Жданов С.К Цветков И.В - Основы физических процессов в плазме и в плазменных установках (2000)
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jɌɒ = jTexp(e3/2E1/2/kBT) = jTexp(4.39E1/2[ȼ/ɫɦ]/T[K]). |
(7.16) |
§45. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ȼ ɩɪɢɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜɵɫɨɤɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ E
(106÷107 ȼ/ɫɦ), ɩɨɦɢɦɨ ɭɜɟɥɢɱɟɧɢɹ ɬɨɤɚ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ ɫɧɢɠɟɧɢɹ ɪɚɛɨɬɵ ɜɵɯɨɞɚ (ɷɮɮɟɤɬɚ ɒɨɬɬɤɢ), ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɨɫɬɢ ɬɨɥɳɢɧɵ ɛɚɪɶɟɪɚ ɩɨɹɜɥɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ – «ɬɭɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ. ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɨɛɭɫɥɨɜɥɟɧɨɟ ɜɟɪɨɹɬɧɨɫɬɶɸ ɩɨɞɛɚɪɶɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ, ɢɦɟɸɳɟɝɨ ɜɨ ɜɧɟɲɧɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɨɝɪɚɧɢɱɟɧɧɭɸ ɲɢɪɢɧɭ, ɧɚɡɵɜɚɟɬɫɹ
ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɪɨɯɨɠɞɟɧɢɹ (ɩɪɨɡɪɚɱɧɨɫɬɢ) ɛɚɪɶɟɪɚ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ Wx, ɜɵɫɨɬɵ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ Wa, ɢ ɞɥɹ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɲɢɪɢɧɵ h ɜɵɪɚɠɚɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ:
Ɋɢɫ. 7.2 ɉɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɧɚ ɝɪɚɧɢɰɟ ɦɟɬɚɥɥ – ɜɚɤɭɭɦ
D(Wx ) = exp(−4π 2me (Wa − Wx ) / h) . |
(7.17) |
Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɪɨɡɪɚɱɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɧɟɩɪɹɦɨɭɝɨɥɶɧɨɣ ɮɨɪɦɵ ɦɨɠɧɨ ɟɝɨ ɪɚɡɞɟɥɢɬɶ ɧɚ ɪɹɞ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɛɚɪɶɟɪɨɜ ɲɢɪɢɧɵ dx, ɢ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɬɶ ɩɨ ɲɢɪɢɧɟ ɛɚɪɶɟɪɚ. ȼ ɢɬɨɝɟ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ ɜɵɪɚɠɚɟɬɫɹ ɮɨɪɦɭɥɨɣ:
D(Wx ) = exp[− |
8π 2me (Wa − Wx )3 / 2 |
θ (ζ )], |
(7.18) |
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3he |
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ɝɞɟ θ(ζ) – ɮɭɧɤɰɢɹ ɇɨɪɞɝɟɣɦɚ, ɜɵɪɚɠɚɸɳɚɹɫɹ ɱɟɪɟɡ ɷɥɥɢɩɬɢɱɟɫɤɢɟ ɢɧɬɟɝɪɚɥɵ,
ɝɞɟ ζ |
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ɲ |
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∆ϕ ɲ |
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e3 / 2 E1 / 2 |
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. ɇɟɤɨɬɨɪɵɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɇɨɪɞɝɟɣɦɚ |
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ϕ a (Wx ) |
Wa − Wx |
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Wa − Wx |
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ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ 7.1. |
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Ɍɚɛɥɢɰɚ 7.1. |
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∆ϕɲ/ ϕa |
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0.1 |
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0.3 |
0.4 |
0.5 |
0.6 |
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1.0 |
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θ |
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0.87 |
0.79 |
0.69 |
0.58 |
0.45 |
0.31 |
0.16 |
0 |
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Ⱦɥɹ 0 < ζ < 1 θ(ζ) ≈ 0.955 – 1.03ζ 2. ɉɥɨɬɧɨɫɬɶ ɬɨɤɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɮɨɪɦɭɥɨɣ Ɏɚɭɥɟɪɚ-ɇɨɪɞɝɟɣɦɚ:
j |
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θ (∆ϕ ɲ / ϕ a ) |
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ɫɦ2 |
eϕ a |
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E / E0 |
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(7.19) |
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EF / eϕ a E 2 [ȼ/ ɫɦ] |
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6.85 |
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EF + eϕ a |
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E[ȼ/ ɫɦ] |
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ɝɞɟ EF – |
ɷɧɟɪɝɢɹ Ɏɟɪɦɢ, B0=e2/(8πh), E0=8π |
2me |
/(3he). ȼɥɢɹɧɢɟ ɦɧɨɠɢɬɟɥɹ E2, |
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ɩɨɞɨɛɧɨ ɜɥɢɹɧɢɸ ɦɧɨɠɢɬɟɥɹ T2 ɜ ɮɨɪɦɭɥɟ Ɋɢɱɚɪɞɫɨɧɚ-Ⱦɷɲɦɚɧɚ, ɧɟɡɧɚɱɢɬɟɥɶɧɨ. Ȼɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨ ɜɥɢɹɧɢɟ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɚ eϕa. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɯ ɨɫɬɪɢɣ ɱɚɳɟ ɜɫɟɝɨ ɹɜɥɹɟɬɫɹ ɩɪɢɱɢɧɨɣ ɩɪɨɛɨɹ ɜɚɤɭɭɦɧɵɯ ɩɪɨɦɟɠɭɬɤɨɜ. Ⱥɜɬɨɷɥɟɤɬɪɨɧɧɵɟ ɤɚɬɨɞɵ ɢɡɝɨɬɨɜɥɹɸɬɫɹ ɜ ɜɢɞɟ ɢɝɥ (ɨɫɬɪɢɣ) ɫ ɛɨɥɶɲɨɣ ɤɪɢɜɢɡɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɤɨɥɨ ɤɨɬɨɪɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɞɨɫɬɢɝɚɟɬ ɛɨɥɟɟ 106 ȼ/ɫɦ.
