Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://cryst.geol.msu.ru/literature/kurs/2015_04_sungatullina.pdf Äàòà èçìåíåíèÿ: Thu Jun 4 13:08:32 2015 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 00:17:00 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 63

. .




MIXING ENERGETICS IN SOLID SOLUTIONS OF HIGH-PRESSURE POLYMORPH MODIFICATIONS OF MAGNESIUM AND CALCIUM SILICATES : , ..

: , ..

: ... ..

2015


......................................................................................................3 1. 1.1. ..................6 1.2. ...................................9 1.3. ..................................14 1.4. MgSiO3.......................................17 1.5. CaSiO3.......................................20 2. 2.1 ......................22 2.2 GULP ­ - ......................................................................................................25 3. MgSiO3........................................................................................................27 4. MgSiO3 - CaSiO3....................................35 .......................................................................................................49 .................................................................50

2



, , . , , . , , . , . . - , , . , . , . . . (, ) , . , .

, GULP (General Utility Lattice Program). MgSiO3 , CaSiO3 Ca Mg, , . , Mg Ca , MgSiO3 Ca,
3


. ,



. : , , , , . , , . , , , , , . , , , . - . - , (1992) 6 MgSiO
3

(3 , ,

Pbca, Pbcn, Pbnm, ­ P21/c, ­ I41/a, ­ R3-, MgSiO3, , , Ca MgSiO3 MgSiO3. . , .. , . - .. ( , . .. , .)
4


.



12-05-00809- « », 12-05-00983- « - ». 15-05-04575 « .» « -» (http://parallel.ru/cluster). . , «CCXRDS-2014» 13-15 2014 . , . .. .,

5


1.
1.1. - . . , , 90% , 1 . , . , , , , . , , . , . , , . , , , , . , , , . [, 1999]. , , . . , .. 2900 30 ( ). 6371 . . 410 : . . 670 .
6



(

2000

)






. D", , . (.1)



1.







. 24-410 . , . , , 220 ( ), [endelhson and Price, 1997]. , 300 , [Williams et al, 2005]. , 2(g,F)SiO3 = (Mg,Fe)2SiO4 () + SiO2 (). 15 1600-1700 , .. , 450 . , 300 .
7


410-670 . «410 » -, «520 » - . , 410 670 « », , , , , (g,Al)(Si,Al) 3 . «670 » , 80% , g- (20%) NaCl. , : CaCl2, -2, -, KAlSi3O8, , MgAl2O4 NaAlSiO4 , CaFe2O4 -, CaTi2O4. 410, 520 670 . ( ) , , 900, 1200 -1300 2700 , 1700, 1900-2000, 2850 . , . . 670-850 : (0.5Mg0.5)Al2Si2O8(..)..; 850-900 : Mg3Al2Si3O12(Mg,Fe)SiO3(), Mg3Al2Si3O12 Al2O3() + (Mg,Fe)SiO3 (), MgAl2O4 (.. ) MgAl2O4 (.. CaFe2O4); 1200 : 1500 : MgAl2O4 (.. ) MgAl2O4 (.. CaTi2O4); SiO2 SiO2 (c..CaCl2),

FeO ( ); 2300 : SiO2 (c..CaCl2) ;

2700 : MgSiO3 (..) MgSiO3 (..CaIrO3); 2850 : MgSiO3 (..CaIrO3) MgSiO3 (..) .
8


1.2. , , - . . . . , 1200 , .. [Funamori et al, 1998]. 1200 CaCl2, . SiO2 ( CaCl2) 50 . 1200 , , -1500 . -100 SiO2 -b2 [ , 1997] . , , , SiO2 [Prewitt, 2003], (210 ). , 200 [Kuwayama et al, 2005]. - , . , , . , SiO2, , , , gSi - MgO
9





, ,


SiO2. , [Murakami et al, 2006] [Oganov and Price, 2005] , . , , CaC l2, [Oganov et al, 2005] . SiO , ,
2



