Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://cryst.geol.msu.ru/literature/kurs/2014_03_marchenko.pdf Äàòà èçìåíåíèÿ: Wed Apr 9 10:09:51 2014 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 00:12:12 2016 Êîäèðîâêà:

..



CaAl2O4

: , ..

: , ..

2014




I

2
3 3 8 16 16 17 18

1.1 1.2 CaAl2O4 1.3 1.2.1 GULP 1.2.2 Quantum Espresso (QE) 1.2.3 TOPOS

II , , 2.1 P21/n CaAl2O4 2.2 2.2.1 2.3 ab-initio 19 19 21 26 29 32 33

1



, . , , , - . CaAl2O4 , , , . CaAl2O4. : , , CaAl2O4; , . . , .. , . - .. ( , . .. , .) QE. 12-05-00809- « », 12-05-00983- « - ». «-» (http://parallel.ru/cluster). , . .. ., . 3 7 2013 . « », TOPOS . : 1) ; 2) ( P21/n ) (. 2.1 . 10,11).

2


I 1.1 .

. . , , , . c [, 2002, 2004; , 2006; Oganov and Price, 2005]. , , . . 30 ( ) 2900 . . 410 : . . 670 . D'' , , . , , (.1). , 840-1700 . 410, 520 670 . ( ) , , 900, 1200-1300 2700 , 1700, 1900-2000, 2850 . , .

3


.1. ) ; ) , , 1200 , (MgAl2O4) [Funamori, Jeanloz et al., 1998]. 1200 [ , , 1961] CaCl2, [Kingma, Cohen et al., 1995]. SiO2 ( aCl2) ~50 . , ~1500 [ Oganov, Gillan and Price, 2005]. , ~100 , SiO2 -PbO2 [Dubrovinsky, Saxena et al, 1997]. , MgSiO
3

(Mg- Pv).

, MgO SiO2 70-80 3000 [Meade et al., 1995; Saxena et al., 1996]; [Shim et al., 2001] 83 1700 . , Mg- Pv [Fiquet et al., 2000]. , , [Shim et al., 2001] [Ono et al., 2005]. 2004 ab4


initio , 2500 K 125 (, D'') Mg-PPV , CaIrO3 Cmcm [Oganov and Ono, 2004] (.2) . . [ Murakami, Hirose, Sata, et al., 2004]. , 75% 650 .

.2. () (). , ­ [Oganov and Ono, 2004]. PV- PPV MgSiO3 LHDAC [Mao et al., 2004, 2005]. , PPV [ Mao et al., 2005]. . [Knittle and Jeanloz, 1986] FeO ~70 . , -, [Mazin, Fey et al., 1998]. ~90 (~2100) Al2O3 Rh2O3, 4% [Funamori, Jeanloz, 1997]. , Al2O3 , . , . 5


[Anderson, 1989; Dziewonski, Anderson, 1981] 670 (.3)

P.3. (). CMB ­ ; Cpx+Opx ­ - ; HS LS ­ - , [Ono, Oganov, 2005]. , , , - . , (Mg,Fe)SiO3, 70% , (Mg,Fe)O (~20%). 10% , Ca, Na, K, Al, Fe, - ( (Mg,Fe)SiO3-Al2O3), (CaSiO3) Ca- (NaAlSiO4) [ .. .., 2010]. , . Mg-Pv Ca-Pv. [Irifune, 1994]. Mg-Pv 6


P-T [Irifune, 1994; Ringwood, 1994]. [Kesson et al., 1998; Hirose et al., 1999; Ono, Ohishi et al.,2005] , CaFe2O4, , [Miyajima et al., 2001; Akaogi et al., 1999; Sanehira et al., 2005]. [Sanehira et al., 2005; Shinmei et al., 2005] , . . CaAl2O4. , , , [ Becker and Kasper, 1957; Ringwood, 1975; Irifune and Tsuchiya, 2007).

