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REVIEWS in MINERALOGY Volume 32
EDITORS:
Mineralogical Society of America
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MINERALOGICAL SOCIETY OF AMERICA
REVIEWS IN MINERALOGY
Volume 32
Structure, Dynamics and Properties
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STRUCTURE, DYNAMICS AND PROPERTIES OF SILICATE MELTS
FOREWORD
EDITORS' PREFACE
iii
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iv
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v
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Tables
Table 1
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STRUCTURE, DYNAMICS AND PROPERTIES
vii
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viii
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ix
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x
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xi
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xii
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xiii
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xiv
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xv
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Chapter 1
STRUCTURAL RELAXATION AND THE GLASS TRANSITION
Cornelius T. Moynihan
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time
- - -
o
_____,..
T
Structural Relaxation in Liquids
(2)
_ H - He _ Tf - T2 _ t
Ho - He T, - T2 T
(4)
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,
6TL __
a
b
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a
P
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Table 1
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8
t
(5)
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9
0.5
720
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x6H (1 - x)6H
'I = Toexp[ RT + RTf 1 (8;
B
'I = TO exp[",,.., /", ,l
(9)
¢(t) = 'L:9iexP[-l dt'hl (11)
,
x6H (1 - x)6H
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¢(t) = exp[-([ dt'/T)f3) (14)
¢(t) = p(t) - Pe = Tf(t) - T2 (l5)
Po - Pe Tl - T2
Tf(t) = To + L 6Tj[1 - ¢(t, tj))
¢(t, tj) = exp[-(!ot-tj d(t' - tj)/T),B]
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Tables
Table 1
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14
Tables
Table 1
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15
Tables
Table 1
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TglT
(22)
B7] 1 [B7] 1
'i) = 'i)oexp[TSc(T) = 'i)oexp T!:::.Cpln(TjTK)
Tables
Table 1
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17
60
1; 50
~
"Q. 40
10
20 30
Na201 mol%
40
1~
~
0-;'
Jf
50
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Moynihan: Structural Relaxation and the Glass Transition
REFERENCES
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Moynihan: Structural Relaxation and the Glass Transition
19
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Chapter 2
SOME APPLICATIONS
D. B. Dingwell
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22
P
dP
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23
"\
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24
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T = n/G
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Dingwell: Relaxation in Silicate Melts: Applications
f ~ s-c
~~ IJ ~
g.
o
Tables
Table 1
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27
;;
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M = K + (4/3)0
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o
c
-
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Table 1
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30
o
o
....
•
•
Tables
Table 1
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Dingwell: Relaxation in Silicate Melts: Applications
::: 1 MAl r;6,~~.. __ _
i,
"" -f- - - - - - --- - - - - - - KEO
AGPAITIC INDEX
Tables
Table 1
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Tables
Table 1
Table 2
Table 3
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'.
..
.
"
-:
..... ..... .. ~ )
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(6)
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TEMPERA TURE
Tables
Table 1
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39
H
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40
Dingwell: Relaxation in Silicate Melts: Applications
a
m m ill ~ ill m ~ ~
"
b
c
(\f \
TEMPERATURE
caC)
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41
] 6
15
14
12
-6
,
u
bD
Tables
Table 1
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Dingwell: Relaxation in Silicate Melts: Applications
•
43
-S
o
>
o
::2'
TEMPERATURE (C)
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Table 1
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44
Tables
Table 1
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45
Tables
Table 1
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MOLAR VOLUME OF THE MELTS
Dingwell: Relaxation in Silicate Melts: Applications
mol%
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Table 1
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47
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'"
..
.•.. -. ....
'"
Tables
Table 1
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49
•
•
~
.. ..
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1
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~
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a
Tables
Table 1
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Tables
Table 1
Table 2
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57
o
::z::
,
::z::
__ of
T----~----~----~
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Dingwell: Relaxation in Silicate Melts: Applications
10
Tables
Table 1
Table 2
Table 3
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61
o
calcalkaline
t
10,OOO/T(K)
Tables
Table 1
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Dingwell: Relaxation in Silicate Melts: Applications
63
REFERENCES
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Dingwell: Relaxation in Silicate Melts: Applications
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Dingwell: Relaxation in Silicate Melts: Applications
65
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Dingwell: Relaxation in Silicate Melts: Applications
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Chapter 3
RHEOLOGY AND CONFIGURATIONAL ENTROPY
P. Richet and Y. Bottinga
o
eo
-
~
.....
o
~
....
...
9
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do/dr = G~ ds/dr .
daldt = G~ ds/dr - air, (8)
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71
...
~ ...
~ ..
TJ = G~ 't'.
