Important Note:

Geochemistry

Main tasks of geochemistry:

• determine relative and absolute abundances of elements and isotopes (in Earth and elsewhere)
• understand distribution and migration of elements in various parts of the Earth (crust, mantle, core, atmosphere, oceans) and in minerals and rocks.

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Part 1: Cosmochemistry

Elemental abundance in Universe determined from

1. analyzing spectra of outer portions of stars and from nebulae
2. then averaging many stars of different kinds

Estimates constantly change.

Specifics almost certainly not known (exact %, for example) but some general facts (or "rules") known.

• Only 10 elements - H, He, C, N, O, Ne, Mg, Si, S, and Fe - all with atomic numbers less than 27, show appreciable abundance. Of these, H and He far outweigh the other 8.
• Abundances show a rapid exponential decrease for elements of the lower atomic numbers, followed by an almost constant value for the heavier elements.
• Elements adjacent to Helium (i. e. Li, Be) are very low in relative abundance
• Elements of even atomic number are more abundant than those of odd atomic number on either side. This regularity was first recognized by Oddo and Harkins (c. 1915) and is sometimes referred to as the Oddo-Harkins rule.
• Isotopes with mass numbers which are multiples of 4 (alpha particle mass number) have enhanced abundances.
• There is a pronounced abundance peak at atomic number 26 and smaller peaks at several other heavier atomic numbers (such as Oxygen)

We can explain relative abundances of elements by seeing how elements form in stars.

A typical star might go through several stages - for example: nebula, proto-star, main sequence star, red giant, supernova/neutron star, black hole

Main sequence stage of star's life: Fusion of hydrogen into helium
Several possible routes -
in one route, C acts as a catalyst; intermediate steps result in the production of N and O, explaining their abundance
Some elements (such as Li, Be, Bo, Sc) used up as part of H fusion process

Red giant stage: In core, He converted to C and O, explaining their abundance
C + O yields Ne, Na, P, Mg, Si, S, Cl and Ar
Mg, Si, S then form Fe, Ni

Supernova stage: Implosion to form neutron star forms some exotic heavy elements.
In fact, can correlate half lives of some short lived heavy elements (like Cf²⁵⁴) with half life of luminosity of supernova.
Explosion results in dispersion of elements into space.

Neutron star: Addition of neutrons to Fe forms heavier elements which are less stable than Fe.
For these heavier elements, relative abundance depends on relative stability.
Elements with even numbers of protons and neutrons are more stable because they have greater nuclear binding energy.

For second, third, etc. generation stars, different processes occur because they have different starting materials as well as being at different stages in their lives.

Composition of our Sun results from its present state of evolution
Most striking feature is extreme abundance of H and He.
About 70 elements found in Sun so far.

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Part 1a: Solar System Composition

Brief look at composition of other bodies in solar system in order to compare with Earth:

• meteorites
• Moon
• other planets (including their atmospheres)
• asteroids

Meteorites - chunks of rock from space that land on Earth

Common minerals in meteorites:

• kamacite, taenite (both Ni-Fe alloys, different crytal structures)
• pyroxene (especially bronzite)
• olivine
• plagioclase

Kinds of meteorites:

• irons
• stones
• stony-irons

Iron meteorites:
Predominantly Ni-Fe alloys
Minor amounts of other minerals such as troilite (FeS)
Types classified according to % Ni:

• hexahedrite
• octahedrite (has Widmanstatten structure, exsolution feature formed by slow cooling)
• ataxite

Stone meteorites:
Chiefly silicates, mostly ferromagnesian
Up to 1/4 metallic Ni-Fe
Types:

• Chondrites
• Achondrites

Chondrites: Contain chondrules (BB-sized round bodies)
Composed chiefly of silicates such as olivine, pyroxene, and plagioclase or glass
Important type is carbonaceous chondrite.

• High content of volatiles, including water and non-biogenic carbon (will later show how determined to be non-biogenic)
• Have same composition as Sun's atmosphere

Achondrites: no chondrules

• Same composition as terrestrial mafic and ultramafic rocks
• Most achondrites are breccias

Stony-iron meteorites: Equal amounts of silicates and Ni-Fe alloys
Many are crystallized silicates which have been brecciated, then invaded by metallic and sulfide melts
Classified according to kind of silicate:

• pallasite (olivine)
• mesosiderite (plagioclase, pyroxene)

Some questions on meteorite origins:

• formed under low pressure? (void spaces in some) or high pressure? (diamonds in some)
• Why are most meteorites breccias?
  Generally believed that meteorites formed from breakup of minor planets (asteroids) which were large enough to be differentiated into Ni-Fe cores and silicate mantles.
  (explanation leads to more questions - number and size of the bodies? what caused the breakup?)
• What process produces chondrules?
  Lunar regolith contains round bodies similar to chondrules, formed by meteorite impact. Maybe surfaces of minor planets had similar material.
  Some chondrules are indistinct. Did some chondrules form by recrystallization?
• Are meteorites that we know about representative of the whole solar system or just the part near Earth?

Moon:

• basalt maria (with extra Fe and Ti)
• anorthosite highlands
• 4 most common moon minerals:
  • pyroxene (augite and others)
  • plagioclase (Ca-rich)
  • olivine (Mg-rich)
  • ilmenite (iron titanium oxide)
• No hydrated minerals.
• No minerals formed by chemical weathering or life processes.
• Depleted in volatiles (probably as a result of how Moon was formed.)

Other planets, etc.:

• Mercury: silicates; relatively large iron core
• Venus: basalt
• Mars: basalt covered with iron oxides; more sulfur in core
• Jupiter and other giant planets in outer solar system: mostly hydrogen
• asteroids: silicates

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Part 2: Composition and Early History of Earth

Most information about Earth's interior comes from geophysical studies:

• Density
• Moment of inertia (gives density distribution)
• Seismic data (gives elastic constants of materials, presence of fluids, location of discontinuities, etc.)
• Heat flow data (gives temperatures, locations and abundances of radioactive elements, mantle convection)
• Magnetic data (gives possible core materials)

Outer core

• liquid - fact helpful in determining internal temperature
• Source of Earth's magnetic field
• Composition of core:
  • Iron-Nickel alloy
  • Lesser amounts (10 % -20 %?) of S, C, Si, and/or iron oxides

Mantle

• Heterogeneous vertically (layered) and laterally due to differences in composition and phase changes
• Composition of upper mantle pretty much limited by geophysics studies and petrological considerations to eclogite and peridotite.
  • Olivine-pyroxene most common type of xenolith in magmas which apparently have deep enough origins to have come from mantle. Assumption is these are leftover material after basalt has been removed
  • Original composition thus peridotite and basalt in some ratio - generally assumed to be 3 parts peridotite to 1 part basalt (called pyrolite)
  • This composition doesn't account for volatiles which erupt from volcanoes.

