Thermodynamic modeling of geological materials: minerals, fluids and melts. I.S.E. Carmichael and H.P. Eugster, Editors

Page 1 Titles REVIEWS IN MINERALOGY THERMODYNAMIC MODELING MINERALS, FLUIDS AND MELTS EDITORS: I.S.E. Carmichael & H.P. Eugster Page 1 Titles COPYRIGHT 1987 Volume 17: THERMODYNAMIC MODELING OF GEOLOGIC MATERIALS: MINERALS, FLUIDS AND MELTS ~~.i~r~~r~:"!':::J~=r~~Yo"i':~~~~ ;X::d~~e;::: ii ~~~:,.e.~:.: 1~'::1~. ~~':::y:~~~~~a~~:'~~~': J~=~~:'! Page 1 Titles REVIEWS IN MINERALOGY FOREWORD VOLUME 17 PREFACE Page 2 Titles geochemist of the century, we wish to dedicate this volume to the memory of V.M. I.S.E. Carmichael August 1987 H.P. Eugster Page 1 Titles Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts TABLE OF CONTENTS Chapter 1 Robert C. Newto THERMODYNAMIC ANALYSIS OF PHASE EQUILIBRIA IN SIMPLE MINERAL SYSTEMS Chapter 2 Alexandra Navrotsk MODELS OF CRYSTALLINE SOLUTIONS Page 2 Titles Chapter 3 Bernard J. Wood Chapter 4 Page 3 Titles 121 Mixing Parameters 123 Solubilities of solids 123 Complex ion equilibria 123 Vapor-phase equilibria 125 Thermal properties Chapter 5 John H. Wear MODELS OF MINERAL SOLUBILITY IN CONCENTRATED Chapter 6 Dimitri A. Sverjenskj CALCULATION OF THE THERMODYNAMIC PROPERTIES OF AQUEOUS SPECIES AND THE SOLUBILITIES OF 181 Standard molal Gibbs free energies of minerals 182 Standard molal Gibbs free energies of gases 182 Standard molal Gibbs free energies of aqueous species 188 Standard molal Gibbs free energies of aqueous complexes 188 Standard molal entropies, heat capacities and volumes of complexes at 25 DC and 1 bar 191 Equation of state coefficients for aqueous complexes 195 Solute species 195 Charged species vii Page 4 Titles Chapter 7 John R. Holloway Page 5 Titles Chapter 8 Page 6 Page 7 Titles Chapter 9 John M. Ferry and Lukas Baumgartn Page 8 Titles Chapter 10 Hans P. Eugster and Lukas Baumgartner MINERAL SOLUBILITIES AND SPECIATION IN SUPER CRITICAL METAMORPHIC FLUIDS Chapter 11 R. G. Berman and T. H. Brown DEVELOPMENT OF MODELS FOR MULTICOMPONENT MELTS: ANALYSIS OF SYNTHETIC SYSTEMS Page 9 Titles Chapter 12 Mark S. Ghiorso Chapter 13 Mark S. Ghiorso and Ian S.E. Carmichael Page 10 Page 1 Titles Chapter 1 Robert C. Newton Page 2 Page 3 Page 4 Page 5 Page 6 Tables Table 1 Page 7 Tables Table 1 Page 8 Page 9 Titles 40~--~~--~~--~~~~~ 1600 Temperature Deg C Page 10 Page 11 Page 12 Page 13 Titles KYANITE SILLIMANITE \h ok! , I , I ,~ , 1--1 200 400 600 800 ~~~ Temperature Oeg C 9 A 10 II B 6S~-A J/K Page 14 Titles z=II'IH-6H'1 + II'IS-6s'l (18) IT\ill'f ~ Page 15 Titles 8 10 12 Tables Table 1 Page 16 Page 17 Titles Temperature °c - - I Synthetic grossular I o t:, Natural grossulor ... I I :'~.