W(q, t) = Ȍ(q, t) Ȍ*(q, t), |
(2.55) |
ɝɞɟ ɡɜɟɡɞɨɱɤɨɣ ɨɛɨɡɧɚɱɚɟɬɫɹ ɤɨɦɩɥɟɤɫɧɨ-ɫɨɩɪɹɠɟɧɧɨɟ |
ɡɧɚɱɟɧɢɟ |
Ȍ-ɮɭɧɤɰɢɢ. |
|
Ɏɭɧɤɰɢɹ Ȍ(q1, …, qn, t) ɧɚɡɵɜɚɟɬɫɹ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ. Ɉɫ-
ɧɨɜɧɵɦ ɟɟ ɫɜɨɣɫɬɜɨɦ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɤɜɚɞɪɚɬ ɟɟ ɦɨɞɭɥɹ ɪɚɜɟɧ ɩɥɨɬɧɨɫɬɢ ɜɟɪɨɹɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɜ ɫɢɫɬɟɦɟ. Ɂɧɚɧɢɟ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɩɨɡɜɨɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɥɸɛɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɤɨɨɪɞɢɧɚɬ. Ⱦɪɭɝɢɦ ɜɚɠɧɵɦ ɫɜɨɣɫɬɜɨɦ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɹɜɥɹɟɬɫɹ ɩɪɢɧɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ, ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: ɟɫɥɢ ɫɢɫɬɟɦɚ ɦɨɠɟɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɫɨɫɬɨɹɧɢɢ, ɨɩɢɫɵɜɚɟɦɨɦ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ Ȍ1(q, t), ɢ ɜ ɫɨɫɬɨɹɧɢɢ, ɨɩɢɫɵɜɚɟɦɨɦ ɮɭɧɤɰɢɟɣ Ȍ2(q, t), ɬɨ
ɥɸɛɚɹ ɥɢɧɟɣɧɚɹ ɤɨɦɛɢɧɚɰɢɹ ɷɬɢɯ ɮɭɧɤɰɢɣ ɬɚɤɠɟ ɨɩɢɫɵɜɚɟɬ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ.
ɉɨɞɨɛɧɨ ɬɨɦɭ, ɤɚɤ ɜ ɤɥɚɫɫɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɟ ɢɡɦɟɧɟɧɢɟ ɤɨɨɪɞɢɧɚɬ, ɨɩɢɫɵɜɚɸɳɢɯ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ, ɩɨɞɱɢɧɹɟɬɫɹ ɧɶɸɬɨɧɨɜɫɤɨɦɭ ɭɪɚɜɧɟɧɢɸ ɞɜɢɠɟɧɢɹ, ɜ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɟ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ, ɨɩɢɫɵɜɚɸɳɚɹ ɫɨɫɬɨɹɧɢɟ ɚɬɨɦɧɨɣ ɫɢɫɬɟɦɵ, ɬɚɤɠɟ ɩɨɞɱɢɧɹɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɞɜɢɠɟɧɢɹ – ɭɪɚɜɧɟɧɢɸ ɒɪɟɞɢɧɝɟɪɚ:
ih w\ |
= ƨȌ, |
(2.56) |
wt |
|
|
ɝɞɟ ƨ – ɨɩɟɪɚɬɨɪ Ƚɚɦɢɥɶɬɨɧɚ (ɝɚɦɢɥɶɬɨɧɢɚɧ), ɢɦɟɸɳɢɣ ɨɫɨɛɵɣ ɜɢɞ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ
|
=2 |
|
§ |
w2 |
|
w2 |
|
w2 · |
=2 |
|
|
ƨ = |
|
¦¨ |
|
|
|
|
|
¸ + V(q) = |
|
¦'i + V(q), (2.57) |
|
2m |
|
wy2 |
wz2 |
2m |
|||||||
|
i |
¨ wx2 |
|
|
¸ |
i |
|||||
|
|
|
© |
i |
|
i |
|
i |
¹ |
|
|
ɝɞɟ V(q) – ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ.
ȼ ɚɬɨɦɧɵɯ ɫɢɫɬɟɦɚɯ ɛɨɥɶɲɭɸ ɪɨɥɶ ɢɝɪɚɸɬ ɬɚɤ ɧɚɡɵɜɚɟɦɵɟ ɫɬɚɰɢɨɧɚɪɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɞɥɹ ɤɨɬɨɪɵɯ ɩɥɨɬɧɨɫɬɶ ɜɟɪɨɹɬɧɨɫɬɢ (2.55) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ. Ɍɨɝɞɚ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ ɞɜɭɯ ɫɨɦɧɨɠɢɬɟɥɟɣ, ɨɞɢɧ ɢɡ ɤɨɬɨɪɵɯ – Ȍ0(q) – ɧɟ
ɡɚɜɢɫɢɬ ɨɬ ɜɪɟɦɟɧɢ, ɚ ɞɪɭɝɨɣ ɹɜɥɹɟɬɫɹ ɩɟɪɢɨɞɢɱɟɫɤɨɣ ɮɭɧɤɰɢɟɣ t:
§ |
|
i |
· |
|
|
|
Ȍ(q, t) = exp ¨ |
|
|
Et ¸ |
Ȍ0(q), |
(2.58) |
|
h |
||||||
© |
|
¹ |
|
|
ɝɞɟ ȿ – ɩɨɫɬɨɹɧɧɨɟ ɱɢɫɥɨ.
51
ɉɨɞɫɬɚɜɥɹɹ (2.58) ɜ (2.56) ɢ ɪɟɲɚɹ ɭɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ, ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ, ɱɬɨ ɜɟɥɢɱɢɧɚ ȿ ɢɦɟɟɬ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɷɧɟɪɝɢɢ, ɤɨɬɨɪɨɣ ɨɛɥɚɞɚɟɬ ɫɢɫɬɟɦɚ ɜ ɡɚɞɚɧɧɨɦ ɫɬɚɰɢɨɧɚɪɧɨɦ ɫɨɫɬɨɹɧɢɢ q. Ⱦɥɹ ɤɨɧɤɪɟɬɧɨɣ ɫɢɫɬɟɦɵ ɱɚɫɬɢɰ ɩɪɢ ɞɚɧɧɨɦ ɜɢɞɟ ɨɩɟɪɚɬɨɪɚ Ƚɚɦɢɥɶɬɨɧɚ ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ ɜɨɡɦɨɠɧɨ ɥɢɲɶ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɞɢɫɤɪɟɬɧɵɯ ɡɧɚɱɟɧɢɹɯ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ. Ɋɚɡɪɟɲɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ȿ ɧɚɡɵɜɚɸɬɫɹ ɫɨɛɫɬɜɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ – ɫɨɛɫɬɜɟɧɧɵɦɢ ɮɭɧɤɰɢɹɦɢ.