Crust:

• Heterogeneous in composition
• Varies in thickness -
  • 5-8 km thick under oceans (under 4 km of water and 1 1/2 km of sediments)
  • about 35 km thick under continents
  • up to 60 km thick under active mountain belts
• Gradual change to more mafic composition with depth
• But not two layers as sometimes said

4 approaches to obtain overall composition of crust:

1. averaging of available rock analyses
2. as #1, but weighted in proportion to rocks' occurrences
3. abundance based on crustal models
4. indirect assessment - estimating mass balance of mafic and felsic rocks to give, through weathering, etc., the observed average composition of sediments (or selected sediment)

Approach #2 used by Clarke and Washington, 1889
Calculations based on more than 5000 "superior" rock analyses
Problem of how to weight different kinds of rocks to strike a reasonable average

• Great bulk of crust is igneous rock or metamorphic rock that was once igneous
• Clarke estimate for upper 10 miles - 95 % igneous or metamorphic, 4 % shale, 0.75 % sandstone, 0.25 % limestone
• Most common rocks by far are granite and basalt.
  • Use some combination of these 2 rocks.
  • What combination?
    • Continents - geologic observation and seismic evidence suggest 1:1 ratio
    • Ocean floors - more basalt

Ronov-Yaroshevsky, 1969, used approach #3.
Based on many thousands of specimens from continents, ocean floors, continental shelves and slopes

Goldschmidt used approach 4
Based on glacial clays in Norway
Gives lower values for Na, Ca (easily removed in weathering)

Material Earth formed from most easily studied by considering the Fe-Mg-Si-O-S equilibrium system, when O>>S and O+S<Fe+Mg+Si (you will get to this kind of equilibrium system later)
Results in 3 essentially immiscible phases (iron present in all):

• iron-magnesium silicate
• iron sulfide
• free iron

Arrange these in order of density and this looks like Earth.
Other elements concentrated in these phases according to their chemical properties (not density)

Chemical properties of elements determined primarily by their electronic configurations; that's why elements in the same group on the periodic table have very similar properties.
Examples:

• Uranium and thorium tend to form silicates and are concentrated in crust.
• Gold and platinum have no tendency to form oxides or silicates but do allow readily with iron and are presumably concentrated in core.

Goldschmidt first recognized primary geochemical differentiation of the elements in 1923.
Coined terms siderophile, chalcophile, lithophile, atmophile

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Part 3: Currently accepted theory for origin and early history of Solar System and Earth:

Step 1: Rotating cloud of gas and dust (nebula) over volume larger than orbit of Pluto

Questions:

• Where did it come from?
• Why was it rotating?

Step 2: Condensation of nebula

Questions:

• Why? (nearby supernova explosion?)
• When? (can get clues from radiometric dating - discussed later)

Step 3: Material collects in central portion of nebula to form Sun.
In remaining material, small groupings of particles form randomly
Because of combined gravitational pull of the group, they attract other particles.
Many bodies grow until they are several kilometers in diameter
Larger bodies sometimes join together by collision and sometimes become fragmented.
Bodies which continue to grow become planets and satellites; those that fragment become interstellar dust, asteroids, comets, etc.

Question: Did Earth form from cold fragments or hot fragments?

• Evidence favors cold accretion
• Compare inert gases to other gases of approximately same molecular weight (water, carbon dioxide, ammonia)
• Inert gases deficient in Earth
• Earth's present gravity field strong enough to hold them; must have been lost by smaller aggregating particles
• Other gases held by particles that formed Earth because they were tied up in compounds such as hydrates, carbonates, etc.
• These compounds would have broken down at temperatures of few hundred degrees so fragments from which Earth formed would have to have been relatively cool.

Question: Was early Earth homogeneous or heterogeneous to start with?
(Reference: Grossman, 1972, Condensation in the primitive Solar nebula, Geochim. Cosmochim. Acta, 36, 597-619)

• Grossman took a gas believed to be similar to nebula material, cooled it and observed order in which material condensed.
• Order was:
  • metallic iron-nickel
  • silicates
  • volatiles
• Suggests that at least part of observed differentiation of Earth and other bodies due to condensation order.

Step 4: planets heat up

Questions:

• Why?
• How hot were they to begin with?
• How much did they heat up?
• How long did it take?
• Are they still heating up?

Two sources of heat:

1. Gravitational potential energy from collapse
2. Radioactive decay (most important)

How fast and how far temperature rose is debatable
Depends on:

• rate of infall
• original distribution of radioactive elements

Also not known whether present temperature rising, falling, or remaining constant
Depends on:

• how much radioactive material still present
• how it's distributed
• amount of heat lost to space

None of which known accurately

Heating up could produce:

• differentiation to form core and mantle?
• crust formation
• plate motions
• magnetic field generation
• loss of volatiles from interior to form atmosphere and ocean

Step 5. Differentiation to form core and mantle? and crust formation.
"iron catastrophe"

• Fe and FeS would be lowest melting material in body of Earth's overall composition and interior pressure.
• As Earth heated, various levels of interior became hot enough to melt iron, perhaps at different times.
• This liquid would aggregate and sink to center
• Time required? (perhaps as little as 100 million years)

Questions:

• How did crust form?
• What was original extent and composition?

Overall chemistry of crust -

• granitic rocks at high levels,
• more mafic rocks toward base,
• ultramafic rocks in mantle underneath

This is reminiscent of layering in differentiated igneous rock bodies and of differentiation observed in labs.
Suggests similar process for formation of crust
Further evidence from Moon - anorthosite layer, flooded by basalts derived from underlying ultramafic layer

When Earth heated, heavier Mg, Fe silicate would move to or remain in mantle; scum of material rich in Al, Si, K, Ca, etc. would rise to surface
Process might take place piecemeal over Earth, because of slightly different temperature, so entire outer part of Earth not necessarily molten at once

None of original crust preserved
Time between accretion and formation of oldest existing rocks would have been tumultuous.
Moon's surface, as well as Mercury, Venus and Mars, indicates intensive meteorite bombardment producing cratered surface; almost certainly Earth's was too
Some of the chemical heterogeneity of Earth's crust and upper mantle may be heritage from the variety of meteor masses that were incorporated into surface material.
Might explain some odd concentrations of tin, iron, and copper ore.
Could it have produced present (and past?) lopsided distributions of continents and ocean basins?

Question: How did continents originate and grow?

• At end of intense bombardment, crustal material probably covered entire planet
• Early crust mostly basalt (inferred from dominance of mafic metamorphic rocks amongst oldest dated varieties)
• Some granitic rocks and ocean basins (inferred from presence of quartzite and a little marble)

Questions:

• Was early crust uniform or contain thicker parts which might have been embryo continents?
• How large were granitic continents?
• How did they originate?
• When did plate motions begin?

It is currently commonly thought that continents:

• were end product of differentiation of mafic magma
• were originally small and scattered
• were moved about by slow currents in mantle beneath
• coalesced and broke apart repeatedly
• grew larger

Mafic lavas came to surface from deep in upper mantle, formed by partial melting of garnet peridotite
Solidifying, lavas became oceanic crust, carried away from spreading centers
At other places, oceanic crust and sediments which had accumulated on it were carried back down and became hot enough to generate felsic and andesitic magmas which produced volcanoes and batholiths on the edges of granitic islands, thus enlarging continents
Process much smaller in scale than at present
Slow and inefficient process but result was silica, alumina, and alkali metals enriched in continents and olivine and pyroxene enriched in upper mantle

Question: Is differentiation to produce continents continuing or are continents simply rearranging themselves?
Other ways of asking same question:

• is total mass of continental material increasing?
• is continental crust generation a one-way process or cyclical?