, , SiO2 . , . MgO/SiO2 > 1 MgO gSiO . , , , , , . . F 70 [Knitle et al, 1986]. , -, . , . ( g0.9Fe0.1)Si. , 70 (-1850 ), 120 (2700 ), .. D" . gSi. ( -) , . [Frost et al, 2004], gSi Fe 3+, Fe2+, . , - Fe
10
2+








,













gSi, : 3Fe2+( ) =2F+( ) + F(), [Frost et al, 2004]. [Oganov and Price, 2005] , Fe
3+

( ,

Fe3+) Mg- Si-. , [Frost et al, 2004] 100 . , . , , , , . , , . , , - . , , - . , , , . - ( D"). .. , 40- XX . , D' (984-2700 ), - D" (2700-2900 ). D" . - . - . , ( 3000 25-70 ) (Mg,Fe)SiO , . [Badro, 2003] - FeSi. , y - ,
11


gSiO lr 125-127 2500-3000, 27002740 , .. D" [Oganov et al, 2005]. , , 1.2%. , gSiO lrO - D", 2700-2890 . [Murakami et al, 2004]. , , -, [Ono et al, 2004] Fe2O3. 30 - Fe2O3 () , 50 [Oganov et al, 2005]. [Oganov et al, 2005] , gSiO (. 2). = 0, , , «» «», . D" . , «» «» , [Oganov et al, 2005], . «» D". MgSiO3 IrO, 130 [, - [Oganov et al, 2005] , , 90 MgSiO3 [ , 1994], O. , , , , - (g,F)SiO, (Mg,Fe)O SiO. Al2O3 130 1500 , .. IrO, , gSiO, . [ .. ., 2010].
12


2. gSiO [Oganov et ; 3xl, ; al, 2005] , , -

22 «».

Mg.

13


1.3. , CaAl4Si2O11, CaAl2Si2O8 ( ) 14 . [Gautron et al, 1996]. , , ( CAS Ca-AlSi ), 1994 . [Ilifune et al, 1994]. CAS . , , : a=5.4 å =12.7 å, P63mc, P62c P63/mmc. , AS , , 3.94 /3, . Ba-, . : P63/mmc. , ¾ , Ca-12, Al Si . , CAS. [Elsevier Science, 1997] CaSiO3 . , , (Mg,Fe)SiO ), CaSiO
3 3

(..

(. ,

7-8 % [, Irifune, 1994]. , , , . [Stacey and Isaak, 2001]. CaSiO3 , , 10- 13 a . CaSiO3 , , . , [Shim et al, 2002; Kurashina et al, 2004], [Stixrude et al, 1996; Chizmeshya et al, 1996; Magyari et al, 2002; Karakas et al, 2005]. CaSiO3
14


[, et al, 1989; Tamai Yagi, 1989; Van et al, 1996; Sheem et al 2000, 2002; Kurashina ey al, 2004; Shieh et al, 2004]. 42 . [, Wentzcovitch et al, 1995; . Chizmeshya et al, 1996; Stixrude et al, 1996] . , , , CaSiO .
3



[Karakas et al, 2005] :

CaSiO3, . , , I4/mcm 16a . I4/mcm - , , I4/mcm . , , 250 a , R-3. [Van et al, 1996 ; Sheam et al, 2002], , [ et al, 1989; Tamai and Yagi, 1989]. , , 600 - 1200 25 ­ 120a , , [Karakas et al, 2005]. , , 2000 - 2500, , CaSiO3 (.3). , [Li et al, 2006] . , , . [Karki and Crain, 1998], . .
15


3. CaSiO3 , [Kurashina ., 2004] [Ono ., 2004]. ]. [Brown Shankland,1981].

16


1.4. MgSiO3 - MgSiO3 (Mg), , . . , Mg- SiO2 MgO 70-80 3000 K [Meade ., 1995, Saxena ., 1996], 83 1700 [Shim ., 2001b], , Mg [: Fiquet .,2000]. , [ Shim ., 2001b] [Ono ., 2005a]. Mg- , [Murakami ., 2004a, 2005; Oganov Ono, 2004]. , - 1 [Umemoto ., 2006]. MgSiO3 , LHDAC 2500 125 [Murakami ., 2004a; Tsuchiya ., 2004a; Oganov Ono, 2004] (.4). D0 ­ -. Mg- , CaIrO3, Cmcm. , b, Mg. SiO6 , a . , , , .

