# Curie’s Constant

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Curie’s constant unlike the others is dependent on the material property that can relate a material magnetic susceptibility to its temperature.This was first derived by a physicist named- Marie Curie.

Curie’s law states that the magnetization in a paramagnetic material is directly proportional to the applied magnetic field.

For eg. if we heat any object, its magnetisation  is said to be inversely proportional to the temperature.

Curie’s temperature is the temperature at which a ferromagnetic substance or material changes in paramagnetic substance or material on heating it. This transition is basically used in storage of optical media for erasing and inserting new data.

Talkin about the physical significance of the curies constant it depends on effective moments of the ions and hence must be some measures of it. However, it is exactly  the same average moment of solid.it is the measure of how strongly a material can sustain magnetic alignment despite thermal fluctuations.

### Curies Constant Represented in SI Unit Form

C = μ0 μB2 ng2 J( J + 1 )/ 3 kB

Here n= number of magnetic  atoms per unit volume

g= lande-g-factor

j= angular momentum quantum number

Kb = boltzmann’s  constant

For a magnetic moment for two level system the formula gets reduced to:

C = nμ0 μ2 / kB

The expressions in Gaussian unit is represented as:

C = μB2 ng2 J( J + 1 )/ 3 kB

C = n μ2 / kB

The constant is used in the curie’s law which states that magnetisation is inversely proportional to temperature for a fixed value of magnetic field.

M = C B/T

This was discovered by Pierre Curie.

The relation between magnetic susceptibility  is denoted by X , and magnetization M and applied magnetic field H is almost linear at the low fields then:

X = dM/dH ≈  M/H

This shows that temperature T is inversely  related to the magnetization  and  paranetcs system of non interacting  magnetic moments.

### Curies Constant Value

Simply, if we take a cubic lattice there is one atom per unit cell. We now are assuming that each atom carries magnetic moment mu= 2muB with the help of curies constant we will get that C (that denotes curies constant) =1.3047 K*A/(T*M).

One of the very important laws in this topic is weiss law:

We already know the mathematical representation of the law which is

M= C*(B/T).

Few terms which helps in understanding curies law better:

Ferromagnetism : It is the property by which certain materials are able to form permanent magnets (like iron)

Magnetic Susceptibility : It is the measurement of how much a substance can get magnetised in a magnetic field.

Paramagnetism : When some materials get weekly attracted by the external magnetic field, then this situation is known as paramagnetism.

Permeability: It measures the ability of a substance to support the formation of magnetic fields within itself.

Curies Poin: It is the point or a temperature above which certain substances lose their permanent magnetic property.

Curies Constant: As discussed, it’s the property depending upon material that relates to materials magnetic susceptibility and temperature.

Curies Weiss Law: It informs us about the magnetic susceptibility that is denoted by letter X of a ferromagnet in the paramagnetic region above the curies point  it is denoted as:

X= C/T-Tc.

C= curies constant

T= absolute temperature

Tc = curie's temperature both measured in kelvin.

### Curie’s Constant Unit

We define the unit of curies constant as:

[K * A/(T * m)]

The magnetic moment μθ is a characteristics number which describes the magnetic property of a single atom or a particle molecule etc.

We can easily calculate the value of curie by dividing the decay rate per second by 3.7 x 10^10 the decay rate is equal to 1 curie. Taking an example of 1 grams of cobalt -60 is equal to 1119 curie  and it is because  4.141 x 10^13/ 3.7 x 10^10 = 1,119 Ci.

### Curies Table of Content

• Curie's Law of Magnetism

• Curies Constant Equation

Curie's Law of Magnetism : it states that magnetization thats M of a paramagnetic substance is directly proportional to the curies constant which is denoted as C and magnetic field which is denoted as B which is inversely proportional to T that is temperature  writing it in equation:

M=C/T*B

C- characteristics  susceptibility to magnetic fields of paramagnetic materials .It totally depends on the strength of the atoms which are forming the substances  and on the density of these moments.

### Limitations of Curie's Law

There are  some failures in these laws, like it fails in the Curie’s Weiss law fails to describe the susceptibility of certain materials these and are considered as the behaviour in the form

1/T-Tc

However, at the temperature which is denoted as T>>Tc the whole expression still holds true, however as soon as we replace Tc by temperature which is higher than curie's temperature that C and if T becomes zero, then the susceptibility becomes infinite . Sometimes it  takes the weiss constant to distinguish it from the temperature of the Weiss point.

There are  a few modifications in these laws :

The Weiss law which was for a paramagnetic material that's written as X = M/H= Mμ0/B= C/T.

Where, μ0 is called the permeability of free space.

M is called as magnetization

B= μ0 is called a magnetic field and C is called the material specific curies constant.

The total magnetic field for curies weiss law is B + lambda M( lambda = weiss molecular field constant).

It  clearly shows that the magnetic susceptibility is inversely proportional to the temperature .

Which is the weiss law

X= C/T-Tc

When temperature Tc is

Tc= C lambda /μ0.

Q1.Define curie’s temperature Tc?

The temperature at which the magnetic core becomes ferromagnetic when it’s below this temperature  and when above this temperature becomes paramagnetic.