Кашурников В.А., Красавин А.В. Современные проблемы физики твердого тела. Часть 2

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ɑɚɫɬɶ 2. ȼɕɋɈɄɈɌȿɆɉȿɊȺɌɍɊɇȺə ɋȼȿɊɏɉɊɈȼɈȾɂɆɈɋɌɖ

Ɂɚɞɚɱɢ

Ɂɚɞɚɱɚ 7.1. Ⱦɨɤɚɡɚɬɶ ɨɩɟɪɚɬɨɪɧɵɟ ɬɨɠɞɟɫɬɜɚ:

)exp(}exp{}exp{ M MM



VVV



iaaaiaaai

iiiiii

)exp(}exp{}exp{ M MM



iaaaiaaai

iiiiii

ɍɤɚɡɚɧɢɟ

: ɩɪɨɞɢɮɮɟɪɟɧɰɢɪɨɜɚɬɶ ɥɟɜɭɸ ɱɚɫɬɶ ɬɨɠɞɟɫɬɜ ɩɨ ɩɟɪɟɦɟɧɧɨɣ

M

Ɂɚɞɚɱɚ 7.2. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɡɚɦɟɧɚ



–t

ɧɟ ɦɟɧɹɟɬ ɫɩɟɤɬɪ ɦɨɞɟɥɢ ɏɚɛɛɚɪ-

ɞɚ, ɟɫɥɢ ɩɟɪɟɫɤɨɤ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɦɟɠɞɭ ɛɥɢɠɚɣɲɢɦɢ ɫɨɫɟɞɹɦɢ.

Ɋɟɲɟɧɢɟ

. Ɋɚɡɨɛɶɟɦ ɭɡɥɵ ɧɚ ɞɜɟ ɩɨɞɪɟɲɟɬɤɢ Ⱥ ɢ Ȼ, ɜɥɨɠɟɧɧɵɟ ɨɞɧɚ ɜ

ɞɪɭɝɭɸ, ɬɚɤ ɱɬɨ ɛɥɢɠɚɣɲɢɦ ɫɨɫɟɞɨɦ ɭɡɥɚ Ⱥ ɨɛɹɡɚɬɟɥɶɧɨ ɹɜɥɹɟɬɫɹ ɭɡɟɥ Ȼ ɢɧɚɨɛɨ-

ɪɨɬ. Ⱦɥɹ ɜɫɟɯ ɭɡɥɨɜ Ⱥ ɫɞɟɥɚɟɦ ɭɧɢɬɚɪɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ

¦¦



aaiU }exp{

ɤɨɬɨɪɨɟ ɦɟɧɹɟɬ ɡɧɚɤ ɨɩɟɪɚɬɨɪɨɜ Ⱥ:.ɗɬɨ ɫɥɟɞɭɟɬ ɢɡ ɨɩɟɪɚ-

ɬɨɪɧɨɝɨ ɬɨɠɞɟɫɬɜɚ:

, ɤɨɬɨɪɨɟ ɧɟɫɥɨɠɧɨ

ɞɨɤɚɡɚɬɶ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɦ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟɦ ɩɨ ɩɚɪɚɦɟɬɪɭ M(ɫɦ. ɡɚɞɚɱɭ 7.1).

ɉɪɢɦɟɧɢɦ ɨɩɟɪɚɬɨɪ U ɤ ɝɚɦɢɥɶɬɨɧɢɚɧɭ ɏɚɛɛɚɪɞɚ:



oo

iiii

aaaa ,

)exp(}exp{}exp{ M MM



VVV



iaaaiaaai

iiiiii

UHU

1

. Ɋɚɫɫɦɨɬɪɢɦ ɩɟɪɟɫɤɨ-

ɤɨɜɵɣ ɱɥɟɧ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɫɟɝɞɚ ɢɦɟɟɦ ɜ ɧɟɦ ɤɨɦɛɢɧɚɰɢɸ a

ɢɥɢ a

+Ȼ

. Ɉɱɟ-

ɜɢɞɧɨ, ɱɬɨ ɭɧɢɬɚɪɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ, ɢɡɦɟɧɹɹ ɡɧɚɤ ɬɨɥɶɤɨ ɨɩɟɪɚɬɨɪɚ Ⱥ, ɢɡɦɟɧɢɬ ɢ

ɜɟɫɶ ɡɧɚɤ ɩɟɪɟɞ ɱɥɟɧɨɦ. Ʌɟɝɤɨ ɩɨɧɹɬɶ, ɱɬɨ ɜ ɤɭɥɨɧɨɜɫɤɨɦ ɱɥɟɧɟ ɱɢɫɥɨ ɢɡɦɟɧɟɧɢɣ

ɡɧɚɤɨɜ ɜɫɟɝɞɚ ɱɟɬɧɨ:

-1

U=U

-1

U=a

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɣ ɱɥɟɧ ɢɧɜɚɪɢɚɧɬɟɧ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɚɤɨɝɨ ɭɧɢ-

ɬɚɪɧɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ. Ⱥ ɬɚɤ ɤɚɤ

11111

UUEUHU

UEUUEUUUUUUHU

\ << <

\ \ \





ɬɨ ɫɩɟɤɬɪ E ɧɟ ɢɡɦɟɧɢɥɫɹ, ɧɨ ɩɪɢ ɷɬɨɦ ɩɟɪɟɫɤɨɤ t ɢɡɦɟɧɢɥɫɹ ɧɚ –t, ɱɬɨ ɢ ɬɪɟɛɨɜɚ-

ɥɨɫɶ ɞɨɤɚɡɚɬɶ.

Ɂɚɞɚɱɚ 7.3. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɝɚɦɢɥɶɬɨɧɢɚɧ ɏɚɛɛɚɪɞɚ (7.3) ɤɨɦɦɭɬɢɪɭɟɬ ɫ

ɨɩɟɪɚɬɨɪɨɦ ɩɨɥɧɨɝɨ ɱɢɫɥɚ ɱɚɫɬɢɰ ɢ ɩɨɥɧɨɣ ɩɪɨɟɤɰɢɢ ɫɩɢɧɚ ɧɚ ɨɫɶ z.

