## Abstract

A simple model considering grain-size distribution is proposed based on the random anisotropy model. When the maximum grain size (D_{m}) is less than the exchange correlation length and induced anisotropies are sufficiently small, the effective magnetic anisotropy constant («K _{1}») is given by using a distribution function (f(D)) for the grain size (D) as «K_{1}» ≈ K_{1} ^{4}{∫_{0}^{Dm} D^{3} f(D)dD} ^{2}/(φ^{6}A_{c}^{3}), where K_{1} is the magnetocrystalline anisotropy constant, φ is a parameter which reflects both the symmetry of «K_{1}» and the total spin rotation angle over the exchange-correlated coupling chain and A_{c} is the exchange stiffness constant. The log-normal distribution function reproduces well the observed grain-size distribution and yields «K _{1}» ≈ K_{1}^{4} «D»^{6} exp(6σ_{D}^{2})/(φ^{6}A_{c} ^{3}), where «D» is the mean grain size and σ _{D} is the geometric standard deviation for the distribution. This result satisfies the well-known «D»^{6} law. However, «K_{1}» increases with increasing σ_{D} even if «D» is constant. Our model has been extended by taking into account the effect of the coherent induced anisotropies on the exchange correlation length. The coercivity (H_{c} ∝ «K _{1}»/J_{s} where J_{s}, is the saturation magnetization) of the nanocrystalline Fe-Nb-B(-P-Cu) alloys with different grain-size distribution have been calculated. Our model explains well the dependence of H_{c} on the grain-size distribution. These results suggest that one should pay attention on not only the mean grain size but also on the grain-size distribution since the inhomogeneity of the grain size increases H_{c}.

Original language | English |
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Pages (from-to) | 2011-2019 |

Number of pages | 9 |

Journal | Materials Transactions |

Volume | 44 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2003 Oct |

Externally published | Yes |

## Keywords

- Grain-size distribution
- Nanocrystalline soft magnetic alloy
- Random anisotropy model
- Structural inhomogeneity

## ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering