Corrections to White Geochemistry book online
Chapter 1.
Fig 1.1 and other periodic tables: Better specify "naturally occurring elements" in the caption, since you are excluding everything beyond Pu.
Page 5, last paragraph of section 1.3.1: imagining the sun, not imaging the sun. (Found by Colette Salyk)
Page 7, second footnote: superscript 4 on '4He' in last line.
Fig. 1.4: For some reason, B, C, Al, and Si are shown above Sc and Ti rather than above Ga and Ge. (Found by Ravi Kanda)
Page 9, second paragraph: Thus the 3d subshell is vacant in period 3 elements (plural) (Colette Salyk)
Page 10, Reference to Fig. 1.6 should be Fig 1.4.
Fig. 1.6: Try to show absolute scale in angstroms?
Page 18: Bizarre to leave abundance of Fe out of the list of common elements in the silicate Earth. Also, not sure I would define silicates as based on tetrahedral coordination...is stishovite a silicate?
Fig. 1.11 caption: in pyroxenes each tetrahedron share two oxygens (sharing only one gives you Si2O7 groups, not chains).
Page 19: Again, pyroxenes have two bridging oxygens per tetrahedron. In amphiboles, you only add half an additional bridging oxygen between tetrahedra (equal number of Q2 and Q3 silicons).
Chapter 2.
Page 23: Better not to state categorically that "equilibrium occurs when the Gibbs Free Energy of the system is lowest" unless you also include "at constant temperature and pressure".
Page 24, bottom: Might want to clarify the definition of pure substance with an example such as water, which is pure unless the process under consideration involves electrolysis, etc.
Page 30: Definitions of exact function and exact differential equation are a bit confused. As I understand it, 2.25 is an exact differential equation if 2.31 is true. From this it follows that there exists at exact function u whose derivative is gien by 2.26.
Pages 33-34: The statistical possibilities considered are "combinations", not "permutations", since the sequence of units is not considered.
Page 34: 6/64 = 0.09375.
Page 35, bottom: "We assume that each block is has..." (two verbs).
Equation 2.52: Better put a "rev" subscript on dQ here, if it is going to serve as a definition of entropy.
Page 38, section 2.4.2.2: Surely once the partition is removed all 16 states are accessible, not only the four versions of the most probable case. So the change in entropy ought to be kln16 = 4kln2.
Page 38, 2.4.2.3, second sentence: "number of states". Third sentence, parenthetical clause: "Such as the thermal insulation".
Page 39, 2.4.3, first sentence: "...inexact differential that is a function...".
Page 39, equation 2.58: This equation is only true for reversible changes. Best to state the inequality and then given the explicit limitation to reversible processes state the equality. It can then also be introduced that E reaches a minimum during the approach to equilibrium at prescribed S and V, which while not very practical sets up the later statement in terms of G, P, and T.
Box 2.1: Units on heat of evaporation? J/kg, J/mol, or extensive J for the total quantity of freon in the air conditioner (J/cycle?). Capitalize K in J/k in the two equations. Should be J/K, not J/T after 0.113 in the line after the two equations.
Page 40, between equations 2.59 and 2.60: enthalpy misspelled.
Page 40, equation 2.65: Again this form is restricted to reversible processes. If the inequality is given then it can be shown that H is a minimum at equilbrium when S and P are prescribed (as in adiabatic reversible pressure changes).
Page 41, section 2.6.1, last paragraph: "heat capacities depend on vibrational frequencies".
Page 42, after equation 2.74: Remarkably, CP-CV is positive even when alpha is negative! This is not quite captured by the present text.
Page 44, section 2.6.4.1, first paragraph: "most mean" should be either "mean" or "most probable".
Equations 2.89 and 2.90: ln is missing in (dlnQ/dT)|V.
Page 46, after equation 2.93: Spin quantum numbers have fractional values, so this is not quite right.
Page 47, last paragraph: Equation 1.125 is the wrong reference, not sure what the right one is.
Equation 2.102: The dT should be in the numerator, the T in the denominator of the integrand! Need a bigger space between the two equations (delta-S-phi and Cp run together). Best to warn the reader right off that both Maier-Kelley and Haas-Fisher are purely empirical forms and that, in particular, since both have positive powers of T they must never be extrapolated beyond the calibrated range.
Page 50: Not sure what you are getting at when you say "the coefficient of thermal expansion is 0 at absolute 0". I think the point is that the Cp integral is done at 1 bar and the volume is integral is taken at the temperature of interest.
Page 50, sections 2.8.1: Must again specify reversible: A reversible adiabatic change is one carried out at constant entropy!
Box 2.3: Better specify nearly ideal solution; if the Fe and Mg atoms tend to cluster, this estimate will not be right.
Page 52, end of section 2.8.3: Don't say "enthalpies of formation for these elements"...you mean compounds. Also, Box 2.4 should be moved to the bottom of the page.
Equation 2.120: Again, dT in numerator, T in denominator.
Box 2.5: Sign error in second equation: integral of -C/T^2 is +c/T.
Table 2.2: Berman (1988) or Holland and Powell (1998) are more accurate and internally consistent than Helgeson (1978). Andalusite misspelled. Should either spell out all minerals or expand abbreviations in the caption. Subscript 8 on chlorite formula misplaced.