Ɂɚɞɚɱɚ 7.4. ɉɭɫɬɶ N

– ɱɢɫɥɨ ɭɡɥɨɜ; M – ɱɢɫɥɨ ɫɩɢɧɨɜ ɜɜɟɪɯ;

– ɱɢɫɥɨ

ɫɩɢɧɨɜ ɜɧɢɡ; N=M+

– ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɨɤɚɡɚɬɶ ɫɥɟɞɭɸɳɢɟ ɫɨɨɬɧɨɲɟɧɢɹ

ɞɥɹ ɷɧɟɪɝɢɢ ɜ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ:

E(M,

, U)=MU+E(M, N

–

,–U),

E(M,

, U)=

U+E(N –M,

,–U).

ɍɤɚɡɚɧɢɟ: ɩɟɪɟɣɬɢ ɤ ɞɵɪɨɱɧɨɦɭ ɩɪɟɞɫɬɚɜɥɟɧɢɸ ɞɥɹ ɷɥɟɤɬɪɨɧɨɜ ɫɨ ɫɩɢ-

ɧɨɦ ɜɧɢɡ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɢ ɫɨ ɫɩɢɧɨɦ ɜɜɟɪɯ ɜɨ ɜɬɨɪɨɦ.

130

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

Ɂɚɞɚɱɚ 7.5. Ɋɚɫɫɱɢɬɚɬɶ ɱɢɫɥɨ ɜɨɡɦɨɠɧɵɯ ɭɡɟɥɶɧɵɯ ɫɨɫɬɨɹɧɢɣ (ɪɚɡɦɟɪ

ɝɢɥɶɛɟɪɬɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ) ɜ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ ɩɪɢ:

1) ɱɢɫɥɟ ɭɡɥɨɜ N

=12, ɱɢɫɥɟ ɷɥɟɤɬɪɨɧɨɜ ɫɨ ɫɩɢɧɨɦ ɜɜɟɪɯ M=4, ɫɨ ɫɩɢɧɨɦ

ɜɧɢɡ

=3;

2) N

=12, M=3,

=3;

3) N

=8, M=4,

=4;

4) N

=8, M=2,

=3.

Ɂɚɞɚɱɚ 7.6. Ɋɟɲɢɬɶ ɢɧɬɟɝɪɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ Ʌɢɛɚ ɢ ȼɭ ɦɟɬɨɞɨɦ Ɏɭɪɶɟ

ɞɥɹ ɩɥɨɬɧɨɫɬɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ U(p) ɢ V(O) ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ ɨɞɧɨɦɟɪɧɨɣ ɦɨ-

ɞɟɥɢ ɏɚɛɛɚɪɞɚ.

Ɂɚɞɚɱɚ 7.7. ɉɨɥɭɱɢɬɶ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢɟ ɫɨɨɬɧɨɲɟɧɢɹ ɞɥɹ ɪɚɡɧɨɫɬɢ ɯɢɦɢ-

ɱɟɫɤɢɯ ɩɨɬɟɧɰɢɚɥɨɜ P

–P

–

ɜɩɪɟɞɟɥɟUo0 ɢ Uof ɞɥɹ ɨɞɧɨɦɟɪɧɨɣ ɦɨɞɟɥɢ ɏɚɛ-

ɛɚɪɞɚ ɢɫɯɨɞɹ ɢɡ ɬɨɱɧɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ (7.15).

ɍɤɚɡɚɧɢɟ

: ɜ ɨɞɧɨɦ ɩɪɟɞɟɥɶɧɨɦ ɫɥɭɱɚɟ ɛɪɚɬɶ ɢɧɬɟɝɪɚɥɶɧɵɣ ɜɚɪɢɚɧɬ (7.15),

ɜɞɪɭɝɨɦ – ɜɵɪɚɠɟɧɢɟ (7.15) ɜ ɜɢɞɟ ɫɭɦɦɵ.

131

ɑɚɫɬɶ 2. ȼɕɋɈɄɈɌȿɆɉȿɊȺɌɍɊɇȺə ɋȼȿɊɏɉɊɈȼɈȾɂɆɈɋɌɖ

8. t-J-ɦɨɞɟɥɶ. ȼɵɜɨɞ ɢɡ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ. Ɇɨɞɢɮɢɤɚɰɢɢ

ȿɳɟ ɨɞɧɚ ɢɡ ɩɨɩɭɥɹɪɧɵɯ ɦɨɞɢɮɢɤɚɰɢɣ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ –

t-J-ɦɨɞɟɥɶ ɩɨɥɭɱɚɟɬɫɹ ɜ ɩɪɟɞɟɥɟ ɫɢɥɶɧɨɝɨ ɤɭɥɨɧɨɜɫɤɨɝɨ ɨɬɬɚɥɤɢɜɚ-

ɧɢɹ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɝɨɜɨɪɹɬ, ɱɬɨ ɤɚɤ ɪɚɡ ɢɦɟɟɬɫɹ

ɛɨɥɶɲɨɟ ɤɭɥɨɧɨɜɫɤɨɟ ɨɬɬɚɥɤɢɜɚɧɢɟ ɧɚ ɦɟɞɧɨɣ ɨɪɛɢɬɚɥɢ. ɉɨɤɚɠɟɦ ɜ

ɷɬɨɦ ɪɚɡɞɟɥɟ ɧɟ ɬɨɥɶɤɨ ɟɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɣ ɜɵɜɨɞ, ɧɨ ɬɚɤɠɟ ɢ ɷɤ-

ɜɢɜɚɥɟɧɬɧɨɫɬɶ ɚɧɬɢɮɟɪɪɨɦɚɝɧɢɬɧɨɣ ɦɨɞɟɥɢ Ƚɟɣɡɟɧɛɟɪɝɚ ɢ ɦɨɞɟɥɢ

ɏɚɛɛɚɪɞɚ ɜɛɥɢɡɢ ɩɨɥɨɜɢɧɧɨɝɨ ɡɚɩɨɥɧɟɧɢɹ ɩɪɢ U/t>>1.

