Intrinsic Planar Defects in Germanium and Their Contribution to the Excess Specific Heat at High Temperatures

Abstract

Excessively high specific heat is usually observed in solids at comparatively high temperatures. It is believed to be associated with anharmonic effects. Using the simple case of elemental germanium with archetypical diamond structure, it is demonstrated that the anharmonicity effect can not fully describe the excess specific heat in germanium. Instead, two types of extended planar defects with a record low formation energy () are proposed, which can account for the discrepancy between theoretical and observed specific heat. These planar defects can be considered as finite distortion of crystal lattice produced by shear phonon modes accompanied by specific reconstruction of interatomic bonds on certain atomic planes. By comparison of experimental and theoretical specific heat, it is found that the germanium sample is subdivided into domains with intrinsic planar defects aligned along a single crystallographic direction.

Planar defects as a way to account for explicit anharmonicity in high temperature thermodynamic properties of silicon

“…In some detail it was discussed in Ref. 18 . Despite not very strict formulation of the method, these local minima can be found as the energy lowering, produced by bond reconstruction.…”

“…We can also mention, that newer data of specific heat obtained by drop calorimeter methods 8 produce substantially lower specific heat values. Earlier we have explained this underestimation of high temperature specific heat measured by drop calorimeters by the effect of planar defects quenching during cooling 18 . The most reliable method of determination of specific heat would be "one-shot measurement" like pulse-heating one [19][20][21] .…”

“…This analogy between defect and anharmonic phonon oscillation was proposed in the number of our recent works [16][17][18] and was successfully used to resolve discrepancies in experimental thermodynamic properties of graphite near the melting temperature 17,[19][20][21] . In the nutshell, this analogy relates strong anharmonicity to finite displacement of atom layers caused by shear phonon modes, and subsequent reconstruction of interatomic bonds.…”

“…As it was demonstrated in Ref. 18 , the concentration of interface sheets is described by the formula:…”

“…14 , where it was demonstrated, that high-temperature specific heat and expansion coefficient in aluminum are mainly described by bulk anharmonicity. It seems, that in covalently bonded materials the situation is opposite, and the large part of anharmonicity present in them is due to transverse anharmonicity (like in germanium 18 ). More than half a century ago, there was a discussion about "microscopic and macroscopic" expansion of solids measured by different methods (by macroscopic dilatometry and microscopic X-Ray diffraction, see e.g.…”