§46. ɂɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɷɦɢɬɬɟɪɚ ɩɪɢ ɬɟɪɦɨ- ɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ
ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ, ɭɧɨɫɢɦɚɹ ɷɥɟɤɬɪɨɧɨɦ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɢ ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ, ɦɨɠɟɬ ɛɵɬɶ ɜɵɱɢɫɥɟɧɚ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɦɚɤɫɜɟɥɥɨɜɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ, ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɷɧɟɪɝɢɹ ɜɵɲɟɞɲɢɯ ɢɡ ɦɟɬɚɥɥɚ ɷɥɟɤɬɪɨɧɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɫɨɨɬɧɨɲɟɧɢɣ ɦɟɠɞɭ ɤɨɦɩɨɧɟɧɬɚɦɢ ɫɤɨɪɨɫɬɢ ɷɥɟɤɬɪɨɧɚ ɜ ɦɟɬɚɥɥɟ v ɢ ɜ ɜɚɤɭɭɦɟ u :
mu |
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− W |
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®u y |
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°¯uz = vz
ɝɞɟ ɨɫɶ x ɧɚɩɪɚɜɥɟɧɚ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ɑɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ ɫɨ ɫɤɨɪɨɫɬɹɦɢ ɜ ɩɪɟɞɟɥɚɯ ɨɬ ux
ɞɨ ux + dux ɡɚɞɚɟɬɫɹ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ Ɇɚɤɫɜɟɥɥɚ :
dN = |
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kBT exp(EF |
/ kBT ) exp(− |
2mWa + m |
2 ux |
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h3 |
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T exp(−eϕ |
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T ) exp(− |
mux 2 |
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du |
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mN |
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2kBT |
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(7.21) |
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ɝɞɟ N = jT/e – ɱɢɫɥɨ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ ɫ ɟɞɢɧɢɰɵ ɩɥɨɳɚɞɢ ɜ ɫɟɤɭɧɞɭ. |
ɋɪɟɞɧɹɹ |
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ɷɧɟɪɝɢɹ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɨɜɟɪɯɧɨɫɬɢ: |
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ux =∞ |
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(7.22) |
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Wx = |
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ux =0 |
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0 |
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ɝɞɟ ε = Wx/kBT. Ⱦɥɹ ɞɜɭɯ ɞɪɭɝɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɤɚɤ ɞɥɹ ɨɛɵɱɧɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ: Wy
ɩɨɥɧɨɣ ɷɧɟɪɝɢɢ ɜɵɥɟɬɚɸɳɟɝɨ
W = Wx + Wy + Wz = 2k
=12 kBT ɢ Wz = 12 kBT . ȼ ɢɬɨɝɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ
ɫɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɬɟɦɩɟɪɚɬɭɪɵ Ɍs:
BTS . |
(7.23) |
ȿɫɥɢ ɦɟɠɞɭ ɤɚɬɨɞɨɦ ɢ ɚɧɨɞɨɦ ɩɨɞɚɬɶ ɬɨɪɦɨɡɹɳɭɸ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ, ɬɨ ɭɫɥɨɜɢɟ ɩɨɩɚɞɚɧɢɹ ɷɥɟɤɬɪɨɧɚ ɧɚ ɤɚɬɨɞ: mev2/2 ≥ -eUa, ɝɞɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɚɧɨɞɟ Ua < 0. Ɍɨɤ ɧɚ ɚɧɨɞ:
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I a = Sa |
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exp( |
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(7.24) |
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ɝɞɟ Iɷ – ɬɨɤ ɫ ɷɦɢɬɬɟɪɚ. Ɇɟɧɹɹ Ua, ɦɨɠɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɹɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ. ɗɤɫɩɟɪɢɦɟɧɬɵ ɩɨɞɬɜɟɪɠɞɚɸɬ ɬɨ, ɱɬɨ ɷɦɢɬɢɪɨɜɚɧɧɵɟ ɷɥɟɤɬɪɨɧɵ ɢɦɟɸɬ ɪɚɫɩɪɟɞɟɥɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ, ɩɪɢɱɟɦ ɬɟɦɩɟɪɚɬɭɪɚ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɦɚɤɫɜɟɥɥɨɜɫɤɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɷɦɢɬɬɟɪɚ. ɉɨɷɬɨɦɭ ɧɚɱɚɥɶɧɵɟ ɷɧɟɪɝɢɢ ɷɦɢɬɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ (ɫ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ 1 ɷȼ ≈ 11600 Ʉ) ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɧɭɥɟɜɵɦɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɷɧɟɪɝɢɹɦɢ, ɩɪɢɨɛɪɟɬɚɟɦɵɦɢ ɜ ɭɫɤɨɪɹɸɳɟɣ ɪɚɡɧɨɫɬɢ ɩɨɬɟɧɰɢɚɥɨɜ ɭɠɟ ɜ ɧɟɫɤɨɥɶɤɨ ɜɨɥɶɬ. Ɉɞɧɚɤɨ ɞɥɹ ɨɯɥɚɠɞɟɧɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɷɦɢɬɬɟɪɚ ɷɬɚ ɷɧɟɪɝɢɹ ɫɭɳɟɫɬɜɟɧɧɚ, ɤ ɬɨɦɭ ɠɟ ɤɚɠɞɵɣ ɷɥɟɤɬɪɨɧ ɩɨɦɢɦɨ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɭɧɨɫɢɬ ɢɡ ɦɟɬɚɥɥɚ ɷɧɟɪɝɢɸ, ɪɚɜɧɭɸ ɪɚɛɨɬɟ ɜɵɯɨɞɚ. Ɇɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɨɯɥɚɠɞɟɧɢɹ w = (jT/e)(2kBTS+eϕa).
ɉɪɢ ɚɜɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɡɚ ɫɱɟɬ «ɬɭɧɧɟɥɶɧɨɝɨ» ɷɮɮɟɤɬɚ ɷɦɢɬɢɪɭɸɬɫɹ ɷɥɟɤɬɪɨɧɵ, ɨɛɥɚɞɚɸɳɢɟ ɷɧɟɪɝɢɟɣ, ɦɟɧɶɲɟɣ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ: E < EF. ɋɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɷɬɨɦ ɫɥɭɱɚɟ W = - ϕa – (EF-E), ɦɨɳɧɨɫɬɶ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɧɚɝɪɟɜɚ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚ ɫɱɟɬ ɩɪɢɯɨɞɚ ɛɨɥɟɟ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɨɛɴɟɦɚ ɦɟɬɚɥɥɚ: w = (jT/e)( EF-E). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɟɪɦɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɨɯɥɚɠɞɟɧɢɟɦ ɩɨɜɟɪɯɧɨɫɬɢ, ɚ ɚɜɬɨɷɥɟɤɬɪɨɧɧɚɹ – ɧɚɝɪɟɜɨɦ (ɷɮɮɟɤɬ ɇɨɬɬɢɧɝɟɦɚ).