7


1.2 CaAl2O4
CaAl2O4 . P21/n [Ito et al, 1980], (SiO2) AlO4, (.4). CaAl2O4 P21/n AlO4- [010].

)

)

.4. ) P21/n CaAl2O4; Ca, ­ Al, - O; ) SiO2. Ca,

: Ca1-6 Ca2-6 Ca3-9. «» 2010 NWA 1934, - 8


[Ma, Kampf, Connolly et al,, 2011]. , CaAl2O4 2,94 /3. P21/c ,
4

m-CaGa2O4 [Ito et al,1980]. AlO

, a O (.5).

.5. P21/ CaAl2O4. Ca, ­ AlO4

- «» [Mikouchi, Zolensky, Ivanova et al, 2009].



, P21/n 2,99 /3. , [Ito et al, 1980] P21/n P21/c =1 (700°) 2 (1300° ). Al P6
3

(.6).

[Janakova, Salavcova, Renaudin et al, 2007], R- Al-O . , .

9


.6. P63 CaAl2O4. , ­ Al-O.

Al . , CaFe2O4 (Pnam) [Becker, Kasper,1957]. Al1 Al2 [001] (.7). , Ca, . =3,973 /3 [Lazic et al,2006]. CaMn2O4 (.7). , Ca, AlO6-. AB2O4 . , (CaTi2O4, CaFe2O4, CaGa2O4 ..) ( , Cmcm Bbmm, Pbcm Pmab .). , : -- -- . [Yamanaka, Uchida and Nakamoto, 2008], CaAl2O4. 10


, CaMn2O4, CaTi2O4 CaFe2O4 , . CaMn2O4 CaTi2O4 30 . CaTi2O4 ( 39 ) Bbmm.

)

)

.7. ) Pnam CaAl2O4; Ca, ­ AlO6; ) .

, CaTi2O4 (Bbmm), , . [Lazic et al, 2006] P21/m CaAl2O4 «» . «» Ca, (.8).

11


.8. P21/m CaAl2O4. Ca, ­ AlO6. , , P-T , CaAl2O4 : P21/m Pnam Al. 1 , CaAl2O4. .1. CaAl2O4. . . P21/n [Ito et al, 1980; Ma, Kampf, Connolly et al,, 2011].
, /3

a, å

b, å

c, å



Z

d aOn, å Ca(1)O6 2.312.68 Ca(2)O6 2.282.71

d AlOn, å AlO4 1.741.77

2.94

8.6996

8.0994

15.217

90.188

12

12


Ca(3)O9 2.353.18 P21/c


2.99

7.95

8.62

10.25

93.10

8

Ca(1)O7 2.213.05 Ca(2)O7 2.282.95

AlO4 1.771.85

(m-CaGa2O4 ) [Ito et al, 1980; Mikouchi, Zolensky, Ivanova et al, 2009] P6
3

P6

3

2.94

8.7402

-

8.0904

-

6

Ca(1)O6 2.472.67 Ca(2)O6

AlO4 1.512.21 1.532.41

( ) [Janakova, Salavcova, Renaudin et al, 2007]

1.982.58 Ca(3)O6 2.482.88 Pnam 3.97 8.92004 10.3155 2.8713 4 CaO8 2.312.48 AlO6 1.871.98 1.911.99 P21/m 3.63 5.556 3.7627 7.056 101.36 2 CaO7 2.352.49 AlO6 1.862.01 1.871.93

CaFe2O4 [Becker, Kasper,1957; Lazic et al, 2006]

P21/m ( ) [Lazic et al, 2006]

13


[Ito et al, 1980] CaAl2O4 . «CA-I», «CA-II», «CA- III» «CAIV» (.9). 600 1500° 10-40 Kb. «CA-I» ­ , . (.2) [ Horkner et al, 1976]. «CAII» m-CaGa2O4, «CA-IV» ­ CaFe2O4, [Reid, Ringwood, 1969].

