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
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ANTI-STOKES
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....
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T = 2" E qi
Tables
Table 1
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... ,
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Tables
Table 1
Page 17
Page 18
Page 19
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a
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longitudinal
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diatomic
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Table 1
Page 22
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(a) RAMAN SCATTERING GEOMETRY
sample
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hy
(b) CONSER V A nON OF WAVE VECTOR
Page 5
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11
~, ='R':-K
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Table 1
Table 2
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Table 2
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Table 1
Page 22
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A'
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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)
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E(x) + [1 - -yz (x)2 + ••• J.
C = ~ [ E(~) + E(~)J
v 2 T 2T·
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g(w) dw
77
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e = nw /k,
( 27)
79
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Table 1
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Titles
en en
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a)
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Temperature (K)
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Page 20
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Lattice DI.tortlon. (Count 100% - all other.)
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Table 1
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C = _A(~)3 ), (W ~~~"ROi7r _
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107
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3NAk a 3 Xu
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n - s Xi
(60)
108
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Table 1
Page 15
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109
Tables
Table 1
Page 16
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110
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Table 1
Page 17
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(d)
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Figure 20, continued.
114
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Table 1
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e
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o
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Ie
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*
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intramolecular
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................ - --
c.
•
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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
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(1. 6)
(1. 7)
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Table 1
Table 2
Page 6
Page 7
Titles
(1.13 )
(1.14)
(1.15)
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(1.17)
Tables
Table 1
Page 8
Titles
\
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134
Tables
Table 1
Page 9
Page 10
Titles
K Br 90 K
-- Simple shell
model
.L
,
,
,
oL
.... -
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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
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wT -w
dw)
Page 15
Titles
= R (~,k) + u(~,k)
Page 16
Titles
o
(2.4)
(2.8)
Page 17
Page 18
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- -e L -f - -
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TRIG.
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Table 1
Table 2
Page 22
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a
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148
Page 23
Page 24
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\
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TEMPERATURE OK
TEMPERATURE DEPENDENCE OF r25( ~ H) MODE
/
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2,0
0,5
150
Page 25
Titles
151
Page 26
Titles
152
Tables
Table 1
Page 27
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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
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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
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1-- R4~
, 3
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kx
t
r
000
Page 8
Page 9
Page 10
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Titles
Fm3m
E R1 R:z R:J
175
Page 12
Page 13
Page 14
Page 15
Tables
Table 1
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0; •
Page 17
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o/\/W\/\
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/\;/\//\/\
\/\~/\/
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
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ill
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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
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H
973K
T
Page 13
Page 14
Page 15
Page 16
Tables
Table 1
Page 17
Page 18
Page 19
Page 20
Titles
e
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Table 1
Page 21
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1600
1500
1400
1300
207
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Table 1
Page 22
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~C1
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Table 1
Page 23
Titles
G
(a)
G
T=t
Ab
(b)
~An
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Ab
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(e)
T=T.
(d)
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Ab
---+ An
G
(e)
T= 1:
(f)
T
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Ab
~ An
Ab
---+ An
209
Page 24
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Titles
G
T=T.
G
T=t
T
Aug
(a)
o
Jd
Aug
(b)
Jd
T,
Aug
(e)
Jd
Page 26
Page 27
Page 28
Page 29
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Titles
II
cI cf .
cI
-II
Page 31
Page 32
Titles
REFERENCES
218
Page 33
Titles
219
Page 34
Titles
220
Page 35
Titles
221
Page 36
Titles
222
Page 37
Titles
223
Page 38
Page 1
Titles
Chapter 7. Alexandra Navrotsky
CR YST AL CHEMICAL CONSTRAINTS on the
Page 2
Titles
<.
..- '
.: _ ....
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o
6H
_ ...........
.... . ....
i
.... -.
226
Page 3
Page 4
Page 5
Tables
Table 1
Table 2
Page 6
Page 7
Page 8
Titles
Table 1
Enthalpies of Substitution Reactions in Silicates
Continued next page
232
-i iz>
Page 9
Titles
-----------------------.-- ... __ .--...