Page 54, section 2.9.1: Better not to say "dU - TdS is the amount of internal energy in the system available for work", this confuses absolute energies and changes in energy (it seems to say that dU - TdS is defined as A). Perhaps just take out "in the system".
Box 2.6: Need to specify that only the volume of steam should be taken as ideal; evidently we are not using the ideal gas law for the heat capacity.
Equation 2.126 is not really the integral of 2.125. It is more like a finite difference version of Equation 2.123.
Page 56, section 2.9.3: The second boxed theorem is only true at constant T and P.
Box 2.7: The references should be to equations 2.129 and 2.130.
Page 57: The unnumbered equation at the bottom of the page does not make sense to me. I would proceed straight to equation 2.132, and then in equation 2.133 I would pull Delta-Sref*(T'-Tref) out of the integral.
Box 2.8 middle paragraph: "Since we may assume" or "Since we are assuming".
Problem 1. Would scan better if you said "adiabatic temperature gradient (dT/dP)|S".
Problem 11. ??? Where did the minus sign come from? Also, this is just a one-step application of the chain rule.
Problem 19. Andalusite misspelled again (but differently).
Chapter 3.
Page 63, section 3.2.1.3, end of first paragraph: "...we are also interested in the precipitation..."
Page 64: Boehmite misspelled the second time. Also, there are at least three phases of Al2O3 and at least 12 phases of H2O...
Figure 3.2, caption: Boehmite misspelled again. Andalusite misspelled again (yet a third way).
Page 64: The albite-orthoclase exchange is binary. I can also write the reaction K-Na = KNa-1.
Page 65, last paragraph: I would not say univariant point, but univariant lines (or curves). And I would not say "fixed pressure or fixed temperature" for a univariant but "along a one-dimensional line or curve in P-T space".
Section 3.2.3: Limiting the discussion to a phase boundary between two phases in a one-component system is not necessary. The Clapeyron equation applies to any unvariant reaction.
Page 66: "...grind anorthite and albite crystals into a fine powder and mix them..."
Page 69, section 3.4.1, second paragraph: The volume of plagioclase is the sum of the partial molar volume of its components weighted by the number of moles of each component present. Also, worth commenting that in some systems the molar volumes are nearly independent of composition and hence can be used to simply interpolate the volume of any composition.
Page 74, after equation 3.33: Better qualify mu_i is always less than or equal to mu_i_o for an ideal solution, lest the reader think this a universal law for all solutions.
Page 75, region (1): Dissolved, not dissolves.
Page 77, top: Kerrick with two k's...observations on the volume, pressure, and temperature (I presume).
Box 3.2: Integral of RT/f df, not RT/P df. Second half of Eq. 3.49 is mangled.
Page 79, last line of section 3.6.3: conentration, singular.
Page 80, Freezing point box: Between Eqns 3.59 and 3.60 the reference to equations 3.56 and 3.57 is wrong, it should be 3.58 and 3.59. The notation in this box is not consistent: sometime mu^o_H2O, sometimes mu^o_H2O_l, etc. Given the convention of putting phase in the superscript, I would use superscripts of o,l and o,ice.
Figure 3.10: No difference in grayscale evident between first and second solvation shells. There is an "and" missing in the last sentence of the caption.
Page 82, second full paragraph: "Immediately adjacent to the ion..."
Page 82, comments for enrichment: Add that electrosriction can lead to negative partial molar volumes for solutes (though you get to this in a few pages anyway). Comment that at very high pressure the dissociation of water becomes much more significant and the pH of neutral solutions shifts dramatically.
Page 83, equation 3.68: I always thought pH was defined as -log[H+] using concentration, not activity. Perhaps I'm wrong; are you sure on this?
Figure 3.11: Reference misspelled.
Equation 3.70: Should be limit as m->0, not infinity!
Page 84, sentence before equation 3.72: delete "and".
Page 86, end of first paragraph: "Table 3.2a summarzies the Debye-Huckel solvent parameters..."
Page 87, bottom: "an ionic species that forms", singular case on verb.
Page 88, middle paragraph: Inconsistent use of molality and molarity.
Page 90: Phase component not really defined. References to Eq. 3.92 is wrong, should be 3.80.
Example 3.5 and elsewhere: The A site of feldspars is not octahedral.
Page 93: Reference to equation 3.97 is wrong; the law of mass action is Equation 3.85. Apparently you added 12 equations at some point.
Box 3.6: p missing of pK2 in last equation. Also sign on pKH2O is wrong, should be +.
Page 94: Second law misstated, inequality is other way around.
Example 3.8: Question should be "what would be the activity of Mg2+ in that fluid". Question says pH 3.5 but answer is calculated using pH 4.0.
Page 98, first paragraph: Choose, not chose.
Page 100: LEO the lion, not lions. Also, my useful mnemonic is that reduction means the charge goes down. Also, the sentence after the magnetite oxidation reaction should is missing an 'is' and loses is misspelled.
Page 102, first full paragraph: Emerged or immersed?
Equation 3.103 is not balanced.
Equation 3.120 is mangled.
Page 107: Statement of equilibrium constant for solution of magnetite should have activity of Fe2+, not 3+, and should have a 2pe term, not 3pe.
Problem 8: Need parentheses around OH in formula for phlogopite.
