标题： 典型元素在Nd$_{2}$Fe$_{14}$$X$ ($X$ = B, C, N, O, F)中的作用 显示英文标题

标题： Role of typical elements in Nd$_{2}$Fe$_{14}$$X$ ($X$ = B, C, N, O, F)

摘要： 钕$_{2}$铁$_{14}X$ ($X$ = B, C, N, O, F) 的磁性性质和结构稳定性通过第一性原理计算进行理论研究，重点研究$X$的作用。我们发现，B 会降低钕$_{2}$铁$_{14}$B 的磁矩（每公式单元）和磁化强度（每体积）。钕的晶体场参数$A_2^0 \langle r^2 \rangle$也没有增强，这表明 B 在钕的单轴磁各向异性中起次要作用。 这些发现与长期以来认为B对Nd$_{2}$Fe$_{14}$B的磁性能有积极影响的观点相矛盾。 当$X$从B变为C、N、O和F时，磁性能和稳定性都发生了显著变化。 Nd$_{2}$Fe$_{14}X$和$\alpha$-Fe 相对于 Nd$_{2}$Fe$_{17}X$的形成能对于$X$ = B 和 C 是负的，而当$X$ = N, O 和 F 时则是正的。这表明 B 在稳定 Nd$_{2}$Fe$_{14}$B 相中起着重要作用。 显示英文摘要

摘要： The magnetic properties and structural stability of Nd$_{2}$Fe$_{14}X$ ($X$ = B, C, N, O, F) are theoretically studied by first-principles calculations focusing on the role of $X$. We find that B reduces the magnetic moment (per formula unit) and magnetization (per volume) in Nd$_{2}$Fe$_{14}$B. The crystal-field parameter $A_2^0 \langle r^2 \rangle$ of Nd is not enhanced either, suggesting that B has minor roles in the uniaxial magnetocrystalline anisotropy of Nd. These findings are in contrast to the long-held belief that B works positively for the magnetic properties of Nd$_{2}$Fe$_{14}$B. As $X$ changes from B to C, N, O and F, both the magnetic properties and stability vary significantly. The formation energies of Nd$_{2}$Fe$_{14}X$ and $\alpha$-Fe relative to that of Nd$_{2}$Fe$_{17}X$ are negative for $X$ = B and C, whereas they are positive when $X$ = N, O and F. This indicates that B plays an important role in stabilizing the Nd$_{2}$Fe$_{14}$B phase.