Ɇɨɥɟɤɭɥɚ ɜɨɞɨɪɨɞɚ ɢ ɨɛɦɟɧɧɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ
ȼ 1927 ɝ. Ƚɚɣɬɥɟɪ ɢ Ʌɨɧɞɨɧ ɩɪɨɜɟɥɢ ɤɜɚɧɬɨɜɨ-ɦɟɯɚɧɢɱɟɫɤɨɟ ɪɚɫɫɦɨɬɪɟɧɢɟ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɢ ɭɫɬɚɧɨɜɢɥɢ, ɱɬɨ ɟɟ ɷɧɟɪɝɢɹ ɡɚɜɢɫɢɬ ɨɬ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɞɜɭɯ ɷɥɟɤɬɪɨɧɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɫɨɫɬɚɜ ɦɨɥɟɤɭɥɵ. Ɇɨɥɟɤɭɥɚ ɜɨɞɨɪɨɞɚ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɹɞɟɪ ɢ ɞɜɭɯ ɷɥɟɤɬɪɨɧɨɜ. Ɋɚɫɩɨɥɨɠɟɧɢɟ ɹɞɟɪ ɢ ɷɥɟɤɬɪɨɧɨɜ ɫ ɨɛɨɡɧɚɱɟɧɢɟɦ ɪɚɫɫɬɨɹɧɢɣ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɪɚɫɫɦɨɬɪɟɧɢɹ, ɫɯɟɦɚɬɢɱɧɨ ɩɪɟɞɫɬɚɜɥɟɧɨ ɧɚ ɪɢɫ. 2.10.
Ɋɢɫ. 2.10. Ɉɛɨɡɧɚɱɟɧɢɟ ɪɚɫɫɬɨɹɧɢɣ ɜ ɦɨɥɟɤɭɥɟ ɜɨɞɨɪɨɞɚ: a, b – ɹɞɪɚ; 1, 2 – ɷɥɟɤɬɪɨɧɵ
Ɂɚɞɚɱɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɹɞɪɚɦɢ R.
ɍɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ ɞɥɹ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɢɦɟɟɬ ɜɢɞ
' |
' |
2 |
|
2m |
ªE U R, r, r |
, r |
, r |
, r |
º |
½ |
< 0, |
(2.59) |
|||
® |
1 |
|
|
= |
2 |
¬ |
a1 |
a2 |
b1 |
b2 |
¼ |
¾ |
|
|
|
¯ |
|
|
|
|
|
|
|
|
|
|
|
¿ |
|
|
|
ɝɞɟ m, ȿ ɢ U – ɦɚɫɫɚ, ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɢ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɱɚɫɬɢɰɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ɚ '1 ɢ '2 – ɨɩɟɪɚɬɨɪɵ Ʌɚɩɥɚɫɚ:
52
|
|
|
' |
|
= |
|
w2 |
+ |
|
w2 |
|
+ |
w2 |
; ' |
2 |
= |
|
w2 |
+ |
|
w2 |
|
+ |
|
w2 |
; |
|
||||||||||
|
|
|
|
wx2 |
|
wy2 |
wz2 |
|
wx2 |
wy2 |
|
|
wz2 |
|
|||||||||||||||||||||||
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||
|
|
|
|
|
|
|
|
|
1 |
|
1 |
|
|
1 |
|
|
|
|
|
|
2 |
|
|
|
2 |
|
|
2 |
|
|
|||||||
U = |
e2 |
|
+ |
|
e2 |
|
– |
|
e2 |
|
– |
|
e2 |
|
|
– |
|
e2 |
|
|
– |
|
e2 |
. (2.60) |
|||||||||||||
4SH |
0 |
R |
4SH |
0 |
r |
4SH |
|
r |
|
|
4SH |
|
r |
|
|
4SH |
|
|
r |
|
4SH |
r |
|||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
0 a1 |
|
|
0 a2 |
|
|
|
|
0 b1 |
|
|
|
|
0 b2 |
||||||||||||
|
ȼɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ |
||||||||||||||||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
Ȍ = Ȍ(x1, y1, z1, x2, y2, z2), |
|
|
|
|
|
|
|
(2.61) |
||||||||||||||||||
ɝɞɟ x1, y1, z1, x2, y2, z2 – ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɝɨ ɢ
ɜɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɨɜ.
ɍɪɚɜɧɟɧɢɟ (2.59) ɪɟɲɚɸɬ ɦɟɬɨɞɨɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɯ ɩɪɢɛɥɢɠɟɧɢɣ.
ɇɭɥɟɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ. Ɋɚɫɫɦɨɬɪɢɦ ɫɥɭɱɚɣ, ɤɨɝɞɚ ɚɬɨɦɵ ɜɨɞɨɪɨɞɚ ɭɞɚɥɟɧɵ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɧɚ ɛɟɫɤɨɧɟɱɧɨɟ ɪɚɫɫɬɨɹɧɢɟ (R = ) ɢ ɧɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɦɟɠɞɭ ɫɨɛɨɣ. ɇɢɡɲɢɣ ɭɪɨɜɟɧɶ ɷɧɟɪɝɢɢ ɢɡɨɥɢɪɨɜɚɧɧɨɝɨ ɚɬɨɦɚ ɨɛɨɡɧɚɱɢɦ ɫɢɦɜɨɥɨɦ ȿ0. Ɍɨɝɞɚ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧ-
ɝɟɪɚ ɞɥɹ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɚɬɨɦɨɜ ɛɭɞɭɬ ɢɦɟɬɶ ɜɢɞ:
ª |
|
|
|
|
|
|
e |
2 |
º |
|
|
|
|
|
|
|
« |
' |
2m |
¨§E |
|
|
|
¸·» |
< |
a |
q |
|
0, |
(2.62) |
|||
|
|
|
||||||||||||||
¬« |
|
1 |
=2 |
© |
0 |
|
4SH0ra1 ¹¼» |
|
1 |
|
|
|
||||
ª |
|
|
2m |
§ |
|
|
e |
2 |
·º |
|
|
q |
|
|
|
|
«' |
|
¨E |
|
|
|
¸» |
< |
b |
0, |
(2.63) |
||||||
|
|
|
|
|||||||||||||
¬« |
|
2 |
=2 |
© |
0 |
|
4SH0rb1 ¹¼» |
|
2 |
|
|
|
||||
ɝɞɟq1 ɢ q2 – ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵɩɟɪɜɨɝɨɢɜɬɨɪɨɝɨɷɥɟɤɬɪɨɧɨɜ.