Problem 11: Formula for K2 is wrong.
Problem 12: Concentration of _solute_ in the vapor is small.
Problem 15: Presumably you mean Fe2+ and Fe3+.
Chapter 4.
Equations 4.8 and 4.8a are redundant.
Page 120: Not clear why you say the WGi for an asymmetric solution depend on pressure after equation 4.17, since you clarify just below that they can also be split into WU, WV,and WS terms.
Figure 4.3: Sketch solvus, spinodal, and critical point on the 3-D G-X-T surface?
Page 122: First paragraph confuses the issues of partial solid solution and complete miscibility. Not clear what good is does to maintain the fiction of pure endmember solids through until after the next paragraph.
Equation 4.20: Sign error, should be -mu^0_1. Also second term should be RT(X2/X1). And then there must be a plus between this term and (dGex/dX2). Also, ideally you should not switch between G_excess in the text and G_ex with a bar in the equations.
Equation 4.21 is not right; again you need a + before the (d2G_ex/dX_2^2). Otherwise setting G_ex to zero gives zero second derivative rather than strictly positive second derivative.
Page 122: X2a and X2b are not the inflection points. The solvus and spinode have gotten all tangled up here. The solvus points, since they both lie on a common tangent, are in equilibrium with one another.
Page 123, first paragraph: "at about 650C _in_ the alkali feldspar solution".
Page 123, end of section 4.3: Again you refer to the solvus point as an inflection point, which it clearly is not. Also, you should introduce here the idea of nucleation of a phase near the opposite limb of the solvus as a way around the kinetic barrier described.
Figure 4.9 caption: The dashed lines should be described as "metastable", not sure what you mean by apparent in this context.
Page 126, last sentence of 4.4.1: where, not we.
Page 126: I wouldn't say univariant and divariant "systems" but rather "assemblages".
Figure 4.11: Caption to part (d) got lost.
Page 128: Your definition of peritectic is tricky. Which phase is eliminated as you lower temperature depends on bulk composition (if you are between fo and en then L will be eliminated, even though En=Fo+L is a peritectic). A more general definition is that the liquid is between the two solids in composition at a eutectic whereas the liquid is not between the solids at a peritectic (and hence it is possible for a solid+liquid assemblage to persist below the peritectic temperature if the bulk composition is right).
Figure 4.14: The uncertainty in the Al2SiO5 triple point is no longer due to sluggish kinetics but to the free energy difference between bulk sillimanite and fibrolite.
Page 131: Displaced equilibria also applies to reactions that are displaced by solution in the vapor phase, I think.
Page 133, section 4.5.2.2, first paragraph: "has _been_ the subject".
Figure 4.16: Shading is messed up. Either shade one-phase regions or two-phase regions but not some of each.
Figure 4.17: The caption statement that experiment show complete solid solution between the Fe end-members is not consistent with the plot. The red 700 C contour should close within the quadrilateral if this is true.
Page 138: The statement of the approach of Spencer and Lindsley repeats what you just said about two independent reactions.
Page 139, little smidge of text: Principles, not principals.
Page 142, first word: either "structures" or "structural elements".
Page 142, last paragraph of 4.6.2: Ghiorso misspelled twice. Also, I object to describing the goal of thermodynamic modelling as restricted to crystallization and cooling. It is equally applicable to melting calculations. Indeed in the batch case it is the same thing. This galls me because I had a reviewer downgrade one of my proposals because he thought Ghiorso's code could not be used for melting...
Page 142, first sentence of section 4.6.2.1: missing 'the' in "argued that simplest model".
Equation 4.61: Extra = sign. Don't need all the fussy j and k stuff in the second summation term since Wjj = 0. Same in equation 4.62.
Page 143 after equation 4.63: should be nu_p,i not nu_p,k.
Page 143 footnote: another novel spelling of Ghiorso.
Page 145 top: This discussion of the numerical method is not quite right. Evidently, the chemical potentials are not all zero at a minimum in G. They are all equal for each component in all the phases, so that G cannot be lowered by moving matter from one phase to another, but that does not mean they are zero. What vanishes at the minimum is the gradient of G with respect to the free compositional variables.
Figure 4.24 caption: Date should be 1995 on Ghiorso and Sack ref.
Page 146: MELTS is not limited to 1 GPa. A more reasonable limit is 3 GPa.
Page 147, top: Another misspelling of Ghiorso. MIXFRAC _is_ available, not _are_.
Page 147: For some reason the chemical potential relation for NaCl, Na+, and Cl- is given twice.
Page 147, after equation 4.72: I would call this a "geometric mean", not multiplicative.
Equation 4.75: Denominator missing.
Page 148, bottom: "Let's return".
Figure 4.25: Odd to put (a) on the bottom and (b) on the top.
Equation 4.95: Should not be an r in the denominator of RHS.
Page 152 last paragraph: remove 'if' from "Consider the case where if a certain fraction...".
Page 154 second paragraph: CaCl_ should be superscript -.
Page 156 top: Fletcher misspelled.
Problem 1 text and table: More trouble with the spelling of andalusite. Also sillimanite, spelled differently in both text and table.
Problem 3: Spelling of parameter.
Problem 4a: Add "intervals".
Problem 7: Gratuitous hyphen in titanomagnetite.
