### Curie Constant Calculator :

Enter the Lattice constant in nanometers(nm), Magnetic moment in μB, and you get the Curie constant in K*A/(T*m).

### Curie Constant Equation :

Curie constant equation C_{(K *A) }in Kelvin per Ampere is equal to the the permeability of free space μ_{0(m/A)} in meter per Ampere and divided by the three and multiply the the Boltzmann constant KB_{(j/k)} in joule per kelvin and multiply the number of atoms carrying the magnetic moment in a unit cell N and divided by the cubie lattice constant a^{3}_{(nm)} in nanometer and multiply the sqauare of the magnetic moment of a single atom μ^{2}_{(T m/A)} in Telsa per meter per Ampere.Hence the curie constant equation can be written as

C_{(}_{K *A)}_{=} μ_{0(m/A)} /(3 *KB_{(j/k)} )* N / a^{3}_{(nm)} *μ^{2}_{(T m/A)}

### Derivation :

M=c /T *B

The curie constant characterizes the susceptibility of the paramagnetic material to the magnetic field its equation is

C= μ_{0} /(3 *KB )* N / a^{3} *μ^{2}

Where

μ_{0} = permeability of free space and its value is 4* π *10^{-7} T m/A

KB = Boltzmann constant and value is 1.381 *10^{-7} J/k

N= number of atoms carrying the magnetic moment in a unit cell

A= lattice constant

μ =magnetic moment of a single atom

### Example:1

Calculate the curie constant? In a number of atoms in a paramagnetic material are 150, lattice constant is 0.5 nm and magnetic moment is 8 μB.

### Answer:

Given that

Lattice a =0.5 nm

Convert it into 1 meter =1000000000 nanometer =0.5 /1000000000 =5*10^{-10} m

Number of atoms N =150

Magnetic moment μ =8 μB

Curie constant formula c = C= μ_{0} /(3 *KB )* N / a^{3} *μ^{2}

C=4* π *10^{-7} / (3* 1.381 *10^{-23}) * 150 / 5*10^{-10} * 8

C=200.3513195 K *A /(T *m)

### Example:2

Calculate the curie constant? In a number of atoms in a paramagnetic material are 250, lattice constant is 9.8 nm and magnetic moment is 26 μB.

### Answer:

Given that

Lattice a =9.8 nm

Convert it into 1 meter =1000000000 nanometer =9.8 /1000000000 =9.8*10^{-09} m

Number of atoms N =250

Magnetic moment μ =26 μB

Curie constant formula c = C= μ_{0} /(3 *KB )* N / a^{3} *μ^{2}

C=4* π *10^{-7} / (3* 1.381 *10^{-23}) * 250 /9.8 *10^{-19} * 26

C=0.468424 K *A /(T *m)