Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://cryst.geol.msu.ru/literature/kurs/2014_04_kolupaeva.pdf Äàòà èçìåíåíèÿ: Thu Jun 5 08:44:42 2014 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 00:12:20 2016 Êîäèðîâêà:

, ..

:

. Thermodynamic properties of high-pressure water ice polymorphs.

414 . .., .., ., .., ., -. , : .., , , : .., ..., ...

2014 .



...........................................................................................3 1. 1.1. .............................................................................4 1.2. ........................................................4 1.3. ..........................................................6 1.3.1. ...........................................9 1.3.2. Ih................................................................................12 1.3.3. II.................................................................................13 1.3.4. III................................................................................15 1.3.5. V................................................................................16 1.3.6. VI...............................................................................18 1.3.7. VI...............................................................................19 2. 2.1. .....................................................................21 2.1.1. I..........................................................................22 2.1.2. II.........................................................................22 2.1.3. III........................................................................23 2.1.4. V........................................................................23 2.1.5. VI........................................................................24 2.1.6. VII.......................................................................24 2.1.7. ................................................................25 2.2. ........................................................................25 2.2.1. ................................................................25 2.2.2. ...................................27 2.2.3. ..........................................28 2.2.4. ....................................................28 2.3.......................................................................................30 ...............................................................................................32 .....................................................................................33

2


.
, . , , , , , , -. , , . . ( ), . 1h, 2, 3, 5, 6 7, , , , , , ,- , .

3


1. .
1.1. . , , . , --, ­ . . 2,423*1022, 0,0004% . , 53- . , 0, 64 . [5] , (, ), - (, , , , ), , , . , . , . [1] 104,5 (. 1), . sp3 . , L- . . 2 , 4 , . [6]

. 1 . [1] 1.2. . 1935 . , 0 ( ), .
4


. , , , - . , .. , . . , . , ­ . , . , () . . , .. , . , - , , «». , «» , , . -, . , : 1) , , 2) . « ». [5] , , . , . [6] , . , , (),
5


, . - , . , , . [5] - , H2O 3+ -. ­ : 1) O-O ( ); 2) O-O (-). , , , . , . (, -) , . [2] 1.3. . 13 (. 2) , . , , . , (I, IV, IX XII) . XII .

6


. 2 . [1] . , X, , , ­ . , . II, VIII ( VII), XI ( Ih, Ih, ), IX ( III) ­ , , , ­ (.., ). , , 4 0,5. , . , ­ , , -......-,
7


«» ­ . , . Ih, III VII XI, IX VIII . , , , , . - , (). ( Ih, Ic, XI) . , (II, III, IX, V, IV, XII, VI), , H2O, . 2 ( VII, VIII) . VII VIII , -.... , 50 , , . 200 . , 0,5 , ( IV V), .. , . VI, VII, VIII, . , , . , . Ih , . Ic , , , , . (SiO2) III IX, Ba(Al2Si3O10) VI. Zn S , , SiO2,
8




,









,



, , Si-O-Si. [4]
Ih Ic II III IV V VI VII VIII IX X XI XII . . . . . . . . . . . . . P63/mmc Fd3-m R-3 P41212 R-3c A2/a P42/nmc Pn-3m I41/amd P41212 Pn-3m Cmc21 I-42d a=4.48 A, =7.31 A a=6.35 A a=7.78 A, alfa=113.1° a=6.73 A, =6.83 A a=7.60 A, alfa=70.1° a=9.22 A, b=7.54 A, =10.35 A, beta=109.2° a=6.27 A, =5.79 A a=3.344 A a=4.656 A,c=6.775 A a=6.73 A, c=6.83 A ( ) a=4.502 A, b=7.798 A, =7.328 A a=8.304 , c=4.024 A Z 4 8 12 12 16 28 10 2 8 12

2 - 8 12

. 1 . [4] 1 . . . . , ( , , , .). () . 1.3.1. . , 180 , . Ih .
9


. Ih, . , 28°, Ih. , 1 , 27.4°. 1 , Ih 70° . (0001) Ih {111} 1, . , Ih Ih, 1. 100 , . -, . , , , , , , , , , , , , . . . . . , ( = 3.0 *-3), 2 *-3, 2.5 *-3. (, , ) , , . , ,
10


. , , , . . , , , , , . . Fe FeS, 38% 53% (1821.6 ), . . ( FeS) 10% 45% (1565 ), , 120 170 . 1/4 1/3 (2634 ), , 900 VI, V, III I. ( 2410.3 ) , -, , , VI, V, III I. 1.9 *
3 -

, 1.4 1.0 * -3.