K = K~ - K; (12)
TJv = Kr't'v
't'p = 1:vK.JK. (14)
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(J' = TJel deelfdt , (15)
(J' = E eel,
TJel = 3 TJ . (19)
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1500
3Rfg atom
1200
900
~~ I' id
y ... IqUI
a
600
'.
...
~~
,
t glass
50~~~~~~~~~~~~~
300
90
60
c.. 70
g-
o 80
~
T (K)
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Tables
Table 1
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75
T (K)
sconr
Tables
Table 1
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76
sconf(T) = sconf(Tg) + J C~Onf I TdT.
weT) = A exp (-BeiTsconf) , (25)
Tables
Table 1
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Temperature dependence of the viscosity
Tables
Table 1
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78
Richet & Bottinga: Rheology and Configurational Entropy
so
~
~ 40
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~
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"
..
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< f:J.S f:J. V > = kB T (aVlaT)p (38)
< ss=« f:J. V > = kB T [(av/aT)p - (av/aT)p] . (39)
Tables
Table 1
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'"
.::
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ACKNOWLEDGMENTS
REFERENCES
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Richet & Bottinga: Rheology and Configurational Entropy
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Richet & Bottinga: Rheology and Configurational Entropy
91
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Richet & Bottinga: Rheology and Configurational Entropy
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Richet & Bottinga: Rheology and Configurational Entropy
9~
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Chapter 4
Sharon L. Webb and Donald B. Dingwell
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96
-
-
~!
~
- r- - - - -
TIME
(2)
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97
>-
:;
log, TIME
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98
Webb & Dingwell: Viscoelasticity
(5)
,
,
>
1+ 'ts 1+ 'ts
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99
K * (00) = K= - Ko + Ko 2 2 + lKo ----:::;- 2
(9)
I . 00 'is
I (oo'tv K= - KO)
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100
~
a
>
,
o
:J
~
,/\
3:
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-
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Table 1
Table 2
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107
-.-
- .. -
loglo 7:1\
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Table 1
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108
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109
M(oo) = p v~ (00).
Tables
Table 1
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110
Webb & Dingwell: Viscoelasticity
2
G'((1)
Tables
Table 1
Table 2
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111
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112
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113
10
>-
:;
o
iovz-c
Tables
Table 1
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114
V = IX v: + I X X v:
K = ~=- v· ap .
1 [ n .... -V· n av 1
(20)
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115
Tables
Table 1
Table 2
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116
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Webb & Dingwell: Viscoelasticity
117
melts is an essential component of progress in understanding viscous deformation in
REFERENCES
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118
Webb & Dingwell: Viscoelasticity
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119
APPENDIX
Mechanical relaxation time
Electrical relaxation time
't =~~------------~~--~~--------------
(AI)
(A2)
Thermal relaxation time
'tt =-=
(A3)
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Chapter 5
ENERGETICS OF SILICATE MELTS
Alexandra Navrotsky
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Navrotsky: Energetics of Silicate Melts
FACTORS AFFECTING MELT ENERGETICS
Major acid-base interactions and polymerization equilibria
(1)
(2)
b
o
a
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Table 2
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[
e
:t
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Navrotsky: Energetics of Silicate Melts
-48b
-og
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Table 2
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Navrotsky: Energetics of Silicate Melts
Temperature (K)
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'"
135
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Table 2
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•
•
•
•
••
11\
Tables
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Navrotsky: Energetics of Silicate Melts
REFERENCES
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Navrotsky: Energetics of Silicate Melts
141
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Navrotsky: Energetics of Silicate Melts
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Navrotsky: Energetics of Silicate Melts
143
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Paul C. Hess
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149
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... ·::::z
..» 0<····· RnO
-175 +--.--.--.--.-.--.--.--.---.--1
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(6)
8:::::::::::::::·.
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ENTHALPY OF SIMPLE "MINERAL" MELTS
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:r:
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Hess: Thermodynamic Mixing Properties and Structure
159
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(21)
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so ,
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169
o
Peraluminous
K (
Peralkaline
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----
Tables
Table 1
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[Z+Z-I]e02
Tables
Table 1
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Hess: Thermodynamic Mixing Properties and Structure
175
5oo,------~r-------~------~r------~
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K
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180
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Tables
Table 1
Table 2
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(A20)
(A21)
(A23)
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184
X s.o,
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Hess: Thermodynamic Mixing Properties and Structure
185
(A30)
Entropy of mixing
(A31)
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186
(0°)(0-2)
K .:.-'--'-___:__
(0-)2
O,----------.----------,-----------r----------~
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Hess: Thermodynamic Mixing Properties and Structure 187
REFERENCES
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188
Hess: Thermodynamic Mixing Properties and Structure
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Hess: Thermodynamic Mixing Properties and Structure
189
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Chapter 7
DYNAMICS AND STRUCTURE OF SILICATE AND OXIDE
Jonathan F. Stebbins
INTRODUCTION
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(2)
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o
A e
-
-~ ,
v - C
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o
-A--
Tables
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on A- __
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Table 1
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201
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Structural effects on chemical shifts
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Stebbins: Dynamics and Structure of Melts: NMR Studies
1 bar
o
o
o
o
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REV032C007_p219-246.pdf
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(j)
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•
2~~~~~~~~~~~~~~~+
..