ȿɫɥɢ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɫɨɜɨɤɭɩɧɨɫɬɶ ɞɜɭɯ ɭɞɚɥɟɧɧɵɯ ɚɬɨɦɨɜ ɤɚɤ ɟɞɢɧɭɸ ɫɢɫɬɟɦɭ, ɬɨ ɟɟ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɛɭɞɟɬ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɨɬɞɟɥɶɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɩɨɫɤɨɥɶɤɭ ɨɧɢ ɞɜɢɠɭɬɫɹ ɧɟɡɚɜɢɫɢɦɨ ɞɪɭɝ ɨɬ ɞɪɭɝɚ:
Ȍ0(q1, q2) = Ȍa(q1) Ȍb(q2), |
(2.64) |
ɚ ɟɟ ɷɧɟɪɝɢɹ ɨɩɪɟɞɟɥɢɬɫɹ ɜɵɪɚɠɟɧɢɟɦ ȿ = 2ȿ0.
ɉɨɫɤɨɥɶɤɭ ɜ ɤɜɚɧɬɨɜɨɣ ɦɟɯɚɧɢɤɟ ɞɟɣɫɬɜɭɟɬ ɩɪɢɧɰɢɩ ɧɟɪɚɡɥɢɱɢɦɨɫɬɢ ɱɚɫɬɢɰ, ɬɨ ɨɛɦɟɧ ɦɟɫɬɚɦɢ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɢɡɦɟɧɢɬ ɷɧɟɪɝɢɸ ɫɢɫɬɟɦɵ, ɬɨɝɞɚ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɨ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɟɣ
53
Ȍ0(q2, q1) = Ȍa(q2) Ȍb(q1), |
(2.65) |
ɚ ɬɚɤɠɟ ɥɢɧɟɣɧɨɣ ɤɨɦɛɢɧɚɰɢɟɣ (2.64) ɢ (2.65): |
|
Ȍ0(q1, q2) = Į Ȍa(q1) Ȍb(q2) + ȕ Ȍa(q2) Ȍb(q1). |
(2.66) |
ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ (2.66) ɨɩɢɫɵɜɚɟɬ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ, ɜ ɤɨɬɨɪɨɣ ɤɚɠɞɵɣ ɷɥɟɤɬɪɨɧ ɢɦɟɟɬ ɧɟɤɨɬɨɪɭɸ ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɨɤɨɥɨ ɚɬɨɦɚ ɚ ɢɥɢ ɚɬɨɦɚ b. ɉɪɢ ɷɬɨɦ |Į|2 ɞɚɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɚ 1 ɭ ɚɬɨɦɚ ɚ, ɚ ɷɥɟɤɬɪɨɧɚ 2 ɭ ɚɬɨɦɚ b, ɚ |ȕ|2 – ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɪɚɬɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ. ȼɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ, ɜɯɨɞɹɳɢɟ ɜ (2.66), ɫɱɢɬɚɸɬɫɹ ɧɨɪɦɢɪɨɜɚɧɧɵɦɢ:
³ |
|
<a q |
|
2 dq ³ |
|
<b q |
|
2 dq 1 |
(2.67) |
|
|
|
|
||||||
ɢ ɨɪɬɨɝɨɧɚɥɶɧɵɦɢ: |
|
||||||||
|
|
³<*a q <b q dq 0, |
(2.68) |
||||||
ɝɞɟ dq – ɷɥɟɦɟɧɬ ɤɨɧɮɢɝɭɪɚɰɢɨɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɷɥɟɤɬɪɨɧɚ. ɉɟɪɜɨɟ ɩɪɢɛɥɢɠɟɧɢɟ. Ⱥɬɨɦɵ ɧɚɱɢɧɚɸɬ ɫɛɥɢɠɚɬɶɫɹ, ɩɪɢ ɷɬɨɦ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɹɞɟɪ, ɧɟɭɱɬɟɧɧɵɟ ɜ (2.62) ɢ (2.63), ɩɪɢɜɟɞɭɬ ɤ ɢɡɦɟɧɟɧɢɸ ɫɨɛɫɬɜɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɷɧɟɪɝɢɢ ɫɢɫɬɟɦɵ:
c |
(2.68) |
E 2E0 E , |
ɝɞɟ Ec – ɩɨɩɪɚɜɤɚ ɤ ɩɨɥɧɨɣ ɷɧɟɪɝɢɢ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ. ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ (2.66) ɹɜɥɹɟɬɫɹ ɪɟɲɟ-
ɧɢɟɦ ɢ ɩɨɥɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ (2.59). ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɟ (2.69) ɢ (2.66) ɜ (2.59) ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɩɨɞɛɨɪɭ ɬɚɤɢɯ ɡɧɚɱɟɧɢɣ Į, ȕ ɢ Ec, ɩɪɢ ɤɨɬɨɪɵɯ ɭɪɚɜɧɟɧɢɟ (2.59) ɢɦɟɟɬ ɪɟɲɟɧɢɟ. ɋɚɦɚ ɩɪɨɰɟɞɭɪɚ ɪɟɲɟɧɢɹ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɡɞɟɫɶ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ. Ɉɫɬɚɧɨɜɢɦɫɹ ɬɨɥɶɤɨ ɧɚ ɪɟɡɭɥɶɬɚɬɚɯ, ɤɨɬɨɪɵɟ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɞɜɚ ɜɨɡɦɨɠɧɵɯ ɪɟɲɟɧɢɹ (ɩɪɢ ɬɨɦ, ɱɬɨ Į = ±ȕ):
– ɩɟɪɜɨɟ ɪɟɲɟɧɢɟ:
< 1 q , q |
|
Dª< |
a |
q |
< |
b |
q |
< |
a |
q |
< |
b |
q |
º, (2.70) |
0 1 2 |
|
¬ |
1 |
|
2 |
|
2 |
|
1 |
¼ |
ɤɨɬɨɪɨɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ
ȿ(1) = 2ȿ + ɋ + Ⱥ; |
(2.71) |
0 |
|
– ɜɬɨɪɨɟ ɪɟɲɟɧɢɟ: |
|
< 2 |
q , q |
|
Dª< |
a |
q |
< |
b |
q |
< |
a |
q |
< |
b |
q |
º, (2.72) |
0 |
1 2 |
|
¬ |
1 |
|
2 |
|
2 |
|
1 |
¼ |
54
ɤɨɬɨɪɨɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɹ |
|
ȿ(2) = 2ȿ + ɋ – Ⱥ. |
(2.73) |
0 |
|
ɂɡ (2.70)–(2.73) ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɣ ɜɵɜɨɞ: ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ <01 ɧɟ ɦɟɧɹɟɬ ɡɧɚɤ ɩɪɢ ɩɟɪɟɫɬɚɧɨɜɤɟ ɷɥɟɤɬɪɨɧɚ ɨɬ ɚɬɨɦɚ ɚ ɤ ɚɬɨɦɭ b. Ɍɚɤɚɹ ɮɭɧɤɰɢɹ ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ ɫɢɦɦɟɬɪɢɱɧɨɣ, ɚ ɮɭɧɤɰɢɹ <02 , ɦɟɧɹɸɳɚɹ ɡɧɚɤ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ, ɧɚɡɵɜɚɟɬɫɹ ɚɧɬɢ-
ɫɢɦɦɟɬɪɢɱɧɨɣ. ɇɚ ɪɢɫ. 2.11 ɫɯɟɦɚɬɢɱɧɨ ɩɨɤɚɡɚɧɚ ɮɨɪɦɚ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɢ ɟɟ ɨɪɢɟɧɬɚɰɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɪɢ ɩɟɪɟɫɬɚɧɨɜɤɟ ɷɥɟɤɬɪɨɧɨɜ.
