マグマの熱力学的性質：レビューと今後の課題

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(4) . Thermodynamic Properties of Magmatic Liquid: Review and Future Directions Toru SUGAWARA῍ Advances in calorimetric measurements for magmatic liquids in the recent two decades are reviewed. This paper summarized previously reported values of heat capacities of silicate glasses and liquids and heats of fusion of minerals. Some of the values for heats of fusion are recalculated using the recently reported heats of vitrification and more reliable heat capacities of solids compared with those previously used. Heats of mixing of silicate liquids are also re-examined using excess enthalpies of glasses, heat capacities of end-members, excess heat capacities of liquids and recalculated values of heats of fusion. Excess enthalpies of pseudobinary silicate liquids are generally within -* kJ/mol and mostly /+* kJ/mol. Although the excess enthalpies reach only -῍ +*ῌ of enthalpies of fusion, those cannot be ignored, because liquidus temperatures and compositions of minerals are greatly a#ected by small excess enthalpies. Based on the compilation of the excess enthalpies by direct and indirect measurements, we found that interactions among network-forming oxides (SiO,, NaAlO,, KAlO,), network-modifying oxides (CaO, MgO) and intermediate oxide (CaAl, O.) control the excess enthalpy of silicate liquid. As a preliminary test for generalized prediction of enthalpy of magmatic liquids, regular solution parameters for K, O-Na, O-CaO-MgO-Al, O--SiO, liquids are determined using compiled calorimetric enthalpies using a least square method. Finally, Adam-Gibbs theory for viscosity and configurational entropy of silicate liquid are reviewed. In order to express Gibbs free energy of magmatic liquids, the following studies will be required in future : (+) measurements of excess heat capacity by drop calorimetry for liquids including interactions between NaAlO,, KAlO, and CaO, MgO, (,) measurements of excess enthalpy by solution calorimetry and relative enthalpy by drop calorimetry for Fe-bearing multicomponent glasses and liquids, and (-) determinations of entropy of mixing and configurational entropy by systematic viscosity measurements for multicomponent silicate liquids. Key words : magma, calorimetry, thermodynamics, silicate melt, enthalpy, entropy. +ῌ ῐ ῎ ῑ ῏. Ekl/mn;)/oB pqrsgtug^_. !"#$%&'. 4vDwExT dcefghijyzD{|#E. ()*+,,-./012 3.45167/89. }~K) (,) tug4à9?9{D. :;)<=>&?@21)A BCBDEF GH. \ PD3{E}~K) 0 (-). 3.E'IJK)L,,-.MNB2 G. &^()pqrsgtug4 /@2. HOHCFD)3.P>Q/RST*+,. ?/ 2 &K)\/. U4 VWXYZK)4[1E\1A ]V4. .P>QL#EK) 1 - . (+) D^_&()àbc4dcefghij. /U()A. 02,῍*+3- ®¯°±²³´µ¶+· 2,1 ¸+¹. Gº»f¼j Institute for Study of the Earth’s Interior, Okayama University at Misasa, 2,1 Yamada, Misasa, Tottori 02,῍*+3-, Japan. e-mail : [email protected]. 3. pqrsgtug3.P>Q&3{/R S12FC/B()4 +32* / P /"B\? ?D0vDwExT¡¢V2 09 3.4£/¤@21D1A ¥¦ P4 §¨ ,* ©/FC/¢V2;\pqrsgt ug3.P>Q&ªB «!]

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(85) H S ! L i, T. H "H L i, T. . . S L # Cp i dT#DHi,Tmi# Cp i dT. S i, ,32. (,a) S i,LT"S Si, ,32# . . . Tf+9i UV3q: eF W:UV3. _`W Tf,9i Z. L i, T. Cp Si Cp iL dT#DSi,Tmi# dT T T. (,b). $% &&' Cp ji j ()*+,' i -'.(ῌ/(012345167 (8Gi, Tmi"8Hi, Tmi9Tmi8Si, Tmi"*) ':; <. 8Hi, Tm (Enthalpy of fusion) < 8Si, Tmi (Entropy of fusion) 0 DS i,Tmi"DH i,Tm/Tmi. (-). SLi,T CpLi,T , ? ]. @+, vibrational entropy and heat caL L pacity, SVib, i, T, CpVib, i, T^ xy'pq ]. @+, configurational entropy and L L heat capacity, SConf, i, T, CpComf, i, T^ JC$Z&['. \ : L L S i,LT"S Vib, i, T#S Conf, i, T. (/a). L L Cp i,LT"Cp Vib, i, T#Cp Conf, i, T. (/b). L L L L &\ SVib, i, T CpVib, i, T ?@ SConf, i, T CpComf, i, T . => : L Cp Vib, i, T dT L S Vib, i, T"

(86) T. => ,32 K .( HSi, ,32 SSi, ,32 ?@+, CpSi ABC DE FGHI =JCKLMN,OPQJCR. . L L S Conf, i, T"S Conf, i, Tf+9i# . (0a) L Cp Conf, i, T dT T. (0b). S3T% CB (Berman, +322 ; Holland and Powell,. UV3eFtu%. +33* ; Berman and Aranovich, +330 ; Gottschalk, +331). s UV3+,+, )JB_v'. CB:;+, . -ῌ, H

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(88) ?bs+,. L i, T. ?Y $Z&['\ :. ¤¥nv¦W§Z ]/ῌ+ῌ+. . S Tf +9i H i,LT"H Si, ,32# Cp i dT#DHVit, i, Ti# . . # . . . . . +,W¨©^ ªdC (0a) (0b) UV3+,W Cp Gi dT. Cp iL dT. (.a). Tf +9i DHi, Tmi"DHVit, i, Ti# . . . HIm

(89) UV3. BC ! X?Y $Z&['\ : . L S Vib, i, T"

(90). G. Cp i, Tf+9i Cp Gi,T dT# dT (1a) T T. ]Cp Gi9Cp Si^dT. . L S # ]Cp i 9Cp i ^dT. &&' Tf+9i i

(91) UV3_` (Fictive. (.b). L L S Conf, i, T"S Conf, i, Tf+9i# . . ]Cp i,LT9Cp Gi,Tf+9i ^. . T. dT. (1b) tem-. Tf +9i perature) ' DHVit, i, Ti .(ab Tf+9i _`. L G &&' S Conf, ! i, Tf+9i Cp i, Tf+9i . WZUV3cUV3TW$Z U. UV3+,' SLConf, i, Tf+9i. Tf+9i . V3, ?dCeFfghi('j . Tf+9i 'tu%. ,OkQl * m

(92) ?dCnok. UV3T'. pqbB _` UV3eFrs. \¤®%B (Richet and Bottinga, +32/) :; SLConf, i, Tf+9i. hi&aeFWtuJCB. Tf+9i _`W¯AUV3 * K . BY_v[ wv% : UV3xyWzvZ. ]° Residual entropy^ )JB :. :;E'j abUV3W {N

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(94) ¦§¦KxmW¨© : ª«¬/®¯°. 107 . :. L HLEx, a, T HLEx, a, Tf+ a

(95) CpEx, a dT. + i . SGTf i, * . . . L Cp Si Cp i dT DSi,Tmi dT T T . . @7 +,0./g%# bA$pRà8 23$[\+,0./7. G. Cp i T dT. (+-). (3). z{'K]# bAc a

(96) .

(97) Tf, i . +,0./+,0./%S!!#. !"# $%&'(

(98). L L S Vib, a, T XiS Vib, i, T . DhiTf + i Tf, i . . Ds iTf + i Tf, i . . . . Cp iL Cp GidT. (+*a). Cp GEx, a, Tf+ a. .

(99). Cp Cp dT T L i. . G i. (+*b). Cp GEx, a dT T. dT. T. (+.a). L S Conf, a, T. ῌL . Xi῍S Conf, i, Tf+ i . $)*+,- ./+,0./123. ῎. . + i Tf, i DHTf+ i DHTf, i , Fig. +7 !% 456 DhTf i Vit, i, T Vit, i, T. 89:;$<= H(Enthalpy of annealing). . S >?@7 +,- ./+,0. Cp i,LT Cp Gi,Tf+ i. . T. . Cp LEx, a Cp GEx, a, Tf+ a . . T.