Evidence for one side:

• General decrease in age of granite bodies toward continental margins suggests amount of continental material increasing.

Evidence for other side:

• no long-term decrease in amount of granite produced per million years
  (one way process should terminate when mantle loses sufficient felsic components and becomes a cumulus of olivine and pyroxene from which basalt can no longer be generated)
• no long term change in composition of granitic rocks
  (granites do become more felsic in preCambrian and Paleozoic but more mafic in Mesozoic)

Questions:
What kind of change in composition might occur in one way process?

• Should granites be more mafic, since felsics decreasing in mantle?
• Or, should granites be more felsic, since felsic sedimentary material is recycled again and again through subduction zones?

Step 6. Origin of atmosphere and ocean
Cold primitive Earth had virtually no atmosphere because gases tied up in compounds or in frozen particles.
As Earth heated up (due to gravitational collapse and radioactivity) gases would be released and accumulate at surface
(This would presumably include water vapor which would condense to form oceans, to be looked at later.)
Gravity would be sufficient to retain all gases except H and He

Example of evidence for degassing: Argon comes from decay of Potassium. Not enough K in surface rocks to supply all Ar in atmosphere. Some Ar must have come from interior.

Questions:

• Did all degassing take place at once, in some warmer stage?
• Or is degassing a gradual process which is still going on?
• If all at once, when?
• If continually, at what speed?

Clues:
Evidence from elemental abundance studies suggest that isotopes of atomic number greater than about 40 are present in about equal amounts.
So when elements in solar system formed, Ar³⁶ = Ar³⁸ = Ar⁴⁰
But Ar⁴⁰ also forms from radioactive decay of K so ratios Ar⁴⁰/Ar³⁶ or Ar⁴⁰/Ar³⁸ constantly increasing
In Earth's interior, ratio is about 5000/1 at present (found in diamonds which are heated to carbonization)

Look at 2 possible extremes:

• all outgassing early, later gases still trapped; Ar⁴⁰/Ar³⁶ ratio in atmosphere should be small
• all outgassing later or continuous; ratio should be closer to 5000/1

Ratio in atmosphere at present is about 300/1 (that is, small); indicates most of atmosphere formed early
Estimates that about 80 % formed in first 500 my; remaining 20 % from volcanic eruptions since then.

Average product of current degassing (from analysis of gases from volcanoes):

• water vapor
• hydrogen
• carbon oxides
• sulfur gases
• hydrogen halides
• nitrogen
• ammonia
• possible hydrocarbons

Bears little resemblance to composition of present atmosphere. Why?

• Hydrogen escapes
• Sulfur and halogen gases dissolve in surface waters and react with rocks
• Carbon dioxide is removed by biologic activity
• Oxygen is added by biologic activity, etc.

We have implied that early atmosphere may have been different than present one.
Look at CO₂ and oxygen for evidence

Question: Was there less CO₂ in past?
Continued evidence of life for more than 3 billion years establishes a fairly definite minimum for the amount of CO₂ in the atmosphere for at least 3 billion years

Question: Was there more CO₂ in past?
Extremely high amounts would produce highly acidic surface waters and greatly speed chemical weathering
(will look at results now, chemical reasons why later)

• silicates would be broken down to free silica
• ions from weathering would accumulate in an enormously concentrated ocean
• highly acid waters would prevent carbonate deposition (at low pH, Ca⁺² and Mg⁺² don't readily combine with HCO₃^-2)

Question: Is there evidence of silicates broken down into free silica?
Banded iron formation - high amounts of silica (chert) in alternating layers with various iron minerals such as magnetite and hematite; restricted to period 2.5 to 1.8 by in age

Question: Evidence of high ion concentration in oceans?
Significant evaporites older than latest preCambrian not found

Question: Evidence of high acid waters preventing carbonate deposition?
Carbonate rocks uncommon in most of preCambrian; become abundant near close of era (especially dolomite) and are continuing to form in large amounts today

Question: Was there less oxygen in past?

• placer deposits of "not too oxidized" minerals (Ex.- uraninite) restricted to early preCambrian
• "red beds" (hematite rich rocks) became more extensive in late preCambrian
• gypsum (a sulfate) deposits rare in preCambrian

Conclusion:
Early preCambrian atmosphere had more carbon dioxide, less oxygen (about 0.1 % of present value)
Great increase in abundance and complexity of organisms in late preCambrian changed carbon dioxide rich atmosphere to oxygen rich atmosphere

Life probably began in oceans.
Water would shield from ultraviolet radiation (ozone does now but little oxygen in primitive atmosphere)
Organisms produce oxygen; some is used to form oxides, some released to atmosphere
PreCambrian banded-iron formations probably formed when iron weathering from rocks in an almost oxygen free environment was washed into plant-containing oxygenated water, oxidized, and precipitated
Later oxygen in atmosphere provided shield, life forms expanded dramatically and moved from water environment.
Little change in atmospheric composition since then.

Origin of oceans:
Water condensed from atmosphere
pH dependent on composition of atmosphere because of dissolved gases included
present pH 8.1- 8.4 in surface waters, slightly lower at depth

Early ocean more acidic (because more carbon dioxide in atmosphere, and thus more dissolved)
Ocean should have obtained dissolved material fairly rapidly in history (due to extensive early weathering)

Question:
Any large changes since?

• more Ca⁺² would mean more gypsum
• less Ca⁺² would mean more Na⁺ minerals (since Ca⁺² less soluble than Na⁺; will look at relative solubilities later)
• more Mg⁺ would mean more sepiolite and brucite
• less Mg⁺ would mean less dolomite

Rock record shows no evidence of change since late preCambrian

For a few elements (notably chlorine, bromine, sulfur, and boron), concentrations in seawater much higher than in surface rocks
Common products of volcanoes and probably added directly to seawater by volcanic activity rather than by erosion
Elements involved with biological activity (C, O, N, P) vary horizontally and vertically because of concentration of organisms in surface layers in warmed waters and because of decaying organisms returning material to seawater

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Part 4: Radiometric Dating

Geochronology - concerned with determining age and history of geologic materials by studying their isotopes

Radioactivity
Discovered in 1896
Natural change from one element to another by emission of particles from nucleus or addition of particles to nucleus

Particles include:

• helium nuclei (alpha particles)
• electrons (beta particles)
• high energy electromagnetic waves (gamma rays)

Decay occurs at constant rate and is not affected by temperature, pressure, chemical combination or any other known thing

Radioactive isotopes - an element capable of spontaneously changing into another element by the emission or addition of particles to its nucleus
Stable isotopes - an isotope which is not radioactive

