diagram and talk about the ferric Fe under more oxidizing conditions, and ferrous Fe under more reducing conditions Discuss the siderite - ferric hydroxide reaction line relative to the reaction FeCO3 + 1/4O2 + 2.5H2O ↔ Fe(OH)3 + HCO3- + H+

or FeCO3 + 2H2O + OH- ↔ Fe(OH)3 + HCO3- + 1/2H2

Then show the natural environment Eh-pH plot (overhead, or computer)

Then overlay soluble Fe diagram over natural environments Talk about soils and climateand chemistry: We don’t get into nuts and bolts of doing it in this class and won’t do any problem sets of this, but wanted you to be introduced to the concept

talk about reactions, which involve H=, which O2 Predict effect of increasing CO2

From Easterbrook 1993Formation of kaolinite from K-spar, also production of gibbsite (bauxite) as H2SiO4 drops as SiO2 is leached.

Orthoclase + carbonic acid + water = kaolinite, + potassium ions + carbonate ions, + silicic acid

4KAlSi3O8 + 4H2CO3 + 18H2O = Al4Si4O10 (OH)8 + 4K+ + 4HCO3- + 8H4SiO4 +kaolinite + H+ = Gibbsite + silicic acid

Two days: lecture and video each day

ISOTOPICS PART I: STABLE ISOTOPES & PART II: GEOCHRONOLOGY (VHS)

1997 Pt I , 23 min Pt.II, 29 min sd color #52820 Part I: Stable Isotopes Presents the definition of isotopes, and the use of isotopes to study the ice ages, the Earth's crust, and groundwater ontamination Part II: Geochronology Covers assessing volcanic hazards, dating of fossil human ancestors, determining the age of the Earth, explanation of

radioactive decay and half-life, and the use of isotopes to study extinction of dinosaurs.What are isotopes?

protons, neutrons, electrons explanation

explain stable and unstable

important stable isotopes in geology:

16O 17O, 18O go through numbers of protons and neutrons: usually look at 16 and 18 because they have bigger difference (Atomic number oxygen = 8)

12C, 13C (note 14C is radioactive) (Atomic number carbon = 6)

32S, 33S, 34S, 36S (usually look at 32 and 34 because they are the most abundant (32=95%, 34=4.2%) (Atomic number sulfur = 16)

36Ar, 38Ar, 40Ar (Atomic number argon = 18)

value increases when the heavier isotopes is more abundant in the sample than in the

standard e.g 18O/16O, 34S/32S, etc

Overhead or computer graphic of climate change

over past 66my from sediment cores and ice

cores Or give as handout

-mention SMOW standard (std mean ocean water)

isotopic ratio for standard

isotopic ratio for sample

slightly different partitioning properties.

Carbonate ion reaction (exchange)

Living things alter reaction from strict equilibrium

mention Kinetic balance vs equilibrium balance

Radiogenic isotopes

40Ar example, stripping of planetary atmospheres Derivation of radiogenic 40Ar from radioactive 40K Others primordial

other comments on usage:

ground water, rainwater, primordial water have different isotopic ratios for O

Bone has C and O, can reflect diet (you are what you eat)

past climate

past temperatures (other than climate)

organic activity, microbial activity

changes in ocean chemistry through time

Carbon and sulfur in hydrocarbons (petroleum prospecting)

Show video, Part I, 23 minutes

C18O32-/C16O3

2-(H218O/H216O)3

Unstable (radioactive) isotopes:

Parent-Daughter idea Nucleus is not energetically favorable, over time it “decays” to become a different nucleus that is more stable

beta decay: (explain origin of beta particle in nucleus, conversion of neutron to a proton

= changes element)

electron capture: (backwards beta decay sort of, usually from K shell, conversion of a proton to a neutron = changes element)

alpha decay: (helium nuclei, 2P,2N)

In each, nucleus can be left in a high energy “excited” state, which when it goes to lower energy state releases gamma rays For electron capture, or X-rays produced when

missing electron in K shell is replaced

Important systems: (ones in bold: go through decay process)

40 K/ 40 Ar electron capture (K=19P, 21N : Ar=18P, 22N) (explain)

half-life 1.3billion years.