§47. Ɏɨɬɨɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɂɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɚɞɚɸɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɮɨɬɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ (Ɏɗɗ). ɉɨɬɨɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɱɚɫɬɶɸ ɨɬɪɚɠɚɟɬɫɹ, ɚ ɱɚɫɬɶɸ ɩɪɨɧɢɤɚɟɬ ɜɧɭɬɪɶ ɬɟɥɚ ɢ ɬɚɦ ɩɨɝɥɨɳɚɟɬɫɹ, ɨɬɞɚɜɚɹ ɷɧɟɪɝɢɸ ɷɥɟɤɬɪɨɧɚɦ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɪɟɨɞɨɥɟɬɶ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢ ɜɵɣɬɢ ɢɡ ɬɟɥɚ. Ɏɗɗ ɛɵɥɚ ɨɛɧɚɪɭɠɟɧɚ Ƚɟɪɰɟɦ 1887 ɝ. Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɵ Ɏɗɗ, ɭɫɬɚɧɨɜɥɟɧɧɵɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɡɚɞɨɥɝɨ ɞɨ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɨɛɨɫɧɨɜɚɧɢɹ, ɫɜɨɞɹɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ:
1.Ɏɨɬɨɷɥɟɤɬɪɨɧɧɵɣ ɬɨɤ ɜ ɪɟɠɢɦɟ ɧɚɫɵɳɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɩɚɞɚɸɳɟɦɭ ɧɚ
ɷɦɢɬɬɟɪ ɩɥɨɬɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɳɧɨɫɬɢ (ɢɥɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɨɛɥɭɱɟɧɢɹ I
[ȼɬ/ɫɦ2])
jɎɗ I (ɡɚɤɨɧ ɋɬɨɥɟɬɨɜɚ – 1889 ɝ.). |
(7.25) |
2. Ɍɟɨɪɟɬɢɱɟɫɤɨɟ ɨɛɨɫɧɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɬɤɪɵɬɨɣ Ʌɟɧɚɪɞɨɦ (1899 ɝ.) ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ – ɦɚɤɫɢɦɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɱɚɫɬɨɬɟ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɟɝɨ ɢɧɬɟɧɫɢɜɧɨɫɬɢ – ɜɩɟɪɜɵɟ ɞɚɥ ɗɣɧɲɬɟɣɧ, ɜɜɟɞɹ ɜ ɮɢɡɢɤɭ ɩɨɧɹɬɢɟ ɨ ɤɜɚɧɬɚɯ ɫɜɟɬɚ (ɮɨɬɨɧɚɯ):
mv2 |
= hν − eϕ a |
(ɡɚɤɨɧ ɗɣɧɲɬɟɣɧɚ). |
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max |
(7.26) |
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2 |
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Ɉɬɤɥɨɧɟɧɢɟ ɨɬ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɛɨɥɶɲɢɯ ɢɧɬɟɧɫɢɜɧɨɫɬɹɯ ɢɡɥɭɱɟɧɢɹ, ɤɨɝɞɚ ɷɥɟɤɬɪɨɧ ɦɨɠɟɬ ɩɨɝɥɨɳɚɬɶ ɧɟɫɤɨɥɶɤɨ n ɮɨɬɨɧɨɜ:
mv2 |
= nhν − eϕ a |
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max |
(7.27) |
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2 |
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3.ɋɥɟɞɫɬɜɢɟɦ ɡɚɤɨɧɚ ɗɣɧɲɬɟɣɧɚ ɹɜɥɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɞɥɢɧɨɜɨɥɧɨɜɨɣ (ɤɪɚɫɧɨɣ) ɝɪɚɧɢɰɵ λ ɨɛɥɚɫɬɢ ɫɩɟɤɬɪɚ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ, ɤɨɬɨɪɨɟ ɦɨɠɟɬ ɜɵɡɵɜɚɬɶ ɮɨɬɨɷɦɢɫɫɢɸ ɷɥɟɤɬɪɨɧɨɜ:
λ < λɝɪ, ɢɥɢ ν > νɝɪ = c/λɝɪ = eϕa/h, |
(7.28) |
ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɪɚɧɢɱɧɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɪɚɛɨɬɭ ɜɵɯɨɞɚ: λɝɪ=12300/( eϕa[ɷȼ]) ɩɪɢ Ɍ = 0 Ʉ. ɉɪɢ Ɍ ≠ 0 Ʉ ɜ ɦɟɬɚɥɥɟ ɢɦɟɸɬɫɹ ɷɥɟɤɬɪɨɧɵ ɫ ɷɧɟɪɝɢɹɦɢ, ɛɨɥɶɲɢɦɢ EF, ɞɥɹ ɧɢɯ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɫɧɢɠɚɟɬɫɹ. ɇɨ ɜ ɯɨɥɨɞɧɨɦ ɦɟɬɚɥɥɟ ɞɨɥɹ ɬɚɤɢɯ ɷɥɟɤɬɪɨɧɨɜ ɤɪɚɣɧɟ ɦɚɥɚ. Ʉɪɨɦɟ ɬɨɝɨ, ɪɚɛɨɬɚ ɜɵɯɨɞɚ, ɚ ɡɧɚɱɢɬ, ɢ ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ (ɷɮɮɟɤɬ ɒɨɬɬɤɢ).
4.Ɏɨɬɨɷɮɮɟɤɬ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɨɦ ɛɟɡɵɧɟɪɰɢɚɥɶɧɨɫɬɢ - ɮɨɬɨɬɨɤ ɩɨɹɜɥɹɟɬɫɹ ɢ ɢɫɱɟɡɚɟɬ ɜɦɟɫɬɟ ɫ ɨɫɜɟɳɟɧɢɟɦ, ɡɚɩɚɡɞɵɜɚɹ ɧɟ ɛɨɥɟɟ ɱɟɦ ɧɚ 10-9 ɫ.
Ɏɨɬɨɷɮɮɟɤɬ ɦɨɠɧɨ ɯɚɪɚɤɬɟɪɢɡɨɜɚɬɶ ɥɢɛɨ ɤɜɚɧɬɨɜɵɦ ɜɵɯɨɞɨɦ Y – ɱɢɫɥɨɦ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɢɧ ɮɨɬɨɧ (Y = 10-3÷10-1), ɥɢɛɨ ɩɥɨɬɧɨɫɬɶɸ ɮɨɬɨɬɨɤɚ jɮ. Ɉɬɧɨɲɟɧɢɟ ɮɨɬɨɬɨɤɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɨɝɨ ɢɡɥɭɱɟɧɢɹ ɜɵɪɚɠɚɟɬ ɫɩɟɤɬɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ ɮɨɬɨɤɚɬɨɞɨɜ, ɚ ɤ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɩɨɬɨɤɚ ɢɡɥɭɱɟɧɢɹ ɫɬɚɧɞɚɪɬɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɫɜɟɬɚ – ɢɧɬɟɝɪɚɥɶɧɭɸ ɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɶ. Ƚɥɭɛɢɧɚ ɜɵɯɨɞɚ ɷɥɟɤɬɪɨɧɨɜ ɢɡ ɦɟɬɚɥɥɨɜ ɫɨɫɬɚɜɥɹɟɬ ɧɚɫɤɨɥɶɤɨ ɚɬɨɦɧɵɯ ɫɥɨɟɜ, ɩɨɷɬɨɦɭ, ɬɟɪɹɹ ɧɚ ɫɜɨɟɦ ɩɭɬɢ ɱɚɫɬɶ ɷɧɟɪɝɢɢ, ɮɨɬɨɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɡ ɦɟɬɚɥɥɨɜ ɢɦɟɸɬ ɧɟɤɨɬɨɪɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɨ ɷɧɟɪɝɢɹɦ ɨɬ ɧɭɥɹ ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɨ ɡɚɤɨɧɭ ɗɣɧɲɬɟɣɧɚ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɬɟɧɰɢɚɥɚ. Ⱦɥɹ ɫɛɨɪɚ ɧɚ ɚɧɨɞ ɜɫɟɯ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ ɜ ɨɩɵɬɚɯ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɤɚɬɨɞ ɜ ɜɢɞɟ ɲɚɪɚ ɢ ɚɧɨɞ ɜ ɜɢɞɟ ɤɨɧɰɟɧɬɪɢɱɟɫɤɨɣ ɤɚɬɨɞɭ ɫɮɟɪɵ, ɱɟɪɟɡ ɭɡɤɨɟ ɨɬɜɟɪɫɬɢɟ ɤɨɬɨɪɨɣ ɧɚ ɤɚɬɨɞ ɩɨɞɚɜɚɥɫɹ ɥɭɱ ɫɜɟɬɚ. Ɋɚɡɧɨɫɬɶ ɡɧɚɱɟɧɢɣ ɬɨɤɚ ɩɪɢ ɞɜɭɯ ɡɚɞɟɪɠɢɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɚɯ -U ɢ -(U + ∆U) ɞɚɟɬ ɱɢɫɥɨ ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ, ɷɧɟɪɝɢɹ ɤɨɬɨɪɵɯ ɩɪɢ ɜɵɥɟɬɟ ɫ ɤɚɬɨɞɚ ɥɟɠɢɬ ɜ ɩɪɟɞɟɥɚɯ ɨɬ eU ɞɨ e(U + ∆U). ɗɬɨɬ ɠɟ ɦɟɬɨɞ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɵ
ɮɨɬɨɷɮɮɟɤɬɚ. Ɂɚɞɟɪɠɢɜɚɸɳɢɣ ɩɨɬɟɧɰɢɚɥ, ɩɪɢ ɤɨɬɨɪɨɦ ɮɨɬɨɬɨɤ ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ, ɨɩɪɟɞɟɥɹɟɬ ɪɚɡɧɨɫɬɶ ɦɟɠɞɭ ɱɚɫɬɨɬɨɣ ɝɚɦɦɚ-ɤɜɚɧɬɚ ν ɢ ɝɪɚɧɢɱɧɨɣ ɱɚɫɬɨɬɨɣ ɮɨɬɨɷɮɮɟɤɬɚ νɝɪ ɞɥɹ ɞɚɧɧɨɝɨ ɦɚɬɟɪɢɚɥɚ: U0 = h(ν - νɝɪ)/e. Ɂɧɚɱɟɧɢɹ U0, ɨɩɪɟɞɟɥɹɟɦɵɟ ɞɥɹ ɪɚɡɧɵɯ ɱɚɫɬɨɬ ɨɛɥɭɱɟɧɢɹ ν, ɥɟɠɚɬ ɧɚ ɩɪɹɦɨɣ, ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɤɨɬɨɪɨɣ ɫ ɨɫɶɸ ɚɛɫɰɢɫɫ ɞɚɟɬ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ.
