The incommensurately modulated NiGe_{1 - x} P_x, ∼ 0.3 ≤ x ≤ ∼ 0.7, solid solution: The 'missing link' between the NiP and MnP structure types

The (3 + 1)-d incommensurately modulated structures of four members of the NiGe_{1 - x} P_x solid solution field have been successfully refined from X-ray powder diffraction data (R_w (all) / R_wp = 2.13 / 3.92; 1.52/4.25; 1.27/3.44 and 2.00/4.03 for x = 0.4, 0.5, 0.6 and 0.7, respectively). The 4-d superspace group symmetry is Amam (0 0 γ) s 0 0 (Z = 4; a = 5.0468 (2), 5.0188(2), 4.9796(2) and 4.9651 (1) Å; b = 6.0636 (3), 6.0576(2), 6.0183(2) and 6.0031 (1) Å; c = 3.4877 (2), 3.4812(2), 3.4593(1) and 3.45442 (7) Å; γ = 0.7769 (2), 0.7467(1), 0.7241(1) and 0.7046(1) for x = 0.4, 0.5, 0.6 and 0.7, respectively). The underlying average structure is of NiAs type while the (in general) incommensurate primary modulation wave-vector, γ c^*, varies continuously and smoothly with composition. The two largest amplitude displacive atomic modulation functions (AMFs), for all samples, were the Ni displacement along b AMF and the Ge/P displacement along a AMF. The refined amplitude of the former was found to systematically increase with P content from 0.215 Å for NiGe_0.6 P_0.4 to 0.294 Å for NiGe_0.3 P_0.7 while the magnitude of the latter was found to increase with P content from 0.177 Å for NiGe_0.6 P_0.4 to 0.253 Å for NiGe_0.3 P_0.7. These displacive shifts significantly modulate the local crystal chemistry i.e. the local interatomic distances and co-ordination polyhedra. This continuously variable, incommensurately modulated, intermediate structure type is shown to provide a natural link or bridge between the two extreme end-member structures i.e. NiGe (of MnP structure type) and NiP by simply choosing the commensurate options with γ = 1 and frac(1, 2) respectively.