(100). ῏ ῑ. dTῐ. L dT S Mix, a. ./%ABCDEFGHIJKL. (+.b). M$NO# Tf, i P (+*a), (+*b) QR # S!TUVW$XV7 YZ# . L Y7 # SMix, a %c a $ZbA+,0. 'K%$[\>?YR]5T!Z\. ./ (Entropy of mixing)# Cp GEx, a, Tf+ i% Tf+ i $. Tf + i Tf, i i. (Richet and Bottinga, +320)# Dh. Tf + i Tf, i i. Dh. %. Tf, i ^_%$[T3UX@7. Zc a z{'K@7 +,- ./$RP (++) (+-) [\# +,0. -ῌ- ῔ΐ῕ῒ῏ῐ῎ῌ G, H ῑ῍ S. L L ./$RP (+.a) (+.b) Sa,L T SVib, a, T SConf, a, T $. à (i, j, k · · · )

(101) bAc a

(102) . (1b) QRs¡# à i bA¢T. d# bAS!ef$<= H S >?2. Yc a

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(104) H à H ~. L L L H a, T XiH i, T H Ex, a, Tf+ a . ;1$[\XV ! : L L HLEx, a, T Ha, T XiHi, T. . (++). Kxm % i aa # a Kxm %) f$R7 Pa # z{'K CpLEx, a XV ! : . L L L S a, T XiS i, T S Mix, a .

(105). . . .

(106). Cp GEx, a dT T. Cp LEx, a dT T. (+/b). L L L L G a, T XiH i, T TS Mix, a H Ex, a, Tf+ a. (+,). P (++) (+,) %$Rh$XV7 # Tf+ a $Zc a

(107) z{+, - ./ HLEx, a, Tf+ a #. Cp LEx, adT (+/a). # Xi % i a a@7 %# i. CpLEx, a CpaL XiCpiL. .

(108). . . .

(109). ῌ T῍ ῎. Cp LEx, adT.

(110). . Cp GEx, a Cp LEx, a ῏ dT

(111) T dTῐ T ῑ. (+/c).

(112) ]. ^. 108. ῌ(G a,L T῏ m i,LT5῍ ῐ ῎ (ni ῑT. -ῌ.

(113) . a i

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(115) ./. L ῌ(S Mix, a῏ ῍ ῐ 5'RlnXi ῎ (ni ῑT. 0#1* ,-23./ 0#1Mix 4 . RTlng iL5+'Xi,WHkT'Tf+'a. L S Mix, a5klnWMix/W*. (+0) 'TlnT/Tf+'aWCp. 467 k 89: #+ ,;.. (+2). -<=> ?@3A*B. R gi ()};#{| i ~. L C% DE Temkin, +3./ ; 7 SMix, a *467. S# ~+S# :J:<<$ L@. Toop and Samis, +30, ; Weill et al., +32* ; Bhattacharya and Viswanath, +32/ ; Blander and Pelton, +321 ; Hillert,. /23g,-i1f4jB*=>. +331 ; Chartrand and Pelton, +333 FGH 3;+*. +II xLI {| Cp. >@> HLEx, a, Tf +'a,. LA CI . I:J:$ C@A. S. >@>. @?@ ()A%A. HEx => K L !M. L Mix, a. L Ex, a. CBC+ D ()L. LNO"#PQR$"STF$A%. "#abI>E=> FNc . U&*'VW C%%& (X@YZ[\]). 7=> . *R$^+_àb7c,$. L@G*M7 C%I >EH. HEx d-. # A*/0$. C. . % DE Thompson, +301 ; Berman and Brown, +32. ; Fei et al., +320 ; Hel#rich and Wood, +323 ; Jackson, +323 ; Mukhopadhayay et al., +33- ; Cheng and Ganguly, +33.. . . IJ$. K. DEeO1f@ab$ , = /2. (+33,) {|LD (+332) *+N M 2. 3g,-I,-hD (*i1. - 9/ -N >?@¡¢£. f4j (Symmetric simple solution, Thompson, +301) +. `¤O=> J*@7 > PY. L L () BC SMix, a HEx, a, Tf +'a. tuvw\$ x£¥7 C%. L S Mix, a5'RXilnXik+'Xiln+'Xi. L Ex, a, Tf+'a. H. 5Xi+'XiWH. ¤O=> ¦1x& (+1a) (+1b). Ytuvw\Q .7 § .7¨L©ª7. >. (%& Qy! HLT «&%&. *C WH , <"lmS. ¬vw\L|¬ ®. #+ HLEx, a, Tf+'an* I= CpLEx, a5CpGEx, a5* . HGT'HST, HLT'HST 7vw\()7. 564j (Regular solution) oE >. CpGT CpLT * £`,@. pq7=>. . (Cp. L Ex, a. Or (+1b) 8ab$. 5Xi (+'Xi) WCp) s&Ytuvw\=>. .ῌ+ (Drop calorimetry). xH9y@pq7*:z7 >@. R¯O SET}U°$%!. >%& CpGEx, a5* C i

(116). T x%vw\0±VS¯E²!. . a>0 (,12ῒ,32 K) 4R¯³W7c LN ! T ,12ῒ,32 K 0 ® 4X²YZ <#X´µ *¶#[> >·\¸¹ºx%Xº»¼.

(117) · ·^j1~5 : ¸¹º »¼. 109.

(118) . fgh i H eH , . (Southard, +3.+ ; Proks et al., +311a) . #PQF# oK + cmL - cm p =Q. S ,32. L T.

(119) !"# $. Tb, U#VWJ=*X. % & ' ( ) (Ginnings and. Y:/d SCQ Z*U=. Corruccini, +3.1 ; Furukawa et al., +3/0 ; Bacon, +311 ;. :bC":?Q F#[\]. Carmichael et al., +311 ; Richet et al., +32, ; Cordfunke. SJ^'()0/23. and Westrum, +322)

(120)

(121) . (Tamura et al., +31/ ; Gaune-Escard and Bros, +31. ;. '() (Lee and Itagaki, +320 ;. Pool et al., +313 ; Ziegler and Navrotsky, +320), j_`. Blachnik et al., +330) *+, #-./+0. jajQbc= ON/+. *1, 2#*345. Setaram MHTC ON Fig. , , . 67891:;< =>?@AB. KL::Ad d +21* K "/. !C"D#EF#$ 67GHIJ. eb m¡S¢ g *MN &Mf. , F#$#KL*&M +ῌ, cm %. glnN£*eb¤:1 ohR# Ar ip,. NOP/+Q RSTUF#&V +ῌ3 g * + W. 67#jkF#/+ Al, O- Pt ¥¦§\l. 67X',. F# (-*ῌ+** mg) =%0/;,. Y Z'1= ?1. = /#m67/VW¨lF#j. : [[\()+F#*=]**^+. kF#F#A=%78*+J + W. (_/ K/s) /`,4-.abc 0d. +QF#S©*nkbQ o¤:= . Z//# HS,1-eHLT /+Q 4\. :ª*p1«Z*+, 4\. fgh i*I", 05j12R. fgh i e/+0*qZ/. STUF##k&V=]**^+/#lmn. +, ;¬fgh. 'J 0&V#3fgh. i#. +323 ; Tarina et al., +33. ; Kojitani and Akaogi, +33/, +331 ;. +ei p HGoTf eHLT b, 4()*lmn/+Q Tf,ei q ,1-. Sugawara and Akaogi, ,**.) B CaMgSi, O0 (Ziegler and. (Navrotsky et al.,. =/5r678bst9uF#v1. Navrotsky, +320) Ni, SiO. Co, SiO. (Sugawara and. := CQ3fgh i#. Akaogi, ,**-a) Fe, O- NaFeSi, O0 $ (Sugawara. ,ei p ,ei p +ei p HGoTf eHGoTf eHLT wx /+, HS,1-eHLT, HGoTf ,1T ,1-. and Akaogi, ,**.) *= CQ :1. ,ei p ,ei p HGoTf eHGoTf / T '%: & ,1T. ,. /:;0CQ CpLT ?Cx CpGT *I". .ῌ-