Ɉɫɧɨɜɧɵɟ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ Ɏɗɗ ɦɟɬɚɥɥɨɜ ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɸɬɫɹ ɬɟɨɪɢɟɣ Ɏɚɭɥɟɪɚ, ɫɨɝɥɚɫɧɨ ɤɨɬɨɪɨɣ ɩɨɫɥɟ ɩɨɝɥɨɳɟɧɢɹ ɜ ɦɟɬɚɥɥɟ ɮɨɬɨɧɚ ɟɝɨ ɷɧɟɪɝɢɹ
ɩɟɪɟɯɨɞɢɬ |
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ɷɥɟɤɬɪɨɧɚɦ |
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ɩɪɨɜɨɞɢɦɨɫɬɢ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɱɟɝɨ |
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ɷɥɟɤɬɪɨɧɧɵɣ ɝɚɡ ɜ ɦɟɬɚɥɥɟ ɨɤɨɥɨ |
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ɟɝɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨɫɬɨɢɬ ɢɡ ɫɦɟɫɢ |
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ɝɚɡɨɜ |
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ɫ |
ɧɨɪɦɚɥɶɧɵɦ |
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(ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ |
Ɏɟɪɦɢ) |
ɢ |
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ɜɨɡɛɭɠɞɟɧɧɵɦ (ɫɞɜɢɧɭɬɵɦ ɧɚ hν) |
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ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɩɨ ɷɧɟɪɝɢɹɦ (ɪɢɫ. |
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7.3). |
Ⱦɥɹ |
ɩɨɞɫɱɟɬɚ |
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ɱɢɫɥɚ |
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ɮɨɬɨɷɥɟɤɬɪɨɧɨɜ |
ɦɨɠɧɨ |
ɩɪɨɜɟɫɬɢ |
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ɬɚɤɨɟ ɠɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɢ |
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ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɱɬɨ ɢ ɩɪɢ ɩɨɞɫɱɟɬɟ |
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ɩɥɨɬɧɨɫɬɢ |
ɬɨɤɚ |
ɬɟɪɦɨɷɦɢɫɫɢɢ, |
Ɋɢɫ. 7.3. Ɏɨɬɨɷɦɢɫɫɢɨɧɧɵɣ ɬɨɤ ɷɥɟɤɬɪɨɧɨɜ ɢɡ |
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ɢɡɦɟɧɢɜ |
ɧɢɠɧɢɣ |
ɩɪɟɞɟɥ |
«ɯɜɨɫɬɚ» ɜɨɡɦɭɳɟɧɧɨɣ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, |
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ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɫ Wa ɧɚ Wa |
- hν, |
ɩɪɟɨɞɨɥɟɜɚɸɳɢɯ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ |
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ɬɟɦ |
ɫɚɦɵɦ |
ɜɤɥɸɱɢɜ |
ɜ |
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ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɷɥɟɤɬɪɨɧɵ, ɤɨɬɨɪɵɟ ɩɪɢɨɛɪɟɬɚɸɬ ɧɟɞɨɫɬɚɸɳɭɸ ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɝɨ ɛɚɪɶɟɪɚ ɷɧɟɪɝɢɸ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɧɵɯ ɤɜɚɧɬɨɜ. Ɍɚɤ ɠɟ, ɤɚɤ ɢ ɞɥɹ ɬɟɪɦɨɷɥɟɤɬɪɨɧɨɜ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɯɨɠɞɟɧɢɹ ɛɚɪɶɟɪɚ, ɬɚɤ ɤɚɤ ɱɚɫɬɶ ɷɥɟɤɬɪɨɧɨɜ ɩɪɢ ɞɜɢɠɟɧɢɢ ɢɡ ɦɟɬɚɥɥɚ ɦɨɠɟɬ ɛɵɬɶ ɨɬɪɚɠɟɧɚ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɪɚɡɞɟɥɚ ɦɟɬɚɥɥ - ɜɚɤɭɭɦ. Ʉɪɨɦɟ ɷɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɭɱɟɫɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɝɥɨɳɟɧɢɹ ɮɨɬɨɧɚ. ɗɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɨɝɥɨɳɚɸɳɟɝɨ ɷɥɟɤɬɪɨɧɚ ɢ ɷɧɟɪɝɢɢ ɝɚɦɦɚɤɜɚɧɬɚ. ȼ ɬɟɨɪɢɢ Ɏɚɭɥɟɪɚ ɷɬɚ ɜɟɪɨɹɬɧɨɫɬɶ ɫɱɢɬɚɟɬɫɹ ɩɨɫɬɨɹɧɧɨɣ ɜɟɥɢɱɢɧɨɣ, ɱɬɨ, ɤɚɤ ɨɤɚɡɚɥɨɫɶ, ɜ ɢɧɬɟɪɜɚɥɟ ɱɚɫɬɨɬ ɨɬ νɝɪ ɞɨ
ɜɵɩɨɥɧɹɟɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɏɚɭɥɟɪɚ:
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°B1T 2 exp( |
hν − hν ɝɪ |
),ν ≤ ν ɝɪ = eϕ a / h |
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jɎ |
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kT |
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(7.29) |
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°°B2T 2 |
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(hν |
− hν ɝɪ )2 |
+ B3 ),ν > ν ɝɪ |
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ɝɞɟ B1, B2, B3 – ɩɨɫɬɨɹɧɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ, ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵɟ A0. Ɂɚɜɢɫɢɦɨɫɬɶ jɮ( kThγ ) ɦɨɠɧɨ ɬɚɤɠɟ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɹɞɨɜ [32]. ɂɡ ɮɨɪɦɭɥɵ Ɏɚɭɥɟɪɚ ɜɢɞɧɨ,
ɱɬɨ ɩɪɢ Ɍ ≈0 jɮ → 0 ɢ νɝɪ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɹɜɥɹɟɬɫɹ ɤɪɚɫɧɨɣ ɝɪɚɧɢɰɟɣ. ɉɪɢ Ɍ ≠ 0 ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɪɟɡɤɨɣ ɝɪɚɧɢɰɵ ɮɨɬɨɷɮɮɟɤɬɚ, ɮɨɬɨɬɨɤ ɩɚɞɚɟɬ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨ ɩɪɢ ν < νɝɪ, ɩɪɢ ν > νɝɪ ɩɥɨɬɧɨɫɬɶ ɮɨɬɨɬɨɤɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɤɜɚɞɪɚɬɭ ɱɚɫɬɨɬɵ ɩɚɞɚɸɳɟɝɨ ɢɡɥɭɱɟɧɢɹ jɎ ν 2. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɨɠɟɧɢɟ νɝɪ ɨɩɪɟɞɟɥɹɸɬ ɩɨ ɢɡɦɟɪɟɧɧɨɣ ɫɩɟɤɬɪɚɥɶɧɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɮɨɬɨɬɨɤɚ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ > 0. ɗɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɝɪɚɮɢɤɟ ɜ ɤɨɨɪɞɢɧɚɬɚɯ x = hν/kT ɢ y = ln( jɎ/T2). ɉɨɥɭɱɟɧɧɚɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɚɹ ɤɪɢɜɚɹ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɚɜɢɫɢɦɨɫɬɢ:
ln( jɎ/T2) = B + F((hν- hνɝɪ)/kT) = B + F(x- hνɝɪ/kT). |
(7.30) |
Ⱦɚɧɧɚɹ ɤɪɢɜɚɹ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ |
ɮɭɧɤɰɢɢ Ɏɚɭɥɟɪɚ F = |
F(hν/kT) ɫɞɜɢɝɨɦ ɩɨ ɨɫɢ y ɧɚ ɤɨɧɫɬɚɧɬɭ B ɢ ɩɨ ɨɫɢ x ɧɚ hνɝɪ/kT (ɪɢɫ. 7.4). ɂɦɟɧɧɨ ɨɩɪɟɞɟɥɟɧɢɟ ɫɞɜɢɝɚ ɩɨ ɨɫɢ x ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɤɪɢɜɨɣ ɞɥɹ ɟɟ ɫɨɜɦɟɳɟɧɢɹ ɫ
ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɤɪɢɜɨɣ Ɏɚɭɥɟɪɚ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɝɪɚɧɢɱɧɭɸ ɱɚɫɬɨɬɭ νɝɪ.