Ɋɢɫ. 2.11. ȼɢɞ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ: ɚ – ɫɢɦɦɟɬɪɢɱɧɚɹ ɮɭɧɤɰɢɹ; ɛ – ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚɹ ɮɭɧɤɰɢɹ
|
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɋ |
ɢ Ⱥ ɪɚɜɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ: |
|
|
|
|
|
|||||||||||||||||||||||||||||||
C |
|
|
e2 |
|
|
|
|
|
e2 |
|
³ |
§ |
1 |
|
1 |
|
1 |
· |
|
< |
|
q |
|
2 |
|
< |
|
q |
|
|
2 dq dq |
, |
(2.74) |
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||||
|
|
4SH |
0 |
R |
|
|
4SH |
0 |
¨ r r |
|
r |
¸ |
|
|
a |
1 |
|
|
|
|
b |
2 |
|
|
1 2 |
|
|
|||||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
© |
|
|
b1 |
|
a1 |
¹ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
A |
e2 |
|
|
§1 |
|
1 |
|
|
1 |
· |
<*a q1 |
<b q1 <*b q2 <a q2 dq1dq2. (2.75) |
||||||||||||||||||||||||||
|
|
³ |
¨ r |
|
|
|
|
|
|
¸ |
||||||||||||||||||||||||||||
4SH |
0 |
r |
|
r |
|
|||||||||||||||||||||||||||||||||
|
|
|
|
© |
|
|
|
b1 |
|
|
|
a1 |
¹ |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
Ʉɨɷɮɮɢɰɢɟɧɬ ɋ ɜɵɪɚɠɚɟɬ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɚɬɨɦɨɜ, ɹɞɪɚ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R, ɚ ɡɚɪɹɞɵ ɷɥɟɤɬɪɨɧɨɜ «ɪɚɡɦɚɡɚɧɵ» ɩɨ ɜɫɟɦɭ ɩɪɨɫɬɪɚɧɫɬɜɭ ɫ ɩɥɨɬɧɨɫɬɹɦɢ ɟ <a q1 2 ɢ ɟ <b q2 2 .
Ʉɨɷɮɮɢɰɢɟɧɬ Ⱥ ɧɟ ɢɦɟɟɬ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɚɧɚɥɨɝɚ, ɯɨɬɹ ɩɨ ɫɭɬɢ ɷɬɨ – ɷɧɟɪɝɢɹ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ ɩɪɢɪɨɞɵ. Ɉɧɚ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ ɱɢɫɬɨ ɤɜɚɧɬɨɜɨɝɨ ɷɮɮɟɤɬɚ – ɧɟɪɚɡɥɢɱɢɦɨɫɬɢ ɱɚɫɬɢɰ, ɩɨɷɬɨɦɭ ɢɦɟɟɬɫɹ ɤɨɧɟɱɧɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ ɷɥɟɤɬɪɨɧɚ 1 ɜ ɨɛɨɥɨɱɤɟ ɚɬɨɦɚ b, ɚ ɷɥɟɤɬɪɨɧɚ 2 – ɜ ɨɛɨɥɨɱɤɟ ɚɬɨɦɚ ɚ, ɬ. ɟ. ɜɟɪɨɹɬɧɨɫɬɶ ɨɛɦɟɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɚɬɨɦɨɜ ɷɥɟɤɬɪɨɧɚɦɢ. ɉɨɷɬɨɦɭ Ⱥ ɧɚɡɵɜɚɸɬ ɨɛɦɟɧɧɨɣ ɷɧɟɪɝɢɟɣ, ɢɥɢ ɨɛɦɟɧɧɵɦ ɢɧɬɟɝɪɚɥɨɦ.
55
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɜ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɞɚɟɬ ɞɜɚ ɡɧɚɱɟɧɢɹ ɫɨɛɫɬɜɟɧɧɨɣ ɷɧɟɪɝɢɢ (2.71) ɢ (2.73). ɂɧɵɦɢ ɫɥɨɜɚɦɢ: ɜɵɪɨɠɞɟɧɧɨɟ ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ ɧɭɥɟɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɪɚɫɩɚɞɚɟɬɫɹ ɧɚ ɞɜɚ ɫɨɫɬɨɹɧɢɹ ɫ ɪɚɡɥɢɱɧɨɣ ɷɧɟɪɝɢɟɣ, ɩɪɢɱɟɦ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɷɬɢɦɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɦɢ ɭɪɨɜɧɹɦɢ ɫɨɫɬɚɜɥɹɟɬ 2Ⱥ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɤɚ ɨɛɦɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɵɦ ɦɨɠɟɬ
ɨɤɚɡɚɬɶɫɹ ɢɥɢ ɫɨɫɬɨɹɧɢɟ <01 , ɢɥɢ ɫɨɫɬɨɹɧɢɟ <02 .
ɉɨɥɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɫɢɫɬɟɦɵ ɞɨɥɠɧɚ ɡɚɜɢɫɟɬɶ ɧɟ ɬɨɥɶɤɨ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ, ɧɨ ɢ ɨɬ ɫɩɢɧɨɜɨɣ ɩɟɪɟɦɟɧɧɨɣ ı, ɤɨɬɨɪɚɹ ɞɢɫɤɪɟɬɧɚ ɢ ɢɦɟɟɬ ɬɨɥɶɤɨ ɞɜɚ ɡɧɚɱɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɞɜɭɦ ɜɨɡɦɨɠɧɵɦ ɨɪɢɟɧɬɚɰɢɹɦ ɫɩɢɧɨɜɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ. ȿɫɥɢ ɩɪɟɧɟɛɪɟɱɶ ɦɚɝɧɢɬɧɵɦ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟɦ ɷɥɟɤɬɪɨɧɨɜ, ɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɧɟ ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɫɩɢɧɨɜ, ɢ ɩɨɥɧɭɸ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ ɦɨɠɧɨ ɛɭɞɟɬ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɩɪɨɢɡɜɟɞɟɧɢɟ ɮɭɧɤɰɢɣ, ɡɚɜɢɫɹɳɢɯ ɢ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ, ɢ ɨɬ ɫɩɢɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬ:
Ȍ(q, ı) = Ȍ0(q1, q2) ij(ı1, ı2), |
(2.76) |
ɝɞɟ ı1, ı2 – ɫɩɢɧɨɜɵɟ ɩɟɪɟɦɟɧɧɵɟ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɷɥɟɤɬɪɨɧɨɜ. Ʉ ɩɨɥɧɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɫɢɫɬɟɦɵ ɷɥɟɤɬɪɨɧɨɜ ɩɪɟɞɴɹɜɥɹ-
ɟɬɫɹ ɫɥɟɞɭɸɳɟɟ ɬɪɟɛɨɜɚɧɢɟ: ɨɧɚ ɞɨɥɠɧɚ ɛɵɬɶ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɟɪɟɫɬɚɧɨɜɤɢ ɞɜɭɯ ɷɥɟɤɬɪɨɧɨɜ, ɬ. ɟ. ɞɨɥɠɧɚ ɦɟɧɹɬɶ ɡɧɚɤ ɩɪɢ ɩɟɪɟɫɬɚɧɨɜɤɟ ɤɚɤ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ, ɬɚɤ ɢ ɫɩɢɧɨɜɵɯ ɤɨɨɪɞɢɧɚɬ. ɉɨɷɬɨɦɭ, ɟɫɥɢ «ɤɨɨɪɞɢɧɚɬɧɚɹ» ɮɭɧɤɰɢɹ ɫɢɦɦɟɬɪɢɱɧɚ, ɬɨ ɫɩɢɧɨɜɚɹ ɞɨɥɠɧɚ ɛɵɬɶ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚ ɢ ɧɚɨɛɨɪɨɬ. ɋɩɢɧɨɜɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɫɢɦɦɟɬɪɢɱɧɚ ɩɪɢ ɩɚɪɚɥɥɟɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɢ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚ ɩɪɢ ɢɯ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɪɟɲɟɧɢɟ ɭɪɚɜɧɟɧɢɹ ɒɪɟɞɢɧɝɟɪɚ, ɨɬɜɟɱɚɸ-
ɳɟɟ ɮɭɧɤɰɢɢ <02 (ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɨɣ), ɬɪɟɛɭɟɬ, ɱɬɨɛɵ ɫɩɢɧɨɜɵɟ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɜ ɦɨɥɟɤɭɥɟ ɜɨɞɨɪɨɞɚ ɪɚɫɩɨɥɚɝɚɥɢɫɶ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ, ɚ ɞɥɹ ɮɭɧɤɰɢɢ <01 (2.70) (ɫɢɦɦɟɬɪɢɱɧɨɣ) ɬɪɟɛɭɟɬɫɹ
ɢɯ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɧɟɪɝɢɹ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɨɤɚɡɵɜɚɟɬɫɹ ɫɜɹɡɚɧɧɨɣ ɫɨ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɟɣ ɫɩɢɧɨɜɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ. ȼɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɤɚ ɨɛɦɟɧɧɨɝɨ ɢɧɬɟ-
56
ɝɪɚɥɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɛɨɥɟɟ ɜɵɝɨɞɧɵɦ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɤɚɤ ɩɚɪɚɥɥɟɥɶɧɨɟ, ɬɚɤ ɢ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨɟ ɢɯ ɪɚɫɩɨɥɨɠɟɧɢɟ. Ɉɛɦɟɧɧɵɣ ɢɧɬɟɝɪɚɥ ɨɱɟɧɶ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɹɞɪɚɦɢ R. Ⱦɥɹ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɪɚɫɱɟɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɩɪɢ ɦɚɥɵɯ R ɨɛɦɟɧɧɵɣ ɢɧɬɟɝɪɚɥ A < 0, ɚ ɩɪɢ ɛɨɥɶɲɢɯ R Ⱥ > 0, ɬ. ɟ. ɢɦɟɟɬ ɦɟɫɬɨ ɢɡɦɟɧɟɧɢɟ ɡɧɚɤɚ. Ʉɪɢɜɵɟ ɞɥɹ ɷɧɟɪ-
ɝɢɣ ȿ (2.71), (2.73) ɢɦɟɸɬ ɜɢɞ, ɩɨ- |
Ɋɢɫ. 2.12. ɗɧɟɪɝɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ |
|
ɤɚɡɚɧɧɵɣ ɧɚ ɪɢɫ. 2.12. |
ɞɜɭɯ ɚɬɨɦɨɜ ɜɨɞɨɪɨɞɚ |
|
(ɫɬɪɟɥɤɚɦɢ ɨɛɨɡɧɚɱɟɧɵ ɫɩɢɧɨɜɵɟ |
||
ɂɡ ɷɬɨɝɨ ɪɢɫɭɧɤɚ ɜɢɞɧɨ, ɱɬɨ |
||
ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ, ɚ0 – ɛɨɪɨɜɫɤɢɣ |
||
ɷɧɟɪɝɢɹ ȿ(1) ɢɦɟɟɬ ɦɢɧɢɦɭɦ ɩɪɢ |
ɪɚɞɢɭɫ ɚɬɨɦɚ ɜɨɞɨɪɨɞɚ) |
|
R ɚ § 1,5, ɩɨɷɬɨɦɭ ɫɢɦɦɟɬɪɢɱɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ < 1 (ɢ ɫɨɨɬ- |
||
0 |
0 |
|
ɜɟɬɫɬɜɟɧɧɨ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚɹ ɮɭɧɤɰɢɹ ij(ı1, ı2)) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɫɬɨɣɱɢɜɨɦɭ ɫɨɫɬɨɹɧɢɸ ɫɢɫɬɟɦɵ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɚɧɬɢɫɢɦɦɟɬɪɢɱɧɚɹ ɮɭɧɤɰɢɹ <02 (ɫ ɩɚɪɚɥɥɟɥɶɧɵɦ ɪɚɫɩɨɥɨɠɟɧɢɟɦ ɫɩɢɧɨɜ) ɢɡɦɟɧɹɟɬɫɹ
ɦɨɧɨɬɨɧɧɨ ɢ ɞɚɟɬ ɧɟɭɫɬɨɣɱɢɜɭɸ ɤɨɦɛɢɧɚɰɢɸ ɞɜɭɯ ɜɨɞɨɪɨɞɧɵɯ ɚɬɨɦɨɜ. ɂɡ ɩɪɢɜɟɞɟɧɧɵɯ ɪɚɫɫɭɠɞɟɧɢɣ ɫɥɟɞɭɟɬ, ɱɬɨ ɭɫɬɨɣɱɢɜɨɦɭ ɫɨɫɬɨɹɧɢɸ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɜɟɧɫɬɜɨ ɧɭɥɸ ɫɭɦɦɚɪɧɨɝɨ ɫɩɢɧɨɜɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ. ɗɬɨɬ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɜɵɜɨɞ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ: ɦɨɥɟɤɭɥɚ ɜɨɞɨɪɨɞɚ ɹɜɥɹɟɬɫɹ ɞɢɚɦɚɝɧɢɬɧɨɣ.