17


. 4. MgSiO

3

, [Murakami .,2004a] [Tsuchiya ., 2004a]. [Brown Shankland,1981]. , . b-- , Mg-O . , . , . [Tsuchiya , 2004a]. , . , - . , [Tsuchiya ., 2004a, 2005b]. - 7,5 -1, D''. [ ., 1999]. ,

18


, D''.



Mg- [ Yagi., 1982; Mao., 1991; Yeganeh-Haeri , 1989; Ross and Hazen, 1990; Funamori., 1996; Fiquet., 2000]. K0 Mg- 254 [Ross Hazen,1990] 273[Mao ., 1991]. , 0 253-264 . , , Mg 250 [Wentzcovitch ., 2004; Tsuchiya ., 2004b, 2005b]. Mg-, Mg- . - , Mg- Mg- [Tsuchiya ., 2004a, 2005b]. , 0 Mg- , , Mg-, , Mg- , Mg- . , - , 1,5% [Tsuchiya ., 2004a], .

19


1.5. CaSiO3 , (Mg,Fe)SiO3- Mg ( 7-8%) Ca- (CaSiO3) [Irifune, 1994]. , , , Ca- , . [Stacey and Isaak, 2001] CaSiO3 10-13 , , , . CaSiO3 , . , [Shim ., 2002; Kurashina ., 2004; Ono . 2004] . [Stixrude ., 1996; Chizmeshya ., 1996; Magyari-Ko¨ .,, 2002; Caracas ., 2005]. Ca- [: Mao ., 1989;Tamai and Yagi, 1989; Wang ., 1996; Shim .,2000a, 2000b, 2002b; Kurashina ., 2004; Ono .,2004; Shieh ., 2004]. , , V0 = 45.54 å3, , 0, 232 288, K0', 3,9-4,5. , , 232 [ Wang ., 1996; Shim ., 2000b] . [:Wentzcovitch ., 1995; Chizmeshya ., 1996; Stixrude ., 1996; Karki and Crain, 1998] . , , , CaSiO3 . [Caracas ., 2005] CaSiO3, , (ab initio) .
20


, , , I4 / mcm, , , , , 165 . I4 / mcm , , I4 / mcm . , , 250 R-3c. K0 [Wang ., 1996;. Shim , 2002], , [Mao ., 1989; Tamai Yagi, 1989]. Ca-. [Ono ., 2004] , 600-1200 25-120, , [Caracas ., 2005]. , 2000 -2500, , CaSiO3 (.3). , - [Li ., 2006a, 2006b] . , , . Ca- [ Karki Crain, 1998], . .

21


2.
2.1 . 90% , [, , 2004]. . [ Gale J.D. Rohl A.L., 2003] -, , - .

A exp(-r/)-C/r

6







o - (-C/r6) . , , , - . «» . (.1) . (Buckingham)


1.









(Lennard-Jones)

(Morse) (Harmonic)





22


«» (General)



«» (Spring) (Three harmonic)



3-

. , . , , (. 1). , . , . , " - " . ( -- ). , R-6. : R -12, . , . , . , , ­ . , : «» (core),
23


, , «» (shell). . «» (Spring) (.1). , , . , , . ( ). (.1). (three harmonic) c k «» [ . ., 2009].

24


2.2 GULP ­ - . : WMIN, EMIN, METAPOCS, PLUTO, CASCADE, GULP . . . , , ( 15-20 å). , . -. -: (.5)

.5. [ , 2012]

25


GULP (General Utility Lattice Program) [J. Gale, 1997] . : · ; · ; · P-T ; · - ; · , - . · , ; · , ; · ; · (electronegativity equilization model); · ; · . , , , , . GULP 4.0 WINDOWS.

26


3. MgSiO3
MgSiO3 (1992) . (. 2) MgSiO3. Pbca. : a=18.227; b=8.819; c=5.179 : 31.33 3
-1

:

MgSiO3.

:

P21/c. :

a=9.605; b=8.813; c=5.166 : 31.22 3
-1

27


MgSiO3.

