ɋɩɟɪɢɦɚɝɧɟɬɢɤɢ. ɉɪɢ ɧɚɥɢɱɢɢ ɮɥɭɤɬɭɚɰɢɣ ɨɛɦɟɧɧɵɯ ɜɡɚɢɦɨɞɟɣɫɬɜɢɣ ɜ ɦɚɝɧɟɬɢɤɟ, ɫɨɫɬɨɹɳɟɦ ɢɡ ɞɜɭɯ ɢɥɢ ɛɨɥɟɟ ɦɚɝɧɢɬɧɵɯ ɩɨɞɫɢɫɬɟɦ, ɫɜɹɡɚɧɧɵɯ ɦɟɠɞɭ ɫɨɛɨɣ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ ɨɛɦɟɧɧɵɦɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹɦɢ, ɜɨɡɦɨɠɧɨ ɨɛɪɚɡɨɜɚɧɢɟ ɫɩɟɪɢɦɚɝɧɢɬɧɨɣ ɫɬɪɭɤɬɭɪɵ. Ɉɧɚ ɞɨ ɧɟɤɨɬɨɪɨɣ ɫɬɟɩɟɧɢ ɩɨɯɨɠɚ ɧɚ ɮɟɪɪɢɦɚɝɧɢɬɧɭɸ ɫɬɪɭɤɬɭɪɭ. ȼɧɟɣ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɩɨɞɪɟɲɟɬɨɤ (ɜ ɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ ɦɚɬɟɪɢɚɥɚɯ) ɢɥɢ ɩɨɞɫɢɫɬɟɦ (ɜ ɚɦɨɪɮɧɵɯ ɦɚɬɟɪɢɚɥɚɯ) ɬɚɤɠɟ ɧɚɩɪɚɜɥɟɧɵ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɞɪɭɝ ɞɪɭɝɭ. Ɉɬɥɢɱɢɟ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɜ ɫɩɟɪɢɦɚɝɧɟɬɢɤɟ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɜ ɨɞɧɨɣ ɢɥɢ ɨɛɟɢɯ ɩɨɞɫɢɫɬɟɦɚɯ ɨɪɢɟɧɬɢɪɭɸɬɫɹ ɫɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ ɜ ɩɪɟɞɟɥɚɯ ɧɟɤɨɬɨɪɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɤɨɧɭɫɚ. Ɍɚɤɚɹ ɫɢɬɭɚɰɢɹ ɜɨɡɧɢɤɚɟɬ ɤɚɤ ɜ ɤɪɢɫɬɚɥɥɢɱɟɫɤɢɯ, ɬɚɤ ɢ ɜ ɚɦɨɪɮɧɵɯ ɦɚɬɟɪɢɚɥɚɯ(ɧɚɩɪɢɦɟɪ, ɜ ɚɦɨɪɮɧɵɯɫɨɟɞɢɧɟɧɢɹɯ Tb–Fe, Tb–Co).
Ɋɢɫ. 2.3. Ɇɚɝɧɢɬɧɵɟ ɫɬɪɭɤɬɭɪɵ:
ɚ – ɫɩɟɪɨɦɚɝɧɢɬɧɚɹ; ɛ – ɚɫɩɟɪɨɦɚɝɧɢɬɧɚɹ; ɜ – ɫɩɟɪɢɦɚɝɧɢɬɧɚɹ
Ⱦɥɹ ɤɨɥɢɱɟɫɬɜɟɧɧɨɝɨ ɨɩɢɫɚɧɢɹ ɦɚɝɧɢɬɧɵɯ ɹɜɥɟɧɢɣ ɜ ɪɚɡɥɢɱɧɵɯ ɜɟɳɟɫɬɜɚɯ ɢɫɩɨɥɶɡɭɸɬ ɬɚɤɢɟ ɩɚɪɚɦɟɬɪɵ, ɤɚɤ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ H, ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɜɟɳɟɫɬɜɚ Ɇ, ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ȼ (ɜɫɟ ɨɧɢ ɹɜɥɹɸɬɫɹ ɜɟɤɬɨɪɧɵɦɢ ɜɟɥɢɱɢɧɚɦɢ).
Ⱦɥɹ ɢɡɦɟɪɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ ɢɫɩɨɥɶɡɭɸɬɫɹ ɟɞɢɧɢɰɵ ɋɂ. Ɉɞɧɚɤɨ ɧɚɪɹɞɭ ɫ ɧɢɦɢ ɜ ɫɩɟɰɢɚɥɶɧɨɣ ɥɢɬɟɪɚɬɭɪɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɢ ɟɞɢɧɢɰɵ ɋȽɋɆ. ȼ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ, ɤɚɤ ɩɪɚɜɢɥɨ, ɢɫɩɨɥɶɡɭɸɬɫɹ ɟɞɢɧɢɰɵ ɋɂ. Ɂɧɚɱɟɧɢɹ ɧɟɤɨɬɨɪɵɯ ɜɟɥɢɱɢɧ, ɡɚɢɦɫɬɜɨɜɚɧɧɵɟ ɢɡ ɪɚɡɥɢɱɧɵɯ ɥɢɬɢɫɬɨɱɧɢɤɨɜ, ɞɚɧɵ ɜ ɟɞɢɧɢɰɚɯ ɨɪɢɝɢɧɚɥɚ (ɜ ɬɚɤɢɯ ɫɥɭɱɚɹɯ ɜ ɬɟɤɫɬɟ ɩɪɢɜɨɞɹɬɫɹɧɟɨɛɯɨɞɢɦɵɟ ɩɨɹɫɧɟɧɢɹ).
