Microscopic to Macroscopic

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Page 1 Titles REVIEWS in Volume 14 MICROSCOPIC to Atomic Environments to s. W. KIEFFER & A. NAVROTSKY, Editors The AUTHORS: SERIES EDITOR: Paul H. Ribbe MINERALOGICAL SOCIETY OF AMERICA Page 1 Titles Mineralogical Society of America ii Page 1 Titles FOREWORD Mineralogical Society of America Short Course MICROSCOPIC to MACROSCOPIC iii Tables Table 1 Table 2 Page 1 Titles TABLE OF CONTENTS MICROSCOPIC TO MACROSCOPIC Chapter 1. Susan Werner Kieffer & Alexandra Navrotsky Chapter 2. Paul McMillan VIBRA TIONAL SPECTROSCOPY in the MINERAL SCIENCES Page 2 Titles Chapter 3. Susan Werner Kieffer SYSTEMATIC RELATIONS to LATTICE VIBRATIONS Chapter 4. Sub rata Ghose LATTICE DYNAMICS, PHASE TRANSITIONS and SOFT MODES " Page 3 Titles Chapter 5. J. Desmond C. McConnell SYMMETR Y ASPECTS of ORDER-DISORDER and the APPLICATION of LANDAU THEORY Chapter 6. Michael A. Carpenter ORDER-DISORDER TRANSFORM A TIONS in Page 4 Page 5 Titles COMPARATIVE CRYSTAL CHEMISTRY and Page 6 Titles Chapter 10. Charles W. Burnham MINERAL STRUCTURE ENERGETICS and MODELING USING the IONIC APPROACH 377 ix Page 7 Titles Chapter 11. Raymond Jeanloz THERMODYNAMICS of PHASE TRANSITIONS Page 1 Titles Chapter 1. Susan Werner Kieffer & Alexandra Navrotsky Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 1 Titles Chapter 2. Paul McMillan VIBRA TIONAL SPECTROSCOPY in the MINERAL SCIENCES Page 2 Titles k = µ Page 3 Titles Table 1. Estimating force constants using Badger's rule. v Tables Table 1 Table 2 Table 3 Page 4 Titles - -:::-z 1/2 + V o Page 5 Titles h Page 6 Titles E (kJ/mol) -- experiment - - harmonic fit •••• Morse curve v a b -- molecular - - harmonic fit Page 7 Page 8 Page 9 Titles ---- n n ('VCO* 00** Tables Table 1 Page 10 Titles Q. Page 11 Titles ANTI-STOKES -1000 .... STOKES E+e * : RAMAN SPECTRUM ;>, .s eo .5 E E-e \. / -e o \ virtual state E 1 Rayleigh SCA TTERING PROCESS n I 19 Page 12 Page 13 Titles - * - Page 14 Titles o 0 a o--c--o o~_...-/o o o--c-o o-c-o o-c-o o o-c-o o o-c-o c o o-c--o o 22 Page 15 Titles T = 2" E qi Tables Table 1 Page 16 Titles ... , o ... , Tables Table 1 Page 17 Page 18 Page 19 Titles a I 1 rr: rr 1 A = 00 k o 20 k = :!:. '" longitudinal acaust i c mod" optic mod" -~ 0 J diatomic o monatomic .!. (n 27 Page 20 Page 21 Titles a b :~ l'~ ""- ~ u: u: Tables Table 1 Page 22 Titles 30 Page 23 Page 24 Page 25 Page 26 Titles 34 Tables Table 1 REV014C002_p35-64.pdf Page 1 Titles e w ) Page 2 Titles T = -'..::...~:--=-""':-­ Page 3 Page 4 Titles (a) RAMAN SCATTERING GEOMETRY sample P z hy (b) CONSER V A nON OF WAVE VECTOR Page 5 Titles 11 ~, ='R':-K Page 6 Page 7 Page 8 Page 9 Page 10 Titles 44 Page 11 Titles 4S Page 12 Page 13 Titles a \. c "\ ~. "0. ? b t( \ _ ..... d·-·······g \ .. 1 Page 14 Page 15 Titles 49 Page 16 Titles A' A" so Tables Table 1 Page 17 Titles A' Y Y Tables Table 1 Page 18 Tables Table 1 Page 19 Titles 53 Tables Table 1 Table 2 Page 20 Titles 54 Tables Table 1 Table 2 Page 21 Titles ... '" '" .. , '" '" RAMAN SHIFT (em-I) '" W A VENUMBERS 55 Tables Table 1 Page 22 Titles A' Page 23 Page 24 Page 25 Titles REFERENCES 59 Page 26 Titles 60 Page 27 Titles 61 Page 28 Titles 62 Page 29 Titles 63 Page 30 Page 1 Titles Chapter 3. Susan Werner Kieffer HEAT CAPACITY and ENTROPY: SYSTEMATIC RELATIONS to LATTICE VIBRATIONS (1) Page 2 Titles . T( K) • .