Ɉɫɧɨɜɧɵɦɢ ɢɬɨɝɚɦɢ ɤɜɚɧɬɨɜɨ-ɦɟɯɚɧɢɱɟɫɫɤɨɝɨ ɪɚɫɫɦɨɬɪɟɧɢɹ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ ɹɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɩɨɥɨɠɟɧɢɹ:
1.ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɨɛ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɫɨɫɬɨɹɧɢɢ ɫɢɫɬɟɦɵ ɧɟ ɜɜɨɞɢɥɨɫɶ ɦɚɝɧɢɬɧɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ, ɨɞɧɚɤɨ ɧɚ ɨɫɧɨɜɚɧɢɢ ɩɪɢɧɰɢɩɚ ɉɚɭɥɢ ɫɞɟɥɚɧ ɜɵɜɨɞ ɨ ɬɨɦ, ɱɬɨ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ ɡɚɜɢɫɢɬ ɨɬ ɫɩɢɧɨɜ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɯ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɢ, ɬ. ɟ. ɨɬ ɦɚɝɧɢɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɫɢɫɬɟɦɵ.
2.ɗɧɟɪɝɢɹ ɫɢɫɬɟɦɵ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɬɨɥɶɤɨ ɤɥɚɫɫɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɣ (ɤɭɥɨɧɨɜɫɤɨɣ) ɷɧɟɪɝɢɟɣ, ɧɨ ɢ ɨɛɦɟɧɧɨɣ ɷɧɟɪɝɢɟɣ,
57
ɢɦɟɸɳɟɣ ɬɚɤɠɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɭɸ ɩɪɢɪɨɞɭ, ɧɨ ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɧɟɪɚɡɥɢɱɢɦɨɫɬɶɸ ɱɚɫɬɢɰ ɢ ɧɟ ɢɦɟɸɳɟɣ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɚɧɚɥɨɝɚ.
ɇɟɤɨɬɨɪɵɟ ɚɫɩɟɤɬɵ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɮɟɪɪɨɦɚɝɧɟɬɢɤɨɜ. Ʉɪɢɬɟɪɢɣ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ
Ɉɫɧɨɜɧɵɟ ɜɵɜɨɞɵ, ɢɡɥɨɠɟɧɧɵɟ ɜɵɲɟ, ɥɟɝɥɢ ɜ ɨɫɧɨɜɭ ɤɜɚɧɬɨɜɨɣ ɬɟɨɪɢɢ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ, ɩɟɪɜɨɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɮɨɪɦɥɟɧɢɟ ɤɨɬɨɪɨɣ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɢɛɥɢɠɟɧɧɨɣ ɦɨɞɟɥɢ ɨɛɦɟɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɚɥɢ ɜ 1928 ɝ. ɫɧɚɱɚɥɚ Ɏɪɟɧɤɟɥɶ, ɚ ɩɨɡɞɧɟɟ – Ƚɟɣɡɟɧɛɟɪɝ.
ɉɨɞɯɨɞ Ɏɪɟɧɤɟɥɹ ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ ɦɨɞɟɥɢ ɝɚɡɚ ɢɡ ɤɨɥɥɟɤɬɢɜɢɡɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɟɬɚɥɥɨɜ ɫ ɭɱɟɬɨɦ ɢɯ ɨɛɦɟɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ȼ ɬɟɨɪɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɫɥɨɜɢɟ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɛɦɟɧɧɚɹ ɫɜɹɡɶ ɞɟɥɚɟɬ ɷɧɟɪɝɟɬɢɱɟɫɤɢ ɜɵɝɨɞɧɵɦ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɟ ɧɚɦɚɝɧɢɱɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ. Ⱦɚɧɧɚɹ ɦɨɞɟɥɶ ɛɥɢɠɟ ɜɫɟɝɨ ɩɨɞɯɨɞɢɬ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɫɜɨɣɫɬɜ ɦɟɬɚɥɥɨɜ ɢ ɫɩɥɚɜɨɜ, ɚɬɨɦɵ ɤɨɬɨɪɵɯ ɢɦɟɸɬ ɧɟɞɨɫɬɪɨɟɧɧɵɟ d-ɫɥɨɢ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵɟ ɫɩɢɧɨɜɵɟ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ.
ɉɨɞɯɨɞ Ƚɟɣɡɟɧɛɟɪɝɚ ɛɨɥɟɟ ɭɞɨɛɟɧ ɞɥɹ ɨɩɢɫɚɧɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ ɜ ɦɟɬɚɥɥɚɯ ɢ ɫɩɥɚɜɚɯ ɪɟɞɤɨɡɟɦɟɥɶɧɨɣ ɝɪɭɩɩɵ ɫ ɧɟɞɨɫɬɪɨɟɧɧɵɦɢ 4f-ɫɥɨɹɦɢ. ɉɪɢ ɬɚɤɨɦ ɩɨɞɯɨɞɟ ɩɪɟɞɩɨɥɚɟɬɫɹ, ɱɬɨ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ, ɨɛɪɚɡɭɸɳɢɟ ɭɩɨɪɹɞɨɱɟɧɧɭɸ ɫɬɪɭɤɬɭɪɭ, ɥɨɤɚɥɢɡɨɜɚɧɵ ɨɤɨɥɨ ɫɜɨɢɯ ɚɬɨɦɨɜ.
Ɋɚɫɱɟɬɵ Ƚɟɣɡɟɧɛɟɪɝɚ ɫɬɚɥɢ ɩɪɹɦɵɦ ɨɛɨɛɳɟɧɢɟɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨ ɫɜɨɣɫɬɜɚɯ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ. Ɋɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɫɢɫɬɟɦɚ, ɫɨɫɬɨɹɳɚɹ ɢɡ N ɜɨɞɨɪɨɞɨɩɨɞɨɛɧɵɯ ɚɬɨɦɨɜ, ɷɥɟɤɬɪɨɧɵ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɜ s-ɫɨɫɬɨɹɧɢɹɯ. Ɉɛɳɢɣ ɯɨɞ ɪɚɫɫɭɠɞɟɧɢɣ ɛɵɥ ɬɚɤɢɦ ɠɟ, ɤɚɤ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ. ȼ ɧɭɥɟɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɫɢɫɬɟɦɚ ɢɡɨɥɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ, ɢɦɟɸɳɢɯ ɨɞɢɧɚɤɨɜɭɸ ɷɧɟɪɝɢɸ ȿ0.