Page 10
Titles
234
Page 11
Page 12
Titles
236
Page 13
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Titles
\
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25
Or--------.-
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238
Tables
Table 1
Table 2
Page 15
Page 16
Page 17
Titles
~:
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Page 19
Page 20
Page 21
Page 22
Page 23
Titles
o
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247
Tables
Table 1
Page 24
Titles
248
Page 25
Titles
249
Tables
Table 1
Page 26
Titles
250
Page 27
Titles
Table 5
M,Mg Exchange Free Energies for Olivines, Pyroxenes, and Amphiboles
-r.i=
+IO.ld
B
. /.
A
251
Tables
Table 1
Page 28
REV014C007_p253-276.pdf
Page 1
Titles
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Page 2
Page 3
Titles
255
Page 4
Titles
An/(Ab + An)(xl)
Tables
Table 1
Page 5
Page 6
Page 7
Page 8
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o
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Tables
Table 1
Page 10
Page 11
Tables
Table 1
Table 2
Page 12
Titles
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Page 13
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Page 7
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Page 8
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Page 10
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10 +\' ~.-
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287
Page 12
Page 13
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289
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Table 1
Table 2
Page 14
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a
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Page 18
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2
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Table 2
Page 19
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ci
WRVENUMBER (CH-i)
10000 7000
,-~--"
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1000 1500
WRVELENGTH (NH)
5000
2000
295
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Table 1
Page 20
Titles
I
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Page 25
Page 26
Titles
302
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Table 1
Page 27
Page 28
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,..
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TEMPERATURE, DC
~
1000
800
600
400
200
o
--
°
Table 2. Selected linear thermal expansivities for polyhedra*
Tables
Table 1
Table 2
Page 14
Page 15
Page 16
Titles
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Page 17
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'!./'!.o
333
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Table 1
Page 18
Page 19
Page 20
Page 21
Titles
3. THE POLYHEDRAL APPROACH
Page 22
Tables
Table 1
Table 2
Page 23
Page 24
Page 25
Tables
Table 1
Page 26
Page 27
Titles
>
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Tables
Table 1
Page 28
Titles
344
Page 29
Page 30
Titles
346
Page 1
Titles
Chapter 10. Charles W. Burnham
MINERAL STRUCTURE ENERGETICS and MODELING
Page 2
Titles
(1)
348
Page 3
Page 4
Titles
DISTANCE
\ REPULSION
,
\
TOTAL
VAN DERj
WAALS, /
1 / COULOMB
Page 5
Titles
351
Page 6
Page 7
Titles
(13)
Page 8
Tables
Table 1
Page 9
Titles
355
Page 10
Page 11
Titles
357
Page 12
Titles
358
Tables
Table 1
Table 2
Page 13
Page 14
Page 15
Page 16
Titles
362
Page 17
Titles
w
o
363
....
....
.....
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......
B~
" ...
,.,'"
Page 18
Page 19
Titles
"''''
~~
"''''
"' ....
0 ....
o bO
~O
:.:u
'"
"'''' ....
;:!~~~
~
....... .-4..-1.-4
!
o
"
-0
~
UUUU
.--(NMM
. ~.~.~ .......
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'"
1\ ....
0· ...
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.... '"
Ie ~~~
j..I ....... N....-l
....... -/\
O ..-INO
p..c;>,?,?~
...... ~;:;:~
'"
"
'"
1\ ....
o~
V:':
NNNNN
365
Page 20
Titles
366
Page 21
Titles
367
Tables
Table 1
Table 2
Page 22
Titles
368
Page 23
Titles
369
Tables
Table 1
Page 24
Titles
370
Page 25
Page 26
Titles
372
Tables
Table 1
Page 27
Page 28
Titles
~ OJ
. In
OJ':': rtl
~g~
:::l .... C
II II II
.... ~
.. ~
........ '"
-g a. ~
... ~ "
. ., ~
.c ~ E
0 ..
.... N
.... N
------
NOM.-IO.-lO
!,....:......:....!,...:......:......:...