Ⱦɥɹ ɷɬɨɝɨ ɮɨɪɦɚɥɶɧɨ ɩɟɪɟɩɢɲɟɦ ɝɚɦɢɥɶɬɨɧɢɚɧ ɏɚɛɛɚɪɞɚ,

ɪɚɡɞɟɥɢɜ ɟɝɨ ɧɚ ɧɟɫɤɨɥɶɤɨ ɫɥɚɝɚɟɦɵɯ:

VTTTH

mixhd

 (8.1)

ɝɞɟ

.}..)1()1{(

.},.)1()1{(

.),.(,

chnaannaantT

chnaantT

chnaantTnUnV

jjii

jjiimix

jjiih

jjiid







VV



VV

VV



VV

VV



VV

VV



VV

¦¦

(8.2)

ɑɚɫɬɶ ɝɚɦɢɥɶɬɨɧɢɚɧɚ T

ɨɩɢɫɵɜɚɟɬ ɤɨɪɪɟɥɢɪɨɜɚɧɧɵɟ ɩɟɪɟɫɤɨɤɢ ɫ

ɭɡɥɚ ɧɚ ɭɡɟɥ ɫɨ ɫɩɢɧɨɦ

V, ɤɨɝɞɚ ɭɡɥɵ ɡɚɧɹɬɵ ɷɥɟɤɬɪɨɧɚɦɢ ɫ ɩɪɨɬɢ-

ɜɨɩɨɥɨɠɧɵɦ ɫɩɢɧɨɦ –

V, ɱɥɟɧ T

, ɧɚɨɛɨɪɨɬ, ɨɩɢɫɵɜɚɟɬ ɩɟɪɟɫɤɨɤɢ ɫ

ɭɡɥɚɦɢ, ɧɟ ɡɚɩɨɥɧɟɧɧɵɦɢ ɷɥɟɤɬɪɨɧɚɦɢ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɫɩɢɧɨɦ,

ɚ T

mix

– ɩɪɨɰɟɫɫɵ ɩɟɪɟɫɤɨɤɚ, ɤɨɝɞɚ ɥɢɛɨ ɨɞɢɧ, ɥɢɛɨ ɞɪɭɝɨɣ (ɧɨ ɧɟ

ɞɜɚ ɨɞɧɨɜɪɟɦɟɧɧɨ) ɭɡɥɵ, ɭɱɚɫɬɜɭɸɳɢɟ ɜ ɩɟɪɟɫɤɨɤɟ, ɡɚɧɹɬɵ ɷɥɟɤ-

ɬɪɨɧɨɦ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɫɩɢɧɨɦ.

ȼ ɩɪɟɞɟɥɟ U/t>>1 ɫɚɦɵɣ ɦɚɥɵɣ ɜɤɥɚɞ ɞɚɟɬ ɱɥɟɧ T

, ɬɚɤ ɤɚɤ

ɷɬɨɬ ɩɪɨɰɟɫɫ ɫɜɹɡɚɧ ɫ ɛɨɥɶɲɨɣ ɞɨɛɚɜɤɨɣ ɤ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ~U.

ɉɨɩɪɨɛɭɟɦ ɢɫɤɥɸɱɢɬɶ ɷɬɨ ɫɥɚɝɚɟɦɨɟ.

Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɨɟ ɭɧɢɬɚɪɧɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɝɚɦɢɥɶɬɨ-

ɧɢɚɧɚ, ɧɟ ɦɟɧɹɸɳɟɟ ɟɝɨ ɫɩɟɤɬɪɚ:

)exp(

)exp( iSHiSH

eff



132

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ S ɦɚɥɨ ɩɨ ɩɚɪɚɦɟɬɪɭ t/U, ɢ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟ-

ɧɢɢ:

]

)1(

)1( HSiHiSHiSH

eff

 

. (8.3)

Ɉɩɪɟɞɟɥɢɦ ɷɮɮɟɤɬɢɜɧɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ ɢ ɭɧɢɬɚɪɧɨɟ ɩɪɟɨɛ-

ɪɚɡɨɜɚɧɢɟ. ɂɳɟɦ S, ɭɞɨɜɥɟɬɜɨɪɹɸɳɟɟ ɫɨɨɬɧɨɲɟɧɢɸ

mixhd

TVTTSi  ],[

. (8.4)

Ɉɬɫɸɞɚ

],[

mixhdeff

TSiVTTH  . (8.5)

ɑɥɟɧɨɦ V ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ, ɬɚɤ ɤɚɤ ɩɪɢ ɛɨɥɶɲɢɯ U ɜɟɪɨɹɬɧɨɫɬɶ

ɧɚɯɨɠɞɟɧɢɹ ɧɚ ɨɞɧɨɦ ɭɡɥɟ ɞɜɭɯ ɷɥɟɤɬɪɨɧɨɜ ɦɚɥɚ. ɉɨ ɷɬɨɣ ɠɟ ɩɪɢ-

ɱɢɧɟ ɩɪɟɧɟɛɪɟɠɟɦ ɢ T

. Ɍɨɝɞɚ ɢɦɟɟɦ:

],[

mixheff

TSiTH # . (8.6)

ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ |n> – ɫɨɛɫɬɜɟɧɧɵɟ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɨɩɟɪɚɬɨɪɚ

+V, ɚ H

– ɫɨɛɫɬɜɟɧɧɵɟ ɷɧɟɪɝɢɢ. Ɍɨɝɞɚ ɢɡ (8.4) ɩɨɥɭɱɚɟɦ:

)(

||||||

|)(||)(|

mix

mixnm

mix

hdhd

mTn

mSn

mTnmSnimSni

mTn

mSVTTnimVTTSni

HH

!

! 

! H!H!

! 

! !

(8.7)

ɉɪɨɫɭɦɦɢɪɭɟɦ ɩɨɫɥɟɞɧɟɟ ɜɵɪɚɠɟɧɢɟ ɜ (8.7) ɢ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɩɨɥ-

ɧɨɬɨɣ ɫɨɛɫɬɜɟɧɧɵɯ ɮɭɧɤɰɢɣ, ɬɨɝɞɚ ɞɥɹ S ɩɨɥɭɱɢɦ:

)(

|||

)(

|||||

¦¦



HH

!

! !



HH

!

