 |
| 我的日历 |
| |
|
| 分类日志 |
| |
|
| 友情链接 |
|
|
| 最新评论 |
|
|
| 搜索日志 |
|
|
| 访问计数 |
|
|
| 获取 RSS |
| |
 | |
| |
布里渊函数[Brillouin Function] [2005-8-31]
iamet 发表在 Ω〖物理〗
| A function arising in the determination of the magnetic dipole moment of electrons in a magnetic field. The interaction energy associated with the magnetic dipoles is
 (1)
where  is the magnetic dipole moment and H is the auxiliary magnetic field. Now, the magnetic dipole moment due to the total angular momentum J of electron orbital motion ad spin is given by
 (2)
where g is the gyromagnetic ratio and  is the Bohr magneton, so
 (3)
where  is the component of the angular momentum in the direction of the field H. Now, quantum mechanics gives
 (4)
where  , ..., j, with j and  the total angular momentum quantum numbers, and
 (5)
Defining
 (6)
where k is Boltzmann's constant and T is the temperature, the mean z-component of the magnetic dipole moment is given by
 (7)
and partition function for  is then given by
  
  (8)
Now, using the partition function gives
 (9)
where
 (10)
is the Brillouin function. In the limit of  , , so
 (11)
while in the limit  ,
 (12)
The average magnetization in the z direction is then given by
 (13)
where  is the number density of dipoles, which can be rewritten in terms of the magnetic susceptibility as
 (14)
where
 (15)
which for becomes
 (16)
which is an explicit form of Curie's law. |
学好数理化，走遍天下都不怕！ | |
|
|
