On the bosonic origin of the elastic constants of the solids

• Elastic stiffness constants, c ij , and elastic compliances, s ij , are defined by different bosons. • The bosons defining the stiffness constant, c ij , are the sound waves (elastic dipole radiation) • The bosons defining the elastic compliances, s ij , are elastic quadrupole radiation. • At the liquid–solid transition, the bosons generated by the elastic quadrupoles order. • The bosons generated by elastic dipoles do not order at a finite temperature. 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 m elting p oint, 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 .