~ .. A· .. :. t'c?@ ., .~ 350f- .. ff .. 4001- 5001- :r: >-::>_ 4501- I I I I 400 600 800 1000 17 Page 18 Page 19 Titles Anorthite • P(Bar)= 22.47T(oC)-587 / 500 Temperature Temperatu re Oeg C Page 20 Titles .d·O 0 .... '" '" " '" '" ~B ~> « ..., ..., '" ° ..., '" ..,. '" '" i u .... '" "'''' '" '" ° '" ° 20 Page 21 Page 22 Titles I- ............. '" I- >;:_____~ 120 700 t.H;,s,298=231.82 kJ , , 4Z0 +QZ = 5AN+GR+2H20 Temperature (K) 22 Tables Table 1 Page 23 Page 24 Page 25 Titles ~ Page 26 Titles 0.2 0.4 0.6 0.8 1.0 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 1 Titles Chapter 2 Alexandra Navrotsky MODELS OF CRYSTALLINE SOLUTIONS Page 2 Titles 0·-------------- + o B Tables Table 1 Page 3 Titles (2) Page 4 Titles (5) o . (9) (10) Page 5 Titles dSmix = -R[x In x + (I-x) In (I-x)] dS(A} = -R In x , dS(B} = -R In (I-x) . RT[x In x + (I-x) In (I-x)] dpO(A} = RT In x. dp'(B} = RT In (I-x) a(A) = x, a(B) = I-x (14) Page 6 Page 7 Titles (25) Page 8 Page 9 Page 10 Titles (41) (42) Tables Table 1 Page 11 Page 12 Page 13 Titles 0.5 0.4 0.3 6V 0.2 coo.s,o.' ,{ · 0.1 0.5 6v 47 Tables Table 1 Table 2 Page 14 Titles 70r--------.---------.--------.--------,--------, 60 48 Tables Table 1 Page 15 Page 16 Titles 50 Tables Table 1 Table 2 Page 17 Page 18 Page 19 Titles (A) + [B] = (B) + [A] . (58) Page 20 Titles ex + 2fJx • Tables Table 1 Page 21 Page 22 Tables Table 1 Page 23 Titles x 630 °C N 0.4 0.6 1.0 r-----..--...,---,....-----r--___, 0.5 X= Fe3+ 3+ X = FeT 1.0 0.5 0.2 0.4 0.6 57 Tables Table 1 Page 24 Page 25 Titles 59 Tables Table 1 Table 2 Table 3 Page 26 Page 27 Titles ~[ " \ iL ' , , 1 ~ , ' Tables Table 1 Page 28 Page 29 Page 30 Page 31 Titles a b .t~ c d Page 32 Page 33 Page 34 Page 35 Page 36 Page 1 Titles Chapter 3 Bernard J. Wood THERMODYNAMICS OF MULTICOMPONENT SYSTEMS (1) Page 2 Titles l' (C) (8) /f (0) t . "''- " . GBC = xlc µ(A) + xlc µ(B) , (2) G(a) = XI µO(A,a) + xIf µO(B,a) + RT(XI In XI + XB" In XIf) (3) G((3) = xl µO(A,(3) + xJ µO(B,(3) + RT(Xlln xl + xJ In XJ) , µ(A) = µO(A,a) + RT In XI . (4) ., µ(B) - µ(A) = µO(B,a) - µO(A,a) + RT In XIf - RT In XI . (5) Page 3 Titles (8) B n+1 B n f" (XJ) . xJ xl Page 4 Titles -t.G12 X-J -t.Gl~ (l-X-J) Page 5 Page 6 Titles (25) Page 7 Titles d1JI d1J-J d1JB" d1J-J s Page 8 Titles s Page 9 Titles -S mix R I Xc 3 Page 10 Page 11 Page 12 Titles 82 Tables Table 1 Table 