${\mathrm{Nd}}_{1+\mathrm{\epsilon }}$${\mathrm{Fe}}_4$${\mathrm{B}}_4$: A composition-modulated compound with incommensurate composite crystal structure

${\mathrm{Nd}}_{1+\mathrm{\epsilon }}$ ${\mathrm{Fe}}_4$ ${\mathrm{B}}_4$ crystallizes with the tetragonal ${\mathrm{Sm}}_{1+\mathrm{\epsilon }}$ ${\mathrm{Fe}}_4$ ${\mathrm{B}}_4$ structure type. It is characterized by two interpenetrating metal substructures with incommensurate translation periods, $c_{\mathrm{Nd}}$ and $c_{\mathrm{Fe}}$. The structure is approximated using a superstructure model of composition ${\mathrm{Nd}}_{19}$(${\mathrm{Fe}}_4$ ${\mathrm{B}}_4$ ${)}_{17}$ with c≃19$c_{\mathrm{Nd}\mathrm{\simeq }}$17$c_{\mathrm{Fe}}$=66.2(1) Å, and refined from single-crystal x-ray data to a consistency index of R=0.12 (2800 contributing reflections, 139 refined parameters). The results reveal rotational and displacive modulations of the Fe tetrahedra chains, Nd atom strings, and B atom pairs. Their periods can be expressed by ${\mathrm{L}}^{\mathrm{rot}}$=${2\mathrm{L}}^{\mathrm{dis}}$=1/(1/${\mathrm{c}}_{\mathrm{rNd}}$-1/${\mathrm{c}}_{\mathrm{Fe}}$). High-resolution electron microscopy reveals 17-Å-spaced Moiré-type fringes, but no commensurately spaced structure segments.