![]() ![]() Elemental solids do not have confounding features existing in compounds due to mixed bonding between different atomic species (including mixed covalent-ionic bonding between the same atomic pairs as well as different bonding types between different pairs). Nevertheless, the dependence of v on m or A can be studied in a family of elemental solids. As a result, the speed of sound for a particular system cannot be predicted analytically and without the explicit knowledge of structure and interactions ( 17), similarly to other system-dependent properties such as viscosity or thermal conductivity. Furthermore, the bonding type and structure are themselves interdependent: Covalent and ionic bonding result in open and close-packed structures, respectively ( 14). Elastic moduli and density also vary with the particular structure that a system adopts. 9 and 10), we note that the speed of sound is governed by the elastic moduli and density, which substantially vary with bonding type: from strong covalent, ionic, or metallic bonding, typically giving a large bonding energy, to intermediate hydrogen bonding, and weak dipole and van der Waals interactions. Thenīefore discussing the experimental data in relation to Eq. The factor f 1 2 is about 1 to 2 and can be dropped in an approximate evaluation of v. Combining v = ( M ρ ) 1 2 and M = f E a 3 gives v = f 1 2 ( E m ) 1 2, where m is the mass of the atom or molecule, and we used m = ρ a 3. The same data imply the proportionality coefficient between M and E a 3 in the range of about 1 to 6. For most strongly bonded solids, f varies in the range of 1 to 4 ( 15, 16). This relation can be derived up to a constant given by the second derivative of the function representing the dependence of energy on volume. In particular, a clear relation was established between the bulk modulus K and the bonding energy E: K = f E a 3, where a is the interatomic separation and f is the proportionality coefficient ( 15, 16). ![]() It has been ascertained that elastic constants are governed by the density of electromagnetic energy in condensed matter phases. The longitudinal speed of sound is v = ( M ρ ) 1 2, where M = K + 4 3 G, K is the bulk modulus, G is the shear modulus, and ρ is the density. ![]()
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