Radiogenic isotopes - an isotope produced by radioactive decay
Non-radiogenic isotopes - an isotope not produced by radioactive decay

Half-life - time for half of element to decay

Parent - the radioactive element which decays
Daughter - an element formed from another by radioactive decay

T (half life) = ln 2/ = 0.6931/

The equation which represents radioactive decay is (derived in most geophysics texts for those who are interested and know a little calculus):

solved for t (age of rock):

Assumptions made in radiometric dating:

• no loss or gain of parent or daughter
• decay rate constant
• half life known
• can measure amounts of parent and daughter accurately (usually use mass spectrometer)

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Part 4a: RbSr dating

Rb⁸⁷ -> Sr⁸⁷ (could also write ⁸⁷Rb, etc.)
Rb commonly substitutes for K in minerals; so method used on K-bearing minerals or rocks which contain them

Decay equation reads:

(Subscript m stands for measured, or in other words, now; o stands for original)

It is easier to measure ratios of atoms rather than absolute numbers so expression usually written:

Could solve for t (age of mineral):

Now measure Sr⁸⁷/Sr⁸⁶ and Rb⁸⁷/Sr⁸⁶ ratios and for reaction ( = 1.39 x 10^-11/yr)
Then estimate (Sr⁸⁷/Sr⁸⁶)_o (Can measure this ratio in coexisting undisturbed minerals which contain no Rb)

Note: Sr⁸⁶_m = Sr⁸⁶_o since Sr⁸⁶ is stable and non-radiogenic
Sr⁸⁶, Sr⁸⁴, and Sr⁸⁸ are all stable and non-radiogenic.
Any could be used; Sr⁸⁶ most abundant and therefore most often used.

Easier mathematics and more accurate way of determining (Sr⁸⁷/Sr⁸⁶)_original:
Equation for straight line is y = ax + b, (where a is slope, b is intercept on y axis)
Equation is in that form (actually y = b + ax) when t is constant (for several minerals in a rock or several rocks of the same age)

If we plot (Sr⁸⁷/Sr⁸⁶)_m vs (Rb⁸⁷/Sr⁸⁶)_m, the values should be different for different rocks and minerals because they would have different initial amounts of Rb.
The slope of the line obtained by connecting these points is -1 and the intercept is (Sr⁸⁷/Sr⁸⁶)_o
Thus we can obtain both the age of the suite and the initial strontium ratio.
These plotted lines are called isochrons.

Isochrons can also be used to determine age of metamorphism.
If whole rock hasn't lost Rb or Sr, but minerals have passed them around during metamorphism, two ages will be obtained - one from dating whole rock and one (metamorphism age) from dating individual minerals in rock.

Another Sr isotope use:
First must know Sr⁸⁷/Sr⁸⁶ in material that made up primitive Earth.
Usually assume it was same as non-Rb⁸⁷ bearing meteorites or about 0.699

During differentiation of crust, behavior of Rb and Sr would be different (different charge, different size).
Rb concentrated in crust, Sr evenly distributed between crust and mantle.
Production of Sr⁸⁷ should thus be faster in crust than in mantle and Sr⁸⁷/Sr⁸⁶ ratios should be higher for crustal material.
Difference in Sr⁸⁷/Sr⁸⁶ ratios, then, is a means for distinguishing igneous rocks that have formed by partial melting of crustal rocks from those that have their origin in differentiation or partial melting of mantle material

Present Sr⁸⁷/Sr⁸⁶ ratio for mantle rock estimated from analyses of recent basalts and gabbros from oceanic environments (direct origin from mantle assumed and no contamination by continental material)
Value is about 0.704
Extrapolation between 0.699 and 0.704 gives reasonable estimate for ratio in mantle at any time in past.
Look at Sr⁸⁷/Sr⁸⁶ ratios for rocks when they formed to determine origin.
(ratio above or consistent with expected mantle ratio?)
(Remember can get Sr⁸⁷/Sr⁸⁶ ratios from isochrons.)

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Part 4b: Uranium, Thorium - Lead dating:

U²³⁸ -> Pb²⁰⁶

U²³⁵ -> Pb²⁰⁷

Th²³² -> Pb²⁰⁸

Commonly use ratio with stable Pb²⁰⁴

One equation might be written:

or:

Must determine ratio (Pb²⁰⁶/Pb²⁰⁴)_o and .
Can find original ratio from associated lead minerals (such as galena) or can use mineral for study that wouldn't have had any original lead (zircon, uraninite, sphene, apatite, monazite, etc.)

By using U²³⁸, U²³⁵, and Th²³², theoretically you get three age determinations and they should agree (concordant ages).
If disagreement, ages are said to be discordant.
This is probably due to gain or loss of material.

Lead-lead method

If equation for U²³⁵ is divided by equation for U²³⁸, we get another equation:

Use of this equation called lead-lead method.
Handy because U²³⁵/U²³⁸ ratio known, as are decay constants.
Can't solve remaining equation directly for t but ages corresponding to different isotope ratios have been plotted and can be obtained from published graphs or tables

Use of Pb-Pb method is good check on U²³⁵, U²³⁸, and Th methods because if lead lost, the ratio of isotopes of remaining lead should not be changed and valid age should still be given.

Can also directly use ratio:

These two quantities increase with time at different rates and if plotted against each other, a curved line is formed (called a concordia curve because all points on the curve have concordant U²³⁸/Pb²⁰⁶ and U²³⁵/Pb²⁰⁷ ages).

If a rock sample has lost no Pb, calculated ages from U²³⁸ and U²³⁵ would be concordant and a point representing the ratio of the above quantities would lie on the concordia curve.

If Pb has been lost, the ages will be discordant and the point representing the ratio will lie below the curve.

Since lead loss would presumably be different for different areas in the sample, several different analyses from different locations in the sample should give several different ratios and thus several different points below the concordia curve.
It can be determined mathematically that these several points will lie on a straight line (called a discordia).

If the discordia line is extended to intersect the concordia curve, upper intersection gives age of rock.
Lower intersection supposedly gives time lead lost but almost never accurate since lead almost never lost all at once but gradually over long time.

Technically could use U²³⁸ -> He⁴, U²³⁵ -> He⁴, or Th²³² -> He⁴
But, helium may be lost since a gas.

Assume that any He present when rock was molten escaped
Therefore, any He present now formed from U or Th after solidification.
He ages thus give solidification ages
(Example: how long it takes for granite batholith to solidify).

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Part 4c: Other Pb uses

1. Can measure average amounts of U²³⁸ and Pb²⁰⁶, or U²³⁵ and Pb²⁰⁷ in rocks at the Earth's surface (usually use recent marine sediments).
Assume no radiogenic lead to start with, can calculate age of Earth's outer portion.

2. Begin with primeval lead (lead present when Earth formed): Pb²⁰⁴, Pb²⁰⁶, Pb²⁰⁷, Pb²⁰⁸ in certain ratios for Earth as whole (usually assume this to be same as ratios in meteorites without U, Th).
With time, radiogenic lead increases, thus higher Pb²⁰⁶/Pb²⁰⁴, etc., ratios with time.
Can get age of Earth (4550-4750 my).

