Relation Between Squareness Factor and the Area Under the Demagnetization Curve of Rare Earth Magnets

This study investigates the correlation between squareness factor (SF) and squareness ratio (SQ) for sintered Nd14.5Dy1.5Fe76Nb1B7, Nd17Fe76.5Cu1.5B5, and Nd16Fe76B8magnets, aiming to expand the range of squareness factors through controlled variations in composition and milling time. The magnets have been fabricated via powder metallurgy and characterized using demagnetization curves. The squareness factor has been determined by the conventional ratio of the knee demagnetization field (Hk) to intrinsic coercivity (iHc). The squareness ratio has been calculated by the ratio between the numerically integrated area under the intrinsic demagnetization curve and the corresponding ideal maximum area of a perfectly square or rectangular loop. Results indicate that the squareness factor varies significantly with alloy composition and milling duration, with values ranging from 0.48 to 0.94. The Nd17Fe76.5Cu1.5B5alloy exhibited the lowest squareness factor (0.48), whereas the Dy-containing Nd14.5Dy1.5Fe76Nb1B7reached the highest one (0.94). Additionally, microstructural analysis revealed heterogeneous grain structures influenced by milling time and elemental composition. Roundness (SD5) and rectangularity (R) parameters have also been introduced to further characterize the loop shape, revealing a general trend in relation to theSQvalues. The findings suggest that standard squareness factor remains the most reliable parameter for defining the squareness of sintered rare-earth magnets, particularly those with well-defined demagnetization curves. In contrast, the squareness ratio while useful for comparison is less effective for magnets with lower squareness factor. This study provides insights into optimizing magnet manufacturing for tailored squareness properties, contributing to improved design and performance of sintered rare-earth-based permanent magnets.