ȼ ɩɟɪɜɨɦ ɩɪɢɛɥɢɠɟɧɢɢ ɧɟɨɛɯɨɞɢɦɨ ɛɵɥɨ ɭɱɢɬɵɜɚɬɶ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɜɫɟɯ ɚɬɨɦɨɜ, ɱɬɨ ɜɵɡɵɜɚɥɨ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɬɪɭɞɧɨɫɬɢ. Ⱦɥɹ ɭɩɪɨɳɟɧɢɹ ɡɚɞɚɱɢ ɭɱɢɬɵɜɚɥɨɫɶ ɬɨɥɶɤɨ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ, ɜɫɟ ɨɫɬɚɥɶɧɵɟ ɜɢɞɵ ɨɬɛɪɚɫɵɜɚɥɢɫɶ.
ɉɨɥɧɚɹ ɷɧɟɪɝɢɹ ɫɢɫɬɟɦɵ, ɤɚɤ ɢ ɞɥɹ ɦɨɥɟɤɭɥɵ ɜɨɞɨɪɨɞɚ, ɛɵɥɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɫɭɦɦɨɣ ɷɧɟɪɝɢɣ ɢɡɨɥɢɪɨɜɚɧɧɵɯ ɚɬɨɦɨɜ Nȿ0, ɷɧɟɪɝɢɢ
58
ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɷɥɟɤɬɪɨɧɨɜ ɢ ɢɨɧɨɜ ɋ ɢ ɨɛɦɟɧɧɨɣ ɷɧɟɪɝɢɢ ȿɨɛɦ. Ⱦɚɥɟɟ ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɢɧɬɟɝɪɚɥɚ ɨɛ-
ɦɟɧɧɨɣ ɷɧɟɪɝɢɢ Aij ɦɟɠɞɭ ɚɬɨɦɚɦɢ i ɢ j. ɉɨɫɥɟ ɫɭɦɦɢɪɨɜɚɧɢɹ ɩɨ ɜɫɟɦ ɩɚɪɚɦ ɚɬɨɦɨɜ ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɜɵɪɚɠɟɧɢɟ
ȿɨɛɦ 2¦AijV2 cosMij , |
(2.77) |
ij |
|
ɝɞɟ ı – ɫɩɢɧɨɜɵɣ ɦɟɯɚɧɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɜ ɟɞɢɧɢɰɚɯ ʄ; ijij – ɭɝɨɥ ɦɟ-
ɠɞɭ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɜɟɤɬɨɪɨɜ ɫɩɢɧɨɜɵɯ ɦɨɦɟɧɬɨɜ.
Ʉɚɤ ɢ ɜ ɦɨɥɟɤɭɥɟ ɜɨɞɨɪɨɞɚ, Aij ɜɯɨɞɢɬ ɜ ɨɛɦɟɧɧɭɸ ɷɧɟɪɝɢɸ ɫɨ
ɡɧɚɤɨɦ ɩɥɸɫ ɩɪɢ ɩɚɪɚɥɥɟɥɶɧɨɦ ɪɚɫɩɨɥɨɠɟɧɢɢ ɫɩɢɧɨɜ ɜɨ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɚɬɨɦɚɯ. ȼɵɪɚɠɟɧɢɟ (2.77) ɦɨɠɧɨ ɭɩɪɨɫɬɢɬɶ, ɟɫɥɢ ɭɱɟɫɬɶ, ɱɬɨ Aij ɛɵɫɬɪɨ ɭɛɵɜɚɟɬ ɩɨ ɦɟɪɟ ɭɜɟɥɢɱɟɧɢɹ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠ-
ɞɭ ɚɬɨɦɚɦɢ. ɉɨɷɬɨɦɭ ɦɨɠɧɨ ɨɝɪɚɧɢɱɢɬɶɫɹ ɭɱɟɬɨɦ ɨɛɦɟɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɨɥɶɤɨ ɦɟɠɞɭ ɫɨɫɟɞɧɢɦɢ ɚɬɨɦɚɦɢ. ȿɫɥɢ ɚɬɨɦ ɢɦɟɟɬ z ɛɥɢɠɚɣɲɢɯ ɫɨɫɟɞɟɣ ɢ ɢɯ ɫɩɢɧɵ ɩɚɪɚɥɥɟɥɶɧɵ (ɭ = 1), ɬɨ ȿɨɛɦ = –NzA
ɩɪɢ A = Aij. ȿɫɥɢ ɧɟ ɜɫɟ ɫɩɢɧɵ ɩɚɪɚɥɥɟɥɶɧɵ ɞɪɭɝ ɞɪɭɝɭ, ɬɨ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɞɚɧɧɵɣ ɚɬɨɦ ɢɦɟɟɬ ɫɩɢɧ ɜɵɛɪɚɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɭ2. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɦɟɧɧɚɹ ɷɧɟɪɝɢɹ ɢɦɟɟɬ ɜɢɞ
ȿ = –Nɭ2zA. |
(2.78) |
ɨɛɦ |
|
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɟɫɥɢ ɞɥɹ ɫɨɫɟɞɧɢɯ ɚɬɨɦɨɜ Ⱥ > 0, ɬɨ ɦɢɧɢɦɭɦ ɨɛɦɟɧɧɨɣ ɷɧɟɪɝɢɢ ɩɨɥɭɱɚɟɬɫɹ ɩɪɢ ɭ = ±1, ɬ. ɟ. ɩɪɢ ɧɚɦɚɝɧɢɱɟɧɧɨɦ ɞɨ ɧɚɫɵɳɟɧɢɹ ɫɨɫɬɨɹɧɢɢ ɫɢɫɬɟɦɵ.
ɉɪɢɧɰɢɩɢɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɜ ɬɟɨɪɢɢ ȼɟɣɫɫɚ ɡɚɜɢɫɢɦɨɫɬɶ ɷɧɟɪɝɢɢ ɨɬ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ ɩɨɫɬɭɥɢɪɨɜɚɥɚɫɶ, ɡɞɟɫɶ ɠɟ ɨɧɚ ɩɨɥɭɱɚɟɬɫɹ ɢɡ ɪɚɫɱɟɬɨɜ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɡɜɟɫɬɧɨ, ɱɬɨ ɷɬɚ ɷɧɟɪɝɢɹ ɹɜɥɹɟɬɫɹ ɨɛɦɟɧɧɨɣ ɢ ɢɦɟɟɬ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɭɸ ɩɪɢɪɨɞɭ. ȼɵɪɚɠɟ-
ɧɢɹ (2.47) ɢ (2.78) ɛɭɞɭɬ ɢɞɟɧɬɢɱɧɵ, ɟɫɥɢ ɩɨɥɨɠɢɬɶ |
|
Ⱥ1 = Ⱥz. |
(2.79) |
Ɂɧɚɱɟɧɢɟ ɝɪɚɧɢɱɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ (ɬɟɦɩɟɪɚɬɭɪɵ Ʉɸɪɢ) ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɩɨ ɜɵɪɚɠɟɧɢɢɸ
Ĭ = 2zȺ/k. |
(2.80) |
ɂɡɥɨɠɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ Ƚɟɣɡɟɧɛɟɪɝɚ ɫɥɢɲɤɨɦ ɝɪɭɛɵ ɞɥɹ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɫɨɝɥɚɫɢɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ. Ɉɞɧɚɤɨ ɢɡ ɧɢɯ ɫɥɟɞɭɸɬ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɜɚɠɧɵɟ ɜɵɜɨɞɵ:
59
Ɍɨɥɶɤɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɋɉɛȽɗɌɍ "ɅɗɌɂ" ɢɦ. ȼ.ɂ. ɍɥɶɹɧɨɜɚ (Ʌɟɧɢɧɚ)
1)ɟɫɥɢ ɨɛɦɟɧɧɵɣ ɢɧɬɟɝɪɚɥ Ⱥ ɩɨɥɨɠɢɬɟɥɟɧ, ɬɨ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɫɨɫɬɨɹɧɢɟɫɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨɣɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶɸ(ɮɟɪɪɨɦɚɝɧɟɬɢɡɦ);
2)ɜɟɥɢɱɢɧɚ ɷɧɟɪɝɢɢ ɨɛɦɟɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɮɟɪɪɨɦɚɝɧɢɬɧɨɣ ɭɩɨɪɹɞɨɱɟɧɧɨɫɬɢ ɜɩɥɨɬɶ ɞɨ
ɬɟɦɩɟɪɚɬɭɪ ɩɨɪɹɞɤɚ 103 Ʉ.
ɉɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɨɛɦɟɧɧɵɣ ɢɧɬɟɝɪɚɥ ɛɭɞɟɬ ɢɦɟɬɶ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ? ɂɡ (2.75) ɫɥɟɞɭɟɬ, ɱɬɨ ɢɧɬɟɝɪɚɥ ɨɛɦɟɧɚ ɦɟɠɞɭ ɥɸɛɨɣ ɩɚɪɨɣ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɨɢɬ ɢɡ ɞɜɭɯ ɱɚɫɬɟɣ: ɱɚɫɬɶ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɸ ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɚɦɢ, ɜɫɟɝɞɚ ɩɨɥɨɠɢɬɟɥɶɧɚ, ɚ ɱɚɫɬɶ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɸ ɷɥɟɤɬɪɨɧɨɜ ɫ ɢɨɧɚɦɢ, ɜɫɟɝɞɚ ɨɬɪɢɰɚɬɟɥɶɧɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɹ Ⱥ > 0 ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ ɩɟɪɜɚɹ ɱɚɫɬɶ ɨɛɦɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ ɛɵɥɚ ɛɨɥɶɲɟ ɜɬɨɪɨɣ. Ɉɬɫɸɞɚ ɫɥɟɞɭɸɬ ɭɫɥɨɜɢɹ, ɫɨɜɨɤɭɩɧɨɫɬɶ ɤɨɬɨɪɵɯ ɩɨɥɭɱɢɥɚ ɧɚɡɜɚɧɢɟ ɤɪɢɬɟɪɢɹ ɮɟɪɪɨɦɚɝɧɟɬɢɡɦɚ:
1)ɜ ɚɬɨɦɟ ɞɨɥɠɧɚ ɫɭɳɟɫɬɜɨɜɚɬɶ ɧɟɡɚɩɨɥɧɟɧɧɚɹ ɨɛɨɥɨɱɤɚ ɫ ɛɨɥɶɲɢɦ ɨɪɛɢɬɚɥɶɧɵɦ ɱɢɫɥɨɦ l (ɷɬɨɦɭ ɬɪɟɛɨɜɚɧɢɸ ɭɞɨɜɥɟɬɜɨɪɹɟɬ d- ɢɥɢ f-ɨɛɨɥɨɱɤɚ);
2)ɪɚɞɢɭɫ ɷɬɨɣ ɨɛɨɥɨɱɤɢ ɞɨɥɠɟɧ ɛɵɬɶ ɦɚɥ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɪɚɫɫɬɨɹɧɢɟɦ ɦɟɠɞɭ ɹɞɪɚɦɢ ɜ ɫɢɫɬɟɦɟ (ɜ ɜɟɳɟɫɬɜɟ).
ɉɟɪɜɨɦɭ ɭɫɥɨɜɢɸ ɭɞɨɜɥɟɬɜɨɪɹɸɬ ɜɫɟ ɩɟɪɟɯɨɞɧɵɟ ɷɥɟɦɟɧɬɵ (Fe, Co, Ni), ɢɯ ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɞɟɪɠɚɬ ɥɸɛɵɟ ɮɟɪɪɨɦɚɝɧɢɬɧɵɟ ɫɩɥɚɜɵ ɢ ɫɨɟɞɢɧɟɧɢɹ. ɋɬɨɱɤɢɡɪɟɧɢɹ ɜɵɩɨɥɧɟɧɢɹ ɜɬɨɪɨɝɨ ɭɫɥɨɜɢɹ, ɩɪɚɜɢɥɶɧɟɟ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɧɟ ɫɚɦɨ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɹɞɪɚɦɢ, ɚ ɨɬɧɨɲɟɧɢɟ ɷɬɨɝɨ ɪɚɫɫɬɨɹɧɢɹ ɤ ɞɢɚɦɟɬɪɭ ɧɟɡɚɩɨɥɧɟɧɧɨɣ ɨɛɨɥɨɱɤɢ V = R/a. ɋɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɚɪɚɦɟɬɪɵ ɞɥɹ ɪɹɞɚ ɩɟɪɟɯɨɞɧɵɯ ɦɟɬɚɥɥɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 2.3, ɢɡ ɤɨɬɨɪɨɣɜɢɞɧɨ, ɱɬɨɭɜɫɟɯɮɟɪɪɨɦɚɝɧɢɬɧɵɯɦɟɬɚɥɥɨɜV > 1,5.
|
|
|
Ɍɚɛɥɢɰɚ 2.3 |
|
ɉɚɪɚɦɟɬɪɵ ɩɟɪɟɯɨɞɧɵɯ ɦɟɬɚɥɥɨɜ |
||
|
|
|
|
Ɇɟɬɚɥɥ |
ɇɟɡɚɩɨɥɧɟɧɧɚɹ ɨɛɨɥɨɱɤɚ |
V |
Ɍɟɦɩɟɪɚɬɭɪɚ Ʉɸɪɢ, Ʉ |
Ti |
3d |
1,12 |
– |
Cr |
3d |
1,13 |
– |
Mn |
3d |
1,47 |
– |
Fe |
3d |
1,63 |
1040 |
Co |
3d |
1,82 |
1400 |
Ni |
3d |
1,97 |
630 |
Mo |
4d |
0,92 |
– |
Gd |
4d |
3,1 |
290 |
W |
5d |
0,79 |
– |
Pt |
5d |
1,23 |
– |
60