§48. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɛɨɦɛɚɪɞɢɪɭɟɦɨɣ ɩɨɬɨɤɨɦ ɷɥɟɤɬɪɨɧɨɜ, ɧɚɡɵɜɚɟɬɫɹ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɟɣ.
ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɚɹ ɫɯɟɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɦɟɬɨɞɨɦ ɡɚɞɟɪɠɢɜɚɸɳɟɝɨ ɩɨɥɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɮɟɪɢɱɟɫɤɨɝɨ ɤɨɥɥɟɤɬɨɪɚ Ʌɭɤɢɪɫɤɨɝɨ ɢ ɉɪɟɥɢɠɚɟɜɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 7.5. Ɂɚɞɟɪɠɢɜɚɸɳɟɟ ɩɨɥɟ
ɩɪɢɤɥɚɞɵɜɚɟɬɫɹ ɦɟɠɞɭ ɦɢɲɟɧɶɸ ɢ ɤɨɥɥɟɤɬɨɪɨɦ. ȿɫɥɢ
ɩɨɬɟɧɰɢɚɥ ɤɨɥɥɟɤɬɨɪɚ ɛɭɞɟɬ ɛɨɥɶɲɟ, ɱɟɦ ɧɚ ɦɢɲɟɧɢ, ɬɨ ɧɚ ɤɨɥɥɟɤɬɨɪ ɩɪɢɞɟɬ ɩɨɥɧɵɣ ɬɨɤ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ Is. ȼɬɨɪɢɱɧɚɹ ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɨɞɧɭ ɩɟɪɜɢɱɧɭɸ ɱɚɫɬɢɰɭ: γe = Ns/Np. ɂɧɬɟɝɪɚɥɶɧɨ ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɬɨɤɨɜ
Ɋɢɫ. 7.5. ɋɯɟɦɚ ɨɩɵɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ
Ɋɢɫ. 7.6. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɩɨ ɷɧɟɪɝɢɹɦ
ɜɬɨɪɢɱɧɵɯ ɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Is/Ip. Ȼɨɥɟɟ ɬɨɱɧɵɦ ɦɟɬɨɞɨɦ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɢɫɩɟɪɫɢɨɧɧɵɯ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɢɥɢ ɦɚɝɧɢɬɧɨɝɨ ɷɧɟɪɝɨɚɧɚɥɢɡɚɬɨɪɚ ɫ ɩɨɥɭɤɪɭɝɨɜɨɣ ɬɪɚɟɤɬɨɪɢɟɣ, ɨɩɢɫɚɧɧɨɝɨ ɜ ɝɥɚɜɟ 5. ɉɨɥɭɱɟɧɧɨɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɟ
ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ (ɪɢɫ. 7.6) ɧɟɡɚɜɢɫɢɦɨ ɨɬ
ɦɚɬɟɪɢɚɥɚ ɢ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɨɞɟɪɠɢɬ ɞɜɚ ɜɵɫɨɤɢɯ
Ɋɢɫ. 7.7. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɢɫɬɢɧɧɨɣ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ W, Mo, C, Be
ɦɚɤɫɢɦɭɦɚ. ɉɟɪɜɵɣ ɜ ɨɛɥɚɫɬɢ ɦɚɥɵɯ ɷɧɟɪɝɢɣ (< 50 ɷȼ) ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɫɬɢɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɤɨɬɨɪɵɟ ɜɵɯɨɞɹɬ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɝɥɨɳɟɧɢɹ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɥɟɤɨ ɧɟ ɜɫɟ ɷɥɟɤɬɪɨɧɵ, ɩɨɥɭɱɢɜɲɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ, ɞɨɛɢɪɚɸɬɫɹ ɞɨ ɩɨɜɟɪɯɧɨɫɬɢ, ɪɚɫɬɪɚɱɢɜɚɹ ɷɧɟɪɝɢɸ ɩɨ ɩɭɬɢ ɧɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɫ ɢɨɧɚɦɢ ɪɟɲɟɬɤɢ ɢ ɞɪɭɝɢɦɢ ɷɥɟɤɬɪɨɧɚɦɢ. ɉɪɟɨɞɨɥɟɜɲɢɟ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ ɢɫɬɢɧɧɵɟ ɜɬɨɪɢɱɧɵɟ ɷɥɟɤɬɪɨɧɵ ɧɚ ɜɵɯɨɞɟ ɢɦɟɸɬ ɷɧɟɪɝɢɢ, ɧɟ ɡɚɜɢɫɹɳɢɟ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɋɚɛɨɬɚ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɬɚɤɠɟ ɧɟ ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɷɦɢɫɫɢɸ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɬɚɤ ɤɚɤ, ɜɨ-ɩɟɪɜɵɯ, ɷɧɟɪɝɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɤɚɤ ɩɪɚɜɢɥɨ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ, ɜɨ-ɜɬɨɪɵɯ, ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɧɟ ɢɡ ɩɨɜɟɪɯɧɨɫɬɧɵɯ ɫɥɨɟɜ, ɚ ɢɡ ɝɥɭɛɢɧɵ ɦɟɬɚɥɥɚ, ɩɨɷɬɨɦɭ ɛɨɥɟɟ ɜɚɠɧɵɦ ɹɜɥɹɟɬɫɹ ɩɨɬɟɪɹ ɷɧɟɪɝɢɢ ɩɪɢ ɞɜɢɠɟɧɢɢ ɷɥɟɤɬɪɨɧɚ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. ȼɬɨɪɨɣ, ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɭɡɤɢɣ ɦɚɤɫɢɦɭɦ ɧɚɯɨɞɢɬɫɹ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɩɟɪɜɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɫɨɯɪɚɧɢɜɲɢɦ ɫɜɨɸ ɫɤɨɪɨɫɬɶ ɩɨɫɥɟ ɨɬɪɚɠɟɧɢɹ. ɉɨɥɨɠɟɧɢɟ ɷɬɨɝɨ ɦɚɤɫɢɦɭɦɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ɉɛɥɚɫɬɶ ɷɧɟɪɝɢɣ ɦɟɠɞɭ ɷɬɢɦɢ ɞɜɭɦɹ ɦɚɤɫɢɦɭɦɚɦɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɟ ɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɦ ɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɫɩɟɤɬɪ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɨɫɬɨɢɬ ɢɡ
Ɋɢɫ. 7.8. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɬɪɚɠɟɧɢɹ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ
ɲɢɪɨɤɨɝɨ ɩɢɤɚ ɜ ɨɛɥɚɫɬɢ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ Wmax, ɤɨɬɨɪɵɣ ɩɪɢɧɚɞɥɟɠɢɬ ɢɫɬɢɧɧɨɜɬɨɪɢɱɧɵɦ ɷɥɟɤɬɪɨɧɚɦ, ɜɵɯɨɞɹɳɢɦ ɫ ɝɥɭɛɢɧɵ 5 - 100 Α ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ, ɢ ɨɱɟɧɶ ɭɡɤɨɝɨ ɩɢɤɚ ɨɬɪɚɠɟɧɧɵɯ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɷɥɟɤɬɪɨɧɨɜ ɜ ɨɛɥɚɫɬɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɣ ɫ ɦɚɤɫɢɦɭɦɨɦ ɩɪɢ ɷɧɟɪɝɢɢ, ɪɚɜɧɨɣ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɫɬɢɧɧɨɣ ɷɥɟɤɬɪɨɧ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɜɜɨɞɹɬ ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ δe= Ns/Np , ɝɞɟ Ns – ɱɢɫɥɨ ɢɫɬɢɧɧɨ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, Ns - ɱɢɫɥɨ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ɩɚɞɚɸɳɢɯ ɧɚ
