. , , ,

,,,

4

.

.18-31 1998 .

: .

.

1

.

, , , . , , .

, , .

. .1 I() , ( ) ( ). , H || c, , . ^ » 104 .

, (, Tb, Dy). I(), , , , (), , ().

, , . Is , . , .

.1. I() ,

( ) ( ).

, ( ). Is J c Is, J =90, . . Is ^ , J =180.

2.


.
. ..

. , , , . .

( Is ), fa, f f:

fa(a i ,ei j)= fa(a i ,ei j)+ f.(a i ,ei j)+ f. (a i ,ei j) (1)

1) fa , a i . fa , - , a i =a = cos (Is,) = cos J . , , a - a . , , . .

fa=K1¢ a 2 + K2¢ a 4 + ...... (2)

K1¢ a 2 K2¢ a 4 . . - ; fa :

fa = K1 sin2J + K2 sin4J +..., (3)

K1 K2 1- 2- . j . , . , Fe, Ni, (a 1, a 2, a 3) Is :

(a 1=cos(Is, [100]); a 2=cos(Is, [010]); a 3=s(Is, [001]). (4)

a 1 , a 2 , a 3, .

[100] . Is fa(a 1, a 2, a 3) . , , (100) a 1 - a 1, a 2 a 3 . (010) (001) a 2 a 3. , fa(a 1, a 2,a 3)

a i ® - a i ( i = 1,2,3) (5)

{110}.

a i ® - a j ( i¹ j = 1,2,3) (6)

a 1 , a 2 , a 3, (5,6), a 21 + a 22 + a 23 , , , .
( a i), a 41 + a 42 + a 43

a 41 + a 42 + a 43 = 1- 2(a 21a 22+a 22a 23+a 21a 23) (7)

(a 21 + a 22 + a 23)2 = 1. ,

a 61 + a 62 + a 63 = 1- 3(a 21a 22+a 22a 23+a 21a 23)+3a 21a 22a 23 (8)

(a 21 + a 22 + a 23)3 = 1.

a i

fa=K1(a 21a 22+a 22a 23+a 21a 23)+K2a 21a 22a 23 (9)

K2a 21a 22a 23, (9), . :

fa=K1(a 21a 22+a 22a 23+a 21a 23) (10)

K1 K2 , .

1>0, (9) [100], [010], [001],
.
1<0, [111], [I11], [1I1], [11I], (9) , .

(9), [100] , 1 , 2, .

, fa Ym l (J ,j ) J - , j - .

fa=S S c mlU ml(J ,j ) , (11)

c ml - , . (11) ( c ml, . . ).

2) f.(ei j ) = ½ [C11(e2xx+ e2yy+ e2zz)] +½ [C44(e2xy+ e2yz+ e2xz)]+

+ C12(exxeyy+ eyyezz+ exxezz ) (12)

3) f.(a i ,ei j ) = B1[(a 21 1/3)exx+(a 22 1/3)eyy+(a 23 1/3)ezz]+

B2[a 1a 2exy+a 2a 3 eyz+a 1a 3exz] , (13)

, a i , ei j- , 1 , 2 , 11 , 44 , 14 .

(a i = const) . , , e(0)i j , f.

f e i j,

f/∂exx= B1(a 21 1/3)+C11e(0)xx + C12(e(0)yy+e(0)zz)=0 ,

f/∂eyy= B1(a 22 1/3)+C11e(0)yy + C12(e(0)zz+e(0)xx)=0 , (14)

f/∂ezz= B1(a 23 1/3)+C11e(0)zz+ C12(e(0)xx+e(0)yy)=0 ,

f/∂ezy= B2a 1a 2+ C44e(0)xy=0,

f/∂eyz= B2a 2a 3+ C44e(0)yz=0, (15)

f/∂exz= B2a 1a 3+ C44e(0)xz=0,

(14), : (∆V/V)0= e(0)xx+ e(0)yy+ e(0)zz ,

.. (∆V/V)0 . (14) (15)

e(0)i i = -[B1/(C11-C12)] [a 2i 1/3], e(0)i j = -(B2/C44)a ia j ; i , j = x, y, z.

(16)

e(0)i j δl/l , β1, β2, β3:

(δl/l)0 = e(0)xx β21+ e(0)yy β22+ e(0)zz β23+ e(0)xy β1 β2+ e(0)yz β2 β3+ e(0)zx β3β1=

= - [B1/(C11-C12)] [a 21 β21+a 22 β22+a 23 β23- 1/3]

(B2/C44)( a 1a 2 β1 β2+a 2a 3 β2 β3+a 3a 1 β3 β1) (17)

δl/l [100] [III]. [100], , (17)

a 1 = β1 = 1, a 2 = a 3 = β2 = β3 = 0,

(δl/l)[100] =λ100 = - 2/3 [B1/(C11-C12)]. (18)

[111]

(δl/l)[111] =λ111 = - 1/3 (B2/C44) , (19)

λ100 λ111 .
(18,19), :

B1=N(∂g1/∂r)r0 , B2= 2Ng1, (20)

- N .
λ100 λ111 g1 :

:

λ100 = -2/3[N/(C11 C12)][∂g1/∂r]r0 ;

λ111 = - 4/3(N/C44)g1

2- - :

λ100 = -16/9[N/(C11 C12)]g1 ; (21)

λ111 = - 16/27[g1+(∂g1/∂r)r0]

3 :

λ100 = -1/3[N/(C11 C12)][6g1 (∂g1/∂r)r0] ;