:

Pbcn. :

a=9.306; b=8.892; c=5.349 : 31.32 3
-1

MgSiO3. I41/a : a=11.501; b=11.501; c=11.480 : 28.58 3
-1

:

28


MgSiO3.



: R3 : a=4.728; b=4.728; c=13.56 : 26.35 3 -1

MgSiO3.

:

Pbnm :

a=4.775; b=4.929; c=6.897 : 24.44 3 -1

2. 6 MgSiO

3

29


() - , (0), , , -- -. , MgSiO3: Pbca (), P21/c (), Pbcn (), I41/a (), R3- () Pbnm (). - , , 0. P21/c , . MgSiO3 , . Pbca P21/c , ; Pbca , P21/c . 1273 , Pbca - Pbcn [Smith,1974; Murakami ,1982], , , 1830 [Kusiro, 1972]. Pbcn . Pbcn, Pbca P21/c [Smith, 1974; .Murakami , 1982], , Pbcn [Lee Heuer, 1987; Shraider ., 1990]. , Pbca , % (Mg2SiO4) (SiO2) , (Mg2SiO4) , [Ringwood, 1975 ; aogi Akimoto, 1977; , 1985] . , , , , Pbca P21/c , I41/a, R3- Pbnm [Kato Kumazawa, 1985; Sawamoto, 1987]. : , , ,
30






[Angel ., 1989; Horiuchi ., 1987], . [Price ., 1987; Matsui, 1988], , , . , [Price , 1989].

0, MgSiO3, , 0 MgSiO3 [Matsui, 1988]. , : , MgSiO 0. , [Murakami ., 1982] 1673 1830. , [Pacalo Gasparik, 1990] MgGeO3. . [ Nos, 1984 ] [Parrinelo Rahman, 1981]. , , 6 (a 2b 3, 480 ) Pbca, 12 (2 2b 3 , 480 ), P21/c Pbcn , 8 (2a1 22 2c , 1280 ) I41/a, 12 (3a1 2 (1 +2 a2) c, 360 ) R3- 27 (3 3b 3c , 540 ) Pbnm. (.3) , (5000 = 5 , ), .
3

,

31


V(rij)=qiqjrij-1-Cicjrij-6+f(Bi+Bj)âexp[(Ai+Aj-rij)/(Bi+Bj)]. F=4.184 -1 q, e Mg Si O +1.565 +2.329 -1.298 A, å 1.0133 0.8436 1.7600
-1

B, å 0.052 0.040 0.150

C,A31/2 0 0 54.0

-1/2

3 . (MAM0K), . , , . - , , [Matsui, 1989]. , Mg Si I41/a, MgSiO3 [kmillan , 1989], , Mg Si, , . , [Angel , 1989]. , ( ) . , , , , . . , Pbnm, , [Matsui, 1988], , . MgSiO3 c / , Pbca [Weidner ., 1978], Pbcn [Vaughan Bas, 1983], I41/a [Akaogi , 1987], R3- [Weidner , 1985] Pbnm [Yeganeh ­
32


Hayry , 1989], Pbca. 4, 300 0 , 22% , 21% , 11% , 6%, 1% Pbca, P21/c, Pbcn, , . Pbca Pbcn , . , , 0 [Matsui, 1988], Si O 1,80å, Si Pbca Pbcn O Si-O, 1,63 å. , 20% , P21/c ( 4), P21/c Pbca Pbcn. I41/a, - Si, . , , O-Si-O Si-O-Si , Si, , [Matsui ., 1984] [Price ., 1987]. , , , Pbca [Skinner, 1966], P21/c [Smith, 1974], I41/a [Scinner, 1966], [Ashida ., 1988], [Knittle et al, 1986], 1353 1633 Pbcn [Murakami ., 1984]. I41/a, . , Pbca, P21/c Pbcn 50 60% . Pbca, P21/c Pbcn, . Pbca [Akaogi ., 1991] [Ashida ., 1988] [Yto ., 1990], , 31,(3) / 983 , 59,(4) 298 110,(4) 298 , .