.9. CaAl2O4 [Ito et al, 1980] .2. CaAl2O4 [Ito et al, 1980]. -I -II -III -IV CaAl2O4 m-CaGa2O4 CaFe2O4 , å b, å . . . . 8.7 c, å 93.1 V, å3 702 155 263 Z 8 (2) 4 8.09 15.21 90.14 1070 12 6.96 2.87 , /3 2.94 2.99 3.39 3.58

7.95 8.62 10.25 4.39 5.07 8.89 10.3

14


«CA- III» . 2 , CaFe2O4. Al
3+

. [Ito et al, 1980]



«CA- II» «CA- III» - «CA-IV» (Pnam). «CA-IV»- P=3 10000, [Reid, Ringwood, 1969] 10 (9000). [Akaogi, Hamada, 1999] 4-8 (7800C­14000C) «CA- III» «CA-IV» (.10)

.10. CaAl2O4 [Akaogi, Hamada, 1999].

15


1.3 .
1.3.1 GULP. . : , , ( 15 -20 º). . . -. [, , 2012]. Program) [Gale J.D., 1992-1994,1997]. GULP (. General Utility Lattice GULP

. ( 4.0) : 1) ( ), ( ), . 2) ( ­, (conjugate gradients) (rfo)). 3) , . 4) . 5) : , , , , . , - . 16


6) P-T . 7) - -. 8) : , . 9) -. 10) . , , , , . GULP .

1.3.2 Quantum Espresso (QE) , . , Quantum Espresso (opEn-Sourse Package for Research in Electronic Structure, Simulation, and Optimization) (www.quantum-espresso.org). , (-, - . ) , PAW. QE Linux. QE . , ld1 [Giannozzi et al, 2009]. QE: 1) - . 2) . 3) . 4) . 5) , . 6) . 7) . 8) . 17


9) (DFPT), . 10) - , . 1.3.3 TOPOS. TOPOS 4.0 [http://www.topos.samsu.ru]. (Systre, 3dt), . TOPOS 4.0 TOPOS TTD, TTO, TTR , RCSR EPINET. [, , 2013]: 1) ( ) 2) . (, , ..). . 3) , . 4) , . 5) - . 6) . . 7) . 8) 9) . ().

18


II , ,

2.1 P21/n CaAl2O4
TOPOS [, , 2013] . P21/n P21/n CaAl2O4, , P1(.10). Systre (Symmetry, Structure (Recognition) and Refinement) [Delgado-Friedrichs and O'Keeffe, 2003] [ Delgado-Friedrichs, 2004] P21/n (.11).

.10. TOPOS. P21/n Systre.

19


P.11. P21/n Systre.

20


2.2

( ) ( ), [Eremin, Talis et al, 2013; Eremin, Talis, Urusov, 2008] . :

(1) qi qj ­ i j, Rij - , : ) V(r)=Aexp( -r/) : (å). ) Al-O (3) ­ r (å), D ­ (å-1), r
0

(2)

r - (å), A ­
­

, (),

­ ­

(),

(å). GULP 3.4.9 [Gale and Rohl, 2003]. , Al2O3, Cr2O3, 3Al2[SiO4]3 a3Cr2[SiO4]3, -. , CaAl2O4, (.3). 21


.3. CaAl2O4.

( ) , eV Ca+1.66 - O-1.36 3843 128627.4 Al+1.89 - O-1.36 9 -1.36 -1.36 O -O 4048.394 ( ) D, eV Ca+1.66 - O-1.36 0.051986

r B, å 0.265 0.14424 5 0.27047 , å-1 1.2
.

,

å

12 12 12

,å-1 2.61

r



,

å 12

, . . . . P21/m P21/c (.4). (.12) P-T P21/c P21/m 900 K. , ­ . , , . , (.13).

22


.12. P21/m P21/c 900 ( ) ( ).

.13. P21/m P21/c 600 ( ) ( ).