Problem 10: This is really labor-intensive!
Problem 11: Better put a label on the table as to which problem it goes with.
Problem 15 Table: why more entries in first column than in second?
Chapter 5.
Page 161, 3rd paragraph: "...more likely to be _in_ equilibrium...", "...where cooling is rapid enough..." (not rapidly).
Page 162 section 5.2.2 second paragraph: "subsequently precipitating", two typos. Extra space later in same line.
Equation 5.15: n_O_2, not n_O.
Equation 5.19: n_O_2 for n_O, n_N for n_H.
Page 165 just before equation 5.20: "...the average velocity..."
Equations 5.21 and 5.23: n_O_2, not n_O.
Page 165 just after equation 5.23: nitrogen, not hydrogen.
Page 166 first footnote: in the present version, van't Hoff equation is 3.96.
Page 166 second footnote: Arrhenius died in 1927, not 1827.
Figure 5.3: The two halves of the figure are not consistent, they do not agree at 300 K and 15 kJ.
Page 166 last paragraph: "In the case of..."
Table 5.1: Would be entertaining to add diamond->graphite, which is like 700 kJ/mol or something, I think.
Page 167 footnote: Also don't confuse it with the law of mass action, since the exponents in the rate equation need not be the stoichiometric coefficients in general.
Page 167 second paragraph: "Second, the values of the exponents _for the reactants_ are the stoichiometric coefficients of the _reactant_ species". Otherwise it sounds inconsistent with the First restriction.
Example 5.1: The question is stated in a confusing manner: "How the concentration of CO2 will change with time after the concentration of CO2 is changed". Better to say we assume that the equilibrium concentration of CO2 is zero and ask about the evolution after CO2 is added.
Page 168 second paragraph: I think you want a one-way reaction arrow, not an equilibrium two-way arrow. The exponent in Equation 5.30 is partly cut-off as I view it.
Example 5.2: Second reaction does not balance; want 1 H2O and 1 H+. Probably want to write the third reaction, even if it not pH dependent. Last line of the box is cut off as I view it.
Page 172: Mysterious euro symbol in first line.
Equation 5.40 and the one before it: subscripts on k+ and k_ missing in denominators.
Box 5.3: Should concede that racemization rates (like all kinetic rates) are temperature dependent, so as a chronometer it involves certain assumptions.
Page 173: It looks like the reference to Eqn 5.60 at the bottom should be to Eqn 5.43.
Page 174: Again, the van't Hoff equation is 3.96.
Figure 5.6: Some minuses missing.
Page 175: It says "activate complex" in a couple places where "activated" is intended.
Page 176: More equation numbering problems.
Page 178: Formatting issue; don't want equation 5.70 by itself on a page the rest of which is taken up by a box. Also, last line of the box is cut off as I view it.
Page 180: Equation 5.73a should show J as a vector. Then, the expression for gradient of a scalar function is incorrect, it needs to be a vector.
Page 181: Fick's 2nd law is equation 5.74, not 5.91. Also, given the way most equations are developed rather than taken as given, it would perhaps be wise to show how Fick's 2nd law arises from conservation of mass (continuity) and Fick's 1st law.
Figure 5.11: More points should be plotted so the curves are smoother and more symmetrical.
Caption to Figure 5.12: This films, not this films.
Equation 5.82: Missing a close-parenthesis.
Page 182, footnote: The reader might not know how to write an IF statement in Excel to test for a negative value. Perhaps a good opportunity to teach them (learning how to use Excel is a big part of learning to be a geochemist, no?).
Box 5.6: More equation numbering problems.
Equation 5.89: Missing "n=" under summation sign.
Equation 5.90: Should use L rather than D for Onsager rather than Fick coefficient.
Equation 5.90a: This is a strange equation. It should either be dc/dt = L d2m/dx2 or if you take an ideal solution approximation you could get back to dm/dt somehow.
Box 5.8 should refer to equation 5.91, not 5.107.
Page 185: In Watson's experiment, the quartz sphere stays solid; in the text your refer to a quartz liquid (at 1200C!).
Page 185: References to Equation 5.92 should be to 5.91. Also, no reason to put arrows over the Ci elements of the C vector.
Page 185: Your "three types of diffusion" (self, chemical and inter-) excludes the important case of multicomponent chemical diffusion, which uses the Fick-Onsager equation, a sort of combination of your treatment of chemical and interdiffusion. The non-ideality of silicate liquids, causing Na chemical potential to be slaved to Si concentration, is much more important in generating uphill diffusion in Watson's (and also, more recently, Lundstrom's) experiments, than any charge or volume counter-diffusion effects. See Liang and Richter papers.
Equation 5.97 is corrupted.
Page 189: Kirkaldy misspelled.
Page 189: Strange to define the r parameter in Stokes-Einstein as an "ionic radius" if the equation only applies to neutral species. Also, the limitation of Stokes-Einstein to diffusion of the major species controlling shear deformation should be mentioned.
Page 190: Adatom or Addatom?
Page 190: It is jarring in the discussion of steps and kinks when you switch from growth to dissolution.
Page 191, top: "Molar volume of each (pure) quartz crystal".
Page 191: If you want another demonstration of the importance of surface energy at small grainsize, you could show Navrotsky's figure based on calorimetry of nanocrystalline a- and g-Al2O3; the relative stability switches at a certain size.