2 Table 3 Page 13 Page 14 Page 15 Page 16 Titles 15 kbar (A) En (B) Fs Tables Table 1 Page 17 Titles XM2·XM1 T Page 18 Page 19 Titles Table 6. Tests of Equilibrium at 11.5 kbar / 800' C 89 Tables Table 1 Table 2 Page 20 Page 21 Titles AS-1 W-2 91 Page 22 Page 23 Titles ACKNOWLEDGEMENTS REFERENCES Page 24 Page 25 Page 26 Page 1 Titles Chapter 4 Kenneth S. Pitzer A THERMODYNAMIC MODEL FOR AQUEOUS Page 2 Page 3 Page 4 Page 5 Page 6 Titles q,-1 Page 7 Titles , , , Page 8 Titles , Page 9 Titles " , Page 10 Titles + I I " , z Page 11 Page 12 Tables Table 1 Page 13 Page 14 Page 15 Titles (44) Page 16 Page 17 Titles '" "' '" . , ..... , , '" '" '" '" '" '" '" '" '" '" ....... -C\J- _Mt- '" '" '" '" .s ~ '" ~ '" e-, "" '" "'''' '" " " '" '" ~ ..... .... '" " "':!:! " + 113 Page 18 Page 19 Titles ~ o , , 00000000.0.000"': , , e-- " , ~~~~~~~~ o "'- '" .~ '" '" o '" c u 9 o Experimental n -3.5 rC02 = 10 otrn includes borates o : Lazar with aragonite t::. : Lazar without aragonite + = Brantley + + DE 167 Tables Table 1 Page 26 Page 27 Titles 169 Tables Table 1 Table 2 Table 3 Page 28 Page 29 Page 30 Titles § .. -e 0 0 ",0 0 '" 0 ",0 '" '" q' s, '0 I .. 9" .. 9" .. 9" 9" II'" J Page 31 Page 32 Page 33 Page 34 Page 1 Titles Chapter 6 Dimitri A. Sverjensky CALCULATION OF THE THERMODYNAMIC PROPERTIES OF AQUEOUS SPECIES AND THE SOLUBILITIES OF Page 2 Tables Table 1 Page 3 Tables Table 1 Page 4 Page 5 Titles ° Page 6 Page 7 Tables Table 1 Table 2 Page 8 Titles ~~~~~'";a:~--:C;C;~ ooooooo~o~o~ ~oooo.:~~..;~,..:~~ C;~~~~";~~~--:~";~ ~~'";"':~ . ... o " "~ !B " " !l" ~ e 0. Z"~ e .. j~ "''' s: ~: -e " ~ ~ ~ .. co .. " . ~ - " sr ~ .. 184 Page 9 Titles + a . In (p + 1)1) 1 (_1_ - 1) Page 10 Titles -------~--.- Page 11 Titles -4 -6 - 8 o o 0.5 KB TEMPERATURE (DEG. C) 5KB 1.5 ALBITE + H+ = 0.5 PARAGONITE + 3.0 QUARTZ + Na+ 500 600 700 TEMPERATURE (DEG. C) 187 Page 12 Page 13 Page 14 Titles CHLORIDE COMPLEXES b3 ~ 1u 0 A. CHLORIDES • •• [c. -I: ~ ~ ~:. ~ -, o '3 s~ABs·(CAL. MOLE-I.DEG-') E. o ZnCI+ ''_'; ~ AgCI2 B • /Z=-I C~(ML'_I)Z+' o 'Z 1 Tables Table 1 Page 16 Titles (67) -----.---- S; - 71.5 I -, I Wn= Tables Table 1 Page 17 Tables Table 1 Page 18 Titles .,;: -'2 A. B c. D. or '" -. cQ '" -. '" , o -I, -'5 194 Page 19 Titles * Page 20 Titles b I * Page 21 Page 22 Titles TEMPERATURE (DEG C) c. ,O~ i '0L:~~ .' ,! . PRESSURE (KB) PRESSURE (KB) Tables Table 1 Page 23 Titles pH ~ TEMPERATURE (DEG. C) D. TEMPERATURE (DEG. C) ~~~_::_ .. - c. Tables Table 1 Table 2 Table 3 Page 24 Page 25 Page 26 Titles