(122) (Solution calotimetry). ,. r$ #rsF#r4tr$. 05j1F#2y<z'V== . /+, RSTUF#=r$. 67# +3.* >? +30* >?@:@{ABC|. :# R/ HF HNO- r\rs. }~?1:DE16 CaTiSiO/ (King et al.,. :'1® (Proks et al., +301 ; Robie and Hemingway,. +3/.) Mn, SiO. (Mah, +30*), Fe, SiO. (Orr, +3/-),. +31,) L (31*ῌ32/ K) / ,PbOB, O- rs. FeTiO- (Naylor and Cook, +3.0) Cb F1b. :'1® oKleppa, +31, ; Navrotsky, +311 ; Akaogi,. =]*+/#lmn'b1|$. +33* ; uvw¯ +33.p *+, ]/# x°$. *1G H, & k5|. MNy'()0/. 2lmn*= CQ. r$]fgh i3[/+Q -.. oIc Proks et al., +311b ; Carmichael et. *'1:1, oT'r. al., +311 ; Adamkovicova et al., +32* ; Stebbins et al., +32,,. $ Oxide melt solution calotimetryp /# 1. +32-, +32. ; Richet and Bottinga, +32.a,b ; Richet, +321 ;. =zbC{X , v§*+Q F#. Richet et al., +33+p,. rsx°$ | #rsx°$(MN. .ῌ,. (Transposed-temperaturedrop calorimetry). , JK}±/t²J^³´µJ , v§#¶~*bC:. = /# *JKE. XN S/":?Q F#. LMN:?Q ONPQCQR (,32 K) GS. r$]i oJ^p '()0/. T JKAQ=%:$% &. r$3, + W67/r$%F##rs.

(123) º» ¼. 110. Fig. ,. The transposed-temperature drop calorimeter (a) and its detector (b). Samples are dropped from outside of the calorimeter at room temperature into the sample chamber at high temperature (Y+2** K). In the calorimetric detector, the thermopile consists of ,2 pairs of thermocouples connected in series. Junctions of thermocouples are arranged symmetrically and are placed alternately between the sample chamber and reference. ++ g /ῌ+/ mg

(124) . RS@AB C (Kosa et al., +33, ; Adamkovicova. Setaram !". et al., +330) '+,-. .ῌ. ῎ῌ῏῍ῒῐῑ (Di#erential scanning calorimetry). #$%&'()*+,-. /$01234 56789:;,. ssq2 J , . <,.-=>?89: @AB. 70 0P7;,. C DH. Tf+Di Vit, i, T. GFTf +Di G i, T. EFH DH GDFH DH Sol i, T. S i, T. Sol i, T. G 'H?,. <,j-$'J[ +ῌ+*. IJ KL4MN89:7;,0ONPQ. K ῌmin $s'?$=0. N89:=>? 89:RS@AB. P7 0[7'. GFTf +Di G GFTf +Di G +Di G EFHSol GD῍FHSol G' C HGFTf a, TDH a, T i, TDH i, T Ex, a. ,0= F DSCG 7 . H?,

(125) TU$'8. , B' +,. 9:VW$X (Tf+DiYTf,Di) Z.J[ 89. $0¡) J[s@¢ £=. :\]^_0àb+cJ[ de. >?¤=0& ¥t ,¦§ DSC. f (+./ῌ,./ h) f89:Ogh 'ij kl$. 7¨,-. F©ª#« +320 ; ©¬ª% +33,G. ῌ. ' Tf,Di P mn- H?,o;,. (/*ῌ+/* mg) 7_ (Au, Pt) . Tf,Di GFTf ,Di G 7s <, DHVit, i, T pqr H Ex, a. $ 0;,<,-=0[ +. qtKL4MN>?NuNvw. ? (Al, O-) 0.JTU5®0P. xyz89:RS@AB C (Navrotsky et al.,. 7qt'H?, syz ¯89:8. +32*, +32-, +33* ; Hovis, +32. ; Hervig and Navrotsky,. 9:VW$qt¥ /*ῌ+** K °$ (Y+*** K) I. +32. ; Hervig et al., +32/) ' IJ7

(126) { . ±²s DSC '³´µ. |B0M}4~c7 K. ¶89:VW$Z!

(127) 789: 0. +,-pt 89:. (Proks et al., +311b ; Adamkovicova et al.,+32* ; Weill. ·¸J[*+,-. F"¹¨ Stebbins et al., +32. ;. et al., +32* ; Kosa et al., +32+ ; Zigo et al., +321) pqr

(128). Lange and Navrotsky, +33- ; Toplis et al., ,**+ ; Tangeman.

(129) cdc&DpK : ¸¹º8"»¶&¼d and Lange, +332, ,**+ ; Roskosz et al., ,**..

(130)

(131) . 111. /

(132) /ῌ+

(133) /ῌ+ῌ+

(134) . !"#

(135) DSC ". @ABC,lk& D - #. $ !"#%

(136) +2** K #&'#. !`&F"G" & ^:; %. !&()

(137) *+, - Fe, O- &.. X0]y

(138) Anderson, +3.0 ; Egorov et al., +31, ; Hirao and. . + (Lange and Navrotsky, +33,)

(139) CaMgSi, O0 &/. Soga, +32, :D&)#

(140) +32* ;< P. Richet. (Lange et al., +33+)

(141) 01/ 23*. " J.F. Stebbins W;;=>w. +,&456+789 (Lange et al., +33. ; DeYoreo.

(142) e#?@&A2$2&*+,"lk&. et al., +33/ ; Sugawara and Akaogi, ,**-b) :;. ^ (Stebbins et al., +32,, +32-, +32. ; Stebbins. . and Carmichael, +32. ; Richet et al., +32,, +320 ; Richet. .ῌ/ . and Bottinga, +32*, +32.a, b, +32/). Richet (&. <=>?&#@ABC,*+,&D. ^BC:; Stebbins &~86 Z. E&F"G"

(143) HI8J5J+KL(. D/L"g}w )

(144) Stebbins (. M !;*+,"N2&O. *+,&~86@&EF&h;. PQ

(145) PRST&NUV&/L*+. &!

(146) Richet (qrEFlkG. , -W&2&M XM YE#. HIJ#wx;

(147) Kl. )

(148) Na " K Z[\ , 23 (Fraser and Bottinga, +32/ ;. k&LY

(149) " , G&MN. Fraser et al., +32/) (1W; SiO, ]\ - 2. ()

(150) O#e Richet (v

(151) &. 3 (Rammensee and Fraser, +321 ; Chastel et al., +321). P. ^tu. G & ^ _HI8J5J+KL. Table + ?@$2&lk"*+,&&. #

(152) !`"2&OPQab"#. o-p&V"L lk"*+,&. )

(153) cdc$2&@ABC,*+,&e2f%g. W;;m() ¡:; :. ]"

(154) Na " K Z[\ , 23h:;

(155) &E# i ' j ( & ) #

(156) k l d Xe CaO-MgO-Al, O--SiO, 3 -i'&*+Dm9. CpGi,T¢ai£biT£ciT¤,£diT¤*./. (+3a). Cpi,LT¢ai£biT. (+3b). ,#

(157) i'R@ABC,*+,&NUV&

(158). !!#

(159) 5Q Cv "5Q Cp &T&UV. $2

(160) n%Qo-pqrs

(161) W;tu. . kld.&n9i'2 (FeO, NiO, SiO,) &M m9. Ev/wx; X0]y

(162) Belton. et al., +31- ; Taniguchi et al., +331 ; Matsuzaki et al., +332 ;. Cv¢Cp¤XTVa,/bT. (,*). !!# a 5QRST

(163) bT 5Q¥TU Fig.. Pagador z1

(164) +332 ; Morita et al., ,*** 23E. - V¦§¨ (gram-atom) )&lk"*+,&. cdc$2&@ABC,*+,! 4:;

(165) *. 5Q&9 @ABC,lk#. +, - FeO, Fe, O-, NiO, CoO 5&.+{|. Cv " Cp & © W X +ῌ > # (Richet and. 4 5 6 + 7 8 (RTlngi) & $ 2 o - p g } : ; . Bottinga, +32*) lk& -R u"lk. (Doyle and Naldrett, +320, +321 ; Doyle, +322 ; Holzheid et. Gª {K«*+,")

(166) ¬&5Qb. al., +331 ; O’Neill and Eggins, ,**, ; Gaillard et al., ,**-). # -R u Dulong-Petit YZ[\®}. L _!&E#

(167) 6; gi 7 S Mix, a .~+9. :; (Haggerty et al., +302 ; Richet and Bottinga, +320 ;. &o-

(168) 6;7!`" . Martens et al., +321). 2&.+{|456+78&#&#

(169) . lk&&]#¯°] &. 89&{|456+78 (HLEx) U 7. !