Concept of half-life: connect probability of decay to half-life In one half-life, a

particular nuclei has 50% chance of decaying Like flipping a coin If one half-life, flip

1000 coins, how many (about) will be heads? 2nd half life, how many heads? and so on Each half-life, half decay

Concept of setting clock to 0 Have to know when the “starting time” is, or what it means Is it since the origin of atoms? Since the origin of the Earth? Since the origin of

a rock? Since something happened to a rock?

Ar is a gas, evaporates when the rock is melted and all 40Ar lost So starts out at 0 Then make new 40Ar through radioactive decay of 40K

Go through a simplified example and have them figure out how much time passed

40K/40Ca beta (K=19P, 21N : Ca=20P, 20N)

238U/206Pb 8alpha + 6beta (4.5by halflife) (decays through several intermediate steps that

are also unstable)

235U/207Pb 7alpha+4beta (710my halflife)

232Th/208Pb 6alpha+4beta (13.9by halflife)

87 Rb/ 87 Sr beta (Rb=37P, 50N : Sr 38P, 49N) (48.8by halflife)

14C/14N beta (C=6P,8N : N=7P,7N) 5730 years

147 Sm/ 143 Nd alpha (Sm=62P,85N : Nd=60P, 83N) (106by halflife)

187Re/187Os beta (Re=75P, 112N : Os=76P, 111N) (43by halflife)

176Lu/176Hf beta (Lu=71P,105N : Hf=72P,104N) (36by halflife)

others

Be-10 2.5 M.Y

Fission

Explanation of 14C systematics:

Steady-state production in the atmosphere by cosmic-rays

14N + neutron (produced by cosmic rays interacting with atoms)⇒ 14C + proton

This carbon becomes incorporated into living things, which maintain a balance of stable carbon (12C, 13C) and 14C related to the balance in the atmosphere

When a living things dies, it stops maintaining the balance with the atmosphere Decay

of 14C causes the amount of 14C in the remains to decline

By measuring how much 14C is left we can determine the amount of time that has passed

If half of the original 14C is left, how old?

If ¼ of the original 14C is left, how old?

Concerns: Unlike other radiometric methods, we don’t measure the amount of daughter (14N) and so we don’t have an actual measurement of the initial 14C We estimate the initial 14C by assuming the amount is related to the amount of 14C produced in the

atmosphere However, the balance of 14C may not have remained the same through time, method has been calibrated against tree rings to see how atmospheric 14C may have changed through time

Can get to intermediate values (not just equal steps of ½) by:

Rb/ Sr systematics and the concept of the isochron:87

Rock clock set to 0 when rock melts All minerals have the same proportion of 87Sr/86Sr (stable and radiogenic are “mixed”)

However, some minerals within the rock have more parent than others (87Rb) once rock solidifies, 87Sr will accumulate more rapidly in minerals with more 87Rb (remind of PARTITIONING) (NOTE: can also do whole rock isochron where rocks with different initial 87Rb are used)

General derivation of graphical relationship:

dN/dt = λN (this is the more general expression of the simplified relationship given above)

integrating with respect to time yields:

But, for 87Sr, some daughter is already present in rock, even after melting To handle this,

we put expression in a form that normalizes to nonradiogenic 86Sr

87Sr/86Sr = 87Sr0/86Sr + 87Rb/86Sr (eλ t -1)

Intercept related to the INITIAL 87Sr

slope related to the age of the rock (t)

Initial 87Sr/86Sr also tells us something It tells us about whether previous separations have taken place If fractional melting takes place, Rb goes with the melted part Then let it sit for a while, get lots of 87Sr So higher 87Sr can tell us that this particular batch of material has been separated from the mantle for a long time.

Also, can reset the minerals (by metamorphism), but whole rock isochron still gives age

of original formation So can get 2 ages: one of when rock 1rst formed, one of when metamorphism occurred

Show Video part II

Geochemistry Puzzle Assignment #3:

Radiometric dating calculations.