ɩɨɜɟɪɯɧɨɫɬɶ ɜ ɟɞɢɧɢɰɭ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɷɦɢɫɫɢɢ ɨɬɪɚɠɟɧɧɵɯ ɨɬ
ɩɨɜɟɪɯɧɨɫɬɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɪɚɠɟɧɢɹ ηe = (Ne+Nu)/Np, ɝɞɟ Ne ɢ Nu - ɭɩɪɭɝɨ ɢ ɧɟɭɩɪɭɝɨ ɨɬɪɚɠɟɧɧɵɟ ɷɥɟɤɬɪɨɧɵ. ɋɭɦɦɚɪɧɵɣ
ɤɨɷɮɮɢɰɢɟɧɬ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ γe = δe + ηe. Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp ɡɚɞɚɟɬɫɹ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ (Kollath):
δ e (Wp ) = (2.72) |
2 Wp |
exp(−2 |
Wp |
) , |
(7.31) |
|
δ e max |
|
Wmax |
Wmax |
|
|
|
ɝɞɟ δemax= 0.35eϕ a , |
Wmax |
– ɡɧɚɱɟɧɢɟ ɢ |
ɩɨɥɨɠɟɧɢɟ |
ɦɚɤɫɢɦɭɦɚ. ɉɨɥɨɠɟɧɢɟ |
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ɦɚɤɫɢɦɭɦɚ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɞɥɹ ɪɚɡɧɵɯ ɦɚɬɟɪɢɚɥɨɜ ɩɪɟɞɫɬɚɜɥɟɧɨ ɜ ɬɚɛɥɢɰɟ 7.2. Ɋɨɫɬ δe ɫ ɷɧɟɪɝɢɟɣ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɫɦɟɧɹɟɬɫɹ ɫɩɚɞɨɦ (ɪɢɫ. 7.7), ɬɚɤ ɤɚɤ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɨɛɪɚɡɨɜɚɧɢɟ ɜɬɨɪɢɱɧɵɯ ɩɪɨɢɫɯɨɞɢɬ ɜɫɟ ɝɥɭɛɠɟ ɢ ɝɥɭɛɠɟ, ɪɚɫɬɭɬ ɩɨɬɟɪɢ ɷɧɟɪɝɢɢ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɦɟɬɚɥɥɟ ɢ ɢɯ ɜɵɯɨɞ ɫɬɚɧɨɜɢɬɫɹ ɜɫɟ ɛɨɥɟɟ ɡɚɬɪɭɞɧɟɧɧɵɦ. ɗɬɢɦ ɠɟ ɨɛɴɹɫɧɹɟɬɫɹ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɫɞɜɢɝɚ ɦɚɤɫɢɦɭɦɚ Wmax ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɞɥɹ ɦɚɬɟɪɢɚɥɨɜ ɫ ɜɵɫɨɤɢɦ ɚɬɨɦɧɵɦ ɱɢɫɥɨɦ (ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɨɥɶɮɪɚɦɚ) ɜ ɫɬɨɪɨɧɭ ɧɢɡɤɢɯ ɷɧɟɪɝɢɣ ɢɡ-ɡɚ ɫɧɢɠɟɧɢɹ ɞɥɢɧɵ ɩɪɨɛɟɝɚ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɜ ɬɜɟɪɞɨɦ ɬɟɥɟ (ɷɥɟɤɬɪɨɧɚɦ, ɩɨɥɭɱɢɜɲɢɦ ɷɧɟɪɝɢɸ ɨɬ ɩɟɪɜɢɱɧɵɯ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɝɱɟ ɜɵɣɬɢ ɢɡ ɬɜɟɪɞɨɝɨ ɬɟɥɚ). Ɂɚɜɢɫɢɦɨɫɬɶ δe ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ α (ɭɝɨɥ ɫ ɧɨɪɦɚɥɶɸ ɤ ɩɨɜɟɪɯɧɨɫɬɢ) ɞɥɹ α < 60ɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
δ e (α ) = δ e (0) / cosβ α , |
(7.32) |
ɝɞɟ β = 1.3 ÷1.5. ɑɟɦ ɛɨɥɶɲɟ α, ɬɟɦ ɦɟɧɶɲɟ ɝɥɭɛɢɧɚ, ɤɨɬɨɪɭɸ ɧɭɠɧɨ ɩɪɟɨɞɨɥɟɬɶ ɜɬɨɪɢɱɧɨɦɭ ɷɥɟɤɬɪɨɧɭ ɞɥɹ ɜɵɯɨɞɚ. ɗɦɩɢɪɢɱɟɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ ɨɬɪɚɠɟɧɢɹ ηe ɞɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɩɚɞɟɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɨɬ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ Wp (ɪɢɫ.7.8) ɢ ɚɬɨɦɧɨɝɨ ɧɨɦɟɪɚ z:
ηe (Wp , z) = Wpm( z)
exp(C(z)) , |
(7.33) |
ɝɞɟ m(z)=0.1382–0.9211z-0.5, C(z)=0.1904–0.2236lnz+0.1292ln2z–0.01491ln3z
(Hunger). Ɂɚɜɢɫɢɦɨɫɬɶ ηe ɨɬɭɝɥɚ ɩɚɞɟɧɢɹ α:
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ηe (α ) = 0.891( |
ηe (0) |
)cosα (Darlington). |
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(7.34) |
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Ɍɚɛɥɢɰɚ |
7.2. |
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Al |
Be |
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C |
ɋ (ɝɪɚɮɢɬ) |
Cu |
Fe |
Mo |
Ni |
Ta |
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Ti |
W |
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(ɚɥɦɚɡ) |
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δemax |
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1.0 |
0.5 |
2.8 |
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1.0 |
1.3 |
1.3 |
1.25 |
1.3 |
1.3 |
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0.9 |
1.4 |
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Wmax[ɷȼ] |
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300 |
200 |
750 |
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300 |
600 |
400 |
375 |
550 |
600 |
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280 |
650 |
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ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɩɪɢɦɟɧɟɧɢɟɦ ɜɬɨɪɢɱɧɨɣ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɹɜɥɹɸɬɫɹ ɷɥɟɤɬɪɨɧɧɵɟ ɭɦɧɨɠɢɬɟɥɢ, ɩɪɢɧɰɢɩ ɞɟɣɫɬɜɢɹ ɤɨɬɨɪɵɯ ɩɪɟɞɫɬɚɜɥɟɧ
ɫɯɟɦɨɣ ɧɚ ɪɢɫ. 7.9. Ɇɚɤɫɢɦɚɥɶɧɨ ɩɨɥɧɨɟ ɩɨɩɚɞɚɧɢɹ ɜɬɨɪɢɱɧɵɯ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɫɥɟɞɭɸɳɢɣ ɷɦɢɬɬɟɪ ɦɨɠɟɬ ɨɛɟɫɩɟɱɢɜɚɬɶɫɹ ɦɚɝɧɢɬɧɨɣ ɢɥɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɮɨɤɭɫɢɪɨɜɤɨɣ.
ȼɬɨɪɢɱɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ
ɉɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɢɨɧɨɜ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɛɥɸɞɚɟɬɫɹ ɷɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɚɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ: γi = ne/ni, ɝɞɟ ne - ɱɢɫɥɨ
ɷɦɢɬɢɪɨɜɚɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ, ni - ɱɢɫɥɨ ɢɨɧɨɜ, ɭɩɚɜɲɢɯ ɧɚ ɬɭ ɠɟ ɩɨɜɟɪɯɧɨɫɬɶ ɡɚ ɬɨ ɠɟ ɜɪɟɦɹ. Ⱦɥɹ ɨɞɧɨɡɚɪɹɞɧɵɯ ɢɨɧɨɜ γi = ne/ni = je/ji, ɩɪɢ ɷɦɢɫɫɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɢɨɧɨɜ ɡɚɪɹɞɨɦ Z γi = Zje/ji. ɗɦɢɫɫɢɹ ɷɥɟɤɬɪɨɧɨɜ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɞɜɭɯ
ɩɪɨɰɟɫɫɨɜ: ɩɟɪɜɵɣ ɩɪɨɰɟɫɫ, ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ ɬɟɥɚ ɡɚ ɫɱɟɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɷɦɢɬɬɟɪɚ ɜ ɩɨɥɟ ɩɪɢɯɨɞɹɳɟɝɨ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɬɟɥɚ ɢɨɧɚ – ɬɚɤɭɸ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ γɩ; ɜɬɨɪɨɣ ɩɪɨɰɟɫɫ ɫɜɹɡɚɧ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɵ ɬɟɥɚ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɚ – ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɷɦɢɫɫɢɸ ɧɚɡɵɜɚɸɬ ɤɢɧɟɬɢɱɟɫɤɨɣ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɦɢɫɫɢɢ γɤ.
ȿɫɥɢ ɩɪɢɫɭɬɫɬɜɭɸɬ ɨɛɚ ɩɪɨɰɟɫɫɚ, ɬɨ γi = γɩ + γɤ. ɉɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ ɉɟɧɧɢɧɝɨɦ ɜ 1928 ɝ. ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ ɡɚɜɢɫɢɦɨɫɬɢ ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɨɧ ɨɛɧɚɪɭɠɢɥ, ɱɬɨ ɷɦɢɫɫɢɹ ɨɫɬɚɟɬɫɹ ɢ ɩɪɢ ɨɱɟɧɶ
ɦɚɥɵɯ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɭɥɟɜɵɯ, ɷɧɟɪɝɢɹɯ ɢɨɧɨɜ. ɂɡ ɷɬɨɝɨ ɦɨɠɧɨ ɛɵɥɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ
ɢɫɩɭɫɤɚɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɧɟ ɫɜɹɡɚɧɨ ɫ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ ɢɨɧɨɜ. ȼ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɛɵɥɨ ɜɵɹɜɥɟɧɨ, ɱɬɨ ɬɚɤɚɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɨɢɫɯɨɞɢɬ ɬɨɥɶɤɨ ɞɥɹ ɢɨɧɨɜ, ɩɨɬɟɧɰɢɚɥ ɢɨɧɢɡɚɰɢɢ ɤɨɬɨɪɵɯ Vi ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ ɪɚɛɨɬɵ ɜɵɯɨɞɚ ɦɚɬɟɪɢɚɥɚ ɷɦɢɬɬɟɪɚ ϕa:
Vi >2ϕa. |
(7.35) |
ɗɬɨ ɧɚɯɨɞɢɬ ɨɛɴɹɫɧɟɧɢɟ ɜ ɦɨɞɟɥɢ ɨɠɟ-ɧɟɣɬɪɚɥɢɡɚɰɢɢ ɢɨɧɚ. ɉɪɢɛɥɢɠɚɹɫɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ ɦɟɬɚɥɥɚ, ɢɨɧ ɢɡɦɟɧɹɟɬ ɫɜɨɢɦ ɩɨɥɟɦ ɩɨɜɟɪɯɧɨɫɬɧɵɣ ɩɨɬɟɧɰɢɚɥɶɧɵɣ ɛɚɪɶɟɪ, ɩɨɧɢɠɚɹ ɟɝɨ. Ɉɞɢɧ ɷɥɟɤɬɪɨɧ, ɢɦɟɹ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E1, ɫɨɜɟɪɲɚɟɬ ɬɭɧɧɟɥɶɧɵɣ ɩɟɪɟɯɨɞ ɢ ɧɟɣɬɪɚɥɢɡɭɟɬ ɢɨɧ (ɪɢɫ. 7.10). ɉɪɢ ɷɬɨɦ
ɜɵɞɟɥɹɟɦɚɹ ɷɧɟɪɝɢɹ Vi – E1 ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɞɚɧɚ ɜɬɨɪɨɦɭ ɷɥɟɤɬɪɨɧɭ, ɢɦɟɸɳɟɦɭ ɜ ɦɟɬɚɥɥɟ ɷɧɟɪɝɢɸ E2. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɜɬɨɪɨɣ ɷɥɟɤɬɪɨɧ ɜɵɲɟɥ ɢɡ ɦɟɬɚɥɥɚ, ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɧɭɥɹ: mv2/2 = Vi – E1 – E2 > 0. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ E1 ɢ E2 ɦɟɧɶɲɟ ϕa, Vi >2ϕa. Ɉɩɵɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ γɩ ɥɢɧɟɣɧɨ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɪɚɡɧɨɫɬɢ Vi -2ϕa ɞɥɹ ɪɚɡɥɢɱɧɵɯ ɩɚɪ ɦɢɲɟɧɶ – ɢɨɧ. Ⱦɥɹ ɱɢɫɬɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɷɬɭ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɷɦɩɢɪɢɱɟɫɤɨɣ ɮɨɪɦɭɥɨɣ:
γɩ ≈ 0.016(Vi -2ϕa)[ɷȼ]. |
(7.36) |
Ʉɨɷɮɮɢɰɢɟɧɬ γɩ ɬɟɦ ɛɨɥɶɲɟ, ɱɟɦ ɛɨɥɶɲɟ ɡɚɪɹɞ ɢɨɧɚ (ɤɪɚɬɧɨɫɬɶ ɢɨɧɢɡɚɰɢɢ): γɩ(A+) < γɩ(A++) < γɩ(A+++). Ⱦɥɹ ɦɢɲɟɧɟɣ, ɩɨɜɟɪɯɧɨɫɬɶ ɤɨɬɨɪɵɯ ɞɨɫɬɚɬɨɱɧɨ ɱɢɫɬɚɹ, γɩ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɷɧɟɪɝɢɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ Ep: dγɩ/dEp ≈ 0. ɉɪɢ ɛɨɥɶɲɨɣ ɜɟɥɢɱɢɧɟ ɪɚɡɧɨɫɬɢ Vi -2ϕa >> kBT ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɢɨɧɧɨɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɩɨɜɟɪɯɧɨɫɬɢ ɦɢɲɟɧɢ. ɉɪɢ ɦɚɥɨɣ ɜɟɥɢɱɢɧɟ ɷɬɨɣ ɪɚɡɧɨɫɬɢ: Vi -2ϕa ≈ kBT ɬɟɪɦɢɱɟɫɤɨɟ ɭɜɟɥɢɱɟɧɢɟ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɨɜ ɩɨɜɵɲɚɟɬ ɜɟɪɨɹɬɧɨɫɬɶ ɷɦɢɫɫɢɢ ɢ γɩ ɪɚɫɬɟɬ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɬɟɦɩɟɪɚɬɭɪɵ, ɩɪɢ ɷɬɨɦ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɦɢɫɫɢɹ ɜɨɡɦɨɠɧɚ ɢ ɩɪɢ Vi < 2ϕa.