, , , . , : 1) ( Ih ± () + ); 2) - (), ; 3) , . [7] , , . [4] Ih, II, III, V, VI VII.
11


1.3.2. Ih. Ih , .. . Ih , P63/mmc. Ih , (. 3). , ­ , , ­ . Ih , . [4]

. 3 Ih. [3] Ih , , ­ . , ­ . ­ 4,4, 4. [5] Ih , (. 3,,), , (. 3,,d). - . 4,b 4,d , . 4, 4, . , -- .
12


. 4 Ih: () (b) ; () (d) . [4] , Ih , 0 . , , 0 . , 2 Ih . -, Ih . [4] 1.3.3. II. II 1964 . . II , R-3. , [111] , . (1), -- (2). , 1/3 (. 5).
13


3 , . II II «» «». II, ,

.

. 5 II, . . [3] II Ih, Ih (.6). , , .



b

14


. 6 Ih () II (b). . Ih, Ih II, . [4] II, , II , . 0.28 0.48 . [4] 1.3.4. III III . , 4 1212. 6.666 å (a) 6.936 å. [3]

. 7 III. [3] III (1) , , (2) . [4]

15


. 8 III [3] 1.3.5. V. V , 2/. -, -, - ( . 9 2 ) ( ­ ), . (4), , . (2 3), 1. 4 2 3, 1. 4 , (.9). [3]

16


. 9 V. [3] V -- ( 86" 132°) -- ( 105°), --. , . 2, , , . , , ( ), , , .. , . -- , , . -, , , , , .

17


. 10 V. [3] III IX, - 41212 , ( V . V , ) , V . , , , . 2/, 0.4-0.5 . [4] 1.3.6. VI. VI , (Al,Si)O2 . , VI , - . VI, VII VIII , , . [4] V

18


. 11. VI. [3] 1.3.7. VII. VII 1. , VII - (.12). VII , - VIII.

. 12. VII. [3] VIII VII ( III) , VIII. 2 15 273 . VII, 150 () VIII.
19


VII . VII VII'. VII VIII ( , ) . , , , , - . , . . , -- , . . VIII VII. , + -. , VII ( X). . , -- -- , . [4]

20


2. .
2.1. . () , -, 2. , P-V-T : 1. Birch-Murnaghan:
P 3 K 2
T

V V

73

V V

53

1

3 4K 4

' T

V V

23

1

,

V , o - () 1

, 298 ;
' KT , K T - 1

. K

T

1 dP ,K V dV

' T

dKT dP

.

Birch-Murnaghan , , KT (T ) V () :
K T (T ) K T (T )
T

KT T

(T
P

T ),

V (T ) V (T ) exp
T

(T )dT ,
T 1V V T
P

() ­ : 2.

.

Vinet, , :
P 3K T 1 x x
2
13

3 exp ( K 2

T

1) 1 x , x

V V

.

3.










,T

G P, T ,

F . 4. Vi



Vi (T , P) .

21


P-V-T , T(K), P(), V(3/). I, II, III, V, VI [Tchijov et al., 1997] - 230-350 , 0-21 . [Lupo, Lewis, 1979], -, . , Birch-Murnaghan Vinet - . , 2 ,

. , , , . 2.1.1. Ih. P-V-T Ih [Tchijov et al., 1997; Lupo, Lewis, 1979; Noya et al., 2007] : [Tchijov et al., 1997]: VIh(T,P) = ((922.8 + 7.27850.001P + 7.502310-5(P/10)2)-1exp((-5.35810-3+1.57610-4(T273.15)+2.77810-7(T-273.15)2+8.8510-9(T-273.15)3+2.77810-10(T-273.15)4) (1+6.04310 P/10)-0.8)) 18000. [Noya et al., 2007], =100-273.15 , = 0.001-2 : VIh(T,P)=18/(0,952350841174924-0,0000774015597958263*T-2,63449072305342E07*T2+2,79542989072675E-10*T3)*(1+P*(-0,000151158764786942+2,10717361580732E08*P-1,59648106419734E-07*T-3,65556200293796E-10*T2))0 [Lupo, Lewis, 1979]: VIh(T,P)=18/(0.9403+0.0001143(P-1)0 [Tchijov et al., 1997]: VII(T,P)=((1169,8+0,0818*P/10)^(-1)*EXP(LN((1,292090,000613383*237,65+0,00000143211*237,65^2-0,00000000285369*237,65^3)/(1,2920922
.737 ,045329345462526 -4

).