(14)
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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J /
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•
•
••
• •
•
-
• •
•
•
"
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•
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8
8
o
8
o
o
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o
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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Stebbins: Dynamics and Structure of Melts: NMR Studies
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Chapter 8
VIBRA TIONAL SPECTROSCOPY OF SILICATE LIQUIDS
Paul F. McMillan and George H. Wolf
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'"
=
:e
'"
~
'"
'"
::
'"
- - - - - - - - - - -
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..
s fa
•
.s
'8
.......
E 2
Tables
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aln V v sv
y: = ---' = ---'
a=.!.(av) =(alnV) ,
vs.sr ), st p
YiT=_.!.(alnVi) = __ 1 (aVi) .
, a st p aviaTp
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~= ~;(:~J: .
--' =--=
coc Vi e
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261
_ 1
s
c
'"
~
:c
...
"
~
"
'"
..,
s
'"
...
...
~
b
Tables
Table 1
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McMillan & Wolf: Spectroscopy of Silicate Liquids
263
Vi dq,
Linewidths and Iineshapes
, 3c2 dq,
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c e -1
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no
a
o
b
Tables
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a
'(, ...
. ~ '.. I
.. '. ,I.!+ttl
-.,,~ .. ,-~ I+.~l I~ h
b
.~
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McMillan & Wolf: Spectroscopy of Silicate Liquids
(f) Raman
(e) Neutron spectrum giro)
(a) Raman
(b) Infrared
tc) Dielectric function
(g) Infrared absorption
(d) IR energy loss
wauenumber cm-I
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.~
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280
-=-~.~
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Tables
Table 1
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282
REV032C008_p283-316.pdf
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McMillan & Wolf: Spectroscopy of Silicate Liquids
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Rllc::all tetrasilicate glasses
Cs
Na
li
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McMillan & Wolf: Spectroscopy of Silicate Liquids
K Si 0
Raman shift (cm-1)
•
Tables
Table 1
Table 2
Table 3
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'"
'"
'"
'"
'"
'"
Tables
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Raman shift (cm-1)
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vv
JM
I ~ I~li
/ / ~/ .. '\
r-/".
..
. .:
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McMillan & Wolf: Spectroscopy of Silicate Liquids
/ !.:.\ ->>
,... I" /
,i. ". \/
j' N~\\ __ 1 .. 7.:\v
\ I'!\ /r- '\
~n~zu/ \
-' \
7IO,ftoJ \
_.
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McMillan & Wolf: Spectroscopy of Silicate Liquids
~ ~
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McMillan & Wolf: Spectroscopy of Silicate Liquids
I
a
b
o
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18
28
48
18
~
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McMillan & Wolf: Spectroscopy of Silicate Liquids
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McMillan & Wolf: Spectroscopy of Silicate Liquids
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McMillan & Wolf: Spectroscopy of Silicate Liquids
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McMillan & Wolf: Spectroscopy of Silicate Liquids
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Chapter 9
X-RA Y SCATTERING AND X-RAY SPECTROSCOPY
Gordon E. Brown, Jr.
Francois Farges
Georges Calas
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Tables
Table 1
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Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies 323
Tables
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(1)
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I' 2
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,,:
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330 Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies
Radial distribution function of silica glass
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334 Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies
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Table 2
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0~9.,"'/\,
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.:
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r,A
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:.-.--'''--,--~
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Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies 345
Tables
Table 1
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q_ .... _ e ~ 0::.::;0
s= k:~ <1"'-
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REV032C009_p349-380.pdf
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(17)
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356 Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies
(20)
&» = "" -1 n (2k)20 + I C 4 k 2 (1 + RIA.)
4 3 2( 1 I)
hn.=--C k -4kcr -+-
'-"I' 3 3 R A.
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Table 2
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a=--""----
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kBT
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Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies 365
5100
5050
5000
ENERGY (eV)
Tables
Table 1
Table 2
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Be
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c
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REV032C009_p381-410.pdf
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[(RO - R)]
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384 Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies
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388 Brown, Farges & Calas: X-ray Scattering and Spectroscopy Studies
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r
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REV032C010_p443-474.pdf
Page 1
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443
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444
D = A exp ( - R (#-T2) ReT)-
Page 3
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445
1500
1200
900
Tables
Table 1
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Titles
446
1 rr (K)
b
1 rr (K)
Page 5
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447
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Titles
448
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Chakraborty: Diffusion in Silicate Melts
449
GLASS
LIQUID
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Chakraborty: Diffusion in Silicate Melts
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451
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452
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453
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454
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455
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456
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457
Use of exact relationships.