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜɨɡɧɢɤɚɟɬ ɜɨɤɪɭɝ ɩɪɨɜɨɞɧɢɤɚ, ɩɨ ɤɨɬɨɪɨɦɭ ɩɪɨɬɟɤɚɟɬ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ. ɗɬɨ ɩɨɥɟ ɹɜɥɹɟɬɫɹ ɜɧɟɲɧɢɦ ɩɨ ɨɬɧɨɲɟɧɢɸ
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ɤ ɫɪɟɞɟ, ɧɚ ɤɨɬɨɪɭɸ ɨɧɨ ɜɨɡɞɟɣɫɬɜɭɟɬ. ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ r ɨɬ ɩɪɨɜɨɞɧɢɤɚ [Ⱥ/ɦ] ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɬɚɤ
H = I/(2ʌr). |
(2.1) |
Ɉɬɫɸɞɚ ɜɢɞɧɨ, ɱɬɨ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɜɨɣɫɬɜ ɫɪɟɞɵ, ɧɚ ɤɨɬɨɪɭɸ ɞɟɣɫɬɜɭɟɬ ɩɨɥɟ.
ȼɨɡɞɟɣɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɫɪɟɞɭ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɜ ɫɪɟɞɟ ɜɨɡɧɢɤɚɟɬ (ɢɥɢ ɢɡɦɟɧɹɟɬɫɹ) ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ M [Ⱥ/ɦ], ɡɧɚɱɟɧɢɟ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɦɚɝɧɢɬɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ ɫɪɟɞɵ ɢ ɫɜɹɡɚɧɨ ɫ H ɫɨɨɬɧɨɲɟɧɢɟɦ:
Ɇ = ȤH, |
(2.2) |
ɝɞɟ Ȥ – ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ (ɛɟɡɪɚɡɦɟɪɧɚɹ ɜɟɥɢɱɢɧɚ). ɂɫɯɨɞɹ ɢɡ (2.2) ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɜɧɭɬ-
ɪɟɧɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜ ɜɟɳɟɫɬɜɟ, ɜɵɡɵɜɚɸɳɟɟ ɩɨɬɨɤ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ. ɉɥɨɬɧɨɫɬɶ ɷɬɨɝɨ ɩɨɬɨɤɚ ɧɚɡɵɜɚɸɬ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɟɣ (ȼ). ȼ ɜɚɤɭɭɦɟ ɜɟɥɢɱɢɧɚ ȼ [Ɍɥ] ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɥɶɤɨ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ:
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ȼ = ȝ0ɇ, |
(2.3) |
ɝɞɟ ȝ |
0 |
= 4ʌ · 10–7 |
Ƚɧ/ɦ – ɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ. |
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ȼ ɥɸɛɨɦ ɜɟɳɟɫɬɜɟ |
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ȼ = ȝ0 ȝɇ, |
(2.4) |
ɝɞɟ ȝ – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ (ɨɛɵɱɧɨ ɫɥɨɜɨ «ɨɬɧɨɫɢɬɟɥɶɧɚɹ» ɨɩɭɫɤɚɸɬ).
ɉɪɨɢɡɜɟɞɟɧɢɟ ȝ0ȝ = ȝɚ ɧɚɡɵɜɚɸɬ ɚɛɫɨɥɸɬɧɨɣ ɦɚɝɧɢɬɧɨɣ ɩɪɨ-
ɧɢɰɚɟɦɨɫɬɶɸ. Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ȝ (ɤɚɤ ɢ ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ Ȥ) ɹɜɥɹɟɬɫɹ ɛɟɡɪɚɡɦɟɪɧɨɣ ɜɟɥɢɱɢɧɨɣ.
ɋɜɹɡɶ ɦɟɠɞɭ ɜɵɲɟɧɚɡɜɚɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɜɵɪɚɠɟɧɢɟɦ:
ȝ = 1 + Ȥ. |
(2.5) |
ɉɨɫɤɨɥɶɤɭ ɜ ɜɚɤɭɭɦɟ (ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɟɳɟɫɬɜɚ) Ȥ = 0, ɬɨ ȝ = 1. ɋɨɝɥɚɫɧɨ (2.4)
ȼ = ȝ0ȝɇ = ȝ0 (1 + Ȥ)ɇ = ȝ0ɇ + ȝ0Ȥɇ = ȝ0ɇ + ȝ0Ɇ = ȼɟ + ȼi, (2.6)
ɝɞɟ ȼɟ – ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɜ ɜɚɤɭɭɦɟ (ɜɧɟɲɧɹɹ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ); ȼi – ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɜ ɜɟɳɟɫɬɜɟ (ɜɧɭɬɪɟɧɧɹɹ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ) ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɇ.
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Ɍɚɛɥɢɰɚ 2.1 |
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ȿɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ |
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ɇɚɢɦɟɧɨɜɚɧɢɟ |
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ɇɚɢɦɟɧɨɜɚɧɢɟ |
Ɉɛɨɡɧɚɱɟɧɢɟ |
Ɇɧɨɠɢɬɟɥɶ |
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ɜɟɥɢɱɢɧɵ |
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ɟɞɢɧɢɰ |
ɟɞɢɧɢɰ |
ɞɥɹ ɩɟɪɟɜɨɞɚ ɟɞɢɧɢɰɵ |
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ɋɂ |
ɋȽɋɆ |
ɋɂ |
ɋȽɋɆ |
ɢɡ ɋȽɋɆ ɜ ɋɂ |
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ɷɪɫɬɟɞ |
Ⱥ/ɦ |
ɗ |
103/4ʌ = 79,5775.. § 80 |
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ |
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ɝɚɭɫɫ |
Ⱥ/ɦ |
Ƚɫ |
103 |
Ɇɚɝɧɢɬɧɚɹ |
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ɝɚɭɫɫ |
Ɍɥ |
Ƚɫ |
10–4 |
ɢɧɞɭɤɰɢɹ |
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Ɇɚɝɧɢɬɧɚɹ |
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4ʌ |
ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ |
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Ɇɚɝɧɢɬɧɚɹ |
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ɩɪɨɧɢɰɚɟɦɨɫɬɶ |
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Ɇɚɝɧɢɬɧɚɹ |
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Ƚɧ/ɦ |
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4ʌ · 10–7 |
ɩɨɫɬɨɹɧɧɚɹ |
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Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɩɨɥɶɡɨɜɚɧɢɹ ɥɢɬɟɪɚɬɭɪɧɵɦɢ ɞɚɧɧɵɦɢ ɜ ɬɚɛɥ. 2.1 ɩɪɢɜɟɞɟɧɵ ɟɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɹ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ ɜ ɋɂ ɢ ɋȽɋɆ, ɚ ɬɚɤɠɟ ɦɧɨɠɢɬɟɥɢ ɞɥɹ ɩɟɪɟɜɨɞɚ ɢɡ ɋȽɋɆ ɜ ɋɂ.