23


.4. P-T P21/m P21/c. .
T=300K


P, 0 1 2 3 4 5 10 T=600K

P21/m
94.60 93.97 93.52 93.08 92.63 92.19 90.01 0 5 6 0 6 4 4 -

P21/m
94.99 94.53 94.08 93.63 93.18 92.74 90.54 1 6 4 4 6 1 5

P21/c
-94.938 -94.371 -93.81 -93.257 -92.708 -92.165 -89.521

, -0.053 -0.165 -0.274 -0.377 -0.478 -0.576 -1.024

P 21 /c
94.71 94.13 93.54 92.99 92.44 92.00 89.32 0 4 5 1 3 5 8

, 0.11 0.159 0.019 -0.089 -0.193 -0.189 -0.686


P, 0 1 2 3 4 5 10 T=900K

P21/m
94.78 94.32 93.87 93.42 92.98 92.53 90.34 2 8 7 8 1 7 4 -

P21/m
95.41 94.95 94.49 94.04 93.59 93.14 90.93 3 4 8 4 3 4 3 -

P21/c
95.42 94.85 94.28 93.73 93.18 92.63 89.97 5 3 9 1 0 3 6

, 0.012 -0.101 -0.209 -0.313 -0.413 -0.511 -0.957

P 21 /c
95.13 94.55 93.96 93.40 92.85 92.23 89.58 2 3 1 5 5 0 6

, 0.35 0.225 0.084 -0.023 -0.126 -0.307 -0.758


P, 0 1 2 3 4 5 10

P21/m
95.37 94.91 94.46 94.00 93.55 93.11 90.90 2 4 0 7 7 0 3 -

P21/m
96.07 95.61 95.15 94.69 94.24 93.79 94.22 8 7 6 8 3 0 3 -

P21/c
96.15 95.57 95.00 94.44 93.88 93.33 90.66 0 4 5 3 8 8 5

, 0.072 -0.043 -0.151 -0.255 -0.355 -0.452 -0.558

P 21 /c
95.78 95.20 94.60 94.04 93.49 92.93 90.20 5 3 6 9 7 9 6

, 0.413 0.289 0.146 0.042 -0.06 -0.171 -0.697

T=1200K


P, 0 1 1.5

P21/m
-96.131 -95.670 -95.212

P21/m
-96.920 -96.452 -96.220

P21/c
-97.047 -96.466 -96.178

, 0.127 0.014 -0.042

P 21 /c
-96.606 -96.020 -95.420

, 0.475 0.35 0.208

24


2 3 4 5 10 15 20 T=1500K

-

95.98 95.52 95.06 94.60 92.36 90.16 88.02

7 5 6 9 2 9 3

-

95.89 95.32 94.76 94.21 91.52 88.95 86.91

2 6 6 2 3 0 7

-0.095 -0.199 -0.3 -0.397 -0.839 -1.219 -1.106

-

94.75 94.30 93.85 91.63 89.45 87.32

6 3 2 0 8 9

-

94.86 94.30 93.74 90.99 88.35 85.81

1 7 6 3 9 5

0.105 0.004 -0.106 -0.637 -1.099 -1.514


P, 0 1 1.5 1.6 1.7 2 3 4 5 10 15

P21/m
-97.021 -96.557

P21/m
97.89 97.42 97.18 97.14 97.09 96.95 96.48 96.02 95.56 93.29 91.08 4 1 6 0 2 1 5 1 1 5 5 -

P21/c
98.07 97.48 97.19 97.14 97.08 96.91 96.33 95.77 95.21 92.51 89.92 6 8 8 0 3 0 9 6 8 2 5

, 0.182 0.067 0.012 0 -0.009 -0.041 -0.146 -0.245 -0.343 -0.783 -1.16

P 21 /c
-97.558 -96.969

, 0.537 0.412

-

96.09 95.63 95.17 94.72 92.48 90.30

5 5 9 4 7 1

-

96.36 95.80 95.24 94.68 91.90 89.26

5 3 7 4 9 1

0.27 0.168 0.068 -0.04 -0.578 -1.04

25


2.2.1 CaAl2O4
(.14) 2.5 P21/c ( 300 ), 1500 P21/c P21/m 4.5 . (800-1500K) P21/n P21/c . 2.5 19 P21/m . , [Ito et al, 1980] . Pnam , . [Lazic et al, 2006; Ito et al, 1980], Pnam

. (.15)

.14 CaAl2O4.

26


0 . Al (Pnam) , . , , (.16). Pnam ( 0 3.97 /3 , 15 4.21 /3).

.15. 0 CaAl2O4.

.16. CaAl2O4 .

27


, , 5.

