No abstract

The Stoner-Wohlfarth model can be used for predicting hysteresis curves of either isotropic or anisotropic nanocrystalline Sm2Co17 type magnets. For isotropic magnets, with Mr/Ms=0.5, the Stoner-Wohlfarth model predicts coercive force of 48% of the anisotropy field. Here, Mr is remanence and Ms is magnetization of saturation. Two texture distributions were compared: Pearson VII and cosn. The calculations indicate that increasing the alignment degree of the grains, the coercivity increases. However, this increase of the coercive force is small. It is found that a very well aligned magnet, with Mr/Ms ratio of 0.96, presents coercivity only ~20% higher than that of the isotropic magnet.

Hysteresis curves were calculated according the Stoner-Wohlfarth (SW) model using values of K2/K1from zero up to 0.25 (where K2is the 2ndorder anisotropy constant and where K1is the 1storder anisotropy constant). The SW calculations assume Nd2Fe14B nanocrystalline magnets with single domain particle size (grain diameter less than 150 nm). The effect of K2on several index of merit of magnets as BHmaxand squareness are discussed. As a general result, increasing K2, the intrinsic coercivity increases. However, the increase of K2almost does not improve the BHmaxof isotropic magnets. It is found that the effect of the K2/K1ratio is coupled with the effect of texture, i.e., the effect of K2is more significant for pronounced texture.

The volume fraction of the single domain size particles can be directly estimated from the initial magnetization of thermally demagnetized magnets. Multi-domain grains present initial magnetization curve with high initial susceptibility, whereas single-domain grains present low susceptibility initial magnetization curve. In the case of single domain size particles, the coercivity mechanism is coherent rotation and the Stoner-Wohlfarth (SW) model can be applied. From the initial magnetization curve of magnets, the volume fraction of grains with diameter less than 0.3 micrometers can be estimated in NdFeB magnets. This is possible because the Nd2Fe14B phase is single domain below 0.3 micrometers.

Hysteresis loops were calculated according the Stoner-Wohlfarth model. Using as values for constants of magnetocrystalline anisotropy K1 =4.5 and K2=0.66 (J m−3), and 1.61 T for magnetization of saturation of Nd2Fe14B, the maximum coercivity for isotropic Nd2Fe14B was predicted as mi0 H = 2.95 T (29.5kOe). For a very well aligned magnet, with Mr/Ms=0.96, following the f (alpha)=cosn(alpha) distribution, the theoretical coercivity limit was estimated as mi0 H = 3.6 T (36 kOe). These estimates are valid for the ternary Nd2Fe14B alloy. It is predicted the upper limit for the coercive field as function of grain size for NdFeB and PrFeB magnets. Addition of Praseodymium is an effective method for increasing coercivity of NdFeB magnets.