2.2.Ⱦɢɚɦɚɝɧɟɬɢɡɦ
Ʉɞɢɚɦɚɝɧɢɬɧɵɦ ɜɟɳɟɫɬɜɚɦ, ɜ ɤɨɬɨɪɵɯ ɞɚɧɧɵɣ ɷɮɮɟɤɬ ɹɜɥɹɟɬɫɹ ɟɞɢɧɫɬɜɟɧɧɵɦ, ɨɬɧɨɫɹɬɫɹ: ɜɫɟ ɢɧɟɪɬɧɵɟ ɝɚɡɵ, ɜɨɞɨɪɨɞ, ɚɡɨɬ, ɯɥɨɪ ɢ ɞɪ.; ɧɟɤɨɬɨɪɵɟ ɦɟɬɚɥɥɵ (ɰɢɧɤ, ɡɨɥɨɬɨ, ɪɬɭɬɶ ɢ ɞɪ.); ɦɟɬɚɥɥɨɢɞɵ (ɤɪɟɦɧɢɣ, ɮɨɫɮɨɪ, ɫɟɪɚ ɢ ɞɪ.), ɚ ɬɚɤɠɟ ɞɟɪɟɜɨ, ɦɪɚɦɨɪ, ɫɬɟɤɥɨ, ɧɟɮɬɶ, ɜɨɞɚ ɢ ɦɧɨɝɢɟ ɞɪɭɝɢɟ ɜɟɳɟɫɬɜɚ.
Ⱦɢɚɦɚɝɧɟɬɢɡɦ ɜɨɡɧɢɤɚɟɬ ɡɚ ɫɱɟɬ ɩɪɟɰɟɫɫɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɨɪɛɢɬɚɥɟɣ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɦɨɥɟɤɭɥ, ɨɬɤɭɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɧ ɫɜɹɡɚɧ ɫ ɨɪɛɢɬɚɥɶɧɵɦ ɞɜɢɠɟɧɢɟɦ ɷɥɟɤɬɪɨɧɨɜ. əɜɥɟɧɢɟ ɞɢɚɦɚɝɧɟɬɢɡɦɚ ɨɛɭɫɥɨɜɥɟɧɨ ɭɦɟɧɶɲɟɧɢɟɦ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɨɪɛɢɬɚɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɜɨ ɜɧɟɲɧɟɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ.
ɂɫɯɨɞɹ ɢɡ ɤɥɚɫɫɢɱɟɫɤɢɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ, ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɚ ɩɨ ɨɪɛɢɬɟ ɦɨɠɧɨ ɫɨɩɨɫɬɚɜɢɬɶ ɫ ɡɚɦɤɧɭɬɵɦ ɤɨɧɬɭɪɨɦ, ɩɨ ɤɨɬɨɪɨɦɭ ɩɪɨɬɟɤɚɟɬ ɬɨɤ. ɉɪɢ ɜɧɟɫɟɧɢɢ ɤɨɧɬɭɪɚ ɫ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜ
ɤɨɧɬɭɪɟ ɜɨɡɧɢɤɚɟɬ ɞɨɛɚɜɨɱɧɚɹ ɷɥɟɤɬɪɨɞɜɢɠɭɳɚɹ ɫɢɥɚ*. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɨɝɨ ɫɢɥɚ ɬɨɤɚ ɜ ɤɨɧɬɭɪɟ ɢɡɦɟɧɢɬɫɹ ɢ ɩɨɹɜɢɬɫɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ, ɧɚɩɪɚɜɥɟɧɧɵɣ ɬɚɤ, ɱɬɨɛɵ ɩɪɟɩɹɬɫɬɜɨɜɚɬɶ ɜɧɟɲ-
* Ɂɚɤɨɧ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ (ɡɚɤɨɧ Ɏɚɪɚɞɟɹ).
33
ɧɟɦɭ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ: ɬ. ɟ. ɧɚɩɪɚɜɥɟɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɨɫɤɨɥɶɤɭ ɫɬɪɭɤɬɭɪɚ ɷɥɟɤɬɪɨɧɧɵɯ ɨɛɨɥɨɱɟɤ ɚɬɨɦɨɜ, ɢɨɧɨɜ ɢ ɦɨɥɟɤɭɥ ɩɪɚɤɬɢɱɟɫɤɢɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɬɨ ɢ ɞɢɚɦɚɝɧɢɬɧɚɹɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ, ɨɫɬɚɜɚɹɫɶɨɬɪɢɰɚɬɟɥɶɧɨɣ, ɫɥɚɛɨɦɟɧɹɟɬɫɹɫ ɬɟɦɩɟɪɚɬɭɪɨɣ.
Ɉɛɴɹɫɧɟɧɢɟ ɞɢɚɦɚɝɧɟɬɢɡɦɚ ɜɩɟɪɜɵɟ ɛɵɥɨ ɞɚɧɨ ɉ. Ʌɚɧɠɟɜɟɧɨɦ ɜ 1905 ɝ. Ɍɟɨɪɢɹ Ʌɚɧɠɟɜɟɧɚ ɛɵɥɚ ɪɚɡɜɢɬɚ ɉɚɭɥɢ (1920), ɚ ɩɨɡɞɧɟɟ ȼɚɧɎɥɟɤ ɪɚɡɪɚɛɨɬɚɥɤɜɚɧɬɨɜɨ-ɦɟɯɚɧɢɱɟɫɤɭɸɬɟɨɪɢɸɞɢɚɦɚɝɧɟɬɢɡɦɚ.