~.-- . • • • - . o -. . / ...., 66 Page 3 Titles T( K) T( K) .,...........---/..- . ao / ,/ • roo 5f- /,/1 /-:A- • - /,~ Of""",.:_ 000 ~J • I~ • If /, • zoo !:: ¥ / .... '.'''''''. " ~ -t /./ soo J} E 1/ ~-, '00 t, " , '. roc l 2 i/ __ .~~ f ~;:--I liOOO j~' / ----=-"" - MgO 51- I~l/ - II 200 I" .00 ~i tf 67 Page 4 Titles 68 Tables Table 1 Page 5 Titles ~a:~~ . ~I~ """ ... ]~ . , !!~- """ ... '" - ., ~~ '0- .. - -;; " , ~~ "'. :::1 ~~o:~ °N~ ~ , t .... ~ " c • ~~ . , .~ """ ... .~ " "~ ", ... ~ ,....~ ~~ . , .. - 69 Page 6 Tables Table 1 Page 7 Titles (3) Tables Table 1 Page 8 Titles N( A) ~. Page 9 Titles e -1 h w Tables Table 1 Page 10 Titles 74 Tables Table 1 Page 11 Titles E(x) + [1 - -yz (x)2 + ••• J. C = ~ [ E(~) + E(~)J v 2 T 2T· Page 12 Page 13 Titles g(w) dw 77 Page 14 Page 15 Titles e = nw /k, ( 27) 79 Tables Table 1 Page 16 Titles en en Page 17 Page 18 Titles a) O:Si,AI=2 Temperature (K) Page 19 Page 20 Page 21 Page 22 Titles o • ...,~ - (~ g !p - - m Page 23 Titles 87 Page 24 Titles W-t v •. 0/51 for: Acou.tlc Mode. v (Count 1135), and Lattice DI.tortlon. (Count 100% - all other.) T 2.5 iii O2.75 700 600 500 200 100 o Page 25 Tables Table 1 Page 26 Titles ~ fs;o, ... Page 27 Page 28 Titles r+ I r+2 r r-2 r-I ~2o- Page 29 Titles I 2 o. (37) Page 30 Titles ~.' 310 ---- w 2 Tables Table 1 REV014C003_p95-126.pdf Page 1 Titles .....,£-------8 w 2 95 Page 2 Tables Table 1 Page 3 Tables Table 1 Page 4 Page 5 Titles .. 9 -z Page 6 Page 7 Titles [ooi-J r, r, Tables Table 1 Page 8 Page 9 Titles Ow • w .. '" .. I '" I • ~ .... ~CX) C/) '" C\I~ + + o • .c: II' ... s: e ~ ~ - '" B III ~ hN _ L o. .2 L "0 o o '" '" J_ +- "0 ~ £ s: s ~ 5 ~ f- L '" OJ c: "0 c: "0 0- . U ., I/) W '" 0 O ",~.'r .. ... · '" .. .. o I . ... . co ~()N 0 0 .. ·f + ' .. .. • I .. .. ~ ~+ I e 0., • • (Q'+ I -.to ~ o i o '" o + ! o _tD -~ 103 Page 10 Page 11 Tables Table 1 Page 12 Titles C = _A_(~)3 ), (W ~~~"ROi7r _ + Page 13 Titles 107 Page 14 Titles 3NAk a 3 Xu ---z-- L S(xi) + 3NAk(1 - --3 - q) K( ) n - s Xi (60) 108 Tables Table 1 Page 15 Titles 109 Tables Table 1 Page 16 Titles 110 Tables Table 1 Page 17 Titles (d) o A o o o E , .... ··'A \ (c) \ ...... _ ;.:::":'~',~~~"""'"'' A 100[\ (b) 600 • ....... ____.:--- l " 11001 ALBITE STISHOVITE 400 (a) ,// I~t =>: 100 .,.'/ 3Jt/ )( 600 , '/ MICROCLINE ..'. Page 18 Titles (d) L o (c) o ,or. 4O~1\ J\~ (b) ~r ~F =C-·-"-· (0) Page 19 Titles o o 'l" (c) (b) Page 20 Titles (c) "'~I lOU \f ~.~ . .E ' ...... ,~:: . .::~ .. - .. o~ \ .... ,.._..:-=:.:.:~;---... , 'M, , "I ~ % contribution of branches (0) Figure 20, continued. 114 Tables Table 1 Page 21 Titles (0) (b) (c) (d) 1 o o o o -; . \,-"".:: ..... , .... ; ........ :r\~:,.;~.~.:=,~~'~~·~'~~ Page 22 Titles (0) (b) (c) (d) J ~*F- ----------------- 1101:: 0 I 200 20 \~_,~:.:=.~=.~~.~~~~ ,I ~I ~ • • • ""'~ I ~. ~r ~n ~ ~[~~ ~ '''':;'I'"',,:;·:;'':.::_·~_A . ~ " ~t ., II j ! 