Page 192: The notation DGr is confusing, since this is the part of DG that does not depend on r! About halfway down there is a typo, is says DGrl for no good reason. Also, in Figure 5.21, the red curve should go through the origin.
Page 193, top: Does viscosity really affect nucleation through the surface energy rather than through the rate of formation of nuclei? This is surprising to me. Also, I assume you don't mean "nucleation rations".
Box 5.9: Enthalpy misspelled.
Page 195: Reference to 3.133 should be to 5.116. Reference to 5.123a needs fixing.
Page 196, first paragraph of section 5.5.4: Better specify "Heats of chemical adsorption are relatively large".
Page 197: What is A? I think around equations 5.128 and 5.129 the text should only talk about the concentration of M.
Page 202, Rate equation: Missing open brace on third term; kL, [L], and kH2O not defined.
Page 207, top: "Let's turn our attention..."
Equations 5.141, 5.143, 5.144: You switched from w to v.
Equation 1.54 can't really be balanced.
Figure 5.37 caption: should refer to equation 5.160?
Problem #6: Derive 5.57 by starting with 5.57?
Chapter 6
Page 216, last paragraph: "Arrhenius defined an acid as a substance..."
Page 217: Second reaction showing amphoteric nature of Al(OH)2+ should have OH- as a reactant, not H2O.
Page 217, first paragraph of section 6.2.1.1: There is an OH+ that should be OH-. Also there is a gratuitous 's' in the italic sentence. And I think it would be useful to caution the reader against confusing balanced chemical reactions with proton balance equations (point out the use of an equals sign rather than reaction arrows).
Page 218, just before Eqn. 6.9: "...is assumed but not written..."
Page 218, just after Eqn. 6.9: Italicize TOT in TOTH.
Page 220: Reaction 6.15a does not parse; leave out H2O as a reactant. In Example 6.1, too many 'ands' in the first sentence. In second line, NaCO3 should Na2CO3. Just after equation 6.22, 'choose' and 'fourth' are misspelled.
Page 221: Table 6.1 headers, missing p on the pKCaHCO3+.
Page 223, end of section 6.2.3: Symbol CT not defined, you have been using SCO2.
Page 224, after equation 6.36: Reference should be to back to RHS of 6.36, not 6.32.
Page 225, Example 6.4: Should refer to problem 3.7, not 3.8. Also, I think both in the example and in the text of section 6.2.5.1, the reference should be to equation 6.37 for calculation of alkalinity.
Page 225, after equation 6.40: references should be to equations 6.39a and 6.39b.
Page 226, top: misspelled stoichiometry.
Example 6.5: Why is equation 6.46 given twice?
Caption to Figure 6.6: Valence misspelled (also on Page 231, three times, where figure 6.6 is described).
Page 231, just after the drawings of the complexes: the word 'concentration' is repeated twice.
Example 6.6: "...substituting into the equilibrium constant expression, we obtain..."
Page 233: Predominately should be predominantly.
Page 234: Do not want to split lines between 10- and 8 in the Pb concentration.
Page 234, first sentence of 6.4.1: 'found' and 'present' are redundant.
Page 234: There is no equation 6.51. Also, the reference at the bottom of the page should be to 6.53 (as presently numbered).
Page 236: Should point out that the effect of Na concentration on Calcite solubility is expressed in equation 6.56 by the activity coefficients of Ca and bicarbonate which, in turn, depend on ionic strength as in the Debye-Huckel law.
Figure 6.14: Why show metastable extensions in part (a) but not in part (b)?
Page 239, first line: dissolved, not dissolve. Also, first sentence of 6.43 should say 'element', not 'elements'.
Page 240: In description of Solver, mean to say "no direct solution".
Page 241, just after equation 6.75: Gratuitous "we ca" before real "we can".
Page 242, section 6.4.4: Want Ag1+, not 3+.
Page 243, before equation 6.84: Either "other metals" or "metals other than Al". Then, missing value for K1 for Fe and label on 6.84a. Also, charge on Fe(OH)4 in 6.84c should be -1, not +1. Also, the sequence of reactions 6.84 is confusing. Finally, why not show neutral Fe(OH)3[aq], the way you do for Al?
Page 244, equation 6.85 and following: better give K as 10-4.4, since that is what is given in the text and in figure 6.22.
Page 246, section 6.5.1.1: "...some hydroxyls are replaced by oxygen...", not the other way around. In section 6.5.2.2, the subscript 4's on Si in the formulas for pyrophyllite and talc are too big.
Page 249, second sentence: Delete "is".
Page 249, between 6.88 and 6.89: The equation uses KYX and the text uses K' for selectivity constant. Also, notation of 6.90 is inadequate to express the fact that X and Y may have different stoichiometric coefficients.
Page 250, intro to section 6.6: It currently says "Soils have concentrations in soils above levels one would predict..."; something is wrong there.
Caption to figure 6.29: "emmersed" should be "immersed".
Page 252, top: Either "constituent oxides' surfaces" or "constituent oxide surfaces".
Caption to Figure 5.31: "dilute" solution.
Page 253, middle paragraph: Logic is messed up in sentence about anion and cation adsorption as function of pH.