.5. CaAl2O4 .
P21/m P, 0 1 2 3 4 5 15 P21/c P, 0 1 2 3 4 5 15 P21/n P, 0 1 2 3 4 5 15 Pnam P, 0 5 10 15 66.05 64.68 63.47 62.40 3.97 4.05 4.13 4.20 3 8 5 6 8.91 8.84 8.78 8.72 10 08 00 58 2.85 2.83 2.82 2.80 23 59 02 55 10.3 10.3 10.2 10.1 944 187 536 957 91.3 90.3 89.4 88.5 87.6 86.8 78.8 2 3 0 2 7 4 3 2.87 2.90 2.93 2.96 2.99 3.02 3.32 4 5 5 5 3 2 9 8.77 8.74 8.71 8.69 8.67 8.64 8.41 09 38 92 60 33 98 12 8.09 8.04 7.99 7.94 7.89 7.84 7.33 36 19 28 51 77 93 57 15.4 15.4 15.3 15.3 15.3 15.3 15.3 371 153 940 746 584 477 303 90.2 90.2 90.2 90.2 90.1 90.1 90.1 6 5 3 0 6 1 2 91.6 90.5 89.5 88.3 87.4 86.6 81.0 4 5 1 4 7 7 2 2.864 2.898 2.932 2.971 3.000 3.028 3.240 8.18 8.12 8.06 8.00 7.95 7.91 7.73 69 69 78 33 82 75 23 8.71 8.68 8.66 8.62 8.60 8.58 8.38 36 63 07 98 64 41 77 10.3 10.3 10.2 10.2 10.2 10.2 10.0 273 097 950 738 578 419 375 95.6 95.5 95.4 95.1 95.1 95.0 95.3 4 4 6 7 2 9 9 V/. å p, / 71.75 71.63 71.03 70.70 70.36 70.04 67.08
3

3.65 3.66 3.69 3.71 3.72 3.74 3.91

3

a, å 8 4 4 2 9 7 2 5.52 5.56 5.51 5.50 5.50 5.49 5.41 92 63 53 86 20 54 33

b, å 3.77 3.74 3.76 3.75 3.74 3.74 3.70 66 56 27 62 50 39 11

c, å 7.00 7.01 6.98 6.96 6.95 6.94 6.83 82 07 17 89 64 42 03

101. 101. 101. 101. 101. 101. 101. 31 45 32 33 34 34 35

28


2.3 ab-initio
- Quantum Espresso [Giannozzi et al, 2009], . () USPP [Vanderbilt,1990]. QE (, , , ) . GGA , , [Perdew, Burke, Ernzelhof, 1996]. «» 60 . 4x4x4 k- . CaAl2O4 ( Pnma, Bbmm). 0 200. , , AlO6 CaOn. 6 8. .6. 200 . ab-initio. CaO9 AlO6 CaO9 AlO6 Pnma d a-O (å) 2â1.9967, 2â2.0116, 1â2.0835, 1â2.1178, 2â2.1078, 1â2.868 d Al-O (å) 1â1.6685, 2â1.6999, 1â1.7032, 2â1.7272 Bbmm d a-O (å) 2â1.9712, 4â2.0013, 2â2.2964, 1â2.4934 d Al-O (å) 1â1.6176, 1â1.6730, 2â1.7184, 2â1.7716 V CaO8 (å3) V AlO6 (å3) V CaO8 (å3) V AlO6 (å3)

, . 7 - 3- [Anderson, 1995]:

P

3 K 2

0

(V0 / V )

7/3

(V0 / V )

5/3

1

3 (K 4

0

4) (V0 / V )

2/3

1
(4)

29


V0 -- P = 0, K0 K0 -- , . .7. Pnam Bbmm ab-initio . Pnma Bbmm K0, 185.56 175.94 K0' 4.056 4.068