3. (variation on 2)
After a time, ore might form (example: galena).
This ore would "sample" the lead at time of formation, which would consist of the primeval lead plus all radioactive lead formed before the time of ore formation (total lead called the common lead).
Thus, age of ore can be determined by comparing its lead ratios to the ratios which would have existed at various times.

4. Stable nuclei atomic weight about 40 and above are present in about same abundance.
Assume when elements formed, same rule applied to unstable elements.
Now U²³⁸ is 140 times as abundant as U²³⁵.
If both once equally abundant, would take 6 billion years to reach present proportion.
Age of Universe? of our part of Universe? of our Solar System nebula?

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Part 4d: Fission-track dating:

U²³⁸ spontaneously breaks down by fission (splits into two large parts).
This is a rare occurrence.
These fission particles pass through the surrounding material with very high energy and leave tube-shaped damage tracks.

These tracks can be counted (etch mineral with HFl, look at under microscope) and thus the number of spontaneous fissions may be counted.
This gives amount of daughter product in sample.

Can determine (generally from measurement of amount of radiation being emitted) current U²³⁸ content in sample.
Essentially have number of daughter atoms and number of remaining parent atoms and can thus determine age.

Useful because can be used on wide variety of substances of wide range of ages.

Disadvantage which turns out to be an advantage:
Fission tracks are "healed" by prolonged heating (millions of years).
Temperature at which healing occurs is different for each mineral.
Each different mineral thus can yield a different age (apparent disadvantage) because each mineral has its clock "restarted" by healing at different temperatures and thus different times.
But temperature history of sample can be determined by comparing different minerals in sample.

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Part 4e: Potassium-Argon dating:

K⁴⁰ undergoes 2 principal kinds of decay, to Ca⁴⁰ and to Ar⁴⁰.
Decay to Ca⁴⁰ not useful, because Ca⁴⁰ most common isotope of Ca and small amount produced radiogenically would be undetectable.
Therefore, use K-Ar.

Since 2 separate decay types are possible, decay equation somewhat more complicated.

Let be total decay constant, _Ar be decay constant for K-Ar reaction, and _Ca be decay constant for K-Ca reaction.
Then decay equation can be written:

Ar⁴⁰_original = 0 for all but very exotic minerals (original Ar a gas, wouldn't survive formation except under very unusual circumstances, such as enormously high pressures).
Therefore, substituting 0 for original Ar and also substituting decay constants:

     t = 1.88 x 109 ln (1+ 9.07 Ar40/K40)

If metamorphism occurs, Ar⁴⁰ already formed will probably be lost and clock reset.
K-Ar methods can therefore be used to date metamorphic events.

Disadvantage to method:

• Ar is gas and will often escape

Advantages to method:

• can be applied to very common and abundant rocks and minerals, since K one of major elements in Earth's crust
• Glauconite in sedimentary rocks can be used and other methods not generally useful for sedimentary rocks
• schists and slates can be dated
• since Rb usually found with K, 2 independent ages can usually be obtained from same sample and compared
• wide range of ages because of length of halflife (from age of Earth to about 5000 years old); no other methods allow dating of rocks a few tens of thousands of years old (important for establishing chronology of recent magnetic reversals)

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Part 4f: Samarium-Neodymium dating:

Techniques same as for Rb-Sr or K-Ar.

Has advantage that both elements are members of rare-earth group and have virtually identical chemical properties.
Both similarly affected by weathering and metamorphic processes.
Sm/Nd ratios would remain unchanged, giving reliable date for original crystallization.

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Part 4g: Carbon dating:

Carbon 14 dating (also called radiocarbon dating)

C¹⁴ formed in upper atmosphere by reaction of N₂ with neutrons produced by cosmic rays.
Reaction is: ₀N¹ + ₇N¹⁴ -> ₆C¹⁴ + ₁H¹
then C¹⁴ decays -> ₇N¹⁴ + _-1⁰
Thus, total amount of C¹⁴ in atmosphere constant.

Carbon in organism has same C¹⁴/C¹² ratio as air or water does as long as organism alive.
When organism dies, C¹⁴ not replenished, disappears, and C¹⁴/C¹² ratio decreases to zero.
C¹⁴/C¹² ratio thus gives age since death.

Limited to very young samples (less than 70,000 years) because of short half-life (5730 years).

Instead of measuring C¹⁴/C¹² ratio in material directly, normally we compare C¹⁴ in sample to C¹⁴ in air by comparing radioactivity of the 2 samples (number of decays per minute per gram of carbon).
A is activity of C¹⁴ in material to be dated and A_o is activity of air.
(Age of sample) t = 19,035 log A_o/A.

Is % C14 really constant?
Known that C14 content of atmosphere increased 10 % in period 6000 to 2000 years ago.
Found by studying tree rings.
Cause not known.
Now changing because of:

• burning of fossil fuels
• nuclear explosions
• possibly through changes in intensity of Earth's magnetic field

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Part 5: Stable Isotopes

Commonly used stable isotopes in geology:

• H¹, H²
• C¹², C¹³
• O¹⁶, O¹⁸
• S³², S³⁴

Atoms of 2 different isotopes of the same element in the same molecule or crystal structure will vibrate at different frequencies.
The difference in frequency depends on the relative difference in mass between the isotopes.
It would be a significant difference for isotopes of hydrogen (where H² is twice the mass of H¹) and insignificant for isotopes of elements such as tungsten (W¹⁸⁶ is 1.03 times mass of W¹⁸⁰).

The lighter isotope vibrates at a higher frequency than the heavier one and is therefore less strongly bonded.

It can, therefore, be more easily removed by physical, chemical, or biological processes.
Degree to which separation occurs is called fractionation.
Theoretical calculations for fractionation are very difficult or impossible.
Therefore, data is usually merely observed experimentally and then one uses tables, graphs, etc. to study natural occurrences.

The extent of isotopic separation (or fractionation) can be expressed by a ratio called the fractionation factor, .
= (R_a/R_b) - 1
where R_a is ratio of isotopes in phase a, R_b is ratio in phase b.

Example: for oxygen at 25 degrees C,

No fractionation number is very far from zero.

Differences between fractionation numbers are very small, so we usually use comparisons between isotopic separation in a particular sample and the corresponding isotopic separation in some standard.
Standards used:

• O, H - sample of sea water called standard mean ocean water (SMOW)
• C and sometimes O - belemnites of the Cretaceous Peedee Formation of South Carolina
• S - troilite from the Canyon Diablo (Arizona) meteorite
• Si - a quartz vein in the Mother Lode of California

These comparisons are given in terms of delta values, , in permil units (parts per thousand).
A positive means the sample contains a higher % of the heavier isotope than a standard and a negative means the sample contains a lower % of the heavier isotope than the standard.

Examples:

1. physical process
Evaporation of water leads to concentration of lighter isotopes of H and O in the vapor phase and heavier isotopes of H and O in the fluid phase.
O in fresh water has values down to -60 permil because light isotope concentrated in vapor escaping from the sea (and then precipitating to form fresh water).

