Figure 1

(a) The $Pn\overline{3}m$ anticuprite structure of Cd(CN)${}_2$: Cd centers are shown as large red spheres, and cyanide ions as small black spheres. The cyanide orientations are disordered; consequently no distinction is made between C and N atoms. Like cuprite itself, two topologically independent networks interpenetrate. Here one is shown in ball-and-stick representation and the other in stick representation. (b) Cadmium off-centering in Cd(CN)${}_2$. Displacement of the Cd${}^{2+}$ ions parallel to one of the $\langle 100\rangle$ crystal axes gives rise to a pseudo-octahedral coordination environment.Reuse & Permissions

Figure 2

Temperature-dependent structural evolution in Cd(CN)${}_2$ as determined using single-crystal x-ray diffraction. With increasing temperature, both the cubic lattice parameter $a$ (open black circles) and the Cd mean-squared displacement $U$(Cd) (filled red squares) decrease. The corresponding linear fits to data are included as guides to the eye; estimated standard errors are smaller than the data points.Reuse & Permissions

Figure 3

Thermal evolution of residual scattering density around the Cd site in the difference Fourier map for Cd(CN)${}_2$. Each cube corresponds to an octant of the unit cell $0\le (x,y,z)\le 1/2$, with the $(1/4,1/4,1/4)$ Cd position at its center and the $\langle 100\rangle$ crystal axes parallel to the cube edges. Isosurfaces are drawn at a level of $\rho =+0.2$ ${\mathrm{e}}^{-}$ Å${}^{-3}$.Reuse & Permissions

Figure 4

Left: Experimental x-ray diffuse scattering patterns collected at 270 K for the $\left(hk0\right)$ and $\left(hkk\right)$ cuts of reciprocal space. Right: the corresponding predicted diffuse scattering from the Monte Carlo model as described in the text.Reuse & Permissions

Figure 5

Correlated Cd${}^{2+}$ displacements in Cd(CN)${}_2$. A requirement that each CN${}^{-}$ be proximal to a single Cd${}^{2+}$ center implies ice-rules-like correlations in Cd${}^{2+}$ displacements. Here, a displacement of one reference Cd${}^{2+}$ center (highlighted) in a downwards direction reduces the number of possible displacement directions from six to three for the Cd${}^{2+}$ center to which it is immediately connected within its covalent network. Of these three ice-rules-allowed directions, one is parallel to the original displacement vector (ferroelectric displacements), and two are perpendicular. Within MC simulations, the coupling parameter $J_{\mathrm{intra}}$ can be used to favor either type of correlated displacement. Similarly, internetwork correlations can be controlled through the coupling parameter $J_{\mathrm{inter}}$. The calculated diffuse scattering patterns shown in Fig. 4 were generated using a pair of $J_{\mathrm{inter}},J_{\mathrm{intra}}$ values that favor ferroelectric displacements within the same network but antiferroelectric displacements between networks.Reuse & Permissions