Relative magnetization and a Face Centered Cubic lattice

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• LagrangeEuler
In summary, the relative magnetization in a simple cubic lattice is given by a formula involving volume, parameter, and integration over the first Brillouin zone. The same formula can be applied to a face cubic centered lattice, with the values for volume and integration boundaries changing accordingly. A reference for this equation would be appreciated.
LagrangeEuler
In case of simple cubic lattice relative magnetization is given by

$$\sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}$$
where ##v## is volume of elementary cell, ##a## is parameter of elementary cell, and integration from ##-\frac{\pi}{a}## to ##\frac{\pi}{a}## is integration over first Brillouin zone.

How relation for relative magnetization looks in case of face cubic centered lattice. What is ##v## and what are integral boundaries in that case? Thanks a lot for the answer.

Last edited:
LagrangeEuler said:
In case of simple cubic lattice relative magnetization is given by

$$\sigma=1-\frac{1}{S}\frac{v}{(2\pi)^3}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\int^{\frac{\pi}{a}}_{-\frac{\pi}{a}}\mbox{d} k_x\mbox{d} k_y\mbox{d}k_z(\mbox{e}^{\frac{E(\vec{k})}{kT}}-1)^{-1}$$
where ##v## is volume of elementary cell, ##a## is parameter of elementary cell, and integration from ##-\frac{\pi}{a}## to ##\frac{\pi}{a}## is integration over first Brillouin zone.

How relation for relative magnetization looks in case of face cubic centered lattice. What is ##v## and what are integral boundaries in that case? Thanks a lot for the answer.
Could you give us a reference for this equation?

1. What is relative magnetization?

Relative magnetization is a measure of the magnetic strength of a material compared to a reference material. It is typically expressed as a ratio or percentage.

2. How is relative magnetization measured?

Relative magnetization is measured using a magnetometer, which measures the strength of a magnetic field produced by a material. The measurement is then compared to a known reference material to determine the relative magnetization.

3. What is a Face Centered Cubic lattice?

A Face Centered Cubic lattice is a type of crystal lattice structure that is commonly found in metals. It consists of a cube with atoms located at each corner and in the center of each face. This lattice structure is known for its high symmetry and stability.

4. How does the Face Centered Cubic lattice affect magnetization?

The Face Centered Cubic lattice has a significant impact on the magnetization of a material. The arrangement of atoms in this lattice creates a strong magnetic field, making it easier for the material to become magnetized.

5. What are some applications of relative magnetization and the Face Centered Cubic lattice?

Relative magnetization and the Face Centered Cubic lattice are important concepts in materials science and have numerous applications. These include the development of new magnetic materials for electronic devices, understanding the magnetic properties of metals, and improving the efficiency of magnetic storage devices.

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