Page 254: Unnumbered equation for total Pb should not have a symbol in SPb. Also, in same equation, missing close bracket on [FeOH2+].
Page 257, after eqn. 6.114: Valence misspelled again.
Page 259, caption to 6.40: should refer to Example 6.10, not 6.9.
Page 262, problem 10: Relevance of eqn. 6.48 not clear.
Chapter 7.
Page 265, first paragraph: I don't think 'concentrational' is a word. Also, I think you leave out one of the key reasons why trace elements are useful, namely Henry's Law and the simple and predictable behavior that results from partition coefficients.
Page 267, heading of section 7.2.1: Goldschmidt misspelled.
Page 267 footnote: The Goldschmidt conferences are annual J
Figure 7.3: Too many shades of grey; hard to tell apart. Also, Th should be double-classified as a "rare-earth and related" as well as a U-series decay product.
Page 271, paragraph on sulfur partitioning: "...and other chalcophile metals and are the source of many economically important..."
Page 271: Do not want to imply that by definition carbonatites from as the result of liquid immiscibility. Wyllie's work has shown that many (all?) do not.
Page 271: Conventional to give ionic radii in ngstroms, not pm, isn't it?
Page 272, in paragraph on charges of REE: Eu can be +2, not 2+ (for consistency). Valence misspelled after Th is always +4.
End of page 272, top of page 273: Why not go ahead and tell people that a Coryell-Masuda diagram is often called a spidergram?
Figure 7.7: It is implied in the text, but should make it explicit in the caption which normalization scheme is used, since Orgueil does not plot at 1 and this may confuse people.
Page 275, third sentence of section 7.2.2.6: Valence again.
Page 276, third paragraph: I think this is the first place you have used roman numerals for valence states. Probably better to say +1 to +8.
Page 276: At end of fourth paragraph, 'silicate' not 'silicates'. At end of fifth paragraph, 'oxide' not 'oxides'.
Caption to Figure 7.9: Missing end-quote on Onias's Flow.
Page 278: Formula for apatite is wrong. Should be Ca5(PO4)3(OH,Cl,F).
Page 279: Definition of incompatible is D < 1. D << 1 defines highly incompatible.
Page 279: Using gamma for activity coefficients here seems to violate the standard set up in Chapter 3 of using lambda when units are mole fraction.
Section 7.4 general comment: You need to update all this to reflect the remarkable success of the Blundy and Wood (after Brice and Onuma) treatments. They have drawn much more attention than the Beattie formulation. They have now accounted for ionic radius effects, electrostatic effects, site population...everything but liquid composition (a significant shortcoming, but still). In particular, the symmetry of the Onuma curve seems to shows that the incompatibility of small ions is not because of "low bonding energy" but rather because of strain associated with shrinking the site to fit the small ion.
Page 282: Equation 7.14 is not right. Where did the standard state terms go? Why are there two equals signs?
Page 284: Please don't use the terms basic and acidic for silicate liquids; they are confusing and obsolete.
Example 7.1: I don't think the constant term in 7.22 reflects additional compositional effects; it is just the intercept, i.e. D at infinite temperature and NBO/T=1. Last sentence of the example: Schofield misspelled.
Page 289, just before olivine exchange reaction: "...thermodynamic data were used to calculate..."
Page 289: The paragraph explaining the symbols in equation 7.37 has somehow gotten displaced down into the next section!
Page 292: I don't think the symbol SDo for CFSE makes sense; SD would be better.
Page 294: Probably want to define pleochroism in a footnote.
Figure 7.19: Two lines are shown for the two orbitals that remain degenerate in part (a), but only one line is shown for this pair in part (c). Also, two lines are shown for the two degenerate high energy orbitals in (b), and two lines (not three) are shown for the three degenerate low energy orbitals in (b). In the two previous figures, only one line is shown for all degenerate orbitals; I would stick with that standard in this figure.
Table 7.7: Why isn't Cu2+ vertically aligned with the other 2+ ions? Why no data on Ni3+? Explain somewhere the relationship of spectroscopic transition energy in cm-1 to molar CFSE (CFSE = NAhcD); (OK I see this in one of the problems at the end)?
Figure 7.20: Components should be Mg2SiO4 and Ni2SiO4, the 2's are missing.
Page 297, first sentence of 7.6: "Igneous geochemistry" or "High-temperature geochemistry" would be preferable to "igneous temperature geochemistry." In last paragraph of introductory section, need to say either "melting and melt extraction in the Earth remain poorly understood" or "remain a poorly understood process" and also replace "observed" with "observe." Also, "emplaced", not "implaced." And, "provided" rather than "provides."
Page 297, equation 7.39: Do not put a bar over Cil, this is not an average of anything. More importantly, you need a (1-F) in the denominator, not an (F-1)!
Also, I would not wait until several pages later to define bulk partition coefficient; it would be too easy for a student to look up the batch melting equation without reading on and miss the distinction with mineral partition coefficients. At least a pointer to the definition below would be good.
Caption to figure 7.21 is totally messed up...the equation for fractional melting liquid composition in the text got superimposed on it.
Equation 7.40 is wrong. Again, no bar over Cil, this is not an average of anything. And the equation should be Cil/Cio = (1/D)[(1-F)^(1/D - 1)]. There is an incorrect "1-" term in there.
