Born - von Karman - Modell

Das Born-von Kármán-Modell ist ein grundlegendes Modell zur Beschreibung der Bewegungen der Atome in einem Kristallgitter.

Das Modell besteht aus zwei Beiträgen:

Diese Näherung besagt, dass die Schwingungen der Atome in einem Gitter wie eine Masse, die linear zwischen zwei Federn eingespannt ist und hin und her schwingen kann, beschrieben werden können (im mehrdimensionalen entsprechend mit 2N Federn bei N Dimensionen). Die Atome können dann mit harmonischen Potentialen wie dem Lorentz-Oszillator und dem Harmonischen Oszillator beschrieben werden.
Diese zeigt, dass die Potenziale quadratisch sind und damit einfacher berechnet werden können.

Als Folge des Modells mit seiner Quantisierung kann man die Quantisierung der Atomschwingungen ansehen, die man Phononen nennt. Wichtig ist das Modell zum Beispiel für die Berechnung der spezifischen Wärme in Festkörpern.

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