Ɋɚɫɫɦɨɬɪɢɦ ɷɥɟɤɬɪɨɧ, ɜɪɚɳɚɸɳɢɣɫɹ ɜɨɤɪɭɝ ɹɞɪɚ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ ɪɚɞɢɭɫɚ R ɫ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɶɸ v0 ɢ ɤɪɭɝɨɜɨɣ ɱɚɫɬɨɬɨɣ Ȧ0.
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɧɟɝɨ ɞɟɣɫɬɜɭɟɬ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ
F0 mv02 R mZ02R, |
(2.7) |
ɤɨɬɨɪɚɹ ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɫɢɥɨɣ ɤɭɥɨɧɨɜɫɤɨɝɨ ɩɪɢɬɹɠɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɤ ɹɞɪɭ (ɪɢɫ. 2.4, ɚ).
ɉɪɢɥɨɠɟɧɢɟ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ ɩɪɢɜɟɞɟɬ ɤ ɜɨɡɧɢɤɧɨɜɟɧɢɸ ɫɢɥɵ Ʌɨɪɟɧɰɚ
FH , ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɡɚɪɹɠɟɧɧɭɸ ɱɚɫɬɢɰɭ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ: |
|
|||||
F |
P |
0 |
HeZ R |
P |
Hev . |
(2.8) |
H |
|
1 |
|
0 1 |
|
|
ɋɢɥɚ FH ɧɚɩɪɚɜɥɟɧɚ ɬɚɤ ɠɟ, ɤɚɤ ɰɟɧɬɪɨɛɟɠɧɚɹ ɫɢɥɚ, ɬ. ɟ. ɩɨ ɪɚ-
ɞɢɭɫɭ. Ɉɧɚ ɧɟɞɨɫɬɚɬɨɱɧɚ ɞɥɹ ɢɡɦɟɧɟɧɢɹ ɪɚɞɢɭɫɚ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ, ɚ ɩɨɫɤɨɥɶɤɭ ɫɢɥɚ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ,
Ɋɢɫ. 2.4. ɋɯɟɦɚɬɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɩɪɟɰɟɫɫɢɢ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ:
ɚ– ɞɜɢɠɟɧɢɟ ɷɥɟɤɬɪɨɧɚ ɩɨ ɨɪɛɢɬɟ ɜ ɦɨɦɟɧɬ ɩɪɢɥɨɠɟɧɢɹ ɩɨɥɹ H;
ɛ– ɩɪɟɰɟɫɫɢɹ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ ɜɨɤɪɭɝ ɩɨɥɹ
34
ɬɨ ɞɥɹ ɭɪɚɜɧɨɜɟɲɢɜɚɧɢɹ ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɷɥɟɤɬɪɨɧ ɫɢɥ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɩɨɥɨɠɢɬɶ ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ (ɤɪɭɝɨɜɨɣ ɱɚɫɬɨɬɵ) ɜɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɩɨ ɨɪɛɢɬɟ. Ɂɧɚɤ ɦɢɧɭɫ ɜ (2.8) ɝɨɜɨɪɢɬ ɨɛ ɭɦɟɧɶɲɟɧɢɢ ɤɪɭɝɨɜɨɣ ɱɚɫɬɨɬɵ, ɬ. ɟ. Z1 Z0. ɇɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɞɜɢɠɟɧɢɟ
ɷɥɟɤɬɪɨɧɚ ɩɨ ɨɪɛɢɬɟ ɜ ɩɪɢɫɭɬɫɬɜɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚɞɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɟɝɨ ɞɜɢɠɟɧɢɟ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ. ɉɨɷɬɨɦɭ ɢɡɦɟɧɟɧɢɟ ɤɪɭɝɨɜɨɣ ɱɚɫɬɨɬɵ ɷɥɟɤɬɪɨɧɚ ɦɨɠɧɨ ɬɪɚɤɬɨɜɚɬɶ ɤɚɤ ɩɟɪɢɨɞɢɱɟɫɤɨɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɩɨɥɨɠɟɧɢɹ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ (ɩɪɟɰɟɫɫɢɹ ɨɪɛɢɬɵ) ɜɨɤɪɭɝ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɹ (ɪɢɫ. 2.4, ɛ). Ɋɟɡɭɥɶɬɢɪɭɸɳɚɹ ɫɢɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
F F F |
mZ2R |
mZ2R P |
HeZ R. |
(2.9) |
||
0 |
H |
1 |
0 |
0 |
1 |
|
Ɋɟɲɚɹ ɤɜɚɞɪɚɬɧɨɟ ɭɪɚɜɧɟɧɢɟ (2.9) ɨɬɧɨɫɢɬɟɥɶɧɨ Z1, ɩɨɥɭɱɢɦ:
Z1 = – |
P |
ɇɟ |
± |
§P |
ɇɟ·2 |
| Z0 |
P |
ɇɟ |
. |
(2.10) |
||
0 |
|
¨ |
0 |
¸ |
Z02 |
0 |
|
|||||
|
2m |
|
© |
2m ¹ |
|
|
2m |
|
|
|||
Ɂɧɚɱɟɧɢɟ P0ɇɟ
2m 2 ɫɨɢɡɦɟɪɢɦɨ ɫ Z02 ɬɨɥɶɤɨ ɜ ɩɨɥɹɯ
~1011 Ⱥ/ɦ, ɩɪɚɤɬɢɱɟɫɤɢ ɧɟ ɞɨɫɬɢɠɢɦɵɯ ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ. ɉɨɷɬɨɦɭ ɩɟɪɜɵɦ ɱɥɟɧɨɦ ɩɨɞ ɡɧɚɤɨɦ ɪɚɞɢɤɚɥɚ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. Ɍɨɝɞɚ ɢɡ (2.10) ɩɨɥɭɱɚɟɦ:
ǻȦ = Ȧ0 – Ȧ1= ȝ0ɇɟ/(2m) = Ȗlȝ0ɇ. |
(2.11) |
ȼɟɥɢɱɢɧɚ ǻȦ ɧɚɡɵɜɚɟɬɫɹ ɥɚɪɦɨɪɨɜɫɤɨɣ ɱɚɫɬɨɬɨɣ ɢɥɢ ɱɚɫɬɨɬɨɣ ɥɚɪɦɨɪɨɜɫɤɨɣ ɩɪɟɰɟɫɫɢɢ. Ʉɚɤ ɜɢɞɧɨ ɢɡ (2.11), ɨɧɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɭɝɥɚ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɟɦ ɇ ɢ ɩɥɨɫɤɨɫɬɶɸ ɨɪɛɢɬɵ.