'"
0>
0,-1""';0'
0'IU""III'"If"-.
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O\Lf"lV"'Ir--
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374
Page 29
Page 30
Titles
376
Tables
Table 1
Page 31
Page 32
Titles
;f-
378
Page 33
Titles
379
Page 34
Titles
..
Q12
0.08
x.
...
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XI. .: ••••
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ooe
b
8
n
2
380
Tables
Table 1
Page 35
Page 36
Titles
382
Page 37
Titles
383
Tables
Table 1
Table 2
Page 38
Page 39
Page 40
Titles
REFERENCES
386
Page 41
Titles
387
Page 42
Titles
388
Page 1
Titles
Chapter 11.
Raymond Jeanloz
THERMODYNAMICS of PHASE TRANSITIONS
Page 2
Page 3
Titles
dP ss;
--= --
-
E
I-
-=====1: t:;,.V
Il t:;,.V < ~
+
Pressure
Page 4
Titles
so; ~ Ttr6Str (3)
Page 5
Titles
SI [el]r [el] ]-1 r [-el]]
Page 6
Titles
I-
'"
'"
S7
'"
'"
( >l 'IOWO~D / r )
~F l= 3
+ + ,0
<Jr<>
-
o
"
cD
W
, ,
2
,
~I I, I, ,I 10
,
E
o~
fl58
Page 7
Titles
.6Sl!.T =In[81] (7)
3R 82
Page 8
Titles
(8)
[as] [aT] dS [aT] [aT] [as]
= [-Tj(8) Cv = _ C~
Page 9
Titles
ss; = £[~~lrdV+ .6Sgeom (11)
Page 10
Titles
[as] [as] [ae]
av T = ae T av T (13a)
Cv [as]
= - - -- (13b)
s av T
[as] = [ap] = aKT , (14)
e v T et y
Page 11
Titles
.tJ.S T = -yCv-
Page 12
Titles
o
.6S}
.6V
PRESSURE
ENTROPY
400
Tables
Table 1
Page 13
Page 14
Titles
Liquid Packing Fraction,e.
t t
E
o o~
Ratio of Holes to A toms, w
R
Page 15
Titles
3 r[ V]-5/3 [V ]-7/3]
PIKo= '2l Vo - Vo' (21)
Page 16
Titles
+0,05 ~
<J
Z
07
0,8
0.6-..
0.9
1.0
1.0
5
(VOl = 7 cm3/atomol)
<J 0(---+----+-1---+----+-1---'- __ --1
<.9
~
o
o 0.2 0.4 0,6 0.8
P/Kol
404
Page 17
Page 18
Titles
CALCULATED
PRESSURE (GPo; KOI = 100 GPo)
dP == ~6® dT
Page 19
Page 20
Page 21
Titles
81 (NoCl-type) Structure
82 (CsC 1- type) Structure
Page 22
Titles
81-82 TRANSITIONS: DATA
Page 23
Titles
!J!3&- [27]1I6[ 6V, ]113
Page 24
Page 25
Page 26
Tables
Table 1
Page 27
Titles
er p er pdInV ot p
1.2
dS = [a~] dT + [as] [a v] dP 1.5
aT v av T ap T
Cv -rCv
= -dT - --dP
Page 28
Page 29
Page 30
Page 31
Titles
35 <00> = - ---- - - - µ
µ-l = .l.[l + _L]
Page 32
Page 33
Page 34
Titles
v» = -- = -----
[ 2 1 ]-113
c = - + - (A5)
vl Vp
r ]112
V = 13K(1-=A
r ]1/2
V = 13K(..L=-M
Page 35
Titles
dlnVp
K'T = OK] = _ [alnK] (A12a)
oP T aln V T
() _ .=.!...(aK] _ -K[~] __ [alnK]
Page 36
Titles
(B 1)
(B4)
Page 37
Titles
(B5)
= ----l- - - ---- exp(-Tlp)
k
Page 38
Titles
REFERENCES
426
Page 39
Page 40
