On the bosonic origin of the elastic constants of the solids

Abstract

It is shown that the elastic compliances, s_ij, are defined, as the elastic stiffness constants, c_ij, by bosons. The constants c_ij are well-known to be given by the velocities of the sound waves, called here Debye-bosons. Sound waves are evidently elastic dipole radiation. The constants s_ij will be shown to originate in a boson type that is identified as elastic quadrupole radiation. Consistent with the conclusion that the two elastic constants are defined by bosons is that they reach a (finite) maximum at the ordering temperature of the respective boson field. The maximum of the elastic compliances s_ij at T_m indicates, that the associated bosons order at the melting point, T_m. We will call these bosons, MP-bosons. The maximum of the constants c_ij is at T = 0. As a consequence, the Debye boson field does not order at a finite temperature. Upon ordering, all MP-bosons condense in one energy state (Bose-Einstein condensation). This is the thermodynamically highest possible order. Additionally, ordered boson fields constrict themselves to the finite volume of a stationary unit. In magnetism, these ordered units are known as domains. The mosaic blocks are identified as the long-range ordered units, created upon ordering of the MP-bosons. Moreover, ordered boson fields attempt to assume the smallest possible volume (magnetostriction). The self-constriction of the ordered MP-boson field that compresses each mosaic block, has to be made responsible for the strong decrease of the lattice parameter below T_m and for the cohesion of the solids up to T_m.