! !!

mix

mTn

nSnn

mTn

nmmSnn

(8.8)

ȼɛɥɢɡɢ ɩɨɥɨɜɢɧɧɨɝɨ ɡɚɩɨɥɧɟɧɢɹ ɩɪɢ ɛɨɥɶɲɨɦ U ɥɸɛɵɟ ɜɨɡɛɭɠɞɟ-

ɧɢɹ ɫɢɫɬɟɦɵ ɧɚɞ ɨɫɧɨɜɧɵɦ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ t/U ɛɭɞɭɬ H

-H

=rU. Ɉɬ-

ɫɸɞɚ

133

ɑɚɫɬɶ 2. ȼɕɋɈɄɈɌȿɆɉȿɊȺɌɍɊɇȺə ɋȼȿɊɏɉɊɈȼɈȾɂɆɈɋɌɖ

mmTnn

mix

¦¦

!





(8.9)

Ɂɞɟɫɶ

mix

T ɢ – ɱɚɫɬɢ ɨɩɟɪɚɬɨɪɚ T

mix

, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɜɟɥɢɱɟ-

ɧɢɸ (ɭɦɟɧɶɲɟɧɢɸ) ɷɧɟɪɝɢɢ.

Ɉɩɪɟɞɟɥɢɦ ɩɪɚɜɢɥɶɧɨ ɡɧɚɤɢ ɜ ɜɵɪɚɠɟɧɢɢ (8.9). ȼ ɜɵɪɚɠɟ-

ɧɢɢ ɞɥɹ T

mix

(8.2) ɩɟɪɜɨɟ ɫɥɚɝɚɟɦɨɟ [~ ] ɩɨ-

ɧɢɠɚɟɬ ɷɧɟɪɝɢɸ ɧɚ U (ɬ.ɟ. ɫɨɜɩɚɞɚɟɬ ɫ ), ɬɚɤ ɤɚɤ ɷɥɟɤɬɪɨɧ ɭɯɨ-

ɞɢɬ ɫ ɞɜɚɠɞɵ ɡɚɩɨɥɧɟɧɧɨɝɨ ɭɡɥɚ j ɧɚ ɩɭɫɬɨɣ ɭɡɟɥ i. ȼɬɨɪɨɟ ɫɥɚɝɚɟ-

ɦɨɟ [],ɧɚɨɛɨɪɨɬ, ɩɨɜɵɲɚɟɬ ɷɧɟɪɝɢɸ ɧɚ U

(ɬ.ɟ. ɫɨɜɩɚɞɚɟɬ ɫ ). ɇɟɫɥɨɠɧɨ ɞɨɤɚɡɚɬɶ, ɱɬɨ ɷɪɦɢɬɨɜɨ-

ɫɨɩɪɹɠɟɧɧɚɹ ɱɚɫɬɶ T

VV



VV



jjii

naan )1(

mix

)1(

VV



VV



jjii

naan

mix

ɫɨɜɩɚɞɚɟɬ ɫ ɩɟɪɜɨɣ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɡɚɦɟɧɵ

ɢ ɞɨɩɨɥɧɹɟɬ ɞɨ ɩɨɥɧɨɝɨ ɫɭɦɦɢɪɨɜɚɧɢɹ (n<m+n>m=n,m) ɜ

(8.9). ɉɨɷɬɨɦɭ ɜ ɢɬɨɝɟ ɢɡ (8.9) ɢɦɟɟɦ, ɢɫɩɨɥɶɡɭɹ ɩɨɥɧɨɬɭ ɜɨɥɧɨɜɵɯ

ɮɭɧɤɰɢɣ:

}.)1(

)1({

VV



VV

VV



VV





jjii

naan

(8.10)

ɍɱɢɬɵɜɚɹ (8.6), ɧɚɣɞɟɦ ɤɨɦɦɭɬɚɬɨɪ i[S, T

mix

]. ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ

,)1(

VV



VV

VV



VV



jjii

naantB

naantA

(8.11)

ɬɨ ɫɨɝɥɚɫɧɨ (8.2) ɢ (8.10) ɧɚɯɨɞɢɦ:

].)1(,)1([

],[

),(,

¦¦

VV



VV

VV



VV





 

jjii

mix

naannaan

TSi

SBAT

(8.12)

134

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

ȼɜɟɞɟɦ ɬɟɩɟɪɶ ɫɩɢɧɨɜɵɟ ɨɩɟɪɚɬɨɪɵ ɫ ɩɨɥɧɨɣ ɩɪɨɟɤɰɢɟɣ ɫɩɢɧɚ

1/2

ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ

),(

iSSSiSSS

nnSaaSaaS

 





pnn







(8.13)

Ʌɟɝɤɨ ɩɪɨɜɟɪɢɬɶ

ɱɬɨ ɜɜɟɞɟɧɧɵɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɨɩɟɪɚɬɨɪɵ ɹɜɥɹɸɬɫɹ

ɨɛɵɱɧɵɦɢ ɨɩɟɪɚɬɨɪɚɦɢ ɫɩɢɧɚ

1/2,

ɩɨɞɱɢɧɹɸɬɫɹ ɜɫɟɦ ɤɨɦɦɭɬɚɰɢ

ɨɧɧɵɦ ɫɨɨɬɧɨɲɟɧɢɹɦ ɢ ɜɵɪɚɠɚɸɬɫɹ ɱɟɪɟɡ ɦɚɬɪɢɰɵ ɉɚɭɥɢ

: S



1/2V

, S



=1/2V



=1/2V

ɂɫɩɨɥɶɡɭɹ

(8.13),

ɩɨɫɥɟ ɝɪɨɦɨɡɞɤɢɯ

ɧɨ ɞɨɫɬɚɬɨɱɧɨ ɩɪɨɫɬɵɯ

ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɢɡ

(8.12)

ɩɨɥɭɱɚɟɦ



jijimix

nnSS

TSi )

(

],[

. (8.14)

Ɉɤɨɧɱɚɬɟɥɶɧɨ

ɭɱɢɬɵɜɚɹ

(8.6),

ɧɚɯɨɞɢɦ ɷɮɮɟɤɬɢɜɧɵɣ ɝɚɦɢɥɶɬɨɧɢ

ɚɧ

ɤɨɬɨɪɵɣ ɢ ɹɜɥɹɟɬɫɹ ɢɫɤɨɦɵɦ ɝɚɦɢɥɶɬɨɧɢɚɧɨɦ

t-J-

ɦɨɞɟɥɢ

(

.}.)1()1{(





VV



VV

jiji

jjiiJt

nnSS

chnaantH

(8.15)

