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Comment on “Nano-particle magnetism with a dispersion of particle sizes” [J. Appl. Phys. 112
, 103915 (2012)]
11.The mean volume is exactly defined from the PDF by ; and in the same way, the mean value of any quantity X related to the particle size can be expressed as . The median diameter Dm (no need to add “of the number distribution”) is defined from the PDF [i.e., from and not f(D)], by the relation: . This defines the one and only median particle diameter.
12.A constant tm in the expression used by El-Hilo would mean that for each temperature T (i.e., each point of the ZFC and FC curves), the system is brought instantly from zero temperature to T and then measured after a time tm. The system should then be demagnetized (i.e., reach the superparamagnetic regime) and cooled down (without any applied field for the ZFC curve) to zero temperature between each measurement point. This is quite unrealistic.
13.Besides, note that in R. W. Chantrell et al. [IEEE Trans. Magn. 27, 3570 (1991)], this distribution is simply referred to as “the distribution of blocking temperatures,” which is highly confusing because it is not the PDF.
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A recent paper1 examines zero field-cooled/field-cooled (ZFC/FC) susceptibility curves for nanoparticle assemblies with a size distribution. It is explained that the “volume and number weighted distribution are equally valid for the representation of distribution functions in nanoparticle magnetic systems” and the usual modelling approach (abrupt transition from a blocked to a superparamagnetic regime, at a given temperature) is compared to the more elaborate one (the “progressive crossover model (PCM)”) introduced in our previous articles.2–4 The importance of the f 0 value is also stressed. In this article, several statements are made in opposition to some of our previously published results. Because we like to believe that these words were driven by a simple “misunderstanding” of our models and analysis, we would like to clarify some points in the present comment.
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