B. '" Tables Table 1 Page 27 Titles TEMPERATURE (DEG. C) Tables Table 1 Page 28 Page 29 Page 30 Page 31 Page 32 Titles 208 Page 33 Page 34 Page 1 Titles Chapter 7 John R. Holloway Page 2 Page 3 Titles F = - dl" I dz, where r is the intermolecular separation. Permanent dipole-permanent dipole forces. These are the easiest to visualize. They 213 Tables Table 1 Table 2 Page 4 Titles Tuu= (1) (2) Page 5 Titles (3) Page 6 Titles b ---------~ - o Tables Table 1 Table 2 Page 7 Page 8 Page 9 Page 10 Titles ~~-------------------------, ~ l!! -: o O+-~---.--~-.--~--.- ~ o 220 Page 11 Page 12 Titles 222 Tables Table 1 Table 2 Page 13 Page 14 Titles METHANE FORMATION ENERGY 1400 1200 1000 800 600 -20+-~--'---~-r--~-'--~~--~-4 400 14001600 10001200 800 O+-~-''-~-'--~~~--'-~--~~ 600 10 20 ... 224 Page 15 Page 16 Titles c+m~=m 00 (7) Page 17 Titles (12) Tables Table 1 Page 18 Tables Table 1 Page 19 Page 20 Tables Table 1 Page 21 Tables Table 1 Page 22 Page 23 Page 24 Page 1 Titles Chapter 8 George H. Brimhall and David A. Crerar Page 2 Page 3 Page 4 Titles 10 0.1 Sc \ I, ". "'1'; Zil .... G • ~:IIi' Mo· .. ··· ,_ \ / ''tot r., f . \: y ~Ni .Cr M "" .. !r··iCOMPATtBLE ELEMENTS) IA 3B 58 78 8 18 3A 5A 7A 2A 48 68 28 4A 6A GROUP in the Periodic Table INCREASING INCOMPATtBILITY ~ ~ 8ULK CONTINENTAL CRUST "'\!!.r (tNCOMPATIBLE ELEMENTS) C. Sa ~ U TI Pb ) ,_ La h Ti ..... ~ . - .... .tf ~ W Ag " ... ~ 1'Sb K~' Sr ,,_... \ .., . , \"L .... :.JIi; M!\t,~' Au ~~.cd Go .!J.S.Bi \ Y ..... _ V ." Cu ~ .. :,tt!..t iN CO ....... Ti ~ Mn .... ~, 'J~1n .L'Si Se j::: ~ Z ~ 0.01 U w E~,OOO a: ­ 3111111C 2IIlIIlC 1111111C 25C 12111 3111111 RAMAN SHIFT (CM-I) 271 Tables Table 1 Page 38 Page 39 Page 40 Titles f}j2 n K(Cni Page 41 Page 42 Titles ..... Moles/ Kg H20 Page 43 Page 44 Page 45 Page 46 REV017C008_p281-322.pdf Page 1 Titles yffl I = I + .. _ Page 2 Titles SO~- HS04 E o '" ..9 ~ I ~: . {I . H2S (oq) ~I~ ~ ~I l~t I I p:~ I I I "I~ -50 I I I l~iI 1 I pH Page 3 Page 4 Page 5 Page 6 Page 7 Titles (42) Page 8 Titles fS = py-po pH =50 Temperature 288 Tables Table 1 Table 2 Page 9 Page 10 Page 11 Titles Domains (4) =1,4) I ..... ReacliOfl Progress Variable rjJ cv cc PY PO Tables Table 1 Table 2 Table 3 Page 12 Page 13 Titles ,., , i 1~~~f;E ,., 0.5 -0.5 -1.0 -1.5 -2.0 4 293 Tables Table 1 Table 2 Page 14 Tables Table 1 Page 15 Titles - _5~[ H : PH~' ~ ~ ";2 1.:[ Jo.OI ~ '" 295 Tables Table 1 Page 16 Page 17 Page 18 Titles = ---- = Page 19 Titles RESIDUAL ENRICHMENT Bj,p Pp I Pp Vw r: Ci,w ~ I o o ... ~ Bj,p 3 2 3 4 PpROTORE BULK z z ~ a::: - 7 6 0.5 1.0 DENSITY 2 1.5 3 o a::: ~ ~ !z PWEATHERED PRODUCT 299 Tables Table 1 Page 20 Titles 7 / / ~ / / surface ...,./ t 3,2 ------ (glee) 2.8 2.6 ---------~----- n= 0.6 --- ... ft. ________ O:? 