Ƚɚɦɢɥɶɬɨɧɢɚɧ (8.15) – ɩɪɟɞɟɥɶɧɵɣ ɫɥɭɱɚɣ ɝɚɦɢɥɶɬɨɧɢɚɧɚ

ɏɚɛɛɚɪɞɚ ɩɪɢ ɛɨɥɶɲɢɯ U ɜɛɥɢɡɢ ɩɨɥɨɜɢɧɧɨɝɨ ɡɚɩɨɥɧɟɧɢɹ. Ɋɨɜɧɨ

ɩɪɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ, ɤɨɝɞɚ ɧɚ ɤɚɠɞɵɣ ɭɡɟɥ ɩɪɢɯɨɞɢɬɫɹ

ɨɞɢɧ ɷɥɟɤɬɪɨɧ, ɩɟɪɟɫɤɨɤɨɜɵɣ ɱɥɟɧ ɡɚɧɭɥɹɟɬɫɹ, ɢ ɦɨɞɟɥɶ (8.15) ɫɬɚ-

ɧɨɜɢɬɫɹ ɚɧɬɢɮɟɪɪɨɦɚɝɧɢɬɧɨɣ ɦɨɞɟɥɶɸ Ƚɟɣɡɟɧɛɟɪɝɚ (ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ

ɧɟɫɭɳɟɫɬɜɟɧɧɨɣ ɩɨɫɬɨɹɧɧɨɣ):



jieff

H )

(

(8.16)

ɫ ɷɮɮɟɤɬɢɜɧɵɦ ɨɛɦɟɧɧɵɦ ɢɧɬɟɝɪɚɥɨɦ J=2t

/U. Ɂɚɦɟɬɢɦ, ɱɬɨ ɜɟɥɢ-

ɱɢɧɚ J~0.1–0.5 ɷȼ (ɬɚɤ ɤɚɤ t~1 ɷȼ, U~3–10 ɷȼ), ɱɬɨ ɜɩɨɥɧɟ ɫɨɝɥɚɫɭ-

ɟɬɫɹ ɫ ɨɰɟɧɤɚɦɢ ɨɛɦɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɚɧɬɢɮɟɪɪɨ-

ɦɚɝɧɢɬɧɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ Ƚɟɣɡɟɧɛɟɪɝɚ ɹɜɥɹɟɬɫɹ ɩɪɟɞɟɥɶɧɵɦ ɫɥɭɱɚ-

ɟɦ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ ɩɪɢ ɛɨɥɶɲɢɯ U ɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ.

135

ɑɚɫɬɶ 2. ȼɕɋɈɄɈɌȿɆɉȿɊȺɌɍɊɇȺə ɋȼȿɊɏɉɊɈȼɈȾɂɆɈɋɌɖ

ɉɨɫɥɟɞɧɟɟ ɜɵɪɚɠɟɧɢɟ (8.16) ɜ ɧɟɫɤɨɥɶɤɨ ɛɨɥɟɟ ɭɩɪɨɳɟɧɧɨɦ ɩɨɞɯɨ-

ɞɟ ɩɨɥɭɱɟɧɨ ɜ ɡɚɞɚɱɟ ɜ ɤɨɧɰɟ ɩɚɪɚɝɪɚɮɚ.

ȼɨɡɜɪɚɳɚɹɫɶ ɤ t-J-ɦɨɞɟɥɢ (8.15), ɡɚɦɟɬɢɦ, ɱɬɨ ɨɩɟɪɚɬɨɪɵ ɜ

ɧɟɣ ɞɟɣɫɬɜɭɸɬ ɜ ɨɝɪɚɧɢɱɟɧɧɨɦ ɝɢɥɶɛɟɪɬɨɜɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɫ ɢɫ-

ɤɥɸɱɟɧɧɵɦɢ ɞɜɭɯɱɚɫɬɢɱɧɵɦ ɫɨɫɬɨɹɧɢɹɦɢ, ɬɚɤ ɱɬɨ ɩɟɪɟɫɤɨɤɢ ɫ ɭɡɥɚ

ɧɚ ɭɡɟɥ ɜɫɟ ɩɟɪɟɧɨɪɦɢɪɨɜɚɧɵ ɤɚɤ

)1(

, VVV

o

iii

naa

. Ɍɚɤɢɦ ɨɛɪɚ-

ɡɨɦ, ɷɥɟɤɬɪɨɧɵ ɫɨ ɫɩɢɧɨɦ ɜɜɟɪɯ ɩɪɢ ɩɟɪɟɞɜɢɠɟɧɢɢ ɩɨ ɪɟɲɟɬɤɟ ɱɭɜ-

ɫɬɜɭɸɬ ɷɥɟɤɬɪɨɧɵ ɫɨ ɫɩɢɧɨɦ ɜɧɢɡ, ɬɚɤ ɱɬɨ ɩɟɪɟɫɤɨɤ ɧɟɜɨɡɦɨɠɟɧ,

ɟɫɥɢ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ ɫɩɢɧ ɡɚɧɹɬ. Ɏɚɤɬɢɱɟɫɤɢ, ɫɢɥɶɧɵɟ ɤɨɪɪɟɥɹ-

ɰɢɢ ɢɫɯɨɞɧɨɣ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ ɜ ɷɬɨɣ ɦɨɞɟɥɢ ɭɱɬɟɧɵ ɬɚɤɢɦ ɡɚɩɪɟ-

ɬɨɦ ɧɚ ɞɜɭɤɪɚɬɧɨɟ (ɫ ɪɚɡɧɵɦɢ ɫɩɢɧɚɦɢ) ɡɚɩɨɥɧɟɧɢɟ ɭɡɥɨɜ.

ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɵɣ ɭɱɟɬ ɫɢɥɶɧɵɯ ɤɨɪɪɟɥɹɰɢɣ

, ɜɨɡɦɨɠɧɨɫɬɶ

ɨɩɢɫɚɧɢɹ ɞɜɢɠɟɧɢɹ ɞɵɪɨɤ ɧɚ ɮɨɧɟ ȺɎɆ-ɭɩɨɪɹɞɨɱɟɧɢɹ, ɚ ɝɥɚɜɧɨɟ –

ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɫɬɨɬɚ, ɨɩɪɟɞɟɥɢɥɢ ɨɱɟɧɶ ɛɨɥɶɲɨɟ ɪɚɫɩɪɨɫɬɪɚɧɟ-

ɧɢɟ ɷɬɨɣ ɦɨɞɟɥɢ ɜ ɬɟɨɪɢɢ ȼɌɋɉ. ɉɪɢ ɷɬɨɦ t-J-ɦɨɞɟɥɶ ɜ ɰɟɥɨɦ ɫɬɚɥɚ

ɤɚɤ ɛɵ ɲɢɪɟ ɫɜɨɟɣ ɢɫɯɨɞɧɨɣ ɦɨɞɟɥɢ (ɏɚɛɛɚɪɞɚ), ɬɚɤ ɱɬɨ ɩɚɪɚɦɟɬɪɵ

t ɢ J ɩɪɢ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɢ ɱɢɫɥɟɧɧɵɯ ɪɚɫɱɟɬɚɯ ɧɟ ɫɱɢɬɚɸɬɫɹ ɫɜɹɡɚɧ-

ɧɵɦɢ ɦɟɠɞɭ ɫɨɛɨɣ ɩɨ ɜɟɥɢɱɢɧɟ.

ɋɭɳɟɫɬɜɭɸɬ ɦɨɞɢɮɢɤɚɰɢɢ ɷɬɨɣ ɦɨɞɟɥɢ, ɧɚɩɪɢɦɟɪ

-ɦɨɞɟɥɶ, ɜ ɤɨɬɨɪɨɣ ɞɨɛɚɜɥɹɟɬɫɹ ɱɥɟɧ ɫ

Jtt 

 t

, ɨɬɜɟɱɚɸɳɢɣ ɡɚ

ɩɟɪɟɫɤɨɤɢ ɱɟɪɟɡ ɭɡɟɥ ɧɚ ɫɥɟɞɭɸɳɢɣ, ɫɨɩɪɨɜɨɠɞɚɟɦɵɟ ɩɟɪɟɜɨɪɨɬɨɦ

ɫɩɢɧɚ, ɢɞɪ. ɗɬɨ ɫɥɚɝɚɟɦɨɟ ɩɨɹɜɥɹɟɬɫɹ ɩɪɢ ɭɱɟɬɟ ɩɨ ɬɟɨɪɢɢ ɜɨɡɦɭ-

ɳɟɧɢɣ ɩɨ ɩɚɪɚɦɟɬɪɭ t/U ɫɥɟɞɭɸɳɢɯ ɱɥɟɧɨɜ ɩɪɢ ɜɵɜɨɞɟ ɢɡ ɦɨɞɟɥɢ

ɏɚɛɛɚɪɞɚ. Ɂɚɱɚɫɬɭɸ ɬɚɤɚɹ ɦɨɞɟɥɶ ɛɨɥɟɟ ɬɨɱɧɨ ɨɩɢɫɵɜɚɟɬ ɧɢɡɤɨɥɟ-

ɠɚɳɢɟ ɜɨɡɛɭɠɞɟɧɢɹ.

Ɂɚɞɚɱɢ

Ɂɚɞɚɱɚ 8.1. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɜɜɟɞɟɧɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹɦɢ (8.3) ɨɩɟɪɚɬɨɪɵ ɹɜ-

ɥɹɸɬɫɹ ɫɩɢɧɨɜɵɦɢ ɨɩɟɪɚɬɨɪɚɦɢ S=1/2.

Ɂɚɞɚɱɚ 8.2. ȼɵɪɚɡɢɬɶ ɤɨɦɦɭɬɚɬɨɪ

(8.2) ɱɟɪɟɡ ɫɩɢɧɨɜɵɟ ɨɩɟɪɚɬɨ-

ɪɵ, ɬ.ɟ. ɩɨɥɭɱɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (8.4).

],[

mix

TSi

Ɂɚɞɚɱɚ 8.3. ɉɨɥɭɱɢɬɶ ɪɨɜɧɨ ɩɪɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ ɡɨɧɵ ɢɡ ɦɨɞɟɥɢ

ɏɚɛɛɚɪɞɚ ɚɧɬɢɮɟɪɪɨɦɚɝɧɢɬɧɭɸ ɦɨɞɟɥɶ Ƚɟɣɡɟɧɛɟɪɝɚ ɩɪɢ t/U<<1.

Ɋɟɲɟɧɢɟ.

Ɋɨɜɧɨ ɩɪɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ, ɫɨɝɥɚɫɧɨ ɡɨɧɧɨɣ ɤɚɪɬɢɧɟ

(ɫɦ. ɪɢɫ. 7.1), ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ (ɧɚɡɨɜɟɦ ɟɝɨ |D>, ɧɢɠɧɹɹ ɯɚɛɛɚɪɞɨɜɫɤɚɹ ɡɨɧɚ)

ɨɬɞɟɥɟɧɨ ɨɬ ɜɨɡɛɭɠɞɟɧɧɵɯ (|E>, ɜ ɜɟɪɯɧɟɣ ɯɚɛɛɚɪɞɨɜɫɤɨɣ ɡɨɧɟ) ɤɨɧɟɱɧɨɣ ɳɟɥɶɸ

136

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

~U. ɗɮɮɟɤɬɢɜɧɵɣ ɝɚɦɢɥɶɬɨɧɢɚɧ ɛɭɞɟɦ ɫɬɪɨɢɬɶ, ɨɬɬɚɥɤɢɜɚɹɫɶ ɨɬ “ɧɭɥɟɜɨɝɨ”, ɤɢɧɟ-

ɬɢɱɟɫɤɨɝɨ ɱɥɟɧɚ ɦɨɞɟɥɢ ɏɚɛɛɚɪɞɚ, ɨɩɢɫɵɜɚɸɳɟɝɨ ɧɨɫɢɬɟɥɢ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ,

ɬɚɤ ɱɬɨ ɩɨɥɧɚɹ ɦɨɞɟɥɶ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:



 

aatHHHH

Ɂɞɟɫɶ

– ɩɨɩɪɚɜɤɚ, ɫɜɹɡɚɧɧɚɹ ɫ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɢ ɡɚɛɪɨɫɨɦ ɜ ɜɟɪɯɧɸɸ ɯɚɛɛɚɪ-