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458
a
qj = ax [JLj - JLn]
~ aJLj ~ aJLk
c: aC~k =,l,...J aC~j·
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459
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460
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C(t ,x)
= C1 +Cz + 2( e1 -Cz) ;... ..!.exp [ -Dl2Tf2t 1 cos [wrrx ]Sin [wrrx i 1
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469
D( N;) = (N; - N2) V J Hz) i( 1 - YO) f ~ dx + Y*] \; Y dx I
N; - N;
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470
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471
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472
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473
( A) = (Llui) J ( w)
(Llui)
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474
REV032C010_p475-504.pdf
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Titles
475
Uncertainties in diffusion data
Page 2
Titles
476
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Titles
477
W(X, n)
1 exp(-£).
2nJ...2
2D = (rlJ...i+r2J...~+ ... +rnJ...~).
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Titles
478
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479
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480
_1 [L ((6r/m))2) + L (6r/rriJ.6r/n))]
6 VkT m t 111 n; mm t
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483
VIII. DIFFUSION DATA IN SILICATE MELTS
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le4/T(K)
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494
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Chakraborty: Diffusion in Silicate Melts
495
REFERENCES
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496
Chakraborty: Diffusion in Silicate Melts
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Chakraborty: Diffusion in Silicate Melts
497
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Chakraborty: Diffusion in Silicate Melts
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499
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Chakraborty: Diffusion in Silicate Melts
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501
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Chakraborty: Diffusion in Silicate Melts
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Chakraborty: Diffusion in Silicate Melts
503
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Page 1
Titles
Chapter 11
PRESSURE EFFECTS ON SILICATE MELT
George H. Wolf and Paul F. McMillan
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Table 1
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512
Tables
Table 1
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Wolf & McMillan: Pressure Effects on Structure and Properties 513
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Titles
516 Wolf & McMillan: Pressure Effects on Structure and Properties
GPa is qualitatively similar to that of stishovite at the same pressure (Williams et aI.,
;:a
Tables
Table 1
Page 13
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Titles
-
a
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Pressure (GPa)
Page 15
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Wolf & McMillan: Pressure Effects on Structure and Properties
519
1 5.0t
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Wolf & McMillan: Pressure Effects on Structure and Properties
523
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Table 2
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Titles
524 Wolf & McMillan: Pressure Effects on Structure and Properties
b
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Wolf & McMillan: Pressure Effects on Structure and Properties 533
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REV032C011_p543-580.pdf
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544 Wolf & McMillan: Pressure Effects on Structure and Properties
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Wolf & McMillan: Pressure Effects on Structure and Properties
547
Tables
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Table 2
Page 6
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Frequency (em -1)
Frequency (em -1)
Tables
Table 1
Page 8
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Wolf & McMillan: Pressure Effects on Structure and Properties 553
REFERENCES
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554 Wolf & McMillan: Pressure Effects on Structure and Properties
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Wolf & McMillan: Pressure Effects on Structure and Properties 555
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556 Wolf & McMillan: Pressure Effects on Structure and Properties
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Wolf & McMillan: Pressure Effects on Structure and Properties 557
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558 Wolf & McMillan: Pressure Effects on Structure and Properties
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Wolf & McMillan: Pressure Effects on Structure and Properties 559
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560 Wolf & McMillan: Pressure Effects on Structure and Properties
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Wolf & McMillan: Pressure Effects on Structure and Properties 561
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Titles
Chapter 12
COMPUTER SIMULATIONS OF SILICATE MELTS
Peter H. Poole
Paul F. McMillan and George H. Wolf
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Titles
564
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Titles
565
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566
N 3 p~
(2)
= - LL¢>;/r;,rj) == LL¢>;/r;,rj) , (3)
Page 25
Titles
567
(6)
(A),ime = (A(r(t)))time = lim ~ r' A(r(t'))dt' (4)
LA(k)P(k)
f A(k)P(k)dk
(A) - s: -.--
.s.
P(k)=e kBT
Page 26
Titles
568
(A)k = !_ tACk) (9)
The molecular dynamics method
Page 27
Titles
569
f·=m·--l (12)
1
1
Page 28
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570
{A} = {A}k = {Atne
Page 29
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571
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572
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Titles
573
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574
Tables
Table 1
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575
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576
,
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577
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578
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579
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580
2 ( (In]
REV032C011_p581-616.pdf
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581
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