Part I Rb/Sr dating example: Age of igneous lunar sample 10044, 30 (from

Papanastassiu et al, 1970; among first dates for lunar rocks ever done)

Mass spectrometer analysis results:

Graph the data

Graphically determine the slope (one could use linear regression, but you can just

“eyeball” the slope with a ruler and pencil)

Calculate the age from the expression:

87Sr/86Sr = 87Sr0/86Sr + 87Rb/86Sr (eλ t -1)

Where the slope = (eλ t -1)

Add 1 to both sides and take the natural log such that

ln(slope+1) = λt

where t=time,

and λ is the decay constant which, for 87Rb is 1.42x10-11 decays per year (this

corresponds to a half-life of 50 billion years)

Using the scatter in the data as a guide, draw what you think are the maximum deviations possible for the slope (if you do linear regression, the regression program should give you

an uncertainty estimate of the slope you can use this value in the calculation) Then calculate the slope in the same way to give you an estimate of the uncertainty Include this uncertainty in your report of the age

AGE of 10044,30: _

Part II: Radiocarbon dating example.

Notes: radiometric analysis (counting of beta decays) is cheaper for larger samples, say 300mg to 4 g total carbon Accelerator Mass Spectrometry is used for smaller samples (say 100mg to 300mg) By convention, all radiocarbon dates are referenced to 1950 Important corrections include corrections for past atmospheric 14C (which was different due to variations in the Earth’s and Sun’s magnetic fields which altered the production rate for 14C) and isotopic fractionation For radiometric analysis, beta decays are counted with a scintillation detector

Suppose you use the radiometric method, counting decays in a 2 gram sample After counting for 24 hours, you record 9763.2 total decays

At this point, calculate the percentage error from counting statistics (hint: the

percentage error = sqrt(counts)*100/counts = 100/sqrt(counts).)

percentage error from counting statistics = _

You do an analogous count on 5 grams of modern carbon in equilibrium with the

atmosphere (counting for 5 days to minimize statistical uncertainty) and derive an activity

of 67.8 decays per minute Percentage error from counting statistics = .Remember that the decay equation is

N = N0e- λ t

where N = the number of atoms remaining, N0 is the initial number, λ is the decay

constant, and t= time

Rearranging and taking the natural log yields:

ln (N/N0) = -λt

N0 , the number of atoms, is proportional to the number of decays per minute per gram

N, the number of atoms initially, is equal to the modern atoms, and is proportional to the number of decays per minute per gram in modern carbon (actually it isn’t exactly equal tothe modern concentration because this has changed somewhat through time)

λ= 1.21x10-4/sec (corresponding to a half life of 5730 years)

Calculate the radiometric age of the sample:

_

Note: The true age can be derived by applying calibration curves to this result to account for changes in atmospheric 14C through time, etc

Variation Diagrams (“visual statistics”):

“interactive” lecture: Concepts are ones understood by practice, not memorization!

topics to integrate: linear regression, distinguishing populations, cluster analysis, dependent variation, and correlations between elements

time-Reviews of: partitioning, previous discussion of the importance of evaluating variation in

a value in order to understand whether you can distinguish populations

A variation diagram is a plot of the variation in concentration of one element in a suite of sample against the variation in concentration of another element

You are doing a survey of flows from a single Hawaiian volcano (say Mona Loa) and its effect on communities through time As part of this study, you want to relate composition to time period of each lava flow

You know that Hawaii eruptions occur from a magma chamber in which the mineral olivine is crystallizing The olivine is denser than the melt, sinking to the bottom

of the chamber, and is effectively removed from the melt

Experiments show that the partition coefficient for Yb in olivine is very low (nearly 0) (Dol/melt for Yb <<1) and the partition coefficient for Ni is high (Dol/melt for

Ni ~ 10)

1) Consider variation diagram, and predict what the plot of many different flows over time would look like:

2) Now, which of these flows is the most recent, and which is older?

3) Consider the plot of 2 flows provided (not shown otherwise the answer to questions above would be obvious!) How much olivine has crystallized between the two?

Math notes for fractional crystallization puzzle with variation diagrams:

Concentration in olivine = D*Concentration in the melt (This is definition of partition coefficient)

Thus:

Let X = the amount of Ni in the olivine

If we consider that there are 20 atoms of Ni total, and 10 million atoms total (about 2ppm

Ni before any crystallization) then we can calculate the concentration of Ni in melt after 50% crystallization as follows:

X/amount atoms in Ol = 10* (20-X)/amount atoms in melt

at 50% crystallization, amount Ol = amount melt = 5 million atoms

(20-By similar calculation, for Yb (D~0, initial Yb also at 2ppm for convenience):

Let Y= number of Yb atoms in Olivine

Y/amount Ol = 0*(20-Y)/amount of melt

Amount of Ol = Amount of melt (as before)