Equation 7.41, however, is perfect. You will want to point out, since it is not plotted, that accumulated fractional melting is close to batch melting for liquid (but not residue) compositions, for incompatible constant partition coefficients.
Page 299: Need to specify that mf in equation 7.43 is a mass fraction in the mode.
Please do not call P the "eutectic proportion" after 7.44; this appears to limit the non-modal melting equation to eutectic situations, which is too restrictive (e.g., it works just as well for peritectics with a negative term in the sum for P). It would be useful also to point out that in real rocks that do not melt at a univariant reaction, P is not constant either, and a numerical treatment is necessary.
Example 7.3: Missing verb "varies" in second sentence. Missing brackets on Sm concentration in third paragraph.
Page 300: A little caution about the differing definitions of F in batch, fractional, and continuous melting. For batch melting, F is the total amount of liquid produced. For fractional melting, F is both the total amount of liquid produced and the total amount extracted. As defined in the Albarde eqution for continuous melting, F is the amount extracted, which is less (especially at small F) than the amount produced.
End of page 300 is another good place to point out that, although aggregate liquids from different melting models look quite similar, the residues are wildly different.
Section 7.6.6.1: Obviously, I could say a lot on this subject. I will try to limit myself to suggestions that will make the text correct without sacrificing clarity. First, need to explicitly exclude subduction zones from a section that begins "most melting in the mantle appears to result from decompression" (though you do say this later). Second, the Langmuir analysis (also given by Hess) describes a bizarre sort of irreversible decompression path, since it conserves entropy during the metastable solid decompression and enthalpy when it brings the system to equilibrium isobarically. The result depends on the step-size, i.e. the magnitude of departure from equilibrium in the thought experiment. We can do a discussion that is almost as simple and actually describes a well-defined isentropic (i.e. adiabatic and reversible) path just by substituting DSm for DHm and integrating Cp/T instead of Cp. There is a full discussion of my objection to this approach in Asimow et al, 1997, Phil Trans Roy Soc A355: 255-281.
Between 7.53 and 7.54, Clapeyron is misspelled. Furthermore, the Clapeyron equation in its simplest form only applies to univariant reactions. I would simply leave (dT/dP)sol as an experimentally determined parameter. Furthermore, the substitution DSm = TmDHm is not right except for a congruently melting compound (it amounts to saying DGm = 0, which means the bulk system as liquid and as solid are in equilibrium with each other). Furthermore, it is not useful to switch to DHm since this parameter is strongly dependent on pressure and DSm is not. We need not get into just how hard it is to define what you mean by DSm in a multicomponent system.
On pages 301-302 you cavalierly go back and forth between energy and enthalpy several times. Replace them all with entropy. Write equation 7.56 as DS =
Integral(Tact, Tpot, Cp/T dT). Write equation 7.57 as DS = Cp ln(Tpot/Tact), which you then expand as a first-order Taylor series since for small steps Tpot ~ Tact, which yields DS ~ (Cp/Tact)(Tpot-Tact). Write equation 7.58 as DS = F DSm. Now when you equate these two you get instead of 7.61 (DT/P)S ~ (T DSm/Cp)(F/P)S. Sure, this looks a lot like 7.61, but it is valid for multicomponent systems and describes a thermodynamic path that makes sense. Don't use 7.63 at all (see previous paragraph).
The curve in Figure 7.24 is good; much better than any of the treatments that have been used such as Klein and Langmuir or McKenzie and Bickle. However, please do not say melting becomes "eutectic-like"; this is a dangerously ill-defined and connotation-rich phrase that never means quite what one wants it to mean. The general behavior that we see is that isobaric melt productivity is low on the solidus and just after the exhaustion of a phase from the residue and increases to maximum values just before phase exhaustions. Note that in the figure you have a typo: "ol+opx+loq" in place of "liq".
So now you can get an equivalent to 7.65 that I would much prefer, namely: (F/P)S = [TVa/Cp - (T/P)F]/[1/(F/T)P + TDSm/Cp]. By not using the slope of the solidus but rather the slope of a constant F contour, you get something that is not tied to batch melting and can be used for any melting process. It is correct for multicomponent systems and it describes an adiabatic reversible process.
Page 303: The estimate of 1.2%/kbar is worse than you say. Even for anhydrous partial melting it can and does vary from 0.2%/kbar to almost 3%/kbar. You can also be more specific about the effects of volatiles...they result in deep melting but at very small productivity.
Page 304: For gss 2gsm, the dihedral angle is exactly, mot approximately zero.
Page 304: I think it is a mistake to associate low porosity with near-fractional melting. Whether melting approaches batch or fractional has more to do with the rate at which the melt moves relative to diffusive equilibration times. It is perfectly possible for low porosity to mean slow melt migration, which allows equilibrium porous flow, an excellent approximation of batch (not fractional) melting. On the other hand, at high porosity the melt moves quickly and does not maintain equilibrium with the residue...now you're looking at something more like continuous melting. So I'm not comfortable with this rather conventional equality of distantly related concepts.
Section 7.6.6.3 is good; it deals with some of the issues I raised above. Note that the date on the Langmuir et al. reference should be 1992.
Page 305: I prefer "depression" of the solidus to "suppression" of the solidus.
