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Weiss Molecular Field Theory of Para magnetism

Weiss modified Langevin theory of paramagnetism by introducing a new concept of internal fields. Weiss assumed that in a real gas, the molecules are mutually influenced by their magnetic moments and consequently, there should exist within the gas a molecular field. This field, produced at any point by all the neighboring molecules, is proportional to and acting in the same sense as the intensity of magnetization. Let this internal molecular field be represented by Hi. Then
            Hi = λM
Here, λ is molecular field coefficient. M is the magnetization.
Then the effecting field is
            He = H + Hi = H + λM

According to Langevin’s theory of paramagnetism,
            M = nm2 μ0H / 3KT = μ0M2s H/3nkT
m = magnetic moment of each atoms,
n = number of atoms per unit volume,
H = magnetic field intensity,
K = Boltzmann’s constant,
T = absolute temperature,
Ms = nm = saturation value of magnetization.

Weiss replaced H by He. Therefore,
        M = = μ0M2s (H + λM) /3nkT                            … (1)

. :    Volume susceptibility χm = M/H = μ0 nm2 (H + λM)/3kTH
i.e.,         χm = μ0nm2 /3kT = + λμ0nm2 /2kT χm
or         χm = (1 – λμ0nm2 /2kT) = μ0nm2 /3kT

. :        χm = (μ0nm2 /3kT) = (μ0nm2 /3k) / T – λμ0 nm2 /(T - λμ0 nm2 /3k) = C/T – θ        … (2)

Eq.(2) is known as Curie Weiss law. The constant θ is known as Curie temperature. Curie Weiss law shows that below Curie temperature (T < θ), susceptibility becomes negative. However, it should be noted that for most of the paramagnetic substances, Curie temperature is quite low so that a situation for which T < θ is rare.

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