(170) *+,&(±²³v#!". 6;.

(171) ^´§¨&µN_ !"!

(172) ¶´ e§¨&` ·a#s!"( lkG L L G -` (Cp Conf, i, Tf+¤i¢Cp i, Tf+¤i¤Cp i, Tf+¤i) . b, "

(173) v/ &c$2 X0]y Di, An.

(174) Table +. Abbreviations, chemical formulae and heat capacities of glass and liquid.. 112. ῍ῌ ῎.

(175) ¢£¢T¤G~¥¦ : §¨©%&ª«¬

(176) Qz, Ab Cp L (Fig. -) Cp Conf, i, Tf+i. L Conf, i, Tf+i. !"#$%&'()* +#,-./01234 567 /ῌ,ῌ, 89 !"#$%:; !,<$%6=>. S,CDET6uva&B : CpGa, Tw῍Xi aixbiTxciT,xdiT*./ ῌ. (,+). AM Richet et al. (+33-b) * K yzCDE12 !,<$% {| !,<$% 6lV}~B /b. /ῌ+ῌ,

(177) Richet. 113. (+321) ?@ABCDEFGHIBJK. -** K y Jd, En, Gr CDET6. ?@ABU%"& ^_` * K & ,32 K . L@MNOPQRS,CDETU%"6A. !,<$% (SGi,,32 SGi,*) jHk#6JK. &V WXYZ[M\] CDETU%"&. p (,+) mOy ; SGi,,32SGi,* jHk#6 Table. ^_à&B ,1*b+*** K cABdefgh. , . N HiPQRS,CDEjHk#T6lVM j. N HiPQRS,+#,T +31* A. Hk#TmO&nopqr st PQR. B

(178) 3q[M Carmichael et al. (+311), Stebbins et al. (+32,, +32-, +32.) oT *. y ; An-Ab-Di i+#,T6M a@r U%"\] +#,T& ^_` Z_@ N HiPQRS,+#,jHk#T VJKL@M (Stebbins et al., +32.) ? Lange and Navrotsky (+33,) T DSC * Na, O-FeOFe, O--SiO, i CaO-FeO-Fe, O--SiO, iy ;. +#,T6Z JU%"& ^_` +#,jHk#T6M Richet and Bottinga (+32/) oT U%"&. J SiO,-Na, O-Li, O-CaO-MgO-SrO i+ #,T6A&V Al, O- 6Ah+#,*d eBjHk#T6JKM. AM Courtial and. Richet (+33-) MgO-Al, O--SiO, iBoT6. Z aiBdeB Al, O- jHk#T6JK Fig. -. Heat capacity of CaSiO- (Wo), CaMgSi, O0 (Di), CaAl, Si, O2 (An), NaAlSiO. (Ne), NaAlSi, O0 (Jd), NaAlSi- O2 (Ab), KAlSi- O2 (Sa) and SiO, (Qz) glasses and liquids. Data from Richet and Bottinga (+32.a, b) and Richet et al. (+32,, +33*, +33+).. Table ,.. a@r Table , A&VM jHk#T6eN HiPQRS,+#,T ¡p *uvL@ : L L Cpa, Tw῍Xi Cpi. ῌ. Partial molar quantities of S,32-S* of glass and heat capacities of glass and liquid.. (,,).

(179) ¦ §. 114. Fig. . An-Ab An-Di Ab-Di .

(180) 21- K (Richet and Bottinga, +32.a, b ; Stebbins et al., +32-, +32.). (Richet, +321 ; Lange and Navrotsky, +33,) !"#$

(181) %&'() *+,-( ./01 234(5$ 36 ./01. 78349: %&, -'#5;<+="#$ > Table + "#? Richet / Al, O- @ABC%& D E F G # 5 H I J ( 5 K Lange and Navrotsky (+33,) DE,-LM(. =$ NO Lange and Navrotsky (+33,) KIJ( P&QRST U 015V+WXYWZ5[. !. \]^_à]^Kb?[ Lc/d5$ Fig. . eW[?f gV#hij Ab-Di . Kklm"#H WZ5$ H. L L L CpAbqDi rXAb CpAb sXDi CpDi q32..XDi XAb,. s--,.0XAb XDi,. (,-). lm"#tu ( Ht SiO,-K, O Kvlm"#H Kw/d5 (Richet and Bottinga, +32/)$ lm x (+-) (+2) "#? HLEx, a lmyz. {|}~ y (RTlngi) DE,- =5 1WZ5K Hd>W H An-Ab-Di _ BC%&W%&,-Kh/d =$ klmGk HLEx, a KZ U /ῌ-ῌ-. BC%& lm. } #5$ /ῌ, ῎῏ῌῑ῍ῐ. } (HTm) } '015`W= ¡WZ5 ¢£ P& lm} ¤¥#5. n?opWi5 :. Fig. .. Compositional variations of heat capacities of An-Di, An-Ab and Ab-Di liquids at +11- K and glasses at 21- K..

(182) 0¸G¹ : ;<= º»¼. 115. Table -. Enthapy of fusion of diopside (kJ/mol) at melting point, +00/ K.. (Stebbins et al., +32- ; Richet and Bottinga, +32.b ; Lange et al. +33+)' Weill et al. (+32*) 32/ K "-QR /0K! Fig. /. Experimental data of relative enthalpies (HjT HS,32, jhL, S or G) of CaMgSi, O0 liquid, supercooled liquid, glass and diopisde. Enthalpies of glasses were calculated using enthalpy of vitrification reported by Weill et al. (+32*). Solid line represents relative enthalpy of diopside calculated from formulation of heat capacity by Richet and Fiquet (+33+). Dotted lines are enthalpies of liquid and glass calculated from heat capacity by Lange and Navrotsky (+33,) and partial molar heat capacity by Richet (+321), respectively.. >$ Diopside NOP".

(183) '. Tf,Di (DHVit, Di, 32/h2/.0i+.1 kJ/mol)' Kelley (+30*). \ CpGDi CpSDi, Ferrier (+302) Carmichael et al., L (+311) \ CpDi 0 K!\ NOP_. ` (Tf,Dih+*,0, Briggs, +31/)

(184) $ (.b) \d WHDi +00/h+.,.1 kJῌmol j

(185) '. Weill et al. (+32*) f /0K!# U NOPm* . VDhiTf+i Tf ,i . +*aX 1D9%$^

(186)

(187) 9A . 1J

(188) ' Stebbins et al. (+32-) _è f\d ,3232/ K NOP. ". ENOP:$% , lK!4 V+ ler z

(189) . NOP , l 32/ K 4

(190) NOPX . !"#$%% &. Tf +iTf,i h..1i+./ kJ ῌ mol(Tf+Di h+*,0 K, g^8 DhDi. ' () *+,-./012. Tf,Dih32/ K) j

(191) ' ]81

(192) ef0. 3456789%$ Diopside :$%;<=. >. L h-/- kJῌmol

(193) $ \ K!\d

(194) CpDi. $ ? 9(@89%$ A7%,-/. d WHDi +00/h+-2.+i,.+ kJῌmol Z[4

(195) ' E Richet. 0( BCDEFGHIJA ' /ῌ,ῌ+. Diopside ῍῔ΐ῎ῒ῏ῑῐῌ. 9(K!D9%C

(196) Diopside LM NOP QR #U /. and Bottinga (+32.b) _`"_` ¡. ¢$% Tf,Dih32/ K £!4

(197) ' ]8. Fig. / S4 T +00/K VWH X Table - ( Di +00/. L h --. kJ ῌ mol ef0K!\d

(198) CpDi. Tf+Di h+**/ K

(199) $ (.b) (+*a) ^8 WHDi +00/ h +-1.1i,.* kJῌmol 4

(200) ' +32* ¤¥.¦( _èf0K! "-.

