Statistical Aspects of Ferromagnetic Nucleation-Field Theory

Abstract

It has been shown by DeBlois that surface flaws decrease the magnitude of the nucleation field of iron whiskers below the ideal theoretical value H_n0=2K₁/M_s. It is assumed here that the number of flaws in area S is determined by a Poisson distribution, with mean number λS (λ=const); that each flaw independently has a magnitude x (in magnetic field intensity units) that is a random variable with distribution function F(x); and that the nucleation field magnitude is H_n=H_n0—x_m, where x_m is the magnitude of the largest flaw on the surface of the specimen, or of a part of it that may be regarded as physically independent. The distribution of observed nucleation fields is then calculated; for large λS, it has an asymptotic form independent of the precise form of F(x), provided F(x) satisfies certain rather general conditions, and identical with the form obtained when F(x)=1—e^μx (μ=const). Comparison with data of DeBlois and Bean gives a fair fit, with λ≈2×10³ cm⁻². A particle of surface area 10⁻⁸ cm², and with this same λ, would be practically certain to have no flaws; with a λ 5000 times as large, it would have probability 0.9 of flawlessness. These conclusions are consistent with the relatively much greater success of ideal crystal theory for fine particles than for bulk material.