On the bosonic origin of the elastic constants of the solids - Ulrich Köbler (Results in Physics)
It is shown that the elastic compliances, sij, are defined, as the elastic stiffness constants, cij, by bosons. The constants cij 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 sij 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 sij at Tm indicates, that the associated bosons order at the melting point, Tm. We will call these bosons, MP-bosons. The maximum of the constants cij 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 Tm and for the cohesion of the solids up to Tm.