(201) ' Diopside WHDi +00/ 2YZ[ Ferrier (+302) \. QR0K!

(202) $ §¨©¥

(203) 4%$

(204)

(205) . ' ] -/- K ^8 +22/ K _àbcdef0. +*** K ª`(vw«89%$

(206) ' 4^4. K!>$ QRLM. \d¬_®K!§¨©1¯°D9 Ziegler. g. WHDi +00/h+,2./i-.- kJῌmol j

(207) VEFe. and Navrotsky (+320) ±² ³mÁ ¬_. \dNOP"A Diopside LM"Dk 1C. _èf0K!Y %>

(208) ' ]8 +/1. K.

(209) + l

(210) dem1n5 0op. ^8 +100 K Û% Diopside µ¶·¶. q D9r LM1s4

(211)

(212) tu9 X' 4^. . 4 Ferrier (+302) vwex-1 Di LMN. Stebbins et al. (+32-) Richet and Bottinga. OP(

(213) Wo yz- d WHDi +00/ {|}~. (+32.b) \ 9(\5z%#d NOP. d4%$

(214) 1 1 D9%$. Tf+i Tf,i ¢$%QR DhDi. g®K!4 WHDi +00/ h+-2./ kJ ῌ mol j

(215) '.

(216) ¼ d. 116.

(217) . 94CDHTm "=7$ Ni, SiO. DHTm @. . TABC

(218) !7$D , E94 . Lange et al. (+33+) Ziegler and Navrotsky (+320)

(219) +.*- K. (Table .) * TAF-@GV{0

(220). !. !7$ 0 H Ni, I"94Crs~0. +10, K " #$%& "' DSC () *. <7 ."')$.J k-. +,- Diopside ./

(221) 0".

(222) .$ (Sugawara and Akaogi, ,**-a) . 1 $2 3 *

(223) -4 Diopside . TAWX/:"94C Ni CH]

(224) Ni-Mg. +0*0 K - .567 +0/* K ". #$. CH];K Z|} Takahashi, +312 ;. ,*ῌ .7 89 2*ῌ +/ K -:". Hart and Davis, +312 ; Beattie et al., +33+\ Ni, SiO. . . *

(225) ;< !" .". 94CDHTm "')$BL"MN-4 (Sugawara and. =7$ >?@

(226) ABC (DHDi +00/ E+-1.1 kJ/. Akaogi, ,**-a). mol) !. Fig. 0 " Table + "! 3 7Rf'z. /ῌ,ῌ,

(227) . Na, Si, O/

(228) K, Si, O/ (Richet and Bottinga, +32/) "1. Diopside '"FGHI DSC CJ. $WX! HO! ZSTU VG. - . K$ L7MNC. L L - Cpconf, TECpTd-R\

(229) DSTm = DSTm. O P

(230) QJRDHTm . "' ST. L CpLT P&"'9P&7 CpConf, T

(231) 27. U V

(232) H "' STU

(233) W. 1 **

(234) .X C .. XY Z[! \ $/. HO¡QRS¢

(235) =T7$ *

(236). "K$ Richet and Bottinga (+32.a, b) ". £ . ]^_àR"#7$ bc Di -()

(237). rsF2 C"1 $ .. $C- DhiTf +didTf,di %

(238) . eK. X! *

(239) - 943I. ()$f9 [ Richet and Bottinga (+320) -!. WXF¤; *

(240) -4 |}¥A2. ghi

(241)

(242) "j&'"[

(243) k$ (l-. DSTm En, Wo, Di "1 $ 0.-῍2.- JῌK-g atom -. +32* )*+mn",o3 Zp"q-. "#7 Jd

(244) Ac DSTm /.- yz /.+. ! STU0\ $rs .. J ῌ K-g atom

(245) :"¦ Jd

(246) Ac PU7 . "1 $etu() Zvw./ A+ "c \ *. < *

(247) ! WXF2 £. !

(248) ",oxk Ryz^_. NaFeSi, O0 WX"f $ Fe- Al-

(249) $". à0BDHTm

(250) DSTm (EDHTm/Tm) Table. . HVk$ *

(251) WX YA2 DSTm. . "[

(252) k. An 0., JῌK-g atom - "#7 Ab, Sa, Ne . {01 Z|} Na, K, Cu, Ag, Mg, Zn\ ~B. DSTm '9¦C ,.3῍-.3 J ῌK-g atom - . D STm 1.+ +*./ J ῌ K-mol -9 (Kubaschewski and. §$RZ- SiO, ¦C DSTm . Alcock, +313) 2"'! R " Pj . (DSCristobalite E+./ J/K-g atom) mb"'9 DSTm W +333. *,3DHTm 45{0I`0"1 $. X¨B SiO,

(253) =7$ *

(254) ©. DSTm

(255) 6 ! k"7}7}. . !$f9 Richards 3

(256) 7$5!$ *. **-[\9 SiO, ªC]tu«7$¬. "#7 ^_àR

(257) 0BDSTm ZJ/K-g atom, 1. '

(258) 1 §$CWX"f $^_7. ]9 .X\ j7" +./. !. `0 (SiO,, TiO,, Al, O-, MgO, CaO, Na, O · · · )

(259) 7$. +0 894 7 {0'9:"94C;

(260). ® `

(261) ¯7ªC]- (model-+) . 0< *k^_àR- Richards 3.

(262) 1 Al Ca,, Na, K "')$a°%±²#$. "' DHTm = >-4C *!DSTm J. . H

(263) C9 CaAl, O., NaAlO,, KAlO, C. 'C3-K[ < .

(264) ¯7ªC]- (model-,) ³ªC]. *[-"5!$ 94CDSTm ^_. ´µyz´µb2{0xL´¶·¸µ. àR Ni, SiO. - (DS +3,- E+0.. J/K-g atom). ^_XWXc M/(MAl)E*./ -9"C9. Ni, SiO. . k" 6 (+3,- K) -?. ;

(265) 0!. = ! (Hirschmann and Ghiorso, +33.) -. MgAl, O. º-¯W0»

(266) 7 Bottinga. 9 94CDSTm FGH -!. and Weill (+31,) ª3">- Fig. 1a . Ni,SiO.. ! KAlO, ¹NaAlO, ¹CaAl, O. ¹.

(267) Table .. Melting temperatures and enthalpies and entropies of fusion of minerals and silicates.. :

(268) 117.

(269) 118. ¨w ©. Fig. 0. Relationships between entropy of fusion of silicate minerals (An, Wo, Di, Py, Co, Qz, Ab, Jd, Ne, Sa, En and Fo) and crystals (Na, Si, O/ and K, Si, O/) and heat capacity or configurational heat capacity of those liquids at fictive temperature. Dotted line represent a + : + corL relation between STm and CpConf, Tf.. SiO, STm SiO,

(270) model-,

(271) model-+ STm SiO, !"#$% & # ' ()* CaAl, O., NaAlO,, KAlO, + ,./ Table . 01 234567 234587). 9 STm model-, SiO,

(272) Fig. 1 b ).0 234567 STm : XSiO, !". " ;9< =>87 STm :? @AB# CDE&F G H 3IJKLM23458 7 STm Cation field strength (Z/(+..Nr),, ZOP Q rO3GRST (U)V 0 WX XSiO, Y0Z[C 3GR \]E ^_)9`. STm "DE;& (Fig. 1c) a b 2345Z. [ STm : ' ( cd (XSiO,) e3GR \] E f , 9 ghiR(Mj E`? ". /E` klmR(Mnj : Z[op"q`' (rs)&tuv wxyz ={|d}0 f ~ #cd"DE; 3 DE& GR<oE`' ( STm "\] ;&? : ` /ῌ-

(273) +32* Sa: d . +*** K V )#' ( mR nj 0? " ¡¢tuub) £)!¤¥ ¦§. Fig. 1. Compositional variations of entropy of fusion of silicate minerals and crystals listed in Table .. (a) Plot of STm for silicate minerals against mole fraction of SiO, by model-+ (An, Jd, Ac, Ne) and model-, (all minerals) ; (b) plot of STm for silicate minerals and Al-free K, Na, Li-silicate crystals against mole fraction of SiO, by model-, ; (c) plot of STm for ortho-, inoand phyllosilicates against cation field strength. The cation field strength is defined as : Z/(+..Nr),, with Z being the nominal cation charge and r the Pauling-Ahrens radius in Angstroms..

