Документ взят из кэша поисковой машины. Адрес оригинального документа : http://shg.phys.msu.ru/educat/vinogradov/Lesson2.pdf
Дата изменения: Wed Mar 12 16:11:34 2008
Дата индексирования: Mon Oct 1 20:37:48 2012
Кодировка:
Поисковые слова: m 1

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

, m , p, d , (1-p). Eo .

E = E0
D = eff E = eff E0
= 0

p

3 2
eff

eff

+

+ (1 - p )
m

3 2
eff

eff

+

=1
d

p 3 p (2 6 p
2 eff

3 2
eff

eff

+

+ (1 - p )
m

3 2
eff

eff

+ =

=1
d

eff

+

d

)

eff

+ (1 - p ) ( 2
2 eff

eff

+

m

)

3

eff

= ( 2 + 3 p eff d + 6(1 - p )
2 eff

eff

+

d

)(
m

2

eff

+

m

)
m

+ 3(1 - p ) eff m = = 4
2 eff

+ 2 ( d +
m

)

eff

+ d

[

6 p - 4 + 6 - 6 p] 2
2 eff

+ [3 p d - 2 d + 3(1 - p ) m - 2
eff

]

eff

- d m = 0

+ [3 ( p - 2 /3) d - 3 ( p - 1 /3)]
1 d - 3 p - 3

- d m = 0
2 ] + 8 d
m

eff

=

2 -[3 p - 3

2 ] ± [3 p - 3 4

1 d - 3 p - 3

d 0

eff

=

1 3 p - 3

1 m + [3 p - 3 4

2 m ]

=

3 2

1 p- 3 0

m

1 p - m > 0 3 1 p - m < 0 3

m

!!

p

3 2
eff

eff

+

+ (1 - p )
m

3 2
eff

eff

+

=1
d

d = 0
p 3 2
eff eff

+

m

3 + (1 - p ) = 1 2
eff

3 p 2
eff eff

eff m

+

3 p -1 = 2
eff

6 p

eff

= ( 3 p - 1) ( 2

+

m

)

6 p

- 2

- ( 3 p - 1)

m

eff

0 = 3p - 1 m 2 ~ m ( p - 1/ 3)

p < 1/ 3 p > 1/ 3

eff

~ m ( p - pc )t ,

t =1

d 0
eff

1 3 p - m + sign ( Re 3 = 4 1 1 p > 3, 3 m 2 p- 3 1 p< , 0 3 = 3 m p - 1 p > 1 , 2 3 3 1 0 p< , 3

m

)

1 [3 p - m ]2 3

Re m > 0 Re m > 0 Re m < 0 Re m < 0

p

3 2
eff

eff

+

+ (1 - p )
m

m = 3 eff
2
eff

+

= 1 3
eff

eff

- 3 p

eff

= 2

eff

+

d

d

(1

eff

- 3 p )
d

=

d

= d /(1 - 3 p ) ~

(

pc - p

)

-q

,

q =1

p = pc = 1/ 3 (m - eff ) 2
ef f

+

+

2 (d - eff ) 2
eff e ff

m

+

=0

d

2(eff )2 - d

- d m = 0

d h= << 1 eff / m = 0.5( h + h 2 + 8h ) h h <<1 m

s = 0.5

. .

div ( E ) = 0

rot E = 0 E = -

, ( ) div ( 0 E0 ) = 0 rot E0 = 0 E0 = -
0 0

div ( E ) = 0 div ( ± 0 ) E = 0 - div ( - 0 ) E = div ( 0 E

E =0 E

)

div ( 0 E ) = div ( 0 E - 0 E0 ) = 0 div ( E - E0 ) = - 0

= -

0

0 = div ( - 0 ) E
( r ) =1 4 Det[
(0 ) lm

]

(

( ij - ri ' rl - rl ')
-1 ( 0 ) lm

(0 ) ij

)

Ej

(

rm - rm '

)

d 3r ' = 3 d r ' = rm - rm ' ) d 3r ' rm - rm ') E
j

=-

1 4 Det[
(0 ) lm

]

(0 ) ij j - ( rl - rl ') -1 )lm ( rm - rm ') (0 1 ( ij - (0 ) ij ) E j r ' i ( rl - rl ') -1 ) (0 ij - E
(0 ) ij

ri '

(

)

lm

(

=-

1 4 Det[
(0 ) lm

]

( ij - +

)

Ej ri '

1

(

rl - rl ')

-1 ( 0 ) lm

(

1 4 Det[
(0 ) lm

]

(

(

ij -

(eff ) ij

rl - rl ')

-1 ( 0 ) lm

(

dsi ' rm - rm ')

)

Ei - E0i = - ri

(r) = ri
(0) kj

=-

( kj -

)

Ej rki '

1

(

rl - rl ' ) ]

-1 (0 ) lm

(

d 3r ' rm - rm ' )

4 Det[ 1 ] ri

(0) lm

(ij - (0)ij ) E j ds ' + ( r - r ') -1 ( r - r ') i 4 Det[(0 ) lm l l ( 0 ) lm m m , . . . .

