Download - Lecture 4_ Para Magnetism


These materials don't possess permanent dipole and hence the magnetic effects are small Since the induced magnetic moment always oppose the applied field, the diamagnetic susceptibility is negative. It is always temperature independent. Diamagnetic materials usually repel the magnetic line of force. Summary Diamagnetism e.g.: Bi, H2O, CO2, Ge, Si etc. Material = (r -1) Cu -9.5x10-6 Al2O3 -5.0x10-6 Au -3.7x10-5 Ge -0.8x10-5 Si -0.3x10-5 Se -1.7x10-5 He -0.5x10-5 Para-magnetism B>B0 , _ is positive, r>1, . The permanent magnetic moment results from the following contributions: 1. The spin or intrinsic moments of the electrons. 2. The orbital motion of the electrons. 3. The spin magnetic moment of the nucleus. A form of magnetism which occurs only in the presence of externally applied magnetic field and materials are attracted to magnetic field. Paramagnetism Paramagnetism is observed in: 1. Metals 2. Atoms and molecules possessing an odd number of electrons, that is free sodium atoms, gaseous nitric oxide etc. 3. A few compounds having an even number of electrons (example Oxygen molecule) 4. Free atoms or ions having a partially filled inner shell e.g. rare earth and actinide elements, ions of some transition elements such as Mn2+ Manganese, platinum, tungsten, some members of rare earth group and ions formed by removing and adding electrons to basic atoms there by creating unpaired spins. Basic assumptions of Langevins classical theory The theory considers the paramagnetic solids in terms of paramagnetic gas, in which each particle is assumed to bear a permanent magnetic moment . Mutual interaction between dipoles is assumed to be negligible. Orientation of permanent magnetic dipole moment. Classical Theory of Paramagnetism TC= _Curies law : ) ( u_=TCCurie-Weiss law : . Langavins analysis . Temperature dependence of paramagnetism - Paramagnetism has net magnetic moments: No field : M=0 Field is applied, low Temp. B Field is applied, and High Temp. B T _ Classical Theory of Paramagnetism :(vector) u cos BEP = The Magnetization(M) =The total magnetic moments per unit volume }}= t ut uu u u u u 0cos0cossincos sindedenaa}= ndn M0cosu } }= = n adeK dn n0 0cossin 2 t uu u t}= t uu u u t0coscos sin 2 deK a}= t uu ut0cossin2dnKeaB . Langavin Function Let dn be the number of moments inclined at an angle between u & u+du When no field is applied dn dA (solid angle) When field is applied dn is proportional to dA x Boltzmann factor . ) sin(cosexp 2 exp u uu t dkTBKkTEKdA dn p|.|



\| =||.|

\| +=}}=aa nae ee endxedxex na aa aaxax1coth11111 u uud dxxsincos ==aaMM 1coth0 = nM =0Langavin function : + =945245 3) (5 3a aaa LTBak= Conclusions from Langavin function: 1. Saturation will occur if a is large enough. Large B or low T is necessary 2. At small a, the magnetization M varies linearly with B. . Relationship between Langavin theory and Curies law For small a, L(a)=a/3=B/3kT, M=M0 L(a) ..3,32020 0kT B f or validconst CurieknC whereTCkTnBMH M