(274) ´µ´ῌ6¶ : ·¸¹Q#º=»¼ ῌ H

(275) L Ex. Di-An !"῍#$%& ' ( HLEx )"*+ , SiO,-MO !-./ %&'0121( H 345678 9+ L Ex. :;( <= >? @ABCDEFGD6H HLEx ?I"J$ K, O-Na, O-CaO-MgO-Al, O--SiO,. !-./KLMNO.PQ3"R# ( /ῌ-ῌ+

(276) Di-An !%&'ST"ῌ6 U(#". VW( Fig. . X$ Y !-./ CpLEx, a Z* #[( -./\ F]%^_N. à. (+2) <b. 119. L +0X L S Mix ZcRXAn ln L L . e,cX fe+dX f An An . L , An. L . .e+cX An f L dXDi ln. L , L , e+dX Anf e,cX Anf

(277). (,0). #H( e $B Weill et al., +32* "¡¢f Table . £ Table + -./¤EF Richet and Fiquet (+33+) ( Di # An ¤"+ (,/) 01. ( Di-An !¥¦§¨# Osborn (+3.,) ( %&'i©ª«"¤¬$ (Fig. 2) XAn Z.* wt eDi # An ¥¦§¨®f \}(¥¦§¨¯°". ¤¬U(# WHZ* "[U(# kq. Di # An ¥¦§ïj y<b .2 \. F 21 K ±B Two-lattice q.<b. (S m i,LTZH i,LTcTS i,LTd L de+cXiLf, WH (n i L Mix. +/ \ F 3* K ±B( #i©¥¦§¨. (,.a). 4²U( Y WH "³ (# kq. WHZc,+ kJῌmol,, Two-lattice q. WHZc+/. m ZH cTS dRTlna S i, T. S i, T. S i, T. S i. (,.b). L kJ ῌ mol, 21 op (+1b) XAn Z/*. #H( i Di R An "gU Di-An ! -./#h$+(]%ij k%HB Di l> CaAl, SiO0 EF Mg, Si, O0 m An l> CaMgSi- O2 m"]nU( (Murphy, +311) op ]. %q.mr XSi + st0 u+ $0$ 1]nvwKLMNO.PQ (Sack and Ghiorso, +33.b ; Sugawara, ,**+) "x$ gLi + yst0. z+ { |0}~ aSiZXSigSiZ+ #(#U &']%#%^_Nà. $+ emSi, TcmLi,Tf # L (S Mix *ZeH i,LTcH Si, TfcTeS i,LTcS Si, Tfd L (n i . de+cXiLf, WH H i,LTcH Si, TZDHTmid ῏ ῐ. ῌ. eCp i,LTcCp Si, TfdT. ῌ῎ ῍. S i,LTcS Si, TZDSTmid ῏ ῐ. ῌ. ῌ῎ ῍. eCp i,LTcCp Si, Tf dT T. (,/). "2( L SMix 9+ , 9q." Y #9. -./ CaAl, Si, O2 # CaMgSi, O0 #+Ym 01 (#[U(q. (+1a) ( ekq.f yY#. 9 -./ . (Tetrahedral sublattice) # G (Interstitial sublattice) "9" $ Si # Al = Ca # Mg U(# [ U ( q . ( e, q . Two-lattice L modelf SMix (+0) "+. Fig. 2. Comparisons between observed and calculated liquids temperatures of An-Di system. (a) Simple oxide model ; (b) two-lattice model..

(278) ¼4 N. 120. molῒ

(279) HLEx/.- kJῌmol HLEx-.2 kJῌmol HLEx. Di An

(280) (Table .) . -. Table /. Excess enthalpies at XSiO,*./ and SiO, contents of cristobalite liquidus at +1.-K in the MXOSiO, system and ionic potential (Z/r) of cation M.. ΐ.ῒ !"#$%& ' 3* K ()*+. ,-./ 0123456 % 76 89:;<; = % >)?@ AB A&

(281) 3C"

(282) D3 E (F#G Table / SiO,-MX O H (MFe, Co, Mn, Zn, Mg, Ca, Na, K) 3 =I JK. L $M9:"B A XLi*./

(283) JReyes and Gaskell, +32- Havrotsky, +33. NO@ P$M1Q6R L +1.- K S),ATU@A)*+,V. Gaskell (+32-) NO@ #EV:. W@XYZ>[ J@X\] F. HLEx ". %%( K= SiO,-MX O HB. ++3 pm ^]R@X_ Jà@X. A H J>{ (+1b) # ¡3E#!. _L #b6R L cR SiO,-MX O H =I. L ?@¢Vgx

(284) 3 %L XSiO,. L ef g3 HLEx d# (+) HLEx & SMix. (D{M. L Ex. (,) 9:% %hijklmHTm &d. /ῌ-ῌ,

(285) . #G (-)SiO, n MO V n3. 6 =IAB HLEx . & n oEnp lD". £3E&¤C#G DE (+) B. %% %q - rs!&G 76 "M. A3F¥ (,) ¦U, HGEx B A. H &#t%$u%%& !"vwj. G/E f

(286) 1§¨¥#D. x#y& 3z#'(%%(D{M. E (-) ¦U, HGEx f

(287) %¨¥#DE. L Ex. SiO,-MX O HB A# @XYZ>[ &|}. 3r. H &|} S),ATU@A)*+ L Ex. ,V~ SiO, )*>A3 HLEx |}. - rDE&G (+) F¥# . ©-G/E. DSC DE&G HVWI#. L gSiO, |}"R S),ATU@A+,-. Vn % HV!ªz-#©-. L ." GK SiO, p $rR XSiO,. G/E «qE~ HLi,THSi, ,32 Ha,L T. L L L gSiO, XSiO, ) E& S),ATU@A -&G (aSiO,. HSa, ,32 &"M EM¬ QE~ HLEx, a,T &. )*+,V l " %. c :. L *./ % EMH HLEx & XSiO,. % (/. L *./ # 6 . #GE XSiO,. L S L S H LEx, a, TJH a, TH a, ,32LῒXiJH i, TH i, ,32L. ῍. (,1).

(288) #~Rl8VM0 1&0 %E 3

(289) `x&C"@X. %r$! (Table .) ®©-G/. `x!V#Ghj2 l3&!. E J1 -z¯ JK +2** KL ~(%. 76 ~l801 Q4&. & ((HV CpSi, CpLi, mHi, Tm &°±#. 56" E&@XYZ>[ H . c6 %M z'²³ ML´ . " %D{M. % 9:3E&#! 3§µ. L Ex. =P SiO,-MX O (MFe, Co, Mn, Zn, Mg, Ca) H% SiO, )V#7, 0. & SiO,-Na, O W K, O H#"% E E SiO,-Na, O W K, O H&~8% HLEx

(290) 3 E9,##G % H( X. L SiO,. *./ # H. L Ex. L S H LEx, a, TJH a, TH a, ,32L. ῌ ῒXi῍ΐ ῔ ῍. ῎. ῌ῎ ῍. ῌ. ῏ῑῐ. ῌ῎ ῍. Cp SidT¶DHi, Tmi¶ ΐ ῔. ῏ ῑ. Cp iLdTῐ (,2). L *./ V: &/#G& 7, XSiO,. EDE ¦U, HGEx ·¸DE J -,L . # HLEx & t ; E < 3 Reyes and. }%¹º»]#F¥# HLEx &"MM!&G.