2. chemical process
If one mixes water made of only O¹⁶ with CO₂ made of only O¹⁸, the isotopes will exchange to yield water and CO₂ with both kinds of isotopes but the water will wind up with a slightly different ratio of O¹⁶/O¹⁸ than the CO₂, because of different bond strengths in the two compounds.

3. biological process
Biological processes are complex and not well understood.

• Example 1: The reduction of sulfate to sulfide uses bacteria as a catalyst.
  The production of sulfide is faster for the lighter isotope of sulfur and this means sulfides have a concentration of lighter isotopes of sulfur and sulfates have a concentration of heavier sulfur isotopes.
  
• Example 2: Photosynthesis by plants favors carbon 12 over carbon 13
  Hydrocarbons formed from living organisms have a C¹²/C¹³ ratio higher than non-biogenic hydrocarbons.
  The high C¹²/C¹³ ratios of coal, petroleum, etc. are a principle evidence of biogenic origin.

Temperature effects:
At high temperatures, the difference between vibrational frequencies of different isotopes is much smaller than at low temperatures.
Thus less separation of isotopes occurs at high temperatures.

This fact can sometimes be used to determine the temperature that prevailed when a certain process was occurring.
Example:
Temperature at time of formation of CaCO₃ precipitated in ocean can be determined by measuring oxygen isotope composition of the carbonate.
Ideally, temperature differences of less than 1 degree C can be determined.

Shows decrease in average temperature of seawater of 5 to 10 degrees C in past 150 my.

Use of stable isotopes to determine source of fluids: (Big ore deposit debate).
Comparison of H²/H¹ ratios and O¹⁸/O¹⁶ ratios for hydrothermal fluids to same ratios for rainwater in that area and to magmatic water.
Ratios of hydrothermal fluid almost same as rainwater but not quite.
Indicates most fluid from rainwater in vicinity but some possibly from magmatic source.

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Part 5a: Meteorite Impacts and Extinctions

Geochemical evidence for impact:
Rocks deposited in the Cretaceous/Tertiary boundary clay layer contain substantial amounts of elements such as iridium which are common in extraterrestrial rocks but rare in Earth rocks.

Geochemical evidence against impact:
These anomalies could also be produced by:

• extensive volcanic activity
• a decrease in sedimentation as a result of extinction of plant and animal species

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Part 6: Low Temperature Geochemistry or Water Geochemistry

Will now look at some chemical reactions of rocks at the surface of the Earth:

• during weathering
• during transportation
• during deposition
• post deposition

Important reminder: "Chemists" usually deal with very simple solutions where they can control the conditions.
Geologists must deal with several complications:

• complex composition of rocks and minerals
• slow rates of reaction (especially at low temperature of Earth's surface)
• grain size and amount of fracturing can significantly influence rates of reaction

Mechanical weathering:

• frost action
• organic activity
• exfoliation
• etc.

Chemical weathering:

• solution
• colloidal suspension
• hydration
• oxidation
• carbonation

At this point, you should review your introductory geology coursework on weathering of rocks and minerals.

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Part 6a: Chemical Equilibrium

For the reversible reaction aA + bB + ... <-> yY + zZ + ...

the equilibrium constant K is defined as

          [Y]y [Z]z ...
     K = ---------------
          [A]a [B]b ...

where values in brackets are concentrations and the coefficients in the equation determine the powers to which the concentrations are to be raised.

Example:

Values of K are given for 25 degrees C and 1 atmosphere pressure, unless otherwise specified.

Concentrations of gases are expressed as partial pressure in atmospheres
(In a mixture of gases, each gas behaves approximately as though it were alone and exerts a pressure independently of the the others. This is its partial pressure.)

Concentrations of solutes in water solutions are given either as moles of solute per liter of solution (molarity) or as moles of solute per kilogram of water (molality)
In dilute solutions (types usually dealt with in geology), the difference between molarity and molality is negligible.

Concentrations of pure solids and pure liquids and of water are included in the equilibrium constant and hence do not appear in the formula.

Once equilibrium is established, a change in concentration of one constituent will lead to changes in the others
(le Chatelier's Principle)

Example: What would be the effect of more CO₂ in the atmosphere? (as in the early history of Earth)
From 2nd equation, increasing [CO₂] results in increased [H₂CO₃].
From 1st equation, increased [H₂CO₃] means more solution of CaCO₃.
Thus, explains why decrease in CO₂ in late preCambrian resulted in more carbonate deposition.

Note that in discussion of equilibrium, nothing has been said about rates of reaction.
Has significance in geology.

Some rules:

• Reactions involving ions in water solution generally almost instantaneous.
• Reactions of ions in silicate melts slow because movements of ions impeded by extreme viscosity of liquid.
• Reactions speeded by rise in temperature (apparently because molecules must be broken down before the substances can react)

(Important)
Many natural systems not in equilibrium but may be considered "stable" because reactions are so slow

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Part 6b: Solubility Products

Solubility product - equilibrium constant for solution of a substance in water

Example: CaSO₄ <-> Ca⁺² + SO₄^-2

K = [Ca⁺²] [SO₄^-2] = 3.4 x 10^-5

Example of how used:
Determine solubility of CaSO₄
Solubility is maximum amount that can be dissolved.
Solubility (in moles per liter) = concentration of Ca⁺² in saturated solution [Ca⁺²]; also = [SO₄^-2]
(Solubility)² = [Ca⁺²] [SO₄^-2] = K = 3.4 x 10^-5
Solubility = 5.8 x 10^-3 M

Solubilities are given for ideal solutions at 25 degrees C.

Effect of raising temperature is usually increased solubility
Some exceptions if solubility reaction gives off heat.

For real solutions:

• Some compounds, when dissolving, react with water (hydolysis) and increase the solubility.
  This is true for many silicates.
• Some compounds, when dissolving, form complex ions with other ions already present in solution, increasing solubility.
  Important process in solution of minerals during weathering.
  Also important in many hydrothermal solutions.
• For non-dilute solutions, ions don't behave independently, and thus we must consider the "activities" (or effective concentrations) of the substances rather than their concentrations
• Some substances produce colloidal suspensions, not true solutions, and don't follow any simple rules or equations.

Uses of solubilities:
From table, determine solubility of ion.
Compare to measured concentration (or activity of non-dilute solution).
This will tell degree of undersaturation and often indicate whether a small change will lead to precipitation.

Example of use:
order of precipitation of evaporites when water evaporates is least undersaturated first to most undersaturated last

Common ion effect -
the decrease in solubility of a salt due to presence of one of its own ions already in the solvent

Example:
(remember, solubility of CaSO₄ in water is 5.8 x 10^-3 M)
Calculate solubility of CaSO₄ in 0.1 M CaCl₂
Solubility of Ca⁺² = x (from CaSO₄) + 0.1M (since 0.1M already in solution)
Obviously, solubility of SO₄^-2 is also x.
K (from table) = 3.4 x 10^-5 = (x + 0.1) (x)
Use quadratic formula and x = 3.4 x 10^-4 M
Thus solubility of CaSO₄ less in CaCl₂ solution than in water.