Y=0 (there is almost no Yb in the olivine In reality there will always be some, but it is often low enough to ignore for this type of calculation)

Thus the concentration of Yb in the melt is

(20-0)/5million = 4ppm The concentration has doubled as the amount of melt was reduced by half

The general equation for the change in the composition of a fractionally crystallizing magma, derived from the type of reasoning given above is:

CiL/Ci0 = F(Di-1) Rayleigh Equation

Where CiL = Concentration in the liquid, Ci0 = initial concentration in the liquid, F = fraction of the liquid crystallized, Di is the total partition coefficient for element i

between solid and liquid

Figure for Variation diagram puzzle (draw on board)

Scatter plots and cluster analysis using variation diagrams:

What can you tell?

two different populations or not? (yes)

If you took a single sample, could you tell to which population it belonged? (Two sources of pottery clay… could you tell which source a particular pot came from?)Answer: depends There is a zone in middle where you would be unsure

More variation = more difficult to distinguish

Variation from both analytical uncertainty, and from natural variation in the source material

Sample: A set of measurements and records from which the total population is inferred Statistics provides a means to assess the uncertainty in the sample and provides guidance and criteria for setting up the sampling method.

Data can be

discrete: can take only restricted values (e.g integers, male-female, etc)

usually plotted on a histogram

continuous: can take any possible number of successive values (limits of

measurement make this “discrete” at some level) Usually plotted as a smooth curve.Chemical data usually continuous, but may apply to discontinuous objects

Comparing a single sample to the distribution of the larger sampling:

Is the single sample a member of the larger sampling?

Depends on where it occurs If very near “peak” larger chance that it is than if it is off onthe side

If sample is within 2sigma standard deviation of mean, often consider it at least not

inconsistent with membership in the group Outside 2 sigma often taken as evidence that

it is outside the group If it is outside 2sigma, there is still a 5% chance that it could belong to the group

e.g you have a particular pot Wonder if clay could have come from a known source, or

if it must be another source Test with a single element

Mean =

Standard deviation of a single sample determined by evaluating how much variation there

is in the entire sampling

SD = sqrt( )

(1-sigma)

Example: mean Yb for pottery from a known clay source = 2ppm Standard deviation for a single measurement for this sampling is ±0.2ppm (1 sigma) or ±0.4ppm (2 sigma) You find a pot with a Yb concentration of 2.4ppm What do you conclude?

[5% chance that the hypothesis that it is from a different source is wrong.]

comparing two populations:

Can you identify which population an individual sample belongs to?

depends More elements helps (remind of scatter plot)

Can you tell the two populations apart?

Introduce T test and Anova test

Simplified approach, often sufficiently rigorous:

Test whether there is overlap between the two means, taking into account SD of the

mean.

SD of the mean ≈ SD of a single measurement/sqrt(number of measurements)

Now taking example above, suppose that you had 16 measurements of pottery from the known clay quarry, and 16 measurements of pottery from the other location which you wondered if it was from that quarry

The mean for the first is 2ppm, and the mean for the 2nd is 2.4ppm The standard

deviation of the first sample is 0.2ppm (1-sigma) and the standard deviation of the secondsample is 0.4ppm (1-sigma - there is more variation from measurement to measurement

in this set of pottery) What can you conclude?

[Differ by much more than 2 sigma, so are different at much greater than the 95%

confidence interval.]

Statistics: Body of concepts and methods used to collect and interpret data and to draw conclusions in situations where uncertainty and variation are present.

Statistical population: Complete set of all possible measurements and record of some qualitative trait, corresponding to the entire collection of units from which inferences are made

Sample: A set of measurements and records from which the total population is inferred Statistics provides a means to assess the uncertainty in the sample and provides guidance and criteria for setting up the sampling method

Some examples of things to test:

Is a particular sample or subsample a member of an identified grouping?

Method: Compare values, taking into account standard deviations

example: The Colossi at Memnon

Are two groups equivalent or different?

Method: Ttest, Anova, Discriminate, Univariate, Nonparametric comparisons (for non-normal distributions)

example: statistical lab assignment

Are two variables within a single grouping correlated to each other?