. , , . , .

ri

V -V

( ( r ') kj -

(0 ) kj

)

Ej rki '

1

(

rl - rl ')

-1 (0 ) lm

(

4 Det[

(0 ) lm

]

d 3r ' rm - rm ') =

V -V

( ( r - r ") kj - ri

1 d 3r " E j ( r - r ") (0 ) kj ) r " r "l -1 ) lm r "m k (0 = 4 Det[ (0 ) lm ]
(0 ) kj

-

V -V

( ( r - r ") kj - r "i

)

1 d 3r " E j ( r - r ") r " r "l -1 ) lm r "m k (0
(0 ) lm

4 Det[

]

( ( r - r ") kj - - ri "

(0 ) kj

)

E j ( r - r ")

1 rk " r "l -1 ) lm r "m (0

=- ( ( r - r ") kj - ri "

(0 ) kj

( ( r - r ") kj -

(0 ) kj

1 + ) E j ( r - r ") r " r "l -1 ) lm r "m k (0 1 ) E j ( r - r ") r " r " r "l -1 ) lm r "m i k (0

ds = grad dV

E j - E0 j = ( ( r - r ") kj - ri " ( ( r - r ") kn -
(0 ) kn

=-

1 - (0 ) kn ) En ( r - r ") rk " r "l -1 ) lm r "m 3 (0 d r" 1 ) En ( r - r ") r " r " -1 r "l (0 ) lm r "m i k = 4 Det[ (0 ) lm ] En ( r - r ") r " r " j k 4 Det[
(0 ) lm

=

( ( r - r ") kn -

(0 ) kn

)

1 r "l
-1 (0 ) lm

] 1 r "l
-1 (0 ) lm

d 3r " r "m -

-

( ( r - r ") kn -

(0 ) kn

)

En ( r - r ") r "k
(0 ) lm

dS r "m

j

4 Det[

]

0

(

( r - r ") kn -
1

(0 ) kn

)

En ( r - r ") L(k j
1 r "l r "m r "m
-1 ( 0 ) lm

)

L

() kj

=

4 Det[ 1

(0 ) lm

]

S

S

r "k
-1 (0 ) lm

r "m

dS j =

=-

4 Det[

(0 ) lm

]

(

r "l

-1 (0 ) lm

)

3/ 2

dS j =

1 Lij = 3
ij

1 E - E0 = v. p. 40

( -0 ) E 1 3 ( - 0 ) E | r - r ' | d r ' - 3 0

1 E - E0 = v. p. 40

( -0 ) E 1 3 ( - 0 ) E | r - r ' | d r ' - 30
= 3

2 0 + F = 30

E

( -0 ) ( 20 + )

( ri - ri ' ) ( rj - rj ' ) 1 1 1 ij Gij = = -3 3 5 4xi x j | r - r ' | 4 | r - r ' | | r - r' |
F = E0 +

(

F ) Gd 3 r '

, = 3 ( - 0 ) / ( 20 + )

F = (1 + G + GG + ...) E

0

F = ( + G + GG + ...) E

0

eff ij

E

0

ij F j =

eff

F

=

= ij +

(G (
s ij1

x1 - x2 )...G =

j

s -1

j

(

x

s -1

- xs ) K s ( x1 ,..., xs ) dx1 ... dx

)

s

K 2 ( =9

) = 12 - 1 2 ( 1 - 0 ) ( 2 - 0 ) ( 20 + 1 ) ( 20 + 2 )
0

-9

( 1 ( 2

-
0

+

) 1 )
0

(2 ( 20

-

0

+

) 2)

, F= = 3 2 1 E E+ 3 30

eff

eff

( - 0 ) ( 2 0 + )

- 0 + 2 0 1 F = 3 E = E - Es + 2 0 3 0 0

eff

2 1 2 eff E = E + F= E+ E 3 30 3 30 eff 1 F = F = E - E = E-E 0 0 E = ( eff -0 ) eff = 3 ( 20 +eff )

eff

E

eff ij

eff

=3

( eff ( 2 0

- +

0

e

) ff )

eff

=

0

3 + 2eff eff = 0 + 0 3 -eff 1 -eff / 3

=

= ij +

(G (
s ij1

x1 - x2 )...G

j

s -1

j

(

x

s -1

- xs ) K s ( x1 ,..., xs ) dx1 ... dx

)

s

==3

( - 0 ) ( 20 + )

eff

= 3p

( incl - mat ) ( 2 mat + incl )
eff

eff = 0 + 0 0 + 0 1 -eff / 3

0 =

m at

eff

=

mat

( incl - mat ) 1+ 2 p ( 2 mat + incl ) ( incl - mat ) 1- p ( 2mat + incl )

0 =

eff

eff

=3

( eff ( 2 0

- +
eff

0

e

) ff )

eff

=0 -

eff

= = 3p

( mat ( 2eff

-

+

) mat )

+ 3(1 - p )

( mat ( 2eff

eff

+

) mat )

=0

G (
ij

x1 - x2 ) K 2 ( x1 , x2 )dx1dx2 = 0
K 4 ( x1 ,..., x4 ) ~
22

a = 81Sp

eff

= +a

22

=0
4

( G (
s

x1 - x2 ) G ( x2 - x3 ) G ( x3 - x4 ) K 4 ( x1 ,..., x4 ) ) dx1 ... dx

pc =

- ( 3a + 12 ) +

(

3a + 12 ) + 72a + 9a
2

2

9a

0, 40 0, 35 0, 30 0, 25 0, 20 0, 15

P

c

0, 10 0, 05 0, 00 2 4 6 8 10

a

, . E fl ( R ) . : ji = ief E k , .

Ei R = Ei + Ei

()

fl

( R)

= ik + Bik R Ek = Aik R Ek
ik

()

()

Aik -

= Bik = 0

, , , p, . , . , , . . , (1-). , , , . , , .

Bik. , ( , , . EMT EMT -1 Bqk = Bqt I - cB
tk
EMT B11 EM 1 - cB11 T E B22MT = E 1 - cB22MT

=0 - pc )
(1- pc )

c = (1 - 3 pc ) ( p pc

)

pc

(1 - p

) (1

N E 4 P = P = N E + P 4 1- N 3 3

. , . pc = 0.145. , .

1 , 2 , 3

ZrC - C . , .

, , Al 2O3

( I) ( 2), ( 3).

Na Li I 10% -. , , - . , , . 2.3 , 9 , : 2.3 9 . . 2.3 9 .