Although crystallographic properties are considered to be intrinsic, several studies have reported significant different values for the lattice constants of the $\mathrm{N}{\mathrm{d}}_2\mathrm{F}{\mathrm{e}}_{14}\mathrm{B}$ phase. In this study, by analyzing rod-shaped isotropic (randomly oriented) and anisotropic ($c$-axis oriented) Nd-Fe-B bulk-sintered magnets, their powdered counterparts, and powder made from grinding a single crystal, we experimentally demonstrate that the lattice constants of the $\mathrm{N}{\mathrm{d}}_2\mathrm{F}{\mathrm{e}}_{14}\mathrm{B}$ phase in the ferromagnetic ordering state depend on the sample texture. The temperature dependence of the lattice constants was investigated by focusing on their expansion associated with ferromagnetic ordering, that is, the spontaneous linear expansion along the $a$-axis (${\lambda }_a$) and $c$-axis (${\lambda }_c$). The ${\lambda }_a$ value of the isotropic (anisotropic) bulk-sintered magnets at 105 K is 10% (2%) smaller while the ${\lambda }_c$ value is 130% (40%) greater than that of the powdered single crystal. These results indicate the presence of an internal stress perpendicular to the $c$-axis in the isotropic and anisotropic bulk-sintered magnets. In addition, we observed that the ratios of the length along the $a$-axis to that along the $c$-axis ($c/a$) for the various Nd-Fe-B magnets as well as those reported previously are correlated to the sample texture. In other words, the $c/a$ values of the sintered magnets are greater than those of the powdered samples. This result suggests that the sample texture and hence the internal stress has a determining effect on the lattice constants.

中文翻译：

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织构对Nd-Fe-B永磁体中Nd2Fe14B晶格常数的影响及其与内应力的关系

尽管晶体学性质被认为是固有的，但一些研究已经报告了晶格常数的显着不同值。 $\mathrm{ñ}{\mathrm{d}}_2\mathrm{F}{\mathrm{Ë}}_{14}\mathrm{乙}$相。在本研究中，通过分析棒状各向同性（随机取向）和各向异性（$C$轴取向的Nd-Fe-B块状烧结磁体，其粉末状对应物以及通过研磨单晶制成的粉末，我们通过实验证明了其晶格常数 $\mathrm{ñ}{\mathrm{d}}_2\mathrm{F}{\mathrm{Ë}}_{14}\mathrm{乙}$铁磁有序状态下的相位取决于样品的质地。通过关注晶格常数与铁磁有序相关的扩展来研究晶格常数的温度依赖性，即沿着晶格常数的自发线性扩展。$\mathrm{一种}$轴（${\lambda }_{\mathrm{一种}}$）和 $C$轴（${\lambda }_C$）。的${\lambda }_{\mathrm{一种}}$ 在105 K时，各向同性（各向异性）块状磁体的值要小10％（2％），而 ${\lambda }_C$值比粉末单晶大130％（40％）。这些结果表明存在垂直于内应力的内应力。$C$各向同性和各向异性块状烧结磁体的轴向。此外，我们观察到沿长度的比例$\mathrm{一种}$轴沿 $C$轴（$C/\mathrm{一种}$）各种Nd-Fe-B磁体以及先前报道的磁体与样品质地相关。换句话说，$C/\mathrm{一种}$烧结磁体的值大于粉末样品的值。该结果表明，样品的质地以及内部应力对晶格常数具有决定性的影响。