Summary
Theg-shifts of conduction electrons in pure and impure alkali metals have been calculated by taking the average over the Fermi surface along the [100], [110] and [111] directions. The conduction-electron wave functions are approximated by taking orthogonalized plane waves orthogonal to the core states and are the irreducible representations in the double group. The calculatedg-shift for Li is —6.7·10−5 which is in satisfactory agreement with the experimental result (—6.1±0.2)·10−5. The temperature dependence of theg-shift is obtained when the integration over theK-vector involves the Fermi-Dirac distribution. Theg value for Li shifts only about 0.3% from a temperature of 4°K to 500°K. The wave functions for the impure alkali metals are obtained by Bardeen expansion to second order around the center of the Brillouin zone.
Riassunto
Si sono calcolati gli spostamentig degli elettroni di conduzione nei metalli alcalini puri e impuri facendo la media sulla superficie di Fermi lungo le direzioni [100], [110] e [111]. Le funzioni d'onda degli elettroni di conduzione, che si sono approssimate con onde piane ortogonalizzate ortogonali agli stati interni, sono le rappresentazioni non riducibili nel gruppo doppio. Si ha per il Li il valore calcolato dello spostamentog di—6.7·10−5, che coincide entro limiti soddisfacenti col valore sperimentale (—6.1±0.2)·10−5. Si ottiene la dipendenza dalla temperatura dello spostamentog quando l'integrazione operata sul vettoreK coinvolge la distribuzione di Fermi-Dirac. Il valore dig per il Li si sposta solo di circa lo 0.3% andando da una temperatura di 4°K a una di 500°K. Si ottengono le funzioni d'onda per i metalli alcalini impuri per mezzo dello sviluppo di Bardeen del secondo ordine intorno al centro della zona di Brillouin.
Резюме
Проводится вычислениеg сдвигов для электронов проводимости в чистых и нечистых щелочных металлах с помощью усреднения по поверхности Ферми вдоль направлений [100], [110] и [111]. Волновые функции электронов проводимости аппроксимируются с помощью ортогонализованных плоских волн, ортогональных состояниям остова, и образуют неприводимые представления в двойной группе. Вычисленныйg сдвит для Li составляет —6.7·10−5, что удовлетворительно согласуется с экспериментальным результатом (—6.1±0.2)·10−5. Температурная зависимостьg сдвига получается посяе интегрирования по всем векторамK, входящим в распределение Ферми-Дирака. Величинаg для лития изменяется только на 0.3% при изменении температуры от 4°K до 500°K. Волновые функции для щелочных металлов с примесями получаются с помощью разложения Бардина второго порядка вблизи центра зоны Бриллюэна.
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This work was supported by the U.S. Army Research Office (Durham), Grant DA-ARO-D-31-124-72-G69, and by the Chinese National Sciences Council.
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Lue, JT. The temperature dependence of theg-shifts of conduction electrons in pure and impure alkali metals. Nuov Cim B 26, 243–262 (1975). https://doi.org/10.1007/BF02755552
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DOI: https://doi.org/10.1007/BF02755552