Size, temperature, and bond nature dependence of elasticity and its derivatives on extensibility, Debye temperature, and heat capacity of nanostructures

Abstract

With the miniaturization of a solid down to nanometer scale, the elasticity, extensibility, Debye temperature, and specific heat capacity of the solid are no longer constant but change with variation of size. These quantities also change with the temperature of the measurement and the nature of the chemical bond involved. The mechanism behind the intriguing tunability and the interdependence of these quantities remain yet a high challenge. A set of analytical solutions is presented herewith showing that the observed trends could be reproduced by taking the fact of bond order deficiency into consideration. Agreement between predictions and observations clarifies that the shortened and strengthened surface bonds dictate intrinsically the observed tunability, yet atoms in the core interior remain as they are in the bulk. The thermally softening of a specimen arises from bond expansion and bond vibration due to the internal energy increases.

Twinning anisotropy of tantalum during nanoindentation

“…quoted Ao et al [43] who proposed that the competition between the surface bond shrinkage and melting temperature variation with size reduction leads to the so called size effect in elastic modulus whereas Gu et al [46] related this size-dependent behaviour to Debye temperature.…”

Mechanical stiffness and dissipation in ultrananocrystalline diamond microresonators

“…2 However, because of the small grain size of UNCD, a significant fraction of atoms are in the grain boundaries or very close to the grain boundaries in UNCD. This significantly influences the bonding nature 41,42 and hence the mechanical behavior of the UNCD films. The influence on Poisson's ratio for this special case has just recently been modeled.…”

Specifics of thermodynamic description of nanocrystals

“…In many cases, embedding a specimen into a matrix or deposition of foreign atoms on its surface results in a crossover from the size-related expansion of the lattice to contraction. As follows from (14), there are two mechanisms that may make lattice contract or expand as the crystal size decreases. These are enhancement of the anharmonicity due to softening of vibration modes of the nanocrystal (reduction of 0 () cl) and contraction/expansion of the lattice due to stress in the surface layer.…”

“…Subsequently, it was established that such thermodynamic properties as isobaric and isochoric heat capacities, Debye temperature etc., also vary with crystal size [13][14]. In addition to affecting the melting transition, reduction of particle size in some cases leads to formation of new polymorphic modifications of the crystal.…”