33





Pbca . . . . . . . . . . . . . . . 18.227 18.146 8.819 8.727 5.179 5.262 90.0 90.0 31.33 31.36 108 84 2.5 3.8 -7187.7

P21/c 9.605 9.600 8.813 8.672 5.166 5.244 108.5 108.5 31.22 31.14 92 2.5 4.1 -7187.7

Pbcn 9.306 9.378 8.892 8.820 5.349 5.458 90.0 90.0 33.32 33.98 112 88 4.0 6.0 -7186.5

I41/a 11.501 11.516 11.501 11.516 11.480 11.523 90.0 90.0 28.58 28.76 154 137 2.2 2.2 -7151.0

R34.728 4.740 4.728 4.740 13.56 13.33 120.0 120.0 26.35 26.03 212 224 2.4 2.8 -7157.0

Pbnm 4.775 4.772 4.929 4.925 6.897 6.942 90.0 90.0 24.44 24.56 247 250 3.2 2.9 -7150.0

a, å b, å c, å , V, 3/ 0, , -110
-5

H, /

4. MgSiO3 0 [Matsui and Price, 1992] Pbca I41/a, Pbca [Krupka ., 1985] I41/a [Yusa ., 1991] 292 32,(3) . , : «» < < «» <, . MgSiO
3,

,

MgSiO3 300 0 , 4, , , , . 0 - , [Angel ., 1989]
34


4. MgSiO3 - CaSiO


3



GULP MgSiO3, MAM0K, [34]. 0 , GULP. - [34] 3%. GULP MAM0K (.6) Ca- (.7) Mg-O Ca-O.

. 6 (Pbcn) MgSiO3(), CaSiO3 ()

35


. 7 (Pbnm) MgSiO3(), CaSiO3

(.5) , CaSiO3-MgSiO3 Ca(Mg) Mg(Ca), Q. PT , . Mg-O O-O Si-O Ca-O 766.742757 652.5051 2157.243 901.783288 0.29 0.09 0.2410 0.304379 0 10.8 0. 0 , , å C, *å

5. , .

36


, . , - . , . , . 6,5 å ( 8), 150160 .

O

Si

Si

O

O

Si

O

O Mg O O Mg

O O Mg O O Mg O Mg O Mg O

O

O O Mg O O Mg Mg O

O

O

O

Si

Si

O

Si

O

Si

O

O Si

Si

O

Si

O

Si

O

O Si

Si

O

Si

O

Si

O

O O Mg O O O O O Mg O Mg O Mg O O O Mg O O O Ca O Mg O

O Mg Mg O

O Mg O

O O Mg O O

O Mg y

x z

O

Si

Si

O

Si

Si O

Si O

O

Si Si

O

Si

Si O

Si O

O

Si

O

Si O

O

O

O Mg O

O Mg O

O O Mg O O Mg Mg O O Mg O

O O O Mg O O Mg Mg

O

O

Si

O

Si

O

Si

O

. 8 Ca MgSiO3 ()
37


Ca - , 3 å. (. 9)

.9 Ca, MgSiO3 , .

(Q), (Q1 Q2). - 0 50 , 300 .( 6,7 10,11).
38


, Q (Ca MgSiO3), Q (Mg CaSiO3), () dH ()

0
-71,27

10
-68,79

15
-67,59

20
-66,42

25
-65,27

30
-64,14

35
-63,03

40
-61,94

45
-60,86

50 -59,80 -56,95 0,49
9,25

-69,61 -66,86

-65,54

-64,24

-62,98

-61,73

-60,51

-59,30

-58,12

0,49
8,29

0,49
8,53

0,49
8,64

0,49
8,77

0,49
8,88

0,49
8,89

0,49
9,01

0,49
9,01

0,49
9,25

.6 Ca-Mg

. 10 Ca MgSiO3 Mg CaSiO3

39


, Q (Ca MgSiO3), Q (Mg CaSiO3), () dH () . 7

0

10

15

20

25

30

35

40

45

50

-63,80

-60,58

-59,06

-57,42

-56,50

-55,19

-54,07

-52,77

-51,58

-49,84

-60,26 0,45 19,16

-56,55 0,46 29,92

-53,81 0,62 28,67

-52,75 0,61 36,51

-51,37 0,62 35,85

-49,64 0,57 44,17

-48,13 0,55 51,65

-46,67 0,57 48,01

-45,20 0,58 49,87

-43,90 0,55 43,05

Ca-Mg

. 11 Ca MgSiO3 Mg CaSiO3 : H = x1x2(x1Q1+x2Q2), , Q1 Q2 Q . 12,13, 14, 15.