Most important solvents at Earth's surface are rainwater and other natural waters.
Rainwater and surface waters are not neutral but actually weak acids or bases.
(reminder: pH = - log [H⁺]
In nature, observed pH's lie mostly in the range of 4 to 9; a typical value for surface waters might be 5.7
Since natural waters are weak acids and bases, we must consider solubility of rocks in weak acids and bases rather than in pure water.

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Part 7: Carbonates

An example of a substance dissolving in a weak acid, calcium carbonate dissolving in surface waters, is represented by the following compound reaction (Equation is not balanced.):

      H2O + CO2 <-> H2CO3 <-> H+ + HCO3-
 
                     +
 
                    CaCO3 <--> Ca+2 + 2HCO3-

This reaction describes the following:

• the weathering of limestones
• the dissolving of limestone to form caves
• the dissolving of marble by ore-bearing solutions in the walls of a fissure
• the precipitation of limestone in the sea
• the precipitation of calcium carbonate as a cementing material in sedimentary rocks
• the precipitation of calcium carbonate where droplets evaporate at the tip of a stalactite
• etc.

We will use this reaction to look at the effect of real life complications on what at first glance might seem to be a relatively simple chemical reaction:

1. effect of pH
Dissolving of CaCO₃ uses up H⁺ (to form HCO₃^-)
Addition of H⁺ (lowering the pH) should increase the solubility
Addition of OH^- (raising the pH) should favor precipitation

2. forest fires, air pollution, volcanic eruptions (all sources of CO₂)
More CO₂ in atmosphere, more H₂CO₃
More CaCO₃ dissolves.

3a. decay of organic matter in air or in aerated water
Produces CO₂
More CO₂, more CaCO₃ dissolves.

3b. decay of organic matter when air is restricted or cut off
Produces CO₂ and/or H₂S and/or ammonia (process varies)
CO₂ and H₂S would make CaCO₃ more soluble
NH₄OH would raise pH and make precipitation of CaCO₃ more likely.
Hard to predict what will happen.

4. temperature changes

1. the solubility of most salts increases with increasing temperature
2. the opposite is true of CaCO₃; its solubility decreases with increasing temperature.
3. the solubility of CO₂, like any other gas, decreases with increasing temperature.

Effect b is greater than effect c.
Thus increasing temperature leads to precipitation.

As an illustration of the effect of temperature, CaCO₃ dissolves at great depth in the ocean, where the water is perennially cold, but precipitates near the surface, especially in the tropics, where the water is warm.

5. effect of pressure
Increase of pressure increases solubility by increasing solubility of CO₂ in water.
In deep parts of ocean, pressure alone would increase the solubility of CaCO₃ to about twice its surface value.
In near surface environments, changing atmospheric pressure can theoretically change amount of CO₂ that dissolves and thus effect solubility of CaCO₃.

6. organic activity

6a. Many organisms use calcium carbonate in the construction of their shells. How they accomplish this is not certain.
Biological precipitation of CaCO₃ is extremely important, however.

6b. Green plants cause precipitation of CaCO₃ by removing CO₂ from water in the process of photosynthesis.
Example: Abundant green algae in the warm waters of the Bahama Banks aid in the precipitation of the limy mud and sand with which the banks are covered.

More exotic complications:

7. CaCO₃ is polymorphous.
The two commonly occurring natural forms are calcite and aragonite; at least one other form (vaterite) can be prepared artificially and is known as a rare mineral in nature.

Solubilities of the various forms are different.
K = 4.5 x 10^-9 for calcite
K = 6.0 x 10^-9 for aragonite

Suppose we establish equilibrium between solid aragonite and its saturated solution.
Then the product of the concentration of the two ions is: [Ca⁺²] [CO₃^-2] = 6.0 x 10^-9
This number is larger than the equilibrium product for calcite; that is - there are too many ions present for the solution to be in equilibrium with solid calcite.
The excess Ca⁺² and CO₃^-2 should therefore combine to form calcite.

This process does happen but not rapidly enough to be observed under natural conditions.
Main reason is that in many cases nuclei are not present for calcite to precipitate around.
Therefore if aragonite is present, it will remain apparently stable for a long time but eventually turn into calcite.

Important question:
If calcite precipitates at lower ion concentrations than are necessary for the precipitation of aragonite, how does aragonite get produced in the first place?
In fact, experiments show that calcite and aragonite often precipitate together.
No satisfactory answer to this question has been found.
It is an observed fact that many polymorphic substances show this same tendency to precipitate first in metastable forms, which change only slowly to the stable varieties.
Living creatures that use CaCO₃ in their shells may precipitate either polymorph, some species favoring one and some the other. Many pelecypods precipitate both in alternate layers.

8. effect of grain size
Very tiny grains show a greater solubility than do large crystals.
(Ions escape most easily from corners and edges; more of these per volume on small grains.)
We should then have two solubility products for each reaction, one for small grains and one for large grains.
(Technically, we should have an infinity of solubility products.)

A solution in equilibrium with small grains will be oversaturated with respect to large grains and therefore the small grains should eventually dissolve and the large ones grow at their expense.
This is common and produces such effects as growth of large grains in limestone and conversion of opal to chalcedony and quartz after precipitation.

9. effects of other electrolytes (electrolyte - something that produces ions when dissolved)

9a. Common ion effect (covered previously) - decrease in solubility of a salt due to the presence of one of its own ions.

9b. Electrolytes which do not supply a common ion generally have the opposite effect; they make the solubility greater.

Consider a Ca⁺² ion in water.
Water is a polar molecule; one end positively charged, the other negative.
All the negative ends of the H₂O molecules surrounding the Ca⁺² ion should be close to the ion, the positive ends pointing outward.
The CO₃^-2 ions should be similarly surrounded.
Thus the H₂O molecules serve as a shield between the positive ions and the negative ions, making it harder for them to get together and precipitate.
(This is why electrolytes tend to dissolve better in water than in non-polar compounds.)
Now if another electrolyte (say NaCl) is added, the Na⁺ and Cl^- ions as well as the water molecules will be attracted to the Ca⁺² and CO₃^-2 ions.
This will mean each Ca⁺², for instance, will be at the middle of a cluster of water molecules and Cl^- ions.
Thus the shielding is increased and the Ca⁺² and CO₃^-2 ions will have even more trouble getting together.

In general, the greater the concentration of the second electrolyte, the more ions of it are present for shielding, and the greater the solubility of the CaCO₃.
Divalent ions shield better than monovalent ions and this effect means that CaCO₃ is more soluble in a solution of 0.1 molar MgSO₄ than in a 0.1 M solution of NaCl.

Of course, the presence of electrolytes should have little effect on the solubility of things that don't ionize much when dissolved, such as H₂CO₃.

10. possible associations of ions to form complexes such as UO₂(CO₃)₂^-2
This removes CO₃^-2 ions from solution and makes CaCO₃ more soluble.