Method: linear regression analysis, non-linear correlation analysis

example: The amount of Pb in a particular lake varies over some time period The amount of fly ash also varies The question arises, are these two correlated, possibly indicating that a primary source of Pb is the fly ash, or the industrial activity that results

in it

Among a large group of samples, can subgroupings be identified?

Method: cluster analysis

example: Are obsidian points from a single quarry with variable composition, or are the points from different quarries?

Among a group of samples with correlated variations among variables, can key correlatedvariations be identified?

Method: Principle component analysis, factor analysis

example: A particular group uses clay from three sources to make a certain type

of pottery But they use different amounts from each source at different times Can the composition of each of the three sources be extracted from the compositions of the composite pots and how they vary?

Reading Geochemical Fingerprints: LAB #1

Experience with Statistics

General notes on MS Excel statistics Access the statistical package by clicking on Data, then on Data Analysis (if data analysis is not available, you need to add it by clicking on the microsoft symbol in the upper left, then on "excel options" you'll have to figure it outfrom there.)

Part I: Simple statistics and comparing two data sets

Use ONE of the following three data sets For that data set, do the following:

A) Consider the basic statistics for at least two variables for each of the two different groups of your data set (e.g Green Glass B and D are one data set but two different groups, B and D-consider them separately) Do this using "Descriptive Statistics" of the Excel Data Analysis package Make sure that the Summary Statistics Box is checked

i) Report results

ii) In one sentence, explain what each of the reported values means (this may require some online searching to learn the difference (for example) among Standard Error, Standard Deviation, and Sample Variance.)

iii) Is the variance for the variable equal or different between the two different groups of your data set (of course it won't be the exact same number-I'm asking that you think about whether they are fairly close or not Think about it - you can actually test this question using the 'F-test two sample for variances facility in Data Analysis)

iv) Considering the Means and Standard Error, would you say that these two groups are the same or different? Explain your reasoning in detail

v) Plot two of the variables on a two-variable variation diagram (for both

groups) Does the statistical answer match what seems reasonable visually?

B) Do a statistical test of the same data set used in (A) to see if the two groups are the same or different

i) Use the t-test, two sample assuming equal variances Report results

ii) The null hypothesis for this test is that the two groups are the same The P value is the probability that the null hypothesis is true (well, simplified for non-

statisticians) Thus, smaller values of P correspond to higher probabilities that the two groups are different So, are your two groups different? (This is a two-tail problem-one tail problems correspond to questions like 'is group B mean larger than group D')

iii) use the t-test, two samples assuming non-equal variances What one thing is different in the output? Explain what this means about how the test is done

Part II Correlation and Regression

A) Is there any correlation between different elements in Green Glass B in Data Set 1? That is, when one element changes, does another element change in a coordinated way, orare variations in the two elements uncoupled from each other?

i) Consider if there is any correlation between MgO (Y axis) and Sm (X axis) Use Regression in the Data Analysis package Report results

ii) At what level of confidence is the overall regression significant? At what level

of confidence is the intercept non-zero? At what level of confidence is the slope non-zero(that is, a correlation exists)?

iii) Plot MgO vs Sm (include in report) Do you see a correlation? Is it

significant do you think?

iv) MgO is compatible in silicate melts, and Sm is incompatible Is the apparent correlation consistent with fractional crystallization producing a correlation? EXPLAIN.B) Sometimes variables are correlated, but do not initially appear to be because of multiple correlations among several variables To understand this, we're going to create a

"fake" data set (which should also help you understand the concept of how geochemical fingerprinting works-and provide a fairly rigorous introduction to using spreadsheets to manipulate data!)

Consider how various sources of materials affect the composition of ceramic or glass materials Set up a spread sheet to calculate the "fake" compositions, such that there are

12 different glass or ceramic samples, each with 5 different elements Each glass or ceramic sample is itself a mixture of three different "source" materials (previous glass materials, clay samples, whatever) The composition of the source materials is given below, as well as the proportions of each source that make up each glass or ceramic sample The compositions are as follows:

i) Graph Yb vs Ni (in the spread sheet program) Are they correlated (using your eye-evaluation of the graph)?

ii) Do a linear regression of Ni = A + B(Yb) Report results Are they correlated (using statistical tests)? (The R2 value is a measure of what fraction of the total variation

in Ni is explained by the correlation to Yb You can also examine the value of B, as well

as the uncertainty in B, and ask if the value of B is significantly different from 0 A value

of 0 means that there is no correlation between Yb and Ni) You can also consider the listed significance of F test, which is a probability that there is no significance to the regression)