200 ~ \>~'''::::::';'~'L '=';r I I L ~ "---;:.. -- - ~ Page 23 Page 24 Tables Table 1 Page 25 Titles e Page 26 Titles 0-- n = Tables Table 1 Page 27 Titles o k o o o ). Page 28 Titles Ie ~ K-- 11~x, Page 29 Titles * Page 30 Titles intramolecular ... °Cl \ .... ,o.:.-s/" ....... ..!~~ ..: . ................ - -- c. • • * Tables Table 1 Page 31 Titles * - Page 32 Titles 126 Page 1 Titles Chapter 4. Subrata Ghose LA TTICE DYNAMICS, PHASE TRANSITIONS and SOFT MODES Page 2 Titles .. Page 3 Titles (1. 6) (1. 7) (1. 8) f [ :2;ir)] (1. 9) Page 4 Page 5 Titles a T, I ••••• .0 S 10 ." L 0, .. , . .. :: t o 0 , • 0,5 I- • I I I I T, 0·." a r x w x 11 f'b 100"K 1 g.o.o,' L branch o o " o , Tables Table 1 Table 2 Page 6 Page 7 Titles (1.13 ) (1.14) (1.15) Q - - - (1.16) (1.17) Tables Table 1 Page 8 Titles \ ~ 134 Tables Table 1 Page 9 Page 10 Titles K Br 90 K -- Simple shell model .L , , , oL .... - " " " oL 7 6 3 136 Tables Table 1 Page 11 Page 12 Titles - ... - - Page 13 Titles a k' ~' q phonon - q phono.n ~ absorption ~ emIssIon 139 Tables Table 1 Page 14 Titles wT -w dw) Page 15 Titles = R (~,k) + u(~,k) Page 16 Titles o (2.4) (2.8) Page 17 Page 18 Titles - -e L -f - - 1iw = LIE 1l 2 2 ~ Page 19 Titles TRIG. f3 05 I I I I I I I I I I I I I 8 145 Page 20 Page 21 Titles , , '~i -~------------------ ---------·-----~~i :. a I t Tables Table 1 Table 2 Page 22 Titles a d.u(-q) 1 0,5 o 200 400 00 148 Page 23 Page 24 Titles \ T qS :u'; I .. , 2,5 a )?--------~ /.,/ I 0 // I c;r - --I----@' I I /1--+-0, : I =q::: __ -:® ,,/ ,/ I ,/ I 0 I ,/ : ~---I---=e; I 'f" _'---- I I ---( I ---I----;@ : /// 0 J /// ~-------®-- b ~ " " d. +. + ) zone boundary t(, 140 )80 _L_j 220 240 150 200 250 300 TEMPERATURE OK TEMPERATURE DEPENDENCE OF r25( ~ H) MODE / o~/ 2,0 0,5 150 Page 25 Titles 151 Page 26 Titles 152 Tables Table 1 Page 27 Page 28 Titles 4.-r---~----r---~--~~--~---,----~---,----~--~ Tables Table 1 Page 29 Page 30 Titles ~~ k - Tables Table 1 Page 31 Page 32 Titles eBa eli Ooxygen o ° o Page 33 Tables Table 1 Page 34 Page 35 Titles Anderson ~cp~;!~ !~~r~~~oaneK~'i;::~~~~I:C BC:r?8:mcRHR OTBOCJrTelU>DO CTnHCTBK. cIIuoBoro 161 Page 36 Titles 162 Page 37 Titles 163 Page 38 Page 1 Titles Chapter 5. J. Desmond C. McConnell SYMMETR Y ASPECTS of ORDER-DISORDER and the APPLICATION of LANDAU THEORY Page 2 Page 3 Titles 2. SHORT RANGE ORDER Page 4 Page 5 Page 6 Tables Table 1 Page 7 Titles kx '" 000 _;,....- R 1-- R4~ , 3 -Y R~\\ -rlRI~§ _.,. - I ~t:::== kx t r 000 Page 8 Page 9 Page 10 Page 11 Titles Fm3m E R1 R:z R:J 175 Page 12 Page 13 Page 14 Page 15 Tables Table 1 Page 16 Titles 0; • Page 17 Page 18 Titles o/\/W\/\ . . ~ TW;""~d even /\;/\//\/\ \/\~/\/ Page 19 Page 20 Titles I '3 C2 x = 2 x = 0 Tables Table 1 Page 21 Titles 1111 c; c2 Tables Table 1 Table 2 Table 3 Page 22 Titles REFERENCES 186 Page 1 Titles Chapter 6. Michael A. Carpenter ORDER-DISORDER TRANSFORM A TIONS in Page 2 Titles T T Tables Table 1 Page 3 Titles -V~ , Page 4 Page 5 Page 6 Titles G H.S I IT ill T 192 Page 7 Page 8 Titles 194 Page 9 Page 10 Titles Table 1. A summary of data for selected cation s«, Si 196 Tables Table 1 Table 2 Page 11 Titles Table I, continued. 197 Tables Table 1 Page 12 Titles H 973K T Page 13 Page 14 Page 15 Page 16 Tables Table 1 Page 17 Page 18 Page 19 Page 20 Titles e TT / -\\ 6'~