ɞɨɜɫɤɭɸ ɡɨɧɭ. ɗɬɭ ɱɚɫɬɶ ɝɚɦɢɥɶɬɨɧɢɚɧɚ ɩɨɥɭɱɢɦ, ɪɚɡɥɨɠɢɜɲɢɫɶ ɞɨ ɜɬɨɪɨɝɨ ɩɨ-

ɪɹɞɤɚ ɩɨ ɬɟɨɪɢɢ ɜɨɡɦɭɳɟɧɢɣ:

DzE

EEDD

DD

ȼɫɟ ɜɨɡɛɭɠɞɟɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɨɬɞɟɥɟɧɵ ɨɬ ɨɫɧɨɜɧɨɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɳɟɥɶɸ ~U,

ɩɨɷɬɨɦɭ ɦɨɠɧɨ ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ ɩɨɥɚɝɚɬɶ

UHH #DDEE

Ɉɬɫɸɞɚ ɢɦɟɟɦ:

DD

DE DE

¦¦

EDzE

ɍɱɬɟɦ ɩɨɥɧɨɬɭ ɢ ɨɪɬɨɧɨɪɦɢɪɨɜɚɧɧɨɫɬɶ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ, ɬ.ɟ.:

¦¦

DEED DE

HHH

1 EE

Ɉɬɤɭɞɚ ɧɟɦɟɞɥɟɧɧɨ ɫɥɟɞɭɟɬ

DD DE

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɧɚɯɨɞɢɦ:

DDDD

ɇɨ ɜ ɫɥɭɱɚɟ ɢɡɨɥɹɬɨɪɚ, ɪɨɜɧɨ ɩɪɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ ɡɨɧ, ɤɨɝɞɚ ɭɪɨɜɟɧɶ

Ɏɟɪɦɢ ɜ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɳɟɥɢ, ɫɪɟɞɧɹɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɪɚɜɧɚ ɧɭɥɸ, ɬ.ɟ.

{DD H

ɉɨɷɬɨɦɭ

DD

ɢɥɢ, ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ:





jiij

iiii

aaaa

ȼ ɩɨɫɥɟɞɧɟɦ ɜɵɪɚɠɟɧɢɢ ɢɦɟɸɬɫɹ ɞɜɚ ɫɥɚɝɚɟɦɵɯ, ɭ ɤɨɬɨɪɵɯ ɷɧɟɪɝɢɹ ɦɢɧɢɦɚɥɶɧɚ.

ɗɬɨ, ɜɨ-ɩɟɪɜɵɯ, ɞɢɚɝɨɧɚɥɶɧɵɣ ɱɥɟɧ

i=j, i'=j', ɬ.ɟ.

137

ɑɚɫɬɶ 2. ȼɕɋɈɄɈɌȿɆɉȿɊȺɌɍɊɇȺə ɋȼȿɊɏɉɊɈȼɈȾɂɆɈɋɌɖ

 G

ɢ, ɜɨ-ɜɬɨɪɵɯ, ɫɥɚɝɚɟɦɨɟ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɫɭɩɟɪɨɛɦɟɧ ɬɢɩɚ

j'V'ĺiV, jVĺi'V', ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɬɚɤ:







 G

ijjiijjiijjiijji

ijijjiji

aaaaaaaaaaaaaaaa

aaaaaaaa

Ɇɨɠɧɨ ɩɨɤɚɡɚɬɶ, ɱɬɨ ɨɫɬɚɥɶɧɵɟ ɫɥɚɝɚɟɦɵɟ ɢɡ-ɡɚ ɩɨɹɜɥɟɧɢɹ ɞɜɨɣɧɵɯ ɡɚɩɨɥɧɟɧɢɣ ɧɚ

ɭɡɥɟ ɫ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦɢ ɫɩɢɧɚɦɢ ɬɭɬ ɠɟ ɭɜɟɥɢɱɢɜɚɸɬ ɷɧɟɪɝɢɸ ɧɚ ɜɟɥɢɱɢɧɭ ~U.

ȼɜɟɞɟɦ ɫɩɢɧɨɜɵɟ ɨɩɟɪɚɬɨɪɵ ɩɨ ɫɥɟɞɭɸɳɢɦ ɡɚɤɨɧɚɦ:











iiii

aaaaSaaSaaS

;;

;

iSSSiSSS

 



;

 



 

iii

SSSS

;

Ⱦɚɥɟɟ, ɩɨɞɫɬɚɜɥɹɹ ɷɬɢ ɫɨɨɬɧɨɲɟɧɢɹ ɜ

, ɩɨɫɥɟ ɩɪɨɫɬɵɯ, ɧɨ ɝɪɨɦɨɡɞɤɢɯ ɩɪɟɨɛɪɚ-

ɡɨɜɚɧɢɣ (ɩɨɥɟɡɧɨ ɱɢɬɚɬɟɥɸ ɭɛɟɞɢɬɶɫɹ ɜ ɫɩɪɚɜɟɞɥɢɜɨɫɬɢ ɩɨɥɭɱɟɧɧɨɝɨ ɧɢɠɟ ɨɬɜɟɬɚ),

ɢ ɤɨɦɛɢɧɢɪɭɹ ɫ

, ɩɨɥɭɱɚɟɦ ɢɫɤɨɦɵɣ ɨɬɜɟɬ (ɬɨɱɧɨ ɩɪɢ ɩɨɥɨɜɢɧɧɨɦ ɡɚɩɨɥɧɟɧɢɢ):

 

jiji

nnnnnSS

;)

(

138

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

9. Ɇɧɨɝɨɡɨɧɧɚɹ ɦɨɞɟɥɶ ɗɦɟɪɢ ɞɥɹ ɩɥɨɫɤɨɫɬɢ CuO

Ʉɚɤ ɦɵ ɨɬɦɟɱɚɥɢ ɪɚɧɟɟ, ɤ ɧɚɫɬɨɹɳɟɦɭ ɦɨɦɟɧɬɭ ɨɛɳɟɩɪɢɧɹ-

ɬɨ, ɱɬɨ ɡɚ ɬɪɚɧɫɩɨɪɬɧɵɟ ɢ ɫɜɟɪɯɩɪɨɜɨɞɹɳɢɟ ɫɜɨɣɫɬɜɚ ȼɌɋɉ ɨɬɜɟ-

ɱɚɸɬ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɷɥɟɤɬɪɨɧɵ ɧɚ ɜɧɟɲɧɢɯ ɨɛɨɥɨɱɤɚɯ ɚɬɨɦɨɜ