.8. ab-initio Pnma Bbmm. Pnma , 0 20 50 100 150 200 , 0 20 50 100 150 V, å3 137.0 4 124.5 4 113.0 5 101.0 6 93.12 a, å 4.99 7 4.81 9 4.64 5 4.44 6 4.30 b, å 9.60 0 9.36 1 9.11 0 8.82 8 8.63 c, å 5.000 4.819 4.645 4.446 4.302 E, (/) -3113.225 -3112.856 -3111.641 -3108.909 -3105.843 30 K ( ) 176 255 362 532 692 V, å3 269.6 5 246.1 2 224.0 7 200.7 5 185.2 1 173.7 1 a, å 8.97 8 8.67 9 8.39 6 8.08 3 7.86 6 7.70 0 b, å 2.88 8 2.80 5 2.72 0 2.62 1 2.54 8 2.49 1 c, å 10.38 8 10.09 8 9.802 9.468 9.231 9.047 E, (/) -3114.036 -3113.687 -3112.518 -3109.862 -3106.863 -3103.744 Bbmm K ( ) 186 267 371 541 704 862 (/3) 3.894 4.267 4.687 5.231 5.670 6.045 (/3) 3.831 4.216 4.644 5.195 5.638


200

87.25

2 4.18 7

1 8.47 9

4.188

-3102.660

852

6.017

P21/m Pnma , 53 (.17). . Pnam . , .

.17. ( ) P21/m Pnma.

31



, : - CaAl2O4. - , , CaAl2O4. - P21/n TOPOS. CaAl2O4 1.66% P21/c, 0.83% - P21/m, 1.5% - P21/n, Pnam ­ 1.3%. GULP QE. ab-initio . - CaAl2O4, : P21/n P21/c, P21/n P21/m, P21/m Pnam P21/m Pnam . ab-initio .

32



.., .. TOPOS 4.0, 2013 .., .. // . 1961. 10. . 837-839. .. // . . 2002. . 172, 4. . 480-485. .. // . . . 4, . 2004. 2. . 3-10. .., .. // . 2006. . 51, 5. . 819-829. .., .. . - .: , 2010. - 140 ; . ISBN 978-5-89118-55-9. .., .. , -- .: , 2012. 428 . ISBN 978-5-891118-581-0 Akaogi M. , Hamada Y., Suzuki T., Kobayashi M., Okada M. High pressure transitions in the system MgAl2O4 ­CaAl2O4: a new hexagonal aluminous phase with implication for the lower mantle // Physics of the Earth and Planetary Interiors 115 (1999). P.67­77 Anderson O.L. Equations of State of Solids for Geophysics and Ceramic Science. Oxford: 1995. 405 p. Anderson D.L. Theory of the Earth. Boston: Blackwell Scientific Publications. 1989. 366

Becker DF, Kasper JS (1957) The structure of calcium ferrite. Acta Cryst. 10: 332­337.

33


Delgado-Friedrichs O.Barycentric drawings of periodic graphs. Lecture Notes Comp. Sci. 2912, 178189 (2004). Delgado-Friedrichs O., M. O'Keeffe. Identification of and symmetry computation for crystal nets. Acta Crystallogr. A59, 351-360 (2003).

Dubrovinsky L.S., Saxena S.K., Lazor P., Ahuja R., Eriksson O., Wills J.M., Johansson B. Experimental and theoretical identification of a new high-pressure phase of silica // Nature. V. 388. P. 362-365. Dziewonski A.M., Anderson D.L. Preliminary reference Earth model // Phys. Earth Planet. Inter. 1981. V. 25. P. 297-356. Eremin NN, Talis RA, Grechanovsky AE, Urusov V.S. (2013) Atomistic computer modeling of the local structure and mixing properties of a grossular­uvarovite solid solution. Moscow University Geology Bulletin 68 2: 72-78. doi:10.3103/S0145875213020026 Eremin NN, Talis RA, Urusov VS. (2008) Computer modeling of the local structure, mixing properties, and stability of binary oxide solid solutions with corundum structure. Crystallography Reports 53 5: 755-763. doi: 10.1134/S1063774508050052 Ito S, Suzuki K, Inagaki M, Naka S (1980) High-pressure modifications of CaAl2O4 and CaGa2O4.Materials Research Bulletin 15: 925-932. Irifune T (1994) Absence of an aluminous phase in the upper part of the Earth's lower mantle. Nature 370: 131­133
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