36 .:n .9 _________ n= 0.8 ------------------------- ---------;~-:-.:------------ ---------------- ~ _----- {\ " 0,'2. ----- ;;) ~ ----------- ~~~ POROSITY ~~ ~~ ------ O 4 _-------- ---- " /s _-------------- n= , t7 ~ ,0 "- s; .. ~W ....,~ 3 >-2 IJJ Cl ~ ::::> 300 Tables Table 1 Page 21 Titles '" '" SUPERGENE ENRICHMENT -TFTTIEF~l 301 Tables Table 1 Table 2 Table 3 Page 22 Page 23 Page 24 Titles .3 . . . .. . . . . . ::::::::::: ·2 ::::::::::: .1 ...= Water P""'1 = Saturated ~ Element o ~ o -60 cc HM WI~ t: :z: -70 MT -80 PY PO .~'\ --- .. ----/_ . ......... , -30 -40 -90 - 304 Page 25 Titles -5 -6 cc -7 "\: ...... ••• protor~ '. -8 -9 -10 s: pH 305 Tables Table 1 Page 26 Page 27 Titles 1.5 10 8 6 « ..., ..., '" ° ..., '" ..,. '" '" i u .... '" "'''' '" '" ° '" ° 20 Page 21 Page 22 Titles I- ............. '" I- >;:_____~ 120 700 t.H;,s,298=231.82 kJ , , 4Z0 +QZ = 5AN+GR+2H20 Temperature (K) 22 Tables Table 1 Page 23 Page 24 Page 25 Titles ~ Page 26 Titles 0.2 0.4 0.6 0.8 1.0 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 1 Titles Chapter 2 Alexandra Navrotsky MODELS OF CRYSTALLINE SOLUTIONS Page 2 Titles 0·-------------- + o B Tables Table 1 Page 3 Titles (2) Page 4 Titles (5) o . (9) (10) Page 5 Titles dSmix = -R[x In x + (I-x) In (I-x)] dS(A} = -R In x , dS(B} = -R In (I-x) . RT[x In x + (I-x) In (I-x)] dpO(A} = RT In x. dp'(B} = RT In (I-x) a(A) = x, a(B) = I-x (14) Page 6 Page 7 Titles (25) Page 8 Page 9 Page 10 Titles (41) (42) Tables Table 1 Page 11 Page 12 Page 13 Titles 0.5 0.4 0.3 6V 0.2 coo.s,o.' ,{ · 0.1 0.5 6v 47 Tables Table 1 Table 2 Page 14 Titles 70r--------.---------.--------.--------,--------, 60 48 Tables Table 1 Page 15 Page 16 Titles 50 Tables Table 1 Table 2 Page 17 Page 18 Page 19 Titles (A) + [B] = (B) + [A] . (58) Page 20 Titles ex + 2fJx • Tables Table 1 Page 21 Page 22 Tables Table 1 Page 23 Titles x 630 °C N 0.4 0.6 1.0 r-----..--...,---,....-----r--___, 0.5 X= Fe3+ 3+ X = FeT 1.0 0.5 0.2 0.4 0.6 57 Tables Table 1 Page 24 Page 25 Titles 59 Tables Table 1 Table 2 Table 3 Page 26 Page 27 Titles ~[ " \ iL ' , , 1 ~ , ' Tables Table 1 Page 28 Page 29 Page 30 Page 31 Titles a b .t~ c d Page 32 Page 33 Page 34 Page 35 Page 36 Page 1 Titles Chapter 3 Bernard J. Wood THERMODYNAMICS OF MULTICOMPONENT SYSTEMS (1) Page 2 Titles l' (C) (8) /f (0) t . "''- " . GBC = xlc μ(A) + xlc μ(B) , (2) G(a) = XI μO(A,a) + xIf μO(B,a) + RT(XI In XI + XB" In XIf) (3) G((3) = xl μO(A,(3) + xJ μO(B,(3) + RT(Xlln xl + xJ In XJ) , μ(A) = μO(A,a) + RT In XI . (4) ., μ(B) - μ(A) = μO(B,a) - μO(A,a) + RT In XIf - RT In XI . (5) Page 3 Titles (8) B n+1 B n f" (XJ) . xJ xl Page 4 Titles -t.G12 X-J -t.Gl~ (l-X-J) Page 5 Page 6 Titles (25) Page 7 Titles d1JI d1J-J d1JB" d1J-J s Page 8 Titles s Page 9 Titles -S mix R I Xc 3 Page 10 Page 11 Page 12 Titles 82 Tables Table 1 Table 2 Table 3 Page 13 Page 14 Page 15 Page 16 Titles 15 kbar (A) En (B) Fs Tables Table 1 Page 17 Titles XM2·XM1 T Page 18 Page 19 Titles Table 6. Tests of Equilibrium at 11.5 kbar / 800' C 89 Tables Table 1 Table 2 Page 20 Page 21 Titles AS-1 W-2 91 Page 22 Page 23 Titles ACKNOWLEDGEMENTS REFERENCES Page 24 Page 25 Page 26 Page 1 Titles Chapter 4 Kenneth S. Pitzer A THERMODYNAMIC MODEL FOR AQUEOUS Page 2 Page 3 Page 4 Page 5 Page 6 Titles q,-1 Page 7 Titles , , , Page 8 Titles , Page 9 Titles " , Page 10 Titles + I I " , z Page 11 Page 12 Tables Table 1 Page 13 Page 14 Page 15 Titles (44) Page 16 Page 17 Titles '" "' '" . , ..... , , '" '" '" '" '" '" '" '" '" '" ....... -C\J- _Mt- '" '" '" '" .s ~ '" ~ '" e-, "" '" "'''' '" " " '" '" ~ ..... .... '" " "':!:! " + 113 Page 18 Page 19 Titles ~ o , , 00000000.0.000"': , , e-- " , ~~~~~~~~ o "'- '" .~ '" '" o '" c u 9 o Experimental n -3.5 rC02 = 10 otrn includes borates o : Lazar with aragonite t::. : Lazar without aragonite + = Brantley + + DE 167 Tables Table 1 Page 26 Page 27 Titles 169 Tables Table 1 Table 2 Table 3 Page 28 Page 29 Page 30 Titles § .. -e 0 0 ",0 0 '" 0 ",0 '" '" q' s, '0 I .. 9" .. 9" .. 9" 9" II'" J Page 31 Page 32 Page 33 Page 34 Page 1 Titles Chapter 6 Dimitri A. Sverjensky CALCULATION OF THE THERMODYNAMIC PROPERTIES OF AQUEOUS SPECIES AND THE SOLUBILITIES OF Page 2 Tables Table 1 Page 3 Tables Table 1 Page 4 Page 5 Titles ° Page 6 Page 7 Tables Table 1 Table 2 Page 8 Titles ~~~~~'";a:~--:C;C;~ ooooooo~o~o~ ~oooo.:~~..;~,..:~~ C;~~~~";~~~--:~";~ ~~'";"':~-2 IJJ Cl ~ ::::> 300 Tables Table 1 Page 21 Titles '" '" SUPERGENE ENRICHMENT -TFTTIEF~l 301 Tables Table 1 Table 2 Table 3 Page 22 Page 23 Page 24 Titles .3 . . . .. . . . . . ::::::::::: ·2 ::::::::::: .1 ...= Water P""'1 = Saturated ~ Element o ~ o -60 cc HM WI~ t: :z: -70 MT -80 PY PO .~'\ --- .. ----/_ . ......... , -30 -40 -90 - 304 Page 25 Titles -5 -6 cc -7 "\: ...... ••• protor~ '. -8 -9 -10 s: pH 305 Tables Table 1 Page 26 Page 27 Titles 1.5 10 8 6