40


.12 MgSiO3 ­ CaSiO3 ( Pbcn)

41


.13 MgSiO3 ­ CaSiO3 ( Pbnm)

42


.14 3D MgSiO3 ­ CaSiO3 ( Pbcn)

. 15 3D MgSiO3 ­ CaSiO3 ( Pbnm)
43


. 8 10 , 20 40 - «». ( S) (Sc)

, . [ . ., . ., 2004] 90%. , ; . : Sc = kN[xlnx+(1-x)ln(1- x)], k ­ , N ­ . mix :

H = x1x2(x1Q1+x2Q2),
mix
mix)

Sc 1500-3000

( Gmix= Hmix-T S ( 16, 17).

44


. 16 1500-3000 MgSiO3-CaSiO3 ( Pbcn)

45


. 17 1500-3000 MgSiO3-CaSiO3 ( Pbnm) . ( )

G :

46


2

3

H x2 G x3

2

T
3

S x2 S x3



.


T

. 18 T-x

G .



O'

G (x) O




,

[ . ., . ., 2004]

. Q1 Q2 [ .. (1971), (1977), ( . (1975)].

G (x)

[Kaufman L., Bernstein H. (1970)].

G (x) T-x

(.18). T-x [ .. (1974)]
47




G .

T-x

G (.18)
. 19. , 2800 995 (2200 ) 20%.

3100 2900 2700 2500 2300 2100 1900 1700 1500 0 20 40 60 80 100

. 19 MgSiO3-CaSiO - , -

3

48


: - . - , MAM0K GULP, (1992) 6 MgSiO
3

(3 ,

, Pbca , Pbcn, Pbnm, ­ P21/c, ­ I41/a, R3-). 2 Ca- . CaSiO3-MgSiO3 Ca(Mg) Mg(Ca), Q. , PT , . : : 19,16 0 51,65 35 « »; 8,29 0 9,25 50 MgSiO3 c . MgSiO3 , «». 50 2200 MgSiO3 15% , 2800 ­ 20%. , , . , MgSiO3 .

49



1. u .. , .. // . 2006. . 51, NQ 5. . 819-829. 2. u .. // .. 2002. . 172,'NQ 4. . 480-485. 3. u .. // . . . 4, . 2004. NQ 2. . 3- 10. 4. u .. . .: , 1986. 160 . 5. u .. , u .. / /. 1999. 1. . 3-14. 6. u .. , u .. //Geos. 2010 . 1961. 10. . 837-839. 8. . ., . . . . 2004. C. 4. . N. 5. . 37-44. 7. .., .. //

9. Badro J., Fiquet G., Guyot F., Rueff J.-P. Iron partitioning in the Earth's mantle: Toward deep lower mantle discontinuity / / Science. 2003. V. 300, 5620. . 789-791. 10. Badro J., Rueff J.P., Vanko G., n G., Fiquet G., Guyot F. Electronic transitions in perovskite: Possible nonconvecting layers in the lower mantle // Science. 2004. V. 305, 5682. . 383-386. 11. Catti, M.;Gazzoni, G.;Ivaldi, G.;Zanini, G. The beta alpha' Phase Transition of Sr2SiO4. I. Order-Disorder in the Structure of the alpha' Form at 383 K, Acta Crystallographica (1983), 39, 674-679 12. Catti, M.;Gazzoni, G.;Ivaldi, G. Structures of twinned Sr2SiO4-beta and of Sr Ba0.1SiO4-alpha, Acta Crystallographica , (1983), 39, 29-34 13. Creer, J.G.;Troup, G.F.J.The Crystal and Magnetic Structures of Mn2GeO4, Solid State Communications (1970), 8, 1183-1188
50
1.9


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