-T8.58510-5)

2.1.2. II.


0,000613383*T+0,00000143211*T^2-0,00000000285369*T^3))*(1+0,00006949*P/10)^(1)))*18000. [Lupo, Lewis, 1979]: VII(T,P) =18/(1,1711+P*8,96*10^(-6)-T*(7,9*10^(-5))) [Noya et al., 2007], =160-240 , = 1.5-6.5 : VII(T,P)=(1/(1,14433822452418+0,00122265991117161*T-7,43638191978609E06*T^2+1,19304099429434E-08*T^3)*(1+(P1500)*(0,0000447616129011325+1,94964457041927E-10*P-4,32256492491825E08*T+3,70285468746897E-10*T^2))^(0,12169924260111))*18. 2.1.3. III. III : [Tchijov et al., 1997]: VIII(T,P)=((0,0010683+0,00000029191*(T-273,15)+0,0000000021658*(T-273,15)^20,000192)*(113,21+0,012057*(186,1-1,335*(T-273,15)-0,1628*(T-273,15)^2)-0,002*((T273,15)-(-27,2)))/(113,21+0,012057*P/10-0,002*((T-273,15)-(-27,2))))*18000. [Tchijov et al., 2004]: VIII(T,P)=((1/(1,1321+1,2057*0,01*P/1000)/1000+0,0058*0,001)*EXP(LN((0,4642*0,001+2 ,885*0,000001*T-5,348*0,000000001*T^2)/(0,4642*10^(-3)+2,885*10^(-6)*237,655,348*10^(-9)*237,65^2))*(((1+5,7/8,5*P/10000)^(-1))/(1+5,7/8,5*0,25)^(-1))))*18000. [Lupo, Lewis, 1979]: VIII(T,P)=1/(1,077*10^(-5)*P+1,1234)*18 [Noya et al., 2007], =240-254 , =2.2-3.4 : VIII(T,P)=(1/(0,786703336967634+0,00210832736847313*T+1,99960619258305E-06*T^21,84038463537938E-08*T^3)*(1+(P-2200)*(-0,000942199651309869+8,65505817946031E07*P-6,29393867370833E-06*T+2,37762743010959E08*T^2))^(0,0120584939360969))*18. 2.1.4. V. V : [Tchijov et al., 1997]: VV(T,P) [Tchijov et al., 2004]: VV(T,P)=((1/(1,1974+0,01963*P/1000-0,001098*(P/1000)^2)/1000) * exp(ln((0,00091090,000001275*T+0,000000003061*T^2)/(0,000910923

=(0,000802*(1-0,000833*(T-272,73)-0,00000495*(T-272,73)^2)*(1-

0,0000207*(P/10-618,4)-0,0000000242*(P/10-618,4)^2))*18000.


0,000001275*237,65+0,000000003061*237,65^2))*(((1+5,2/13,3*P/0,0001)^(7,86))/(1+5,2/13,3*0,5)^(-7,86))))*18000. [Lupo, Lewis, 1979]: VV(T,P)= 18/(1,2466+1,14*10^(-5)*P-T*1,82*10^(-4)) [Noya et al., 2007], =220-270 , =3,5-6,0 : VV(T,P)=(1/(1.12539931432053+0.00128483603234289*T-2.98274348159903E-06*T^27.02406478308055E-10*T^3)*(1+(P-3500)*(0.00153875621744445+1.2274049292906E10*P-0.0000117010301223628*T+2.37810923985949E08*T^2))^(0.067677348798317))*18. 2.1.5. VI. VI : [, 1993], VI , 10 , 233-293 : VVI(T,P)=(0.00079011+0.00000010513*(T-273.15)+0.00000000037347*(T-273.15)^20.000038)*(129.45+0.0082074*(625.9+0.06086*(T-273.15)-0.0008571*(T-273.15)^2)0.0005*(T-273.15+35.5))/(129.45+0.0082074*P/10-0.0005*(T-273.15+35.5))*18000. [Lupo, Lewis, 1979]: VVI(T,P)= (0,7812+0,000046*T-P*0,00000597)*18 [Noya et al., 2007], =175-325 , =8.0-20 : VVI(T,P)= (1/(1.42078121075434-0.000187677677865978*T-0.0000003027773242824*T^24.33076797788539E-11*T^3)*(1+(P8000)*(0.0000299426388503466+2.31719203820454E-10*P+9.42422956620525E09*T+1.61691965587817E-10*T^2))^(0.103284780340502))*18. 2.1.6. VII. VII BirchMurnaghan, [Fei et al., 1993] =300-700 , =60-200 . Birch-Murnaghan P-V VII 300 , (1): V = 12.3(±0.2) 3/, KT = 23.9(±0.7) , K T=º(P) V () = V(P,T=300K).
' T

