Diamagnetism and paramagnetism

Diamagnetism and paramagnetism :

Those magnetic materials which are slightly repelled by applied magnetic field are known as diamagnetic materials. The diamagnetism inside material can be explained with the help of Lenz’s law. Atoms or molecule of the diamagnetism material in generally have filled outer most orbital (filled valence shell). When external magnetic field is applied on the material the materials gets magnetized in such a way that it oppose the applied magnetic field due to the change in magnetic moment of individual atoms or molecules.

Diamagnetism:

  1. \(\chi_r=\mu_r -1\), \(\mu_r<1,\chi_r=-ve\)
  2. \(\chi=\frac{M}{H}\),

H=\(\frac{magnetic field strength}{magnetization}\)

\(\Rightarrow M=\chi_r H\Rightarrow\) direction of \(\vec M\) is opposite to \(\vec H\)

  1. Lenz’s law is used to explain origin of \vec M
  2. \(B=\mu H \Rightarrow B=\mu_\circ H+\mu_\circ M\)

B=magnetic induction or magnetic flux density inside material

  1. Aluminum oxide (-1.81\(\times 10^{-5}\) SI unit =\(\chi\)), Gold (\(\chi=-3.44 \times 106{-5}\)), mercury(\(\chi=-2.85\times 10^{-5}\)), NaCl(\(\chi=-1.41\times 10^{-5}\)) etc.

Paramagnetism:

  1. Paramagnetism is appear in material due to the presence of permanent magnetic dipole moment of atom and molecules.
  2. At room temperature in the absence of magnetic field all magnetic dipoles have random orientation due to thermal enwrgy.
  3. When magnetic field is applied there is rotation of individual magnetic moment along the direction of magnetic field. So, magnetization is along the direction \(\vec M\). So,

$$\vec M=\mu_\circ H$$

$$\vec M=\mu_circ(\vec M+\vec M)$$

$$\chi_p=\frac{M}{H}\Rightarrow M=\chi_p H$$

$$\vec B=\mu_\circ \vec H(1+\chi_p)$$

$$\frac{B}{H}=\mu_\circ(1+\chi_p)$$

$$\frac{\mu}{\mu_\circ}=\mu_r=1+\chi_p$$

$$\Rightarrow \chi_p=\mu_-1$$

$$\mu_r>1, \chi_p>0$$

  1. It is temperature dependent quantity. As temperature of specimen increases magnetization decreases. As a result, paramagnetic susceptibility also decreases.

$$\chi_p \propto\frac{1}{T}$$

$$\chi_p=\frac{c}{T}$$

Example: sodium is paramagnetic, aluminum, chromium, chromium chloride, zincronium and titanium are paramagnetic at room temperature.

Ferromagnetism and anti-ferromagnetism:

Ferromagnetism:

  1. Certain metallic material have permanent magnetic dipole moment in the absence of external magnetic field and have small applied magnetic field

$$\chi_f=\frac{dM}{dH}$$

  1. Magnetic susceptibility of material is in the order of \(10^6\) for ferromagnetic material as,

H<<M

So, $$B=\mu_\circ(H+M)$$

$$B\simeq \mu_\circ M$$

  1. Magnetic flux density of magnetic induction inside material is due to un cancelled electron spin or due to the net spin magnetic moment of adjacent atom. This spin magnetic is present even in the absence of magnetic field.
  2. The small regions of ferromagnetic moment of individual atoms are completely parallel to each other. The region has attain saturation magnetization kwon as domains.

Domain:

The saturation magnetization of individual domain is equal to the magnetic moment of each atom times the number of atoms present in the domain. For example; Iron has net magnetic moment 2.22 \(\mu_B\) , cobalt atom has magnetic moment 1.72 \(mu_B\) and Nickel has magnetic moment 0.50 \(\mu_B\).

Anti-ferromagnetism:

  1. This is the phenomena of magnetic moment coupling between adjacent atoms or ions.
  2. This coupling of magnetic moment results in an anti-parallel alignment i.e. the alignment of spin magnetic moment of exactly opposite direction in such that opposite magnetic moments cancel one another.
  3. The solid has no net magnetic moment.
  4. Example: manganese oxide is a ceramic material and that is ionic in character display this types of character (anti-ferromagnetism}
  5. Manganese oxide

The net magnetic moment associated with \(o^{-2}\) ion is zero due to the completely cancellation of both spin and orbital magnetic moment.

  1. The manganese ion \(Mn^{2+}\) posses a net magnetic moment i.e. predominantly in spin origin. The arrangement of manganese ion in the crystal structure is such that adjacent ion are anti-parallel alignment as shown in figure.
fig: antiferromagnetism
fig: antiferromagnetism

References:

Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.

Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.

Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.

Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.

Raghavan, V. Material Science and Engineering. 4th . New Delhi: Pretence-Hall of India, 2003.

Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004

1. Some relations:

(\chi_r=\mu_r -1\), \(\mu_r<1,\chi_r=-ve\)

\(\chi=\frac{M}{H}\)

$$\frac{B}{H}=\mu_\circ(1+\chi_p)$$

$$\frac{\mu}{\mu_\circ}=\mu_r=1+\chi_p$$

$$\Rightarrow \chi_p=\mu_-1$$

$$\mu_r>1, \chi_p>0$$

 $$B=\mu_\circ(H+M)$$

$$B\simeq \mu_\circ M$$

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