Figure 1

Comparison of x-ray-diffraction patterns (top) and Fourier transformed EXAFS spectra (bottom) for amorphous and crystallized phases of ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ demonstrates anticorrelation between the long-range and short-range order. Establishment of long-range order in the crystalline phase is evidenced by the appearance of sharp Bragg diffraction peaks. At the same time, the peaks in the Fourier transforms of EXAFS (reproduced after Ref. 6), especially at the Ge and Te $K$ edges, become broader and have significantly lower intensity in the crystalline phase indicative of the increased disorder compared to the amorphous phase.Reuse & Permissions

Figure 2

Comparison of CDD maps for Si (covalent bonds), NaCl (ionic bonds), and Cu (metallic bonds). The electron charge pileup (red spots midway between the Si atoms) is a signature of covalent bonding.Reuse & Permissions

Figure 3

Two-dimensional (slice, left panel) and three-dimensional (isosurface, right panel) representations of charge density difference demonstrating the formation of covalent bonds, calculated for silicon using castep code. Note that the two panels show the result of the same simulation.Reuse & Permissions

Figure 4

The structure of rhombohedral GeTe with shorter (solid lines) and longer (dashed lines) Ge-Te bonds (upper panel). Considering the strong bonding energy hierarchy between the shorter and longer bonds demonstrated by the CDD map (lower panel) obtained from DFT simulations, where the red shaded regions in the CDD map show the electron charge pileup along the shorter bonds that is indicative of covalent bonding, the structure can be effectively viewed as layered taking into account only the shorter Ge-Te bonds (a cutoff distance of 2.9 Å).Reuse & Permissions

Figure 5

Top panel: a single buckled layer of the ideal GeTe. Lower panel (left) shows a smaller fragment of the layer including three Te atoms covalently (two conventional covalent bonds and one dative bond) bonded to Ge atoms. Both Ge and Te atoms are threefold coordinated and no lone-pair electrons exist. As a result of Sb doping (Sb atoms are shown in magenta) and different responses to the rupture of conventional covalent and dative bonds (see text), the Te atoms become twofold coordinated and possess $p$ orbitals with lone-pair electrons, directed along the broken Ge-Te bonds (lower right-hand panel). The vacant Ge site is indicated by a dotted circle. Because of the low coordination numbers, the Te atoms can rather easily move in the directions indicated by the double-ended arrow.Reuse & Permissions

Figure 6

Schematic of the formation of three-center four-electron Te-Ge-Te bonds (upper panel) utilizing Te lone-pair electrons of the twofold coordinated Te atoms located around the Ge vacancy. Te atoms are shown in orange, Ge atoms in blue, Sb atoms in magenta, and the Ge-site vacancy is shown as an empty circle. The color of the covalent bonds represent the origin of the bonding electrons (see text for more detail). The lower panel shows the result of DFT simulation of the three-center Te-Ge-Te bond complexes. Two CDD slices—separated by a black dashed line—one for each of the two $3c$-$4e$ bonds, are shown on the right. The oval-shaped image on the left zooms into one of the three-center four-electron bonds. The CDD is projected onto a plane going through the atoms participating in the three-center bonds with the atoms in front of the slice being brighter in color than those behind the slice; the red spots of similar size and color midway between the Ge and Te atoms in the CDD map indicate covalent(like) interaction of similar strength on both sides of the central Ge atom along the Te-Ge-Te bond direction. Note that, because of the two-dimensional nature of the CDD maps, the charge distribution along the two other Ge-Te bonds (centered on the same Ge atoms) that are not contained within the slices used to visualize the CDD for the $3c$-$4e$ bonds is not shown.Reuse & Permissions

Figure 7

Local distortion around a $3c$-$4e$ bond in Sb-substituted GeTe resulting in an increased disorder of the crystalline phase.Reuse & Permissions

Figure 8

CDD maps comparing three-center two-electron ($3c$-$2e$) and three-center four-electron ($3c$-$4e$) bonds between the layers. While for the $3c$-$4e$ bond there is a charge pileup on both sides of the central Ge atom indicative of covalent(like) interactions, for the $3c$-$2e$ bond the charge is concentrated only along the shorter Ge-Te bond. The crystal orientation is the same as in Fig. 4.Reuse & Permissions

Figure 9

Temperature dependence of MSRD for Ge-Te bonds in binary GeTe and ${\mathrm{Ge}}_8{\mathrm{Bb}}_2{\mathrm{Te}}_{11}$ demonstrating significantly softer Ge-Te bonds in the latter.Reuse & Permissions

Figure 10

Relaxation of identically distorted crystalline structures for (a) the ideal GeTe material and (b) Sb-doped GeTe. Ge atoms are shown as green, Te atoms as orange, and Sb atoms as magenta balls, respectively. Bonds are shown (as dual-color) sticks between atoms located at distances smaller than 3 Å. See text for details.Reuse & Permissions

Figure 11

Fragments of “defective octahedral Ge sites” in the crystalline (left) and amorphous (right) phases with the corresponding CDD isosurfaces. Despite very similar atomic structures, indicating minute atomic motion, the character of interatomic interaction changes drastically as illustrated by the shown CDD isosurfaces (grey) obtained through DFT simulations. While in the crystalline phase the central Ge atom has covalentlike interactions with four Te neighbors, as evidenced by an electron charge pileup midway between the atoms, in the amorphous phase, it is covalently bonded to only three Te atoms. [The “amorphous” fragment is from a structure that we have studied in a previous work (Ref. 17).]Reuse & Permissions