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Comptes Rendus Physique
Volume 17, n° 3-4
pages 389-405 (mars 2016)
Doi : 10.1016/j.crhy.2015.12.009
Structure of covalently bonded materials: From the Peierls distortion to Phase-Change Materials
Structure des matériaux covalents : de la distorsion de Peierls aux matériaux à changement de phase
 

Fig. 1




Fig. 1 : 

A large number of group V, VII and VII structures can be related to a deformation (symmetry breaking) of a simple cubic structure. Polonium is the exception. The short covalent bonds are in bold and the long Van der Waals bonds are in light. The coordination numbers of groups V, VI and VII are respectively 3(+3), 2(+4) and 1(+5).


Fig. 2




Fig. 2 : 

Dispersion relation E (k ) and density of states of undistorted and distorted chain. The energy gain is the consequence of the downwards shift (arrow) of the occupied energy levels close to the Fermi energy (in red). Upper right insert: original drawing in Peierls’ Les Houches lecture notes.


Fig. 3




Fig. 3 : 

Energy landscape corresponding to Eq. (7). Peierls non-distorted (left) and distorted (right). The red point corresponds to the energy minimum.


Fig. 4




Fig. 4 : 

Energy landscape in the case of the resonant bonding. The vibration ellipsoid is very elongated along a direction at 45°.


Fig. 5




Fig. 5 : 

Energy as a function of the distortion parameter η (schematic). The reference energy is the energy of the undistorted structure. The different curves can be seen in different ways: (1) as a function of the element in a periodic table, (2) as a function of the volume (or pressure), (3) as a function of the ratio p /q .


Fig. 6




Fig. 6 : 

Short and long distances of the A7 structure of arsenic measured by EXAFS.


Fig. 7




Fig. 7 : 

Schematic density of state of state of the Se or Te structure (SLL)n . From left to right: bonding band, lone pair band and unoccupied anti-bonding band.


Fig. 8




Fig. 8 : 

Electronic energies of Te in different environments. TeII (a) and TeIII (b) have the same electronic energy but if Te transfers an electron to Ge, the TeIII (c) configuration is more stable. β is the modulus of the resonance integral ppπ .


Fig. 9




Fig. 9 : 

Densities of states and Peierls distortion. Left: non-distorted. Middle: Peierls distorted in liquid with a dip at the Fermi level at E F . Right: Peierls distortion of a crystal with a gap at E F .


Fig. 10




Fig. 10 : 

Geometry of the three-body correlation function p (r 1 ,r 2 ) for three almost aligned atoms.


Fig. 11




Fig. 11 : 

(Left) Experimental setup (D4 diffractometer at ILL). (Right) Pair correlation functions of liquid alloys of As and Sb and coordination numbers. One observes a continuous disappearance of the Peierls distortion when Sb is added to As.


Fig. 12




Fig. 12 : 

Energies of diamond, graphite and polymeric chain as a function of the hardness p of the repulsive potential. Right scale: difference diamond–graphite. Graphite is the most stable structure for soft repulsive potentials p <3.3, i.e. only for C.


Fig. 13




Fig. 13 : 

Phase diagram of the alloy Gex Te1x and crystallographic structures of the compound GeTe. In green, the region of negative thermal expansion (NTE).


Fig. 14




Fig. 14 : 

Temperature evolution of the atomic volume of liquid alloys Gex Te1x .


Fig. 15




Fig. 15 : 

Structure factor of Ge15 Te85 . The prepeak at ∼1 Å−1 is the signature of a Peierls distortion in the liquid. It diminishes gradually when the temperature increases as well as the second main peak.


Fig. 16




Fig. 16 : 

Distances of the successive nearest-neighbor average distances as a function of the temperature of liquid As2 Te3 .


Fig. 17




Fig. 17 : 

Upper panel: low- and high-temperature structures of Ge15 Te85 . Lower panel: probability densities of two distances (r 1 ,r 2 ).


Fig. 18




Fig. 18 : 

Blue curve: vibrational amplitude (in red) at the temperature kB T , just below the Peierls energy ΔE P . A reduction of the volume at the same temperature transforms the blue curve into the green curve, for which the vibrational amplitude and entropy are higher.


Fig. 19




Fig. 19 : 

The operation principle of a PCM device is based on the reversible switching between a crystalline and an amorphous phase that show a contrast in their optical and electrical properties [39].


Fig. 20




Fig. 20 : 

Ternary phase diagram of GeSbTe. Tie line of Phase-Change Materials and eutectic composition Ge15 Te85 .


Fig. 21




Fig. 21 : 

Bond length distribution around a Ge atom in crystalline, liquid and relaxed amorphous GeTe. The panels represent the probability density f (r 1 ,r 2 ) of having a bond of length r 1 almost aligned with a bond of length r 2 (angular deviations smaller than 25°). (a) liquid phase at T =1100 K, (b) relaxed glass obtained by substituting Sn with Ge in a-SnTe and (c) crystal. All three systems are calculated at the same density: the density of the amorphous phase. The white open circles correspond to the maxima (r 1 ,r 2 ) in crystalline GeTe at the crystalline density. The plots show that the Peierls distortion amplitude (r 2 /r 1 or η (5)) in relaxed amorphous GeTe is larger than in the crystalline phase (figure adapted from [40]).

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