[題目] 統計力學

[brianw ()]

[領域]  統計力學

[來源]  考試題目

[題目]

      One can view a crystal growing process as putting atoms on a regular
lattice under constant T and P. Assuming these atoms are identical and
there are N of them, find the number of vacancies, n, due to thermal agitations
in the growing process. We assume at low T ,i.e. N>>n. Let "v" be the volume
per unit cell and "u" the effective energy cost for creating a vacancy.

Find entropy first and minimize the Gibbs free energy in order to determine
n. And comment on the generalized partition function. System can exchange
its energy and volume with the heat reservoir.


[瓶頸]

      看不太懂題目 想法是 會不會是N個 particle要去造成這n個空額
      (vacancy查字典的意思) 就 N 取 n 寫出 entropy 或 partition function.
      但 N>>n 又想不到這條件要做什麼了
      或者把 Grand partition function 寫成 (1+z exp[-u/kT])^n?
      不太知道怎麼 minimize the Gibbs free energy

謝謝!

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推 kermomo:應該是說，你要堆N個原子在晶格上，他要問的是:在給定的TP
→ kermomo:下，會有多少空隙產生(像岩漿快速冷卻時會有氣泡產生的感
→ kermomo:覺吧?) Gibbs Energy那段應該是微分求極值，解n
→ brianw:謝樓上 想再請問一下 微分是對什麼微呢? N取n正確嗎 @_@
推 kermomo:應該是對n微吧(哪個n使得Gibbs Energy有極值)， N是原子數
→ kermomo:n是空隙數，題目有提到在低溫下N>>n
→ brianw:多謝!已解決