Ʉɚɤ ɫɥɟɞɭɟɬ ɢɡ ɪɚɡɞ. 1.1, ɢɡɦɟɧɟɧɢɟ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ:
ǻȝ = – |
ɟR2 |
(2.12) |
A ǻȦ, |
||
|
2 |
|
ɝɞɟ Rŏ – ɩɪɨɟɤɰɢɹ ɪɚɞɢɭɫɚ ɨɪɛɢɬɵ ɷɥɟɤɬɪɨɧɚ ɧɚ ɩɥɨɫɤɨɫɬɶ, ɩɟɪɩɟɧ-
ɞɢɤɭɥɹɪɧɭɸ ɧɚɩɪɚɜɥɟɧɢɸ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. Ɂɧɚɤ «ɦɢɧɭɫ» ɜ (2.12) ɝɨɜɨɪɢɬ ɨ ɬɨɦ, ɱɬɨ ǻȝ ɚɧɬɢɩɚɪɚɥɥɟɥɶɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ.
ɉɪɟɞɵɞɭɳɢɟ ɪɚɫɫɭɠɞɟɧɢɹ ɤɚɫɚɥɢɫɶ ɩɪɨɫɬɟɣɲɟɝɨ ɚɬɨɦɚ, ɢɦɟɸɳɟɝɨ ɨɞɢɧ ɷɥɟɤɬɪɨɧ, ɜɪɚɳɚɸɳɢɣɫɹ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ. ȼ ɫɥɭɱɚɟ
35
ɦɧɨɝɨɷɥɟɤɬɪɨɧɧɨɝɨ ɚɬɨɦɚ ɨɪɛɢɬɵ ɢɦɟɸɬ ɷɥɥɢɩɬɢɱɟɫɤɭɸ ɮɨɪɦɭ, ɬ. ɟ. ɩɟɪɟɦɟɧɧɵɣ ɪɚɞɢɭɫ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɜɵɲɟ 0 Ʉ ɨɪɢɟɧɬɚɰɢɹ ɨɪɛɢɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɹ ɢɡɦɟɧɹɟɬɫɹ ɡɚ ɫɱɟɬ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢɡɦɟɧɹɟɬɫɹ ɢ ɩɪɨɟɤɰɢɹ ɪɚɞɢɭɫɚ ɧɚ ɩɥɨɫɤɨɫɬɶ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɭɸ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ. Ⱦɥɹ ɭɱɟɬɚ ɷɬɢɯ ɢɡɦɟɧɟɧɢɣ ɦɨɠɧɨ ɜɜɟɫɬɢ ɫɪɟɞɧɢɟ ɩɨ ɜɪɟɦɟɧɢ ɡɧɚɱɟɧɢɹ
RA2 . ɉɪɢ ɪɚɜɧɨɜɟɪɨɹɬɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɷɥɟɤɬɪɨɧɧɵɯ ɨɪɛɢɬ ɚɬɨɦɚ
R2 = 2 R2 , (2.13)
A |
3 |
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ɝɞɟ R2 – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɤɜɚɞɪɚɬɚ ɪɚɞɢɭɫɚ ɨɪɛɢɬɵ.
Ɇɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ (ɢɡɦɟɧɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ) ɝɪɚɦɦɚɬɨɦɚ ɜɟɳɟɫɬɜɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
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ǻɆ |
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ɟ P0 |
ɇ |
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(2.14) |
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ɝɞɟ NȺ – ɱɢɫɥɨ Ⱥɜɨɝɚɞɪɨ.
Ⱦɢɚɦɚɝɧɢɬɧɭɸ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɝɪɚɦɦ-ɚɬɨɦɚ ɜɟɳɟɫɬɜɚ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ
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'M Ⱥ |
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Ȥ |
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= –N |
ɟ P0 |
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(2.15) |
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ȼɵɪɚɠɟɧɢɟ (2.15) ɧɚɡɵɜɚɟɬɫɹ ɮɨɪɦɭɥɨɣ Ʌɚɧɠɟɜɟɧɚ–ɉɚɭɥɢ. ɂɡ ɧɟɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɞɢɚɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɡɚɜɢɫɢɬ ɨɬ ɪɚɞɢɭɫɨɜ ɷɥɟɤɬɪɨɧɧɵɯ ɨɪɛɢɬ ɚɬɨɦɚ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ. Ɋɚɫɱɟɬɵ ȤȺ ɩɨ (2.15) ɫɨɜɩɚɞɚɸɬ ɩɨ ɩɨɪɹɞɤɭ ɜɟɥɢɱɢɧɵ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ
ɞɚɧɧɵɦɢ. Ɂɧɚɱɟɧɢɹ ȤȺ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɞɢɚɦɚɝɧɢɬɧɵɯ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨɜ ɢ ɦɟɬɚɥɥɨɜ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥ. 2.2.