ɉɪɢ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɤɢɧɟɬɢɱɟɫɤɚɹ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɚɹ ɷɦɢɫɫɢɹ ɩɪɟɨɛɥɚɞɚɟɬ ɧɚɞ ɩɨɬɟɧɰɢɚɥɶɧɨɣ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɛɵɥɨ ɨɛɧɚɪɭɠɟɧɨ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɩɨɪɨɝɨɜɨɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɟɪɜɢɱɧɵɯ ɢɨɧɨɜ (Ep)ɝɪ 1.5 ɤɷȼ, ɦɟɧɶɲɟ ɤɨɬɨɪɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ γɤ ≈ 0. ȼ ɩɪɢɩɨɪɨɝɨɜɨɣ ɨɛɥɚɫɬɢ ɷɧɟɪɝɢɣ ɢɨɧɨɜ (Ep < 10 ɤɷȼ) ɤɨɷɮɮɢɰɢɟɧɬ ɷɦɢɫɫɢɢ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɷɧɟɪɝɢɢ: γɤ = ɋ(Ep - (Ep)ɝɪ), ɝɞɟ ɋ = const. Ⱦɥɹ ɱɢɫɬɵɯ ɦɟɬɚɥɥɨɜ ɋ ≤ 0.2 10-2 ɷȼ-1. ɉɪɢ ɛɨɥɟɟ ɜɵɫɨɤɢɯ ɷɧɟɪɝɢɹɯ γɤ Ep1/2 . ɉɪɢ ɨɛɥɭɱɟɧɢɢ ɦɨɧɨɤɪɢɫɬɚɥɥɨɜ ɤɨɷɮɮɢɰɢɟɧɬ γɤ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɩɚɞɟɧɢɹ ɢɨɧɨɜ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɪɢɱɟɦ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ ɧɨɫɢɬ ɩɟɪɢɨɞɢɱɟɫɤɢɣ ɯɚɪɚɤɬɟɪ: ɩɨɥɨɠɟɧɢɹ ɦɚɤɫɢɦɭɦɨɜ ɫɨɜɩɚɞɚɸɬ ɫ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɩɚɞɚɸɳɢɯ ɢɨɧɨɜ ɜɞɨɥɶ ɤɪɢɫɬɚɥɥɨɝɪɚɮɢɱɟɫɤɢɯ ɧɚɩɪɚɜɥɟɧɢɣ ɜ ɦɨɧɨɤɪɢɫɬɚɥɥɟ. ɋɨɜɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ (ɦɨɞɟɥɶ ɉɚɪɢɥɢɫɚ, ɉɟɬɪɨɜɚ, Ʉɢɲɢɧɟɜɫɤɨɝɨ) ɨɫɧɨɜɵɜɚɸɬɫɹ ɧɚ ɞɜɭɯɷɬɚɩɧɨɫɬɢ ɩɪɨɰɟɫɫɚ. ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɨɧɚ ɩɟɪɟɞɚɟɬɫɹ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɟ ɦɟɬɚɥɥɚ ɫ ɨɛɪɚɡɨɜɚɧɢɟɦ «ɞɵɪɨɤ» (ɩɨɥɭɱɚɹ ɷɧɟɪɝɢɸ, ɷɥɟɤɬɪɨɧɵ ɚɬɨɦɨɜ ɫɨɜɟɪɲɚɸɬ ɦɟɠɡɨɧɧɵɣ ɩɟɪɟɯɨɞ ɜ ɡɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɨɛɪɚɡɭɹ ɞɵɪɤɢ). ɇɚ ɜɬɨɪɨɦ ɷɬɚɩɟ ɩɪɨɢɫɯɨɞɢɬ ɪɟɤɨɦɛɢɧɚɰɢɹ ɞɵɪɤɢ ɢ ɷɥɟɤɬɪɨɧɚ ɩɪɨɜɨɞɢɦɨɫɬɢ ɦɟɬɚɥɥɚ ɫ ɩɟɪɟɞɚɱɟɣ ɜɵɞɟɥɹɸɳɟɣɫɹ ɷɧɟɪɝɢɢ ɡɚ ɫɱɟɬ ɨɠɟ-ɩɪɨɰɟɫɫɚ ɞɪɭɝɨɦɭ ɷɥɟɤɬɪɨɧɭ ɩɪɨɜɨɞɢɦɨɫɬɢ, ɤɨɬɨɪɵɣ ɷɦɢɬɢɪɭɟɬɫɹ ɢɡ ɦɢɲɟɧɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɬɨɪɨɣ ɷɬɚɩ ɤɢɧɟɬɢɱɟɫɤɨɣ ɢɨɧɧɨ-ɷɥɟɤɬɪɨɧɧɨɣ ɷɦɢɫɫɢɢ ɛɥɢɡɨɤ ɩɨ ɩɪɢɪɨɞɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɦɢɫɫɢɢ.
ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ
ɂɨɧɧɚɹ ɷɦɢɫɫɢɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɬɟɪɦɢɱɟɫɤɨɣ ɞɟɫɨɪɛɰɢɢ ɱɚɫɬɢɰ ɫ ɩɨɜɟɪɯɧɨɫɬɢ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɧɚɡɵɜɚɟɬɫɹ ɩɨɜɟɪɯɧɨɫɬɧɨɣ ɢɨɧɢɡɚɰɢɟɣ. ȼ ɜɢɞɟ ɢɨɧɨɜ ɦɨɝɭɬ ɢɫɩɚɪɹɬɶɫɹ ɤɚɤ ɚɬɨɦɵ ɫɚɦɨɝɨ ɧɚɝɪɟɬɨɝɨ ɬɟɥɚ (ɧɚɩɪɢɦɟɪ, ɦɟɬɚɥɥɚ), ɬɚɤ ɢ ɚɬɨɦɵ ɢ ɦɨɥɟɤɭɥɵ, ɤɨɬɨɪɵɟ ɩɨɩɚɥɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ ɢɡ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɵ. ɑɚɫɬɶ ɢɡ ɧɢɯ ɩɨɫɥɟ ɚɞɫɨɪɛɢɪɨɜɚɧɢɹ ɢɫɩɚɪɹɸɬɫɹ ɨɛɪɚɬɧɨ ɜ ɝɚɡ, ɧɨ ɭɠɟ ɜ ɜɢɞɟ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɥɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɉɨɜɟɪɯɧɨɫɬɧɚɹ ɢɨɧɢɡɚɰɢɹ ɛɵɥɚ ɨɬɤɪɵɬɚ Ʌɟɧɝɦɸɪɨɦ ɢ Ʉɢɧɝɞɨɧɨɦ (1923 ɝ.), ɤɨɬɨɪɵɟ ɨɛɧɚɪɭɠɢɥɢ ɜ ɰɢɥɢɧɞɪɢɱɟɫɤɨɦ ɞɢɨɞɟ, ɡɚɩɨɥɧɟɧɧɨɦ ɩɚɪɚɦɢ ɰɟɡɢɹ, ɬɨɤ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɋɬɟɩɟɧɶ ɩɨɜɟɪɯɧɨɫɬɧɨɣ