Thus there are so many things that can effect the solubility of CaCO₃ in H₂CO₃ that in many cases it is impossible to predict whether CaCO₃ will dissolve or precipitate or only qualitative reasoning can occur.
Example: We might be able to predict that precipitation would occur as temperature was raised but not be able to predict at exactly what temperature the precipitation would occur.

The fact that CaCO₃ is observed to be dissolving in some parts of the ocean and precipitating in other parts and that only slight shifts in the ocean environment can change precipitation to dissolving implies that seawater is essentially saturated in CaCO₃.

Other simple carbonates enter into equilibria like the CaCO₃ equilibrium according to reactions that can be symbolized:
XCO₃ + H₂CO₃ <--> X⁺² + 2HCO₃^- with X standing for Fe, Sr, Mn, etc.

Replacement of one carbonate by another is often observed, both in sedimentary rocks and veins.
For example, the replacement of calcite by siderite should follow the equation:
CaCO₃ + Fe⁺² <--> Ca⁺² + FeCO₃

We can obtain the equilibrium constant for this reaction as follows:

            [Ca+2]      [Ca+2][CO3-2]      4.5 x 10-9
       K = -------- =  -------------  = ------------ = 225
            [Fe+2]      [Fe+2][CO3-2]      2.0 x 10-11

This means that a solution of 1 M [Ca⁺²] would be at equilibrium with 1/225 M [Fe⁺²].
If the ratio of Ca⁺² to Fe⁺² were decreased (more Fe⁺² added or Ca⁺² removed), in order to reestablish equilibrium, some of the iron would replace the Ca⁺² in CaCO₃ to produce more siderite.

The Dolomite Problem:
Dolomite rock is one of the commonest sedimentary materials.
There are thick and extensive beds in strata of all ages.
But - Efforts to prepare dolomite in the laboratory under normal sedimentary conditions have failed.
No dolomite is observed forming in nature today in ordinary sedimentary environments.
There is no geologic evidence to indicate that formation took place in the past under unusual conditions of temperature and pressure.
So how does dolomite form?

Clue 1 - look at structure of dolomite
Anions are CO₃^-2 group.
Cations are regularly alternating Ca⁺² and Mg⁺².
The regular alternation is important.
This is a special, highly-ordered crystalline structure; perhaps it takes a long time to grow.

Clue 2 - free energy levels indicate the following reactions which produce dolomite can occur spontaneously:
(will explain later how free energy works)

• CaCO₃ + Mg⁺² + 2HCO₃^- <--> CaMg(CO₃)₂ + H₂CO₃
• 2CaCO₃ + Mg⁺² <--> CaMg(CO₃)² + Ca⁺²

Clue 3 - geologic evidence
Poor preservation of fossils in dolomite
Coarseness of grains
Commonly observed cavities and pore spaces

All clues suggest that dolomites in older strata did not form as primary deposits but are instead altered CaCO₃ deposits.

Currently accepted theory:
Dolomite is formed by a reaction between Mg⁺² ions and a CaCO₃ sediment.
The Mg⁺² may come from seawater in contact with the limy sediment or buried with it, from ions taken up in the original CaCO₃ structure (particularly in shells), or from later solutions moving through the sediment.

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Part 8: Colloids

Colloidal dispersion - particles in size range between that of true solution (10^-7 mm) and suspensions (greater than 10^-3 mm)

How to tell colloidal dispersion from suspension:

• even in field of microscope, colloidal particles can't be seen
• when allowed to stand, colloid doesn't change; particles in suspension settle out

How to tell colloidal dispersion from true solution:

• colloids scatter light (Tyndall effect), often look milky when seen in reflected light
• can observe Brownian motion of colloidal particles under microscope (result of bombardment by water molecules)
• colloids diffuse very slowly (through a membrane, for example)
• colloids effects on vapor pressure, boiling point and melting point of water not predictable
  (unlike substance in solution; for example: solution lowers freezing point)
• colored diffusion bands form in colloidal gels when an electrolyte is allowed to diffuse (Liesegang rings); process not understood; may be origin of colored bands in agate

Electric charges characteristic of colloids.
Due to adsorption of ions on particles
What determines amount of charge and sign of charge not understood.

Colloids are thermodynamically unstable.
According to free energy calculations (will look at later), the particles should spontaneously grow larger.
Electric charge is what keeps colloid particles dispersed.
Reducing or removing charge causes flocculation.
Thus most colloidal dispersions destroyed by adding electrolytes.

Apparent confusion:
Must have electrolyte to form colloid (to get ions which are adsorbed) but more electrolyte causes precipitation.
Key apparently is amount and kind of ions present, but process not completely understood.

Protective colloids - the presence of a second colloid sometimes makes a colloid more stable
Examples:

• organic colloids protect iron hydroxide and manganese dioxide colloids
• silica colloids protect gold and mercury sulfide and may have an important effect in ore formation

The role of electric charge in colloidal flocculation leads to three general rules useful in geology:

• particles remain suspended in fresh water longer than in sea water
• salt lakes are clear due to flocculation of colloidal material carried into them
• many "poisonous" materials (copper, selenium, arsenic, lead, etc.) are removed by this process; obviously good for us

Some ions adsorbed on colloids are held tightly; some weakly.
Depends on type of force, type of colloid and type of ion.
Usually attachment is weak enough so some ions are easily replaced by others.
Important fact is that some surfaces or some kinds of colloidal particles hold adsorbed ions more strongly.

In geology, ion exchange is very important.
Examples:

• mechanism for redistribution of metal ions between solutions and sediments
  Explains why cobalt and lead found with manganese since these ions are easily adsorbed on manganese diioxide sols
• influence of adsorbed ions on substance

Especially important for clays.
Clays with adsorbed Na⁺ are sticky and impervious to water; clays with Ca⁺² are granular, easily worked, readily permeable.
That's why gypsum often added to yards to convert Na⁺ clays to Ca⁺² type.

The effect of heat on colloids not understood.
Important because of hydrothermal studies.

Two forms of colloidal dispersions:
1. sol

• clear, transparent liquid
• individual particles?
• example: dissolved gelatine

2. gel

• solid network of fibers in which water trapped?

Which form depends on:

• concentration
• methods of preparation
• time of standing

Two types of colloidal substances:
1. hydrophilic

• probably have much adsorbed water
• dissolves directly to form colloidal dispersions
• dispersion stable indefinitely
• readily forms gels and process of gelation reversible

2. hydrophobic

• must be obtained indirectly (by precipitation from a true solution, passage of electric current, etc.)
• less stable than hydrophilic
• hard to form gels and gelation not reversible

Some compounds difficult to classify.
Example: silica

• stable indefinitely
• forms gel readily
• doesn't spontaneously disperse

Some common natural colloids:

• silica
• clay minerals
• limonite
• manganese dioxide

1. silica

Colloidal characteristics:

• cryptocrystalline or amorphous
• has Liesegang rings
• coagulated by electrolytes
• round nodules resemble laboratory made gels
• shrinkage cracks in nodules
• etc.

silica in the laboratory:<