Ɂɧɚɱɟɧɢɹ ȤȺ ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɞɢɚɦɚɝɧɟɬɢɤɨɜ |
Ɍɚɛɥɢɰɚ 2.2 |
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ɏɢɦɢɱɟɫɤɢɣ ɫɢɦɜɨɥ |
Si |
Ge |
Cu |
Ag |
Au |
Ȥ · 106 |
–3 |
–8 |
–6 |
–22 |
–30 |
Ʉɚɤ ɜɢɞɧɨ ɢɡ ɷɬɨɣ ɬɚɛɥɢɰɵ, ɞɢɚɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɛɨɥɶɲɢɧɫɬɜɚ ɜɟɳɟɫɬɜ ɨɱɟɧɶ ɦɚɥɚ, ɜɨɬ ɩɨɱɟɦɭ ɞɢɚɦɚɝɧɢɬɧɵɣ ɷɮɮɟɤɬ ɧɟ ɧɚɲɟɥ ɩɪɢɦɟɧɟɧɢɹ ɜ ɬɟɯɧɢɤɟ. Ɉɞɧɚɤɨ ɜ ɧɟɤɨɬɨɪɵɯ ɜɟɳɟɫɬɜɚɯ ɷɬɨɬ ɷɮɮɟɤɬ ɩɪɨɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨ (ɜɢɫɦɭɬ, ɫɭɪɶɦɚ, ɝɪɚɮɢɬ). ɉɨɜɵɲɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɢ ɧɚɛɥɸɞɚɸɬɫɹ ɜ
36
«ɫɜɟɪɯɞɢɚɦɚɝɧɟɬɢɤɚɯ» – ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɚɯ ɢ ɧɟɤɨɬɨɪɵɯ ɦɨɞɢɮɢɤɚɰɢɹɯ ɭɝɥɟɪɨɞɚ (ɮɭɥɥɟɪɟɧɚɯ ɢ ɭɝɥɟɪɨɞɧɵɯ ɧɚɧɨɬɪɭɛɤɚɯ).
ɋɥɚɛɵɣ ɞɢɚɦɚɝɧɢɬɧɵɣ ɷɮɮɟɤɬ ɫɭɳɟɫɬɜɭɟɬ ɜɨ ɜɫɟɯ ɜɟɳɟɫɬɜɚɯ, ɧɨ ɩɪɢ ɧɚɥɢɱɢɢ ɛɨɥɟɟ ɫɢɥɶɧɨɝɨ ɷɮɮɟɤɬɚ (ɧɚɩɪɢɦɟɪ, ɩɚɪɚɦɚɝɧɢɬɧɨɝɨ), ɤɨɬɨɪɵɣ ɨɛɵɱɧɨ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɝɨɪɚɡɞɨ ɛɨɥɶɲɟɣ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɸ, ɫɭɦɦɚɪɧɚɹɦɚɝɧɢɬɧɚɹɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶɨɤɚɡɵɜɚɟɬɫɹɩɨɥɨɠɢɬɟɥɶɧɨɣ.
2.3. ɉɚɪɚɦɚɝɧɟɬɢɡɦ
ɉɚɪɚɦɚɝɧɟɬɢɡɦɨɦ ɨɛɥɚɞɚɸɬ ɜɫɟ ɚɬɨɦɵ, ɢɨɧɵ ɢ ɦɨɥɟɤɭɥɵ, ɢɦɟɸɳɢɟ ɜ ɨɛɨɥɨɱɤɟ ɧɟɱɟɬɧɨɟ ɱɢɫɥɨ ɷɥɟɤɬɪɨɧɨɜ, ɬɚɤ ɤɚɤ ɩɪɢ ɷɬɨɦ ɩɨɥɧɵɣ ɫɩɢɧ ɷɥɟɤɬɪɨɧɧɨɣ ɫɢɫɬɟɦɵ ɜɫɟɝɞɚ ɨɬɥɢɱɟɧ ɨɬ ɧɭɥɹ: ɚɬɨɦɵ ɳɟɥɨɱɧɵɯ ɦɟɬɚɥɥɨɜ, ɨɤɢɫɶ ɚɡɨɬɚ, ɫɜɨɛɨɞɧɵɟ ɪɚɞɢɤɚɥɵ ɨɪɝɚɧɢɱɟɫɤɢɯ ɫɨɟɞɢɧɟɧɢɣ ɢ ɞɪ. ɉɚɪɚɦɚɝɧɢɬɧɵ ɜɫɟ ɚɬɨɦɵ ɢ ɢɨɧɵ ɩɟɪɟɯɨɞɧɵɯ ɷɥɟɦɟɧɬɨɜ – ɤɚɤ ɜ ɫɜɨɛɨɞɧɨɦ, ɬɚɤ ɢ ɜ ɤɪɢɫɬɚɥɥɢɱɟɫɤɨɦ ɫɨɫɬɨɹɧɢɹɯ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɟɨɛɯɨɞɢɦɵɦ ɩɪɢɡɧɚɤɨɦ ɩɚɪɚɦɚɝɧɢɬɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜɟɳɟɫɬɜɚ ɹɜɥɹɟɬɫɹ ɧɚɥɢɱɢɟ ɭ ɟɝɨ ɚɬɨɦɨɜ ɫɨɛɫɬɜɟɧɧɵɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ȝɦ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɷɥɟɦɟɧɬɚɪɧɵɟ ɦɚɝɧɢ-
ɬɢɤɢ (ɦɚɝɧɢɬɧɵɟ ɫɬɪɟɥɤɢ).
ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɭɩɨɪɹɞɨɱɟɧɧɨɦɭ ɪɚɫɩɨɥɨɠɟɧɢɸ ɦɚɝɧɢɬɢɤɨɜ ɩɪɟɩɹɬɫɬɜɭɟɬ ɬɟɩɥɨɜɚɹ ɷɧɟɪɝɢɹ. Ʉɚɤ ɩɨɤɚɡɵɜɚɸɬ ɪɚɫɱɟɬɵ, ɷɧɟɪɝɢɹ ɦɚɝɧɢɬɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɨɫɟɞɧɢɯ ɦɚɝɧɢɬɢɤɨɜ ɫɨɫɬɚɜɥɹɟɬ ~10–23 Ⱦɠ, ɱɬɨ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɹɟɬɫɹ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ ɩɪɢ Ɍ = 1 Ʉ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɛɨɥɟɟ ɜɵɫɨɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɦɚɝɧɢɬɢɤɢ ɪɚɡɭɩɨɪɹɞɨɱɟɧɵ ɢ ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɪɚɜɧɚ ɧɭɥɸ. ɉɪɢ ɧɚɥɢɱɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɚɝɧɢɬɢɤɢ ɩɨɥɭɱɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɩɨɥɟɦ ~ ȝɦɇ, ɱɬɨ ɨɪɢɟɧɬɢɪɭɟɬ ɢɯ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɩɨɥɹ, ɢ ɜ ɪɟɡɭɥɶ-
ɬɚɬɟ ɩɨɹɜɥɹɟɬɫɹ ɧɟɧɭɥɟɜɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ.