(291) ±²±#ΐµ8¶ : ·¸¹{Cº»¼

(292) . 5T Cp. HLEx . . ῍!"#ῒ$%&'. (()+/ kJ/mol) *+,-./01 234HLEx 56῔78-95:;<= %ῒ8->?@AB. /C; DE@/ DSC $% FGHI. LM TS= NFGOῑ. 2JK. 2KPLM TL= QR. G EX, a. 121. [* opM . N-; (Tf+Sa STf+Si [Tf,Sa STf,Si) C. %C U (-,) L G2Tf+Sa = ,Sa = H LEx, a, T[HG2Tf = Ex, a, TSC \2H a, TSH a, ,32. S Xi 2H . L i, T. +Si = S HG2Tf =S i, ,32 . . . TSC G#$%5; V. VW ;< L S H LEx, a, TL[2H a, TLSH a, TS =. . . . N'NopMuvwxyz{@TN :. Cp Si dT\DHi, Tmi \ . . . . Cp Li dT (,3). * H LEx, a, TL @TN ]^" . ῍!"#. ῒ$%C_`<&'@a-; (()/ kJ/mol) C; ῎EC TL C TS '@34b-C DSC $% c 2#῏ῒ de cfR#gh. ;<JKLM. HIE= @>? b;01 iFEj0V. k;l7mn@AB/C; DE@/ (,) opM HGEx C῍!"#ῒ$%q. rs ^"C t -+/ opM uvwxyz{tU%| : (-*). . +Sa= +Sa= +Si= SHG2Tf \ XiHG2Tf }U U (++) C *[HG2Tf a, ,32 a, ,32 i, ,32. SXiH . 5~Z H. L Ex, a, T. . ;<GbC. . (-.). L ,Sa = ] . (HG2Tf Ex, a, TSC ) C ῍ ! " # ῒ $ % Ha, T S. +Sa= +Si = HG2Tf C HLi,T SHG2Tf c CpLEX, a 5U (--) a, ,32 i, ,32. ]C HLEx, a, T @TN +Sa= +Si = U (--) Ha,L T SHG2Tf C HLi,T SHG2Tf 5C a, ,32 i, ,32. opM_#5;<C ,Sa = H LEx, a, T[HG2Tf Ex, a, TSC. \ . . . \ . . . Xi2Cp iLSCp Gi=dT. Cp LEx, adTS . . . Cp LEx, adT. (-/). 5T ]@ (-) opM HGEx C_#qrs ]^"U (--) ^"C_`< 2++ C_# @. j<;-N= *a-;mn HLEx, a, T @T. G2Tf+Si = i, ,32. SXi2H SH. . ,Sa = S2H Sol SHG2Tf = a, TSC a, TSC. ^"/. L G2Tf+Sa = ,Sa = H LEx, a, T[HG2Tf = Ex, a, TSC \2H a, TSH a, ,32 L i, T. Sol ,Sa = ,Si = SHG2Tf = HG2Tf Ex, a, TSC [Xi2H i, TSC i, TSC. . G2Tf,Sa = ,Sa = ,Sa = HG2Tf SXiHG2Tf Ex, a, T [H a, T i, T. G2Tf +Si = i, ,32. dT. Ce4 opMCVopM. VW TL C TS X4YZ. . L Ex, a. (--). L S #ῒ H a, TLSH a, TS @TN U (,2) T C ,32 K 5. S Xi. Cp. =. . L L NC; ῎E@/@ CpEx, a, T HEx, a, T. ,Sa = +Sa = SHG2Tf = S2HG2Tf a, TSC a, ,32 ,Si = +Si = \Xi2HG2Tf SHG2Tf = i, TSC i, ,32. (-+). . C- U (-+) , 5_#5;<C. . S . . . . . vwxyz{5), kJῌmol § ¨ ©1]C@. . 401 ++ CpLEX, a[* C%4-N ªK.

(293). «¬@,- HLEx, a, T % ®-¯°. +Si = SXi2H i,LTSHG2Tf =S i, ,32 . \X i . ,Sa = @/ t¤ HG2Tf Ex, a, TSC $%&. 'C Tf+Sa ¥%&'5¦ῐ<+u. L G2Tf+Sa = ,Sa = H LEx, a, T[HG2Tf = Ex, a, TSC \2H a, TSH a, ,32. . @01 C]/j* N<;-; CpLEX, a .@¡¢ £ῌ -C; DE. Cp GEx, a dT. /C¦ZN. 2Cp iLSCp Gi=dT. /ῌ-ῌ-

(294) . ±²±wxyz{5%Ue]C.

(295). 2Cp iLSCp Gi=dT. 5³8CC -é 9 2῔Z CaO-Al,O--SiO, 9= HLEx *+

(296) . . L G \ 2Cp Ex, aSCp Ex, a=dT. (-,). 2῔Z SiO,-CaAl,Si,O2-CaSiO-, CaAl,Si,O2-Ca,AlSi,O1-.

(297) U¼ V. 122. CaSiO- H

(298)

(299) . &:

(300) / HLEx @&"L. (+)

(301) . ;:

(302) /,,M3Ni. L Ex.

(303) !"#$. j012345;A&"W ?-,F. %&'"#()

(304) *'. ]

(305) ij012345

(306)

(307) /"A"'. +, (,)

(308) !

(309) . "/'. -./ 0123456.78. L *./ /B"An/, kJῌmol

(310) An-Di HLEx XAn. '012345 9: ;<=>. (Fig. 3a) ,=0B:CW+3+,-. ?@AB+C D"E

(311) /@A>

(312)

(313) F. 9$àb3

(314) HLEx n/.- kJ ῌ mol, Two-lattice a. GHI'" (-) F' HLEx (Table /). b3

(315) HLExn-.2 kJῌmol DE

(316) . /JKLM3N&"OPQ& HLEx /. Ab-Di $%M3Nij012345"C. R'S!"!TLUV+, &W. ,@PL (Fig. 3c) HGEx ' b52/. &XIYZ##'+[ HLEx . :) 9_ -/ /B"A CpLEx, a*

(317) L XAb /B. \])' H ^ S. "A HLEx 0.- kJ ῌ mol 6? &W&_ (,-) /. L Ex. L Mix.

(318) _/B"A. $`'ab3

(319) cdUV+,W+

(320) %e

(321) ,?

(322) /

(323) /7f"A H ?- L Ex. CpLEx, a U>L +-1- K+31- K /&A HLEx+/-- kJῌmol 3+, ,+ (k). HaL &g],A"?./ h&$. "-:

(324) By(k)/;:

(325) . %ij012345' ?-(k)

(326). ;F&A" @A Ab-Di @F'. b52"A_ (-/) * (--) / HLEx l-/>. HLEx @ij' !T/JK&A".

(327) &- 9_ -/ /Bm Tf+na o

(328) )/p"A+,. W GH/UV SiO,-K, O HLEx F'. A, /q&- 'B H 6./r&A. I (Table /)

(329) M3NI. -sb52.*'t/ LuA/v w. ij' JL (Richet and Bottinga, +32/) /. b52/x&A Table + ' Table . : B. &A"UV+,. L Ex. yzl{0' b52 91V[ Courtial et al., ,*** ;. M3N$%'&Aij012345@. Bouhifd et al., ,**, "A012345. K/N&A" (Fig. 3a, b, c, d, f, g, i, j) ,. |>

(330) & ,78/&A HLEx |}~@-. HLEx HGEx x _ 9_ -/ /B"A CpLinCpGi ¡/@. 2

(331) M3N HaL By HLEx 3+,A" w.