Caption to figure 7.27: The cartoon is not so readily adapted to plume volcanism because you don't have passive spreading out in all directions radial from a point!
Equation 7.68: You use Cil in the equation and C' in the text for the same concept.
Page 307, end of first paragraph: It should be D=0, not D=O. Again, since "acid" melt is an historical term, I would simply avoid using it.
Page 308: Worth pointing out the similarity between in situ crystallization and continuous melting? Worth pointing out that equilibrium crystallization is the reverse of equilibrium melting, but not so for fractional processes?
End of page 310: "Fewer" rather than "few." Ref to figure 7.33 should be to 7.32.
Page 311 top: "Functions" plural.
Page 311, first sentence of 7.8: "Element" or "elements'", but not "elements".
Page 311: "No good constraints on the absolute value of F"...we do know the thickness of the oceanic crust, which is FB*(Pf-Po). There is more to life than trace elements...
Page 311 short paragraph beginning "This all works out nicely": "compatible elements", not "element".
Page 312, sentence beginning "Partial melting produces a much steeper slope...": there is a gratuitous 'of' in here.
Page 313, references: Two errors in the reference between Hauri and Irving.
Problem 5: Tetrahedral misspelled.
Problem 6b refers to problem one; I assume it should refer to 6a. In 6a, it is seriously confusing to use DO for octahedral CFSE and D0 (zero rather than letter O) for the spectroscopic number, since the crystal field theory fractional value goes between these two concepts.
For problem 7 I would have the student plot the solid residue concentration also, so that they can learn the lesson that you need to look at residues not liquids to tell batch melting from accumulated fractional.
Chapter 8.
Page 318 first paragraph: "...salts in the ocean had built up through geologic time at a rate proportional to their delivery by rivers." (two mistakes) I think you should also mention that Kelvin derived a similarly young age based on the heat flow from the Earth (though this one is wrong both because of radioactivity and because of solid-state convection).
Page 319 first full paragraph: By this time the precedent
for "the second point" has become lost in the depths of time.
Page 319 second full paragraph: "...two isotopes of the same element are chemically identical..." Also, need somewhere to explain nuclear notation (i.e. left superscript for A, left subscript for Z).
Page 320: That the strong force becomes weaker than the electromagnetic force at 10-14 m misses the point. At this distance the strong interaction drops to exactly zero; to exchange virtual pions over longer distance would violate the uncertainty principle because they have a rest mass of 0.15 times the proton mass. The EM force is long-range because photons have no rest mass.
Figure 8.1: The point labeled 1H obviously should be 2H...a free proton has no nuclear binding energy relative to free nucleons! Hydrogen should be at (1,0) rather than (0,1).
Page 322: Should point out that the stable configuration of two protons and two neutrons is the alpha particle or 4He, and point back to the big anomalous binding energy in Figure 8.1.
Page 323 first paragraph: Slightly confusing. It mixes the idea of even-even (no net-spin, hence integer angular momentum) with closed shells (zero angular momentum). Probably want to explain that nuclear angular momentum is significant because of nuclear magnetic resonance.
Figure 8.4 Arrow for 6.090 MeV alpha should go all the
way to the ground state line.
Page 325: Better retract or qualify your statement that the neutrino is massless...the evidence for oscillation between neutrino flavors is becoming pretty strong.
Page 325: Near end of neutrino paragraph, "statistical" not "statistically".
Page 326 very top: Go the extra mile and point out that the masses of the pion and W are the reasons why the strong and weak forces are short range.
Page 329: "...can be calculated by the statistical technique of linear regression..."
Example 8.2 third paragraph: "...the names are shown to the left of the cell."
Page 331 end of second paragraph: Too many "is"'s in the parenthetical sentence.
Figure 8.11: Label 143Nd/144Nd ratios along right-hand axis of diagram?
Example 8.4 middle paragraph: gratuitous 'a' after '2.22'. If you take my suggestion for Figure 8.11 then at the end of this example you can refer the reader back to the figure to see where the calculated numbers would plot.
Page 338 first paragraph: "...not until the development of a new analytical technique..." and might be worth adding "...which employed a conventional thermal ionization mass spectrometer but with the unusual twist of accelerating negatively charged compound oxyanions of Re and Os."
Figure 8.14a: In legend, misspelled "Pyrenees". Slightly confusing to use different scale in part (c).
Page 340 last paragraph: Delete 'in' from sentence: "However, it appears that even the thin, basaltic oceanic crust..."
Page 341 first full paragraph: Need to delete one of the two "seawater is about"'s. Then, you need to give the 187Os/188Os ratio of seawater, not the 187Os/186Os ratio, to be consistent with other numbers.
End of page 341: "for the price of one".
Page 342 top: The U in 238U got accidentally superscripted, and of course the 232Th/238U ratio is k, not m.
Equations 8.33 and 8.34: Traditional to label radiogenic 206 and 207 as (206Pb/204Pb)* rather than D206Pb/204Pb, isn't it? Between these two equations the reference to 8.38 should be to 8.33. A little after eqn. 8.34 there is a 204 that is not superscripted.
Page 342 paragraph beginning "Because the half-life": Need a verb in "All systems that begin with a common initial isotopic composition at time t0 plot along a straight line..."
Page 343 second paragraph: "Since the parent-daughter ratio..." (singular).