ȼ 1895 ɝ. ɉ. ɀ. Ʉɸɪɢ ɧɚ ɨɫɧɨɜɟ ɢɫɫɥɟɞɨɜɚɧɢɣ ɦɚɝɧɢɬɧɵɯ ɫɜɨɣɫɬɜ ɝɚɡɨɨɛɪɚɡɧɨɝɨ ɤɢɫɥɨɪɨɞɚ, ɪɚɫɬɜɨɪɨɜ ɧɟɤɨɬɨɪɵɯ ɫɨɥɟɣ, ɚ ɬɚɤɠɟ ɮɟɪɪɨɦɚɝɧɢɬɧɵɯ ɦɟɬɚɥɥɨɜ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɚɯ ɜɵɲɟ Ɍɋ ɩɨɤɚ-
ɡɚɥ, ɱɬɨ ɢɯ ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɫɢɥɶɧɨ ɡɚɜɢɫɢɬ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ (ɡɚɤɨɧ Ʉɸɪɢ):
Ȥ = ɋ/Ɍ, |
(2.16) |
ɝɞɟ ɋ – ɩɨɫɬɨɹɧɧɚɹ Ʉɸɪɢ.
37
Ʉɚɤ ɩɨɤɚɡɚɥɢ ɞɚɥɶɧɟɣɲɢɟ ɢɫɫɥɟɞɨɜɚɧɢɹ, ɧɟ ɭ ɜɫɟɯ ɩɚɪɚɦɚɝɧɢɬɧɵɯ ɜɟɳɟɫɬɜ ɦɚɝɧɢɬɧɚɹ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɩɨɞɱɢɧɹɟɬɫɹ ɡɚɤɨɧɭ Ʉɸɪɢ. ɇɟɤɨɬɨɪɵɟ ɦɚɬɟɪɢɚɥɵ ɢɦɟɸɬ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜɵɪɚɠɟɧɢɟɦ
Ȥ = ɋ/(Ɍ – ǻ), |
(2.17) |
ɝɞɟ ǻ – ɩɨɫɬɨɹɧɧɚɹ ȼɟɣɫɫɚ, ɪɚɡɥɢɱɧɚɹ ɞɥɹ ɪɚɡɧɵɯ ɜɟɳɟɫɬɜ. Ɂɧɚɱɟɧɢɟ
ǻɦɨɠɟɬ ɛɵɬɶ ɛɨɥɶɲɟ ɢɥɢ ɦɟɧɶɲɟ ɧɭɥɹ.
ȼɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ ɢ/ɢɥɢ ɩɪɢ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɩɚɪɚɦɚɝɧɟɬɢɤɨɜ ɫɬɪɟɦɢɬɫɹ ɤ ɧɚɫɵɳɟɧɢɸ. Ɉɞɧɚɤɨ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɧɚɫɵɳɟɧɢɹ (ɤɨɝɞɚ ɜɫɟ ɦɚɝɧɢɬɢɤɢ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɧɟɲɧɟɝɨ ɩɨɥɹ) ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɧɟɨɛɯɨɞɢ-
ɦɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ ɩɨɪɹɞɤɚ 1011 Ⱥ/ɦ, ɚ ɩɪɢ Ɍ = 1 Ʉ – 3·105 Ⱥ/ɦ. ɉɟɪɜɚɹ ɤɥɚɫɫɢɱɟɫɤɚɹ ɬɟɨɪɢɹ ɩɚɪɚɦɚɝɧɟɬɢɡɦɚ ɛɵɥɚ ɪɚɡɪɚɛɨɬɚɧɚ Ʌɚɧɠɟɜɟɧɨɦ ɜ 1905 ɝ. ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɨɜ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɢɞɟɚɥɶɧɵɣ ɝɚɡ ɢɡ N ɦɚɝɧɢɬɢɤɨɜ, ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɜ ɫɮɟɪɢɱɟɫɤɨɦ ɟɞɢɧɢɱɧɨɦ ɨɛɴɟɦɟ. Ʉɚɠɞɵɣ ɦɚɝɧɢɬɢɤ ɢɦɟɟɬ ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ȝɦ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɡɚ ɫɱɟɬ ɬɟɩɥɨɜɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚɩɪɚɜɥɟɧɢɹ ɷɬɢɯ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɪɚɜɧɨɜɟɪɨɹɬɧɵ ɢ ɫɭɦɦɚɪɧɚɹ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ ɪɚɜɧɚ ɧɭɥɸ. ɉɪɢ ɧɚɥɢɱɢɢ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɦɚɝɧɢɬɢɤɢ ɩɨɥɭɱɚɸɬ ɞɨɩɨɥɧɢ-
ɬɟɥɶɧɭɸ ɷɧɟɪɝɢɸ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫ ɩɨɥɟɦ:
ȿɦ = ȝ0ȝɦɇcos ș, |
(2.18) |
ɝɞɟ ș – ɭɝɨɥ ɦɟɠɞɭ ɧɚɩɪɚɜɥɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɧɟɲɧɟɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȼɨɡɧɢɤɚɟɬ ɨɪɢɟɧɬɚɰɢɹ ɦɚɝɧɢɬɢɤɨɜ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸɩɨɥɹ, ɤɨɬɨɪɨɣ ɩɪɟɩɹɬɫɬɜɭɟɬɬɟɩɥɨɜɚɹɷɧɟɪɝɢɹȿɌ §kT.
ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɪɚɫɩɪɟɞɟɥɟɧɢɹ Ȼɨɥɶɰɦɚɧɚ ɜɟɪɨɹɬɧɨɫɬɶ ɧɚɯɨɠɞɟɧɢɹ dN ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɜɧɭɬɪɢ ɬɟɥɟɫɧɨɝɨ ɭɝɥɚ dȍ (ɪɢɫ. 2.5) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
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dN = Ⱥexp ¨ |
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ɝɞɟ Ⱥ – ɩɨɫɬɨɹɧɧɚɹ; exp ¨§ |
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Ɋɢɫ. 2.5. ɍɩɨɪɹɞɨɱɟɧɢɟ ɦɚɝɧɢɬɧɵɯ ɦɨɦɟɧɬɨɜ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ
Ɉɛɨɡɧɚɱɢɦ |
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(2.20) |
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ɉɨɞɫɬɚɜɢɜ (2.20) ɜ (2.19) ɢ ɩɪɨɢɧɬɟɝɪɢɪɨɜɚɜ (2.19) ɩɨ ɜɫɟɦɭ |
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ɨɛɴɟɦɭ, ɩɨɥɭɱɢɦ: |
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>exp(a) exp( a)@ |
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N = 2ʌA ³exp(a cos T)sin TdT 2S |
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sh a. (2.21) |
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ɂɡ (2.21) ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ Ⱥ: |
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Ⱥ = |
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ɉɪɨɟɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ dN ɱɚɫɬɢɰ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
dM = ȝɦdN cos ș. |
(2.23) |
Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɫɭɦɦɚɪɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɩɪɨɢɧɬɟɝɪɢɪɭɟɦ (2.23) ɩɨ ɜɫɟɦɭ ɫɮɟɪɢɱɟɫɤɨɦɭ ɨɛɴɟɦɭ ɫ ɭɱɟɬɨɦ (2.19), (2.20)
ɢ (2.22):
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2ʌ ³ exp(a cos T)sin Tcos TdT = |
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ɝɞɟ L(a) = ¨cth a |
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¸ – ɮɭɧɤɰɢɹ Ʌɚɧɠɟɜɟɧɚ. |
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ɂɡ (2.20), ɩɨɥɨɠɢɜ ȝɦ = ȝB, ɜ ɩɨɥɟ ɇ = 8·105 Ⱥ/ɦ ɩɪɢ ɤɨɦɧɚɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ ɩɨɥɭɱɢɦ ɚ § 1/400.
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Ɍɨɥɶɤɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɋɉɛȽɗɌɍ "ɅɗɌɂ" ɢɦ. ȼ.ɂ. ɍɥɶɹɧɨɜɚ (Ʌɟɧɢɧɚ)
ȼ ɷɬɨɦ ɫɥɭɱɚɟ L(a) § ɚ/3 ɢ ɜɵɪɚɠɟɧɢɟ (2.24) ɩɪɢɦɟɬ ɜɢɞ
Ɇ = |
P P2 NH |
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ɚ ɦɚɝɧɢɬɧɭɸ ɜɨɫɩɪɢɢɦɱɢɜɨɫɬɶ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɬɚɤ:
Ȥ = Ɇ/ɇ = |
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ɝɞɟ ɩɨɫɬɨɹɧɧɚɹ Ʉɸɪɢ: |
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ȼɵɪɚɠɟɧɢɟ (2.26) ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɦ ɨɛɴɹɫɧɟɧɢɟɦ ɷɦɩɢɪɢɱɟɫɤɨɝɨ ɡɚɤɨɧɚ Ʉɸɪɢ (ɫɪ. ɫ (2.16)).
ɉɪɢ ɨɱɟɧɶ ɧɢɡɤɢɯ ɬɟɦɩɟɪɚɬɭɪɚɯ ɢ/ɢɥɢ ɫɢɥɶɧɵɯ ɦɚɝɧɢɬɧɵɯ ɩɨɥɹɯ, ɤɨɝɞɚ ȝ0ȝɦɇ >> kT, ɥɢɧɟɣɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ Ɇ ɨɬ ɇ (ɫɦ. (2.25)) ɧɚɪɭɲɚɟɬɫɹ ɢ Ɇ ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ ɫɜɨɟɦɭ ɦɚɤɫɢɦɚɥɶɧɨɦɭ ɡɧɚɱɟɧɢɸ Nȝɦ, ɬ. ɟ. ɤ ɧɚɫɵɳɟɧɢɸ.
ȼ ɬɟɨɪɢɢ Ʌɚɧɠɟɜɟɧɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ, ɱɬɨ ɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɚɬɨɦɨɜ (ɷɥɟɦɟɧɬɚɪɧɵɯ ɦɚɝɧɢɬɢɤɨɜ) ɧɟ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɞɪɭɝ ɫ ɞɪɭɝɨɦ. ȼɟɣɫɫ ɩɪɟɞɩɨɥɨɠɢɥ, ɱɬɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɷɥɟɦɟɧɬɚɪɧɵɯ ɦɚɝɧɢɬɢɤɨɜ ɩɪɢɜɟɞɟɬ ɤ ɢɯ ɜɡɚɢɦɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɢ ɩɨɹɜɥɟɧɢɸ ɧɚɦɚɝɧɢ-
ɱɟɧɧɨɫɬɢ – ɜɧɭɬɪɟɧɧɟɝɨ ɦɨɥɟɤɭɥɹɪɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɝɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚ ɩɚɪɚɦɚɝɧɟɬɢɤ ɛɭɞɟɬ ɞɟɣɫɬɜɨɜɚɬɶ ɧɟ ɬɨɥɶɤɨ ɜɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ,
ɧɨ ɢ ɜɧɭɬɪɟɧɧɟɟ – ɦɨɥɟɤɭɥɹɪɧɨɟ: |
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ɇɷɮ = ɇ + nM, |
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ɝɞɟ n – ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ. |
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ɉɨɞɫɬɚɜɢɜ (2.28) ɜ (2.25), ɩɨɥɭɱɢɦ |
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Ɇ = |
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ɨɬɤɭɞɚ |
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Ȥ = Ɇ/ɇ = |
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T nC |
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ɝɞɟ ǻ – ɩɨɫɬɨɹɧɧɚɹ ȼɟɣɫɫɚ.
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