Figure 1

Selected two-dimensional (2D) x-ray diffraction images collected while heating a sample of $\mathrm{C}{\mathrm{Br}}_4$ between room temperature and $383\mathrm{K}$. (a) Room temperature (RT), (b) $323\mathrm{K}$, (c) $358\mathrm{K}$ (arrows indicate sharp and circular diffuse patterns), (d) $378\mathrm{K}$.Reuse & Permissions

Figure 2

Four rotation photographs of a near single plastic crystal of $\mathrm{C}{\mathrm{Br}}_4$ held at a $338\mathrm{K}$ isotherm after cooling from the melt. Each individual oscillation image is a 5° rotation angle image. (a) is taken fairly close to an ⟨001⟩ orientation, (b) is taken near the midway point between a ⟨110⟩ and a ⟨332⟩ orientation, (c) is taken tilted a further $\sim 15°$ away from the [001] zone axis orientation relative to (a) around the ${\left[020\right]}^{*}$ reciprocal lattice direction, while (d) is taken tilted a few degrees away from a [112] zone axis orientation towards a [113] zone axis orientation (see the text for details).Reuse & Permissions

Figure 3

(a) A 5° rotation angle image taken at an estimated average orientation of $\sim 8.5°$ degrees to an ⟨001⟩ orientation around the ${\left[020\right]}^{*}$ reciprocal lattice direction. Diffuse streaking along the ${\left[220\right]}^{*}$ reciprocal lattice direction is marked by the doubled-headed arrow and the label $\mathbf{q}$ while the orthogonal directions of the atomic shifts responsible are labeled by the displacement eigenvector ${\mathbf{e}}_{\mu }\left(\mathbf{q}\right)$ and the single-headed arrow. (b) A drawn to scale Ewald sphere construction of the $h0l^{*}$ plane of reciprocal space for an incident beam orientation along $[00,-1]$ (the solid Ewald sphere line) and tilted away from the $[00,-1]$ direction around the ${\left[020\right]}^{*}$ axis by $\varphi \sim 10°$ (the dashed Ewald sphere line). The filled circles correspond to allowed Bragg reflections of the $Fm\text{−}3m$ average structure while the open circles are not allowed by the face-centered lattice. Allowed reflections immediately above and below project onto the open circle positions shown (the projection direction is perpendicular to the drawing plane).Reuse & Permissions

Figure 4

(a) a 5° rotation angle image taken at an estimated average orientation of $\sim 8.5°$ to a $[-1,-1,0]$ orientation around the ${[2,-2,0]}^{*}$ reciprocal lattice direction. (b) A drawn to scale Ewald sphere construction of the $hh{l}^{*}$ plane of reciprocal space for an incident beam orientation tilted by 6.00° from the $[-1,-1,0]$ orientation around the ${[2,-2,0]}^{*}$ reciprocal lattice direction (the solid Ewald sphere line) and by $\sim 15.26°$ from the $[-1,-1,0]$ orientation around the ${[2,-2,0]}^{*}$ reciprocal lattice direction (the dashed Ewald sphere line). The filled circles correspond to allowed Bragg reflections of the $Fm\text{−}3m$ average structure while the open circles are not allowed by the face-centered lattice. Allowed fcc Bragg reflections immediately above and below project onto the open circle positions shown (the projection direction is perpendicular to the drawing plane).Reuse & Permissions

Figure 5

(Color) (a) A three-dimensional representation of the reciprocal space of $\alpha \text{−}\mathrm{C}{\mathrm{Br}}_4$, with the ${\left[111\right]}^{*}$ reciprocal lattice direction as the vertical axis. The $n=1$, 2, and 3 sheets of $\frac{1}{2}$ ${\{1,1,0\}}^{*}$ diffuse are shown as light blue, green, and lavender, respectively. Small colored spheres represent allowed reflections of the fcc lattice (${⟨200⟩}^{*}$ fuchsia, ${⟨111⟩}^{*}$ turquoise, ${⟨220⟩}^{*}$ green, ${⟨113⟩}^{*}$ yellow, ${⟨420⟩}^{*}$ purple, ${⟨331⟩}^{*}$ red, ${⟨422⟩}^{*}$ turquoise, and ${⟨333⟩}^{*}$ dark blue). (b) and (c) Two-dimensional cross sections of the reciprocal space perpendicular to the ${\left[111\right]}^{*}$ and ${\left[022\right]}^{*}$ reciprocal lattice directions, respectively. Solid lines represent the observed diffuse and filled circles represent observed reflections in these planes. Open circles representing allowed reflections just above or below the cross section are added to facilitate comparison to the observed images of Fig. 2 and the Ewald constructions in Figs. 3, 4.Reuse & Permissions

Figure 6

(Color online) Various high symmetry ways of orienting individual tetrahedra within the $Fm\text{−}3m$ average structure unit cell of $\alpha \text{−}\mathrm{C}{\mathrm{Br}}_4$ (tetrahedra on the front face of the cell are indicated with a +). (a) and (b) show long-range ordered, symmetry equivalent $F\text{−}43m$ $(\mathbf{a}={\mathbf{a}}_{\mathrm{p}}$, $\mathbf{b}={\mathbf{b}}_{\mathrm{p}}$, $\mathbf{c}={\mathbf{c}}_{\mathrm{p}}$, $p$ for the $Fm\text{−}3m$ parent) structures. (c)–(h) show the six symmetry equivalent ways of orienting the next highest symmetry, fully ordered $I-42m$ (${\mathbf{a}}^{\prime }=\frac{1}{2}({\mathbf{a}}_{\mathrm{p}}+{\mathbf{b}}_{\mathrm{p}})$, ${\mathit{b}}^{\prime }=\frac{1}{2}(-{\mathbf{a}}_{\mathrm{p}}+{\mathbf{b}}_{\mathrm{p}})$, ${\mathbf{c}}^{\prime }={\mathbf{c}}_{\mathrm{p}}$) option. Note that (c) is obtained from (a) by rotating the tetrahedra by 45° around the ${\mathbf{c}}_{\mathrm{p}}$ direction.Reuse & Permissions

Figure 7

(Color online) (a) A single layer, unit cell thick portion of a random $\mathrm{C}{\mathrm{Br}}_4$ molecular distribution in projection along an ${⟨001⟩}_{\mathrm{p}}$ direction (the tetrahedra have been drawn smaller than they actually are for the purposes of clarity). The C atom of each molecule is anchored to the fcc sites of the $Fm\text{−}3m$ average structure while each molecule is assumed to be in one or other of the six possible molecular orientations shown in Figs. 6c, 6d, 6e, 6f, 6g, 6h to h. The corresponding Fourier transformed reciprocal space corresponding to this random real space distribution is shown in (b) along the [001] direction and (c) along the [111] direction.Reuse & Permissions

Figure 8

(Color online) Representation of the 10 (nonsymmetry equivalent) distinct nearest-neighbor molecular configurations, along with their frequency of occurrence in the case of a random distribution. The shortest intermolecular Br-Br separations distances for these 10 distinct configurations are also shown. An equivalent set of interactions occurs along all twelve such $\frac{1}{2}{⟨110⟩}_{\mathrm{p}}$ separations surrounding any one particular $\mathrm{C}{\mathrm{Br}}_4$ molecule.Reuse & Permissions

Figure 9

(Color online) Representation of the real space distribution obtained for a censored Frenkel model after removal of the two local configurations shown in Figs. 8a, 8b involving Br-Br separation distances of 2.466 and $2.550\mathrm{\AA }$, respectively, and its corresponding reciprocal space projection along [001] in (b) and along [111] in (c).Reuse & Permissions

Figure 10

Calculated diffraction patterns in projection along (a) [100] and (b) [111], respectively, after Monte Carlo relaxation as described in the text.Reuse & Permissions

Figure 11

Ball and stick drawing of the crystal structure of $\beta \text{−}\mathrm{C}{\mathrm{Br}}_4$ oriented so as to emphasize the fcc molecular arrangement. The fcc subcell is indicated with solid lines, whereas the monoclinic cell of the $\beta$ phase is indicated with dashed lines.Reuse & Permissions