2005/08/31 | 布里渊函数[Brillouin Function]
类别(Ω〖物理〗) | 评论(0) | 阅读(196) | 发表于 20:51
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.
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