Actually, Yb and Ni ARE correlated, but that correlation is masked because Ni also varieswith MgO, hiding the correlation to Yb You can see this by doing a different regression

iii) Do a regression to the expression Ni = A + B(Yb) + C(MgO) Again examine the value for R2 (which is now 1 because we have created a fake set of data that must be exactly correlated, thus all of the variation in the data is explained by the correlation) Also, examine the values for B and C and whether those values are significantly different from 0 (that is, they are more than 2 sigma different from 0) Consider the signficance of

F test Discuss results

Data Set 1) Volcanic Glass beads from the Moon.

First Set of Beads (Green Glass B)

Second Set of Beads (Green Glass D)

Data Set 2) Gryphaea population-size data (be sure to use all data, recognizing that the

data for each population are in two columns:

Data Set 3) Use some data of interest to you There must be at least two sets of data,

e.g pottery from two different sites, lava from two different volcanoes, or from two different flows from the same volcano, obsidian points used by two different groups of people, sediment samples from two different lakes, or a single lake but representing different periods of time etc You must have at least 5 separate measurements for each data set

You must have at least 2 measured variables for each set of data e.g analysis of at least

2 elements, measurement of at least 2 dimensional values, etc

Analytical Methods, X-ray methods

Diffraction analysis (XRD, TEM):

Concept: measure the angle at which incoming X-rays constructively interfere from a crystalline material

Use: Identifies mineralogy of sample, chemistry indirectly Can get qualitative (kinds of minerals present) or quantitative (proportions of minerals) information Mineralogy reveals information both about source and processing Firing, for example, alters

mineralogy of pottery while leaving its chemistry mostly unchanged

Can also reveal information about defects in crystals or size of microcrystalline materials (broadening of peaks)

Discuss concept of diffraction:

Explain concept of X-ray wavelength

(error in picture: n=the number of wavelengths, not the number of d spacings, so it can be due to the angle, as well

as the number of d spacings.)

where the constructively interfere defined by the

Bragg equation: nλ = 2dsinθ

Use known and fixed value for wavelength (anode of Cu for example, want long

wavelength so won’t excite) Knowing θ allows us to determine d which is unique to each mineral which has a unique spacing of atoms in the crystal structure

Note: mention TEM, TEM also useful in observing microstructures and defects

(note: 100*sqrtN/N

= 100/sqrtN)

X-ray emission spectroscopy:

concept: kick electron out of its spot, then when it falls back in, measure the

characteristic energy emitted

Use: determine chemical composition of materials for elements with X-ray emission not easily absorbed by atoms in good vacuum (usually elements heavier than about Ne)

Discuss X-ray excitation, Inner shell electrons quantum energy levels

Principle Quantum number (K,L,M,N shells)

Angular Quantum number () shape of sub shell

Magnetic Quantum number (J), refers to orientation of , -, 0, or 

spin Quantum number (s) , + or – one-half

by voltage drop imposed on charged electrons

SEM (backscatter and X-ray emission) valuable for examining textures, small scale

compositional variations

Proton excitation (PIXE= Particle induced X-ray emission) Don’t penetrate surface,

useful for extremely thin samples (air samples), or where only extreme surface is of

interest Lower background (explain background) so more sensitive

Methods of X-ray analysis:

energy dispersive (Pulse height analysis related to energy of photon)

wave-length dispersive (diffraction crystal and angle method)

Energy is proportional to 1/λ

Counting statistics:

S.D (as a percent)= 100/sqrt(N) where N = number of pulses accumulated

X-ray absorption spectroscopy

concept: absorbing energy to kick out electron, vs emitting energy when electron falls

back into its spot)

XANES: (X-ray Absorption Near Edge-Structure Spectroscopy) Monochromotic focusedbeam, look at small samples, get more detailed information about state of atom in target

material

<XANES can provide information about vacant orbitals, electronic configuration and site symmetry of the absorbing atom The

absolute position of the edge contains information about the oxidation state of the absorbing atom In the near edge region, multiple

scattering events dominate Theoretical multiple scattering calculations are compared with experimental XANES spectra in order to

determine the geometrical arrangement of the atoms surrounding the absorbing atom.>