The magnetic properties of packings of cylinders

Powders of magnetic particles are used e.g. in additive manufacturing of magnets, necessitating an investigation of the properties of such powders. In this work we consider hard magnetic particles modeled as infinitely long cylinders in 2D and randomly packed in a square container. The particles have a nonlinear magnetization curve with defined remanence and coercivity and their radii follow a lognormal distribution with the standard deviation distinguishing different packings. Using a finite element approach we calculate the average and standard deviation of the magnetization of the individual particles in the packings and from these subtract the value of the corresponding regions in a solid square box to remove the shape demagnetization effect of the overall packing. We find that at applied fields close to the coercivity the average magnetization of the individual particles have the highest probability to deviate 5% from the average magnetization in the corresponding regions in the box. Away from the coercivity the packings have an near-identical magnetization to the solid box. Considering the magnetization internally in each particle, near the coercivity the standard deviation of the magnetization has the highest probability to deviate 10% from the standard deviation in magnetization in the corresponding region in the box. Thus while the overall magnetization in a packing appear to be the same as in a solid box, near the coercivity there is a larger variation of magnetization both between and within the magnetic particles, compared to a solid box.