=4.2(±0.5). VII

24


P-V-T VII , :
T

V ( P, T ) V ( P, T

30 0K ) exp
3 00 K

( P, T )dT ,

V ( P, T

300K ) - ,

(1), (P,) ­ , :
(T , P) (T )(1 K K
T T

P) ,

­ , , VII =0.9.

P-V-T VII , [Lupo, Lewis, 1979], , , VIII: VVII(T,P)= 18/(1,5422+(0,00000558)*P-T*0,000101). 2.1.7. . [ Lupo, Lewis, 1979]. VL(T,P) = 1,0014+(T-273,15)*3,4*10-4+(T-278,15)2(8,6*10-7)-(P/22400)+P*3,4*10
5 -

*e-3

400/P

, [Wagner, Pruss, 2002]. 2.2. . 2.2.1. . (. 13). [ ., 2010]. . ­ .

25


1,15

V, 3/
1,05

I

0,95

III
0,85

L V

II

0,75

VI

0,65

VII
0,55 170 220 270 320 370 420 470 520 570

,

. 13 V(T). , ­ : al., 2007];

­

[Lupo, Lewis, 1979];

­

[Noya et

­

[Tchijov et al., 1997];

­

[Tchijov et al., 2004];

­

[, 1993];

­

[Fei et al.,

1993]; [Wagner, Pruss, 2002]. (. 2).
Ih [Lupo, Lewis, 1979] [Noya et al., 2007] [Tchijov et al., 1997] II [Lupo, Lewis, 1979] [Noya et al., 2007] [Tchijov et al., 1997] III [Lupo, Lewis, 1979] [Noya et al., 2007] [, 1993] [Tchijov et al., 2004] V [Lupo, Lewis, 1979] [Noya et al., 2007] [, 1993] V,cm3/g T=250 K 1,0668 1,0965 1,0638 T=220 K 0,84065 0,8342 0,82673 T=250 K 0,86932 0,8656 0,85984 0,8697 T=250 K 0,79485 0,7929 0,795 , K-1 P=1000 bar 9,1583E-05 1,8941E-04 1,3870E-04 P=4000 bar 6,6411E-05 2,4000E-04 3,2155E-04 P=2500 bar 0,0000E+00 2,8249E-04 8,7150E-04 2,4786E-04 P=5000 bar 1,4463E-04 2,5404E-04 1,2933E-04 26 , bar-1 1,4611E-05 9,6468E-06 1,4773E-07 7,5322E-06 5,8380E-06 6,7628E-05 9,3626E-06 1,2540E-05 1,0375E-04 , bar 68442 103661 6769106 132763 171292 14787 106808 79745 9639

9,0613E-06 5,9178E-06 7,1731E-05

110360 168981 13941


[Tchijov et al., 2004] VI [Lupo, Lewis, 1979] [Noya et al., 2007] [, 1993] VII [Lupo, Lewis, 1979] [Fei et al., 1993] L [Lupo, Lewis, 1979]

0,7913 T=300 K 0,72336 0,7345 0,7297 T=300 K 0,60555 0,62634 T=300 K 0,87385

3,2600E-04 P=12000 bar 6,3592E-05 2,4856E-04 1,6654E-04 P=25000 bar 1,6700E-04 4,3232E-05 P=5000 bar 4,2300E-04

8,2532E-06 4,3907E-06 5,8933E-05 3,6200E-06

121166 227757 16969 276243

1,7972E-05

55642

. 2 . 2.2.2. ­ , 1 . . , : =1/V(V/T)P. (. 14, . 2). . ­ , , .
,
-1

,

27


. 14 . ( . 13), ­ : ­ 220 , ­ 250 , ­ 300 . 2.2.3.

. . :

=-1/V(V/P)


T



=1/
, . , , .