λ111 = - 2/3[N/C44] [2g1+(∂g1/∂r) r0]

(16), (13) (12) :

f(0).= [B21/(C11 C12)] ∑ (a 2i-1/3)2 - B22/C44 ∑ a 2ia 2j , (i , j=1,2,3)

f(0).= ½ C11 [B21/(C11 C12)2] ∑ (a 2i-1/3)2 + ½ C44 B22∑ a 2ia 2j+

+C12[B21/(C11 C12)2] ∑ (a 2i-1/3)(a 2j-1/3), (i , j=1,2,3)

,

1) ∑a 2 i =1 (i =1,2,3) ;

2) ∑a 4 i =1 2 ∑ a 2 i a 2j (i , j=1,2,3) ;

3) ∑ (a 2i-1/3)2= 2/3 2 ∑ a 2ia 2j (i , j=1,2,3, i>j) ;

4) ∑ (a 2i-1/3)(a 2j-1/3) = ∑ a 2ia 2j 1/3 (i , j=1,2,3, i>j) ;

f(0).= [B21/(C11 C12)][ 2/3 2 ∑ a 2ia 2j] - B22/C44 ∑ a 2ia 2j ,

(i , j=1,2,3, i>j) (22)

f(0).= ½ C11 [B21/(C11 C12)2] [ 2/3 2 ∑ a 2ia 2j] + ½ C44 B22∑ a 2ia 2j+

+C12[B21/(C11 C12)2] ∑ a 2ia 2j 1/3 ,

(i , j=1,2,3,i>j) (23)

(21) (23) (1) (10), (18) (19), :

f =(K1+∆K1)∑ a 2ia 2j (i , j=1,2,3, i>j) (24)

∆K1 ,

∆K1= [2B21/(C11 C12)] + [B22/C44] [C11{B21/(C11 C12)2}]+

+ [½ C44 (B22/C244)]+[ C12 {B21/(C11 C12)2] =

= [B21/(C11 C12)] ½[B22/C44]=9/4 l 2100(C11-C12) 9/2l 2111C44

(25)

(24), , .

2. .

. . , ,
. - .

Kn(T)/Kn(0) = [Is (T)/Is (0)]n(2n+1) , (26)

n . , K1≈ I3s K2≈ I10s. P (26) . - .


, . .

H.=U1+U2+U3 (27)

U1 , , - ; U2 , , ; U3 ( ).

U1 U2 105 . , , , , 102 (, ) 103104 . , , ( s-), (, d- ), , . - U1 U2 . .

U3, , .


,
. , , . , , (Fe, Ni) , (, ). , U3 U1 U2 . , U3, U1 U2.

.
- , , , , () . .

, , , , .


[,
U1 U2 (27)].

- - .
, , - , . , . , , - ,
.

, , :

1) - ,
- (
);

2) ,
( ). , - , - . , , . , .

3.

, Is. , K1.

[110] Vi , , : V0100= V0I00 =V00I0 =V0001 =V00I 0 =V000I =1/6 V, V .

) 180 . , [100] _{010], , [100] [010]. 180 .

,

V0I00= V00I0 =0

I= 2/3 (2) - ½ Is

) 90 . ,
[100] [010], , [001] [001]. V100=V010=V/2,V001=V00I=0

I = (2) - ½ Is

, 90 ,

∆l/l=1/3[(d l/l)[001] (d l/l)[100]]=1/3[(d l/l)[001] (d l/l)[010]] = (1/3)(3/4) l 100 = ¼ l 100

(28)

(d l/l)[001] (a 1 = a 2 = 0, a 3 = 1 ),

(d l/l)[100] (a 2 = a 3 = 0, a 1 = 1 ),

(d l/l)[010] (a 1 = a 3 = 0, a 2 = 1 ),

, (28) , I= (2) - ½ Is, 90 , .
) . 180 90 , , , [110] (001) . J - . I=Is cos J . [110]

(d l/l)[110] = - 1/2l 100 + 3/4l 100 (a 21+a 22) + 3/2l 111a 1a 2 ,

a 1 = cos(p /4-J ), a 2 = sin(p /4-J ) ,

(d l/l)[110] = ¼ l 100 + ¾ l 111 (2cos2J -1) » ¼ l 100 + ¾ l 111 (2(I/Is)2 -1).

, , . . , . . .

.2 . , : 10. . (). , , , . R1 R2 . R3 , R4 . x3,x4 ”

. R5 . R6 , , . - .

, . , , 30x10-6. 5, l 1 10 , 10-4-10-3 . : - 30 / , , .. , , . :

- ;

- ( ) ;

- ( ) .

.

:

,

,

,

.

.

( 1) 3414 0,35 , , ( 2) , .. ( 3). :

1. .

” U , 10 . . Ĕ , 1.

. 2, , .

.

5-10 .

. , 100 ”.

2 , 5-6 .

2 3.

: 1. , .1.2.

2. ,

, () .

3. .

3. .

, .

, .2 .

, :

l =∆l/l=g (∆R/R),

∆R .

R = 200 O ,

g = 2 - .

g =f(H) ( = 100 / = H/J, , J ).

g =f(H) , .

. 2. .

.

.. : , 1971,

.. , , 1981

.. . . , 1974, . 375-380.

.

? ? ?

?

?

, ? ?

K1 ?

. , ?

?

Is (100) , j - Is [001]. j [111].



4 .

 

 

 

! , , , .
. , :