ɦɟɞɢ ɢ ɤɢɫɥɨɪɨɞɚ. ɉɪɢ ɷɬɨɦ d-ɨɪɛɢɬɚɥɶ ɢɨɧɚ ɦɟɞɢ Cu

, ɷɥɟɤɬɪɨɧɵ

ɤɨɬɨɪɨɣ ɜ ɨɫɧɨɜɧɨɦ ɭɱɚɫɬɜɭɸɬ ɜ ɩɟɪɟɧɨɫɟ ɡɚɪɹɞɚ, ɢɦɟɟɬ -ɫɢɦ-

ɦɟɬɪɢɸ. Ɉɧɚ ɝɢɛɪɢɞɢɡɭɟɬɫɹ ɫ ɞɜɭɦɹ ɪ-ɨɪɛɢɬɚɥɹɦɢ (p



ɢ p

) ɢɨɧɚ O

2–

ȼ ɨɬɫɭɬɫɬɜɢɟ ɞɨɩɢɪɨɜɚɧɢɹ (ɨɞɧɚ ɞɵɪɤɚ ɧɚ ɤɚɠɞɭɸ ɷɥɟɦɟɧɬɚɪɧɭɸ

ɹɱɟɣɤɭ ɜ ɩɥɨɫɤɨɫɬɢ CuO

) ȼɌɋɉ ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɸɬɫɹ ɦɨɞɟɥɶɸ

ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɫɨ ɫɩɢɧɨɦ 1/2, ɱɬɨ ɨɬɪɚɠɚɟɬ

ɚɧɬɢɮɟɪɪɨɦɚɝɧɟɬɢɡɦ ɷɬɢɯ ɫɨɟɞɢɧɟɧɢɣ. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɞɜɢɠɟɧɢɹ

ɞɵɪɨɤ ɜ ɩɥɨɫɤɨɫɬɢ CuO

ɫ ɭɱɟɬɨɦ ɜɫɟɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɷɥɟɤɬɪɨɧɧɨɣ

ɫɬɪɭɤɬɭɪɵ ȼɌɋɉ, ɪɚɡɥɢɱɢɹ ɚɬɨɦɧɵɯ ɭɪɨɜɧɟɣ ɧɚ ɦɟɞɧɵɯ ɢ ɤɢɫɥɨ-

ɪɨɞɧɵɯ ɭɡɥɚɯ, ɚ ɬɚɤɠɟ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɧɚ ɭɡɥɚɯ ɦɟɞɢ,

ɤɢɫɥɨɪɨɞɚ ɢ ɦɟɠɞɭ ɧɢɦɢ, ɗɦɟɪɢ ɩɪɟɞɥɨɠɢɥ ɫɜɨɸ ɦɨɞɟɥɶ [86]. Ɉɧɚ

ɩɪɚɜɢɥɶɧɨ ɨɩɢɫɵɜɚɟɬ ɬɨɩɨɥɨɝɢɸ ɩɥɨɫɤɨɫɬɢ CuO

, ɬ.ɟ. ɭɱɢɬɵɜɚɟɬ,

ɱɬɨ ɛɥɢɠɚɣɲɢɦɢ ɫɨɫɟɞɹɦɢ ɚɬɨɦɨɜ ɦɟɞɢ ɹɜɥɹɸɬɫɹ ɱɟɬɵɪɟ ɚɬɨɦɚ

ɤɢɫɥɨɪɨɞɚ ɢ ɧɚɨɛɨɪɨɬ, ɞɜɢɠɟɧɢɟ ɧɨɫɢɬɟɥɟɣ ɫ ɤɢɫɥɨɪɨɞɧɵɯ ɨɪɛɢɬɚ-

ɥɟɣ ɧɚ ɦɟɞɧɵɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɚ ɞɜɚ ɛɥɢɠɚɣɲɢɯ ɦɟɞɧɵɯ ɭɡɥɚ (ɫɦ.

ɪɢɫ. 3.4). ɗɦɟɪɢ ɩɪɟɞɥɨɠɢɥ ɨɬɫɱɢɬɵɜɚɬɶ ɫɨɫɬɨɹɧɢɹ ɨɬ ɩɨɥɧɨɫɬɶɸ

ɡɚɩɨɥɧɟɧɧɵɯ p- ɢ d-ɨɪɛɢɬɚɥɟɣ, ɬ.ɟ. ɨɩɢɫɵɜɚɬɶ ɜɫɟ ɞɵɪɨɱɧɵɦɢ ɧɨɫɢ-

ɬɟɥɹɦɢ.

Ƚɚɦɢɥɶɬɨɧɢɚɧ ɞɜɭɦɟɪɧɨɣ

ɦɧɨɝɨɡɨɧɧɨɣ ɦɨɞɟɥɢ ɗɦɟɪɢ ɜ ɞɵ-

ɪɨɱɧɨɦ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:





¦¦¦

¦¦

V!

pnpn

V!





H

kiE

nnVnnUnnU

nchpdtH

(9.1)

ɝɞɟ ɢ – ɨɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ ɞɵɪɤɢ ɜ ɫɨɫɬɨɹɧɢɹɯ ɢ p





ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; <ik> ɨɡɧɚɱɚɟɬ ɫɭɦɦɢɪɨɜɚɧɢɟ ɩɨ ɛɥɢɠɚɣɲɢɦ

ɫɨɫɟɞɹɦ; ɢɧɞɟɤɫ i ɨɬɧɨɫɢɬɫɹ ɤ ɭɡɥɚɦ ɦɟɞɢ, ɢɧɞɟɤɫ k – ɤ ɭɡɥɚɦ ɤɢɫɥɨ-

ɪɨɞɚ;–ɱɢɫɥɚ ɡɚɩɨɥɧɟɧɢɹ ɦɟɞɧɵɯ ɢ ɤɢɫɥɨ-



VVV



kkkiii

ppnddn ,

139

Кашурников В.А., Красавин А.В. Современные проблемы физики твердого тела. Часть 2 - Высокотемпературная сверхпроводимость

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