. 14 . ( . 13), ­ : ­ 220 , ­ 250 , ­ 300 . [Shimizu et al,1996]. 2.2.4. . ( ):

28


, ­ . (. 3), [Tchijov, 2003].
T, 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 P, 20 1000 60 1000 10 2500 10 5000 30 3000 50 2500 50 4000 50 5000 30 10000 30 15000 70 10000 70 15000 00 25000 00 40000 50 25000 50 40000 00 2000 00 6000 C, - - /* Lupo Noya 93 97 04 Fei Wagner 2,5 0,86 2 1,27 1,92 2,3 0,52 1,99 2,42 2,2 0,52 1,83 2,45 2,5 0,52 1,84 2,57 2,5 2,45 2,16 2,5 1,17 2,11 1,04 2,5 1,15 2,01 1,03 2,2 0,48 1,75 0,81 2,3 0,46 1,42 0,75 2,6 0,48 1,91 1,07 2,7 0,46 1,55 1,00 2,5 1,21 0,32 2,25 1,35 0,30 2,6 1,36 0,82 2,25 1,57 0,78 3,9 2,85 2,93 3,6 3,08 3,14

Ih II

III V VI

VII

L

. 3 . , : , ­ , . : . () (. 16).

29


. 16 . . 2.3.. : 1) 2, 1h, 2, 3, 5, 6 7, . , 2. 2) 2 : , , . 3) . . 4) , , - - (, , , .), . 5) , .

30


, Ih- : Ih . 6) ,

. . 7) , . . 8) , . 9) . ­ , .

31


.
. ( ), . 1h, 2, 3, 5, 6 7, , , , , ,- . , , V(T), , , .

32


:
1. 2. 3. 4. 5. 6. 7. ru.wikipedia.org water.sevo44.ru www1.lsbu.ac.uk .., .. // . . .: , 1988. .., .. , . .: - , 2010. . ., . ., . . -

. 2006. . 75(1). . 64­85.

, - // , 2014, . 454, 3, . 1­6. 8. .., .., .. 2: // , 2010, . 44, 2, 1-22 9. 10. 11. .. Lupo M. J., Lewis J.S. Mass-Radius Relationships in Icy Satellites // ICARUS, 40, Noya E.G., Menduina C., Aragones J.L., Vega C. Equation of state, thermal expansion // . 1993. . 2. . 113­123. 157-170 , 1979 coefficient, and isothermal compressibility for ices Ih, II, III, V, and VI, as obtained from computer simulation // J. Phys. Chem. C 2007, 111, 15877-15888 12. 13. 14. 15. 16. Tchijov V., Keller J., Rodriguez-Romo S. Kinetics of Phase Transitions Induce by Tchijov V., Ayala R. B., Leon G.C., Nagornov O. Thermodinamics of high-pressure Choukroun M., Grasset O. Thermodynamic model for water and high-pressure ices up Fei Y., Mao H., Hemley R.J. Thermal expansivity, bulk modulus, and melting curve of Fortes A. D., Wood I. G., Tuckerc M. G., Marshall W. G. The P­V­T equation of Chock-Wave Loaing in Ice // J. Phys. Chem. B 1997, 101, 6215-6218 ice polymorphs: ices III and V // J. of Physics and Chemistry of Solids 65 (2004) 1277-1283 to 2,2 GPa and down to the metastable domain // J. of Chemical Physics 127, 124506 (2007) H2O-ice VII to 20 GPa // J. Chem. Phys. 1993. V. 99 (7). P. 5369­5373. state of D2O ice VI determined by neutron powder diffraction in the range 0 < P < 2.6 GPa and 120 < T < 330 K, and the isothermal equation of state of D2O ice VII from 2 to 7 GPa at room temperature // J. of Applied Crystallography ISSN 0021-8898, 2012 17. Frank M.R., Fei Y., Jingzhu H. Constraining the equation of state of fluid 2 to 80
33

GPa using the melting curve, bulk modulus, and thermal expansivity of the ice VII //


Geochimica et Cosmochimica Acta. 2004. V. 68(13). P. 2781­2790. 18. Gagnon R.E., Kiefte H., Clouter M.J. Acoustic velocities and densities of polycrystalline ice Ih, II, III, V, and VI by Brillouin spectroscopy // J. Chem. Phys. 1990. V. 92. P. 1909­1914. 19. Tchijov V. Heat capacity of high-pressure ice polymorphs // J. of Physics and Chemistry of Solids 65 (2004) 851-854

34