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