Determination of the dispersion magnetic moment of the nanoparticles in magnetic fluid

At the initial part of the magnetization curve of paramagnet its magnetization on the theory of Langevin proportional to the square of the magnetic moment P of paramagnetic particles: М in= ( nP 2 B /(3 kT )), where the n - concentration of particle, B - magnetic induction, T - temperature, k - Boltzmann constant. Saturation magnetization, measured at the final part of the magnetization curve is proportional to the magnetic moment in the first degree: М sat = nР. At the presence of dispersion of the magnetic moment of the particle measured magnetization М in and М sat averaged. In the result turns М in= n ( Р 2) mid В /(3 kТ ) М sat = nP mid, where ( Р 2) mid и Р mid - middle values Р 2 and Р. Since the value of the magnetic moment of particular paramagnetic particle is random variable, at any function of the distribution of particles on values P, dispersion distribution D can be found by the formula: D = ( Р 2) mid - ( Р mid) 2, received values (Р 2 ) mid и ( Р mid) 2 from experimental magnetization curve. The method is illustrated determining the dispersions of distribution of the magnetic moments of nanoparticles 3 magnetic fluids.