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Titles
REVIEWS IN MINERALOGY
THERMODYNAMIC MODELING
MINERALS, FLUIDS AND MELTS
EDITORS: I.S.E. Carmichael & H.P. Eugster
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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
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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
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Chapter 3 Bernard J. Wood
Chapter 4
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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
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Chapter 7
John R. Holloway
Page 5
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Chapter 8
Page 6
Page 7
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Chapter 9 John M. Ferry and Lukas Baumgartn
Page 8
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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
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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
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40~--~~--~~--~~~~~
1600
Temperature Deg C
Page 10
Page 11
Page 12
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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
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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
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.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
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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
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(A) + [B] = (B) + [A] .
(58)
Page 20
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ex + 2fJx •
Tables
Table 1
Page 21
Page 22
Tables
Table 1
Page 23
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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
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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
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XM2·XM1 T
Page 18
Page 19
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Table 6. Tests of Equilibrium at 11.5 kbar / 800' C
89
Tables
Table 1
Table 2
Page 20
Page 21
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AS-1
W-2
91
Page 22
Page 23
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ACKNOWLEDGEMENTS
REFERENCES
Page 24
Page 25
Page 26
Page 1
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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-
'"
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.s
~
'"
~
'"
e-,
"" '"
"''''
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~ .....
....
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"':!:!
" +
113
Page 18
Page 19
Titles
~
o
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...... ro N CI) eo r(J t..
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o
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- ~~.~
., "'-
r(J ctI ro ro
bO.c· ..... ..,..::.::~
oJ
co ~co
---- .....
eo ctI ttl "0
c
115
Tables
Table 1
Page 20
Page 21
Page 22
Titles
E
E
Q
o
'"
118
Page 23
Page 24
Titles
4.0
3.0
::;:
E 2.0
Kieserite
150
Tables
Table 1
Table 2
Page 25
Titles
i ' , .
Page 26
Titles
mKCI
if
1
..
o 2 .')-! ).
.,.L...f/l I I ~ I
,.
Tables
Table 1
Table 2
Page 27
Page 28
Titles
o
E
Solid Phases:
o Sylvite (KCI)
A Sylvite + Halite
•
012340123' .-
mNaCI
124
Tables
Table 1
Page 29
Page 30
Page 31
Page 32
Titles
,
Page 33
Tables
Table 1
Page 34
Tables
Table 1
Page 35
Titles
...
....
0.1
-------..
-.. ........
............
} 4-1
} 2-1
I
Tables
Table 1
Page 36
Titles
o
o
Tables
Table 1
Page 37
Page 38
Titles
co =
Tables
Table 1
Table 2
Page 39
Tables
Table 1
Page 40
Tables
Table 1
Table 2
Page 41
Tables
Table 1
Table 2
Page 42
Titles
o
Page 43
Page 44
Page 45
Page 46
Page 1
Titles
Chapter 5 John H. Weare
Page 2
Page 3
Page 4
Page 5
Page 6
Page 7
Page 8
Page 9
Page 10
Page 11
Page 12
Titles
... . 6~G,IA I x µ
- - - .003 .004 .005 .006 .007 .008
504
a
.2
154
Tables
Table 1
Table 2
Page 13
Page 14
Titles
10 TEMPERATURE = 2000C
3
TEMPERATURE =
.:
/-l' -----
//";' ---
f~/ ----
;f
t
6
TEMPERATURE = 150°C
TEMPERATURE = 250°C
+
6
mNaCI
2 3 4
mNaCI
2
oIL
o
'0
',-------~~~~-----
TEMPERATURE = wooe
Nael =Om
o 0.4 0.8 1.2 16 2.0 24 2.8
m No2S04
0.002
8' 0.006
E 0.004
0010
0.008
Page 15
Page 16
Titles
-'" -
'7~ ~
,
3
158
Page 17
Titles
159
Page 18
Page 19
Page 20
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.....
-£
=
Page 22
Page 23
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20 40 60 80 100
m Mg 1m Mg (S.W.)
165
Tables
Table 1
Table 2
Page 24
Page 25
Titles
a:::
i
~
........ _
::;;:
:::>
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;~~~~";~~~--:~";~
~~'";"':~<=!~'";~~~"';<=!
oooooooo..:.:~~~
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..,
.;o~~~,.:~.;~
w
~
o
r
w
§
I
ri ri N
I I ,
o ... _
~ ~ ~
C!~~~~~"':~
~~~~~~--:~
, I I
Oa)M";";a)O~ 0'> M °
oO_ ..... ..,;t ..... a..o ° ..0 V"\
...........
ON~O~"'N~ 0 - -
... -o
...........
..
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s:
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co ..
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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~-
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o
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~: .
{I . H2S (oq)
~I~ ~
~I l~t
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-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
<,
' .
....
' .
. ~ .
A .. • ••
"" '.
'.
. .
4
2
Ag
'.
-- ...
'<, • •••••
. ' .......
0.5
pH
Low pH
307
Page 28
Page 29
Titles
Weathered gneiss
Pallid zone
E
o
u
u
~
. 0.6 --
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
AVERAGE GRAIN DENSITY (g/cc)
309
Tables
Table 1
Page 30
Page 31
Page 32
Page 33
Page 34
Page 35
Page 36
Page 37
Page 38
Page 39
Page 40
Page 41
Page 42
Page 1
Titles
Chapter 9 John M. Ferry and Lukas Baumgartner
, . µ, laP ,
, , "
Page 2
Titles
*
Page 3
Titles
, ,
(7)
, , , ,
Page 4
Titles
(14 )
Page 5
Titles
t~~]
[aT JdV
Page 6
Page 7
Page 8
Page 9
Titles
( 48)
Page 10
Titles
8rr2N2 f J J
332
(55)
(56)
Page 11
Titles
rL S± r
rb=. rr ~
m m
Page 12
Titles
[a~] = 0
aV T
(a~p) = 0
Page 13
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b = Ix.b.
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