作者brianw ()
看板Physics
标题[题目] 统计力学
时间Wed Feb 22 15:07:26 2012
[领域] 统计力学
[来源] 考试题目
[题目]
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.
[瓶颈]
看不太懂题目 想法是 会不会是N个 particle要去造成这n个空额
(vacancy查字典的意思) 就 N 取 n 写出 entropy 或 partition function.
但 N>>n 又想不到这条件要做什麽了
或者把 Grand partition function 写成 (1+z exp[-u/kT])^n?
不太知道怎麽 minimize the Gibbs free energy
谢谢!
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 114.45.5.144
1F：推 kermomo:应该是说，你要堆N个原子在晶格上，他要问的是:在给定的TP 02/22 18:59
2F：→ kermomo:下，会有多少空隙产生(像岩浆快速冷却时会有气泡产生的感 02/22 19:00
3F：→ kermomo:觉吧?) Gibbs Energy那段应该是微分求极值，解n 02/22 19:01
4F：→ brianw:谢楼上 想再请问一下 微分是对什麽微呢? N取n正确吗 @_@ 02/22 20:13
5F：推 kermomo:应该是对n微吧(哪个n使得Gibbs Energy有极值)， N是原子数 02/23 09:53
6F：→ kermomo:n是空隙数，题目有提到在低温下N>>n 02/23 09:55
7F：→ brianw:多谢!已解决 02/23 13:03