(332) (Fig. -) ?-$%L. Table 0 /?.- ,+b52/7f) , . (Tf+na, Tf+ni ¢Tf+na ¢Tf+nj) LB£. HLEx Fig. 3 /PL 'B Fig. 3. (XiTf+ni ¤XjTf+nj) M/N"¥/. HLEx 94 DSC

(333) /"A "C,. JK&A" 9+, A, ¦§. +11- K

(334) & CpLEX, a*

(335)

(336) F'+. , M3N HLEx F]'L

(337) . [ _ (+-) / H /S!&'" 5

(338) . ¨©NM3Nij012345F]>

(339) L. 6 HLEx

(340) /&A_ (+1b) 7&A3+. K/p"AUªL

(341) F«¬ Table 1. L Ex. /,,0® WH Xi*./ /Bm. ,ij0123458L An-Di An-Ab Ab-Di (Fig. 3a, b, c)

(342) $. ij012345?.- -«& HLEx $`. %9:

(343) / HGEx, HGEx (k)

(344) b5. /'L¯C °¬'|}~O

(345) . G Ex. 2"A_ (--) }~],- H. ?C /@A± ²'-. 91. ' b52"A"A_ (-/) / }~],. V[ SiO, Si.O2, CaSiO- Ca,Si,O0 HLEx gram for-. L Ex. 9:

(346) H. - HLEx 9:

(347) y(k)/ HLEx 9;:. mula weight 78/³~&- °/ /@A´³Pµ.

(348) . <b52@AB ,+'. /xQ&A"a3²'

(349) ,R@. L

(350) F ,+/Bm:

(351) ;:. L M3NOL =¶ 9/῎,῎, ·¸.

(352) HLEx 'L = b52I. :012345y01N¹45

(353) ºSGH/. YZ/ 6.-

(354) /xY+C ,+. SiO,, NaAlO,, KAlO, AIYZ&. U>&A;:

(355) '" (, kJ/. AUV F Xi*./ /B"A 1V[ Ab-Di . mol) (k)/;:

(356) An-Ab-Di . ῍ *.,/CaO¤*.,/MgO ´

(357) *.,/SiO, ¤*.,/NaAlO,ῌ. ? An-Fo (Fig. 3d) By An-Wo (Fig. 3m) /B. ³PµT»A"UV

(358) F

(359) Pµ. "AI+,AB "C, HLEx /+/ kJῌmol. /xQ&A" *./ a3

(360) Ab-Sa .

(361) :

(362) Table 0.. Data list of excess enthalpy of silicate liquids.. 123.

(363) 124. ῍ῌ ῎. Fig. 3. Excess enthalpies of pseudobinary silicate liquids and glasses. (a) An-Di ; (b) An-Ab ; (c) Ab-Di ; (d) An-Fo ; (e) An-.Qz ; (f) Ab-.Qz ; (g) Sa-.Qz ; (h) Di-Qz ; (i) Ab-Sa ; (j) En-Wo ; (k) Wo-Ak ; (l) Wo-Ge ; (m) An-Wo ; (n) An-Ak ; (o) Di-Ak ; (p) An-Ge. Dotted lines in each figure represent variations of HLEx approximated with a symmetric simple solution..

(364) :

(365) . Fig. 3.. Continued. 125.

(366) »¼ >. 126. < NF-NM )239 HLEx f g/ . Table 1. Regular solution parameters (Wij) and excess enthalpies at Xi¹*./ of pseudobinary silicate liquids.. L h* ij HLEx 9f

(367) SiO,-Mx O 6 XSiO,. //Y T/ kDI lm*/9 *noX pq@rs . tui=>. (+)NF / NM "DEv^ NF 9w!

(368) Yx nAy^?z

(369) {" #d01n9Tv ^$|9}~ tu

(370) (,) tu*) LM 1 R IM 9l

(371) $( D nxnAy^9? , 6s i=>T% 9 ipq>=>$%&'( Y

(372) NM q%-uL/ D In NF-NM-IM !)23&u D Y/GHT /ῌ-ῌ.. K, O-Na, O-CaO-MgOAl, O--SiO,

(373) . ῍ *.,/KAlO, . *.,/NaAlO,ῌ.

(374) *.,/ . ))A '(n)*. gram formula weight HLEx

(375) . y+ tu . "# Ay. +

(376) . % _ DI. ,. ! "#$%&'( )* + ,-./. , . )*y+/tu,L - !*. . Ay. % .$( M. 01 )23 Table 2 4* 5. + ¡ / )+0 DT. Wo-Ak 6/ An-Ge 6 HLEx 789: ;. $%&'(¢T£ D M+ 5i<. <. ¤/

(377) ¥¦*'(9 Table 0. =>

(378) ?@A (network former,. _/: HLEx £(& K, O-Na, O-CaO-MgO-. NF)

(379) BC@A (network modifier, NM) "DE. Al, O--SiO, 6=> +11- K "#$%&. !@A (Intermediate, IM) F

(380) GHDI. '(f12£ D A*/§d. SiO, NaAlO,, KAlO, NF CaO / MgO . HLEx /* 3¨n©49ª5. NM /

(381) JI Bottinga and Weill (+31,) 9K. 9 6« Ghiorso and Sack (+33/) DY/$.

(382) DI CaAl, O. NF LM NaAlO, N KAlO,. 1 ©4

(383) 7T986)9¬lT®. /O

(384) PQ R CaOSAl, O- / NM /

(385) . ¯

(386) HLEx /)+0 D HLEx O§d. JI/GHT : UV 1. . NF / NM WXT Y/IZ CaAl, O. IM /[* Table 2 . Ghiorso and Sack (+33/) 86pq>=>. "# Si, Al, Mg, Ca, Na "DE K * . , 6 " H\ Ab-Di 6. ° SiO,, Al, O-, Mg, SiO., CaSiO-, Na, SiO- "D. SiO, / NaAlO, 9 MgO ]E CaO /*. E KAlSiO. /

(387) T

(388) ±uf12². , 6 NF / NM )23901 . ¤:³

(389) 6«Dx

(390) 0 ´ Mg,. R An-Fo 6 SiO, / CaAl, O. 9 MgO /. SiO. =>$%&'(µ

(391) 5Table .. *: NF / NM "DE IM / NM )23. ;<¶·< : 7T9¸ /6«. I DI

(392) . +11- K ,/.+ kJ ῌ mol 8 9 . , 6. 0 1 ) 2 3 ^ _ / : /. Ghiorso and Sack (+33/) £ D HLEx kDI. NF-IM, NM-NM, NM-IM )23à , 6b. =f

(393) :. W HLEx 9cQ NF-NM NF-NF )23d à , 6 H 9/9 5Table 2 e L Ex. H LEx5recalculated<¹H LEx5original<º,/.+X LFo kJ/mol (-0).

(394) Table 2. Enthalpy change of exchange reaction in silicate liquids and a classification of interactions.. :

(395) 127.

(396) º» ¼. 128. H (original) Ghiorso and Sack (+33/) L Ex. ῌ

(397) HLEx ῑ

(398) HLEx

(399) . . Berman (+322)

(400) HS,32, Berman and Brown (+32/). Table 3. Regular solution parameters, Wij (kJ/mol,) of silicate liquids determned based on the calorimetric enthalpies and of MELTS (Ghiorso and Sack, +33/).. Richet and Fiquet (+33+) Courtial et al. (,***) Bouhifd et al. (,**,)

(401) CpSi, Table . DHTmi !

(402) " Table +. CpLi ῍#$ % (, a)

(403) +11- K !& An, Ab, Di, Fo, En, Qz, Ak, Ge, Sa '()*+,(-.. /012*+,(-.3 Table 0 45)6780129: HLEx ;!

(404) "% (++)

(405) Ha,L +11- < =3> An-Ab-Di ?'() @ #$ Navrotsky et al., (+323)

(406) ;ABCD> # ῌ EF.,G/H#I J#$ Ha,L +11- G/ Ghiorso and Sack (+33/) 012 *+,(-. =K6 Fo '()F.,LM

(407) I B6NO3 HLEx, a, +11- PQ 6$ Ghiorso and Sack (+33/) C0129:36$῍#$#. R#78012 (An, Ab, Di, En, Ak, Ge, Jd, Ne, Sa, Py, Cd, Mw) *+,(-. S6$T HLEx, a, +11- . UV

(408) </ HLEx, a, +11- ῍#$ H LEx, a, +11-WXiXjWij . (-1). Xῌ (Wij) E6 YZ[>\] ^_`

(409) E K,O-Na,O-CaO-MgO-Al,O--SiO, ?'() Wij 3 Ghiorso and Sack (+33/) Cab6 ; Table 3 3 R! LM WAlcK 3 WNacK defgC Ab-Sa ?F., h/. #$ %