Strukturelle Umklapp-Vorgänge in metastabilen β1-Kupfer-Zink-Mischkristallen bei tiefen und höheren Temperaturen (I). Gitterdynamische Skizze1)

The quantity of the shear-modulus G′ = (c₁₁ – c₁₂)/2 is a measure for the probability of structural Umklapp-processes to occur in metastable β₁-Cu-Zn-solid solutions. Such processes take place, if G′ = G′(T, x) would fall below a critical limit, G′_crit, e.g. by lowering of temperature T or/and Zn-concentration x, because the Fermi-contribution to G′will sink in the 1^st and with him additional the Coulomb-contribution in te 2^nd case. Both ones are the authoritative stabilizing factors for β₁ and therefore specific fo its lattice-dynamical behaviour, especially in the longwavy range of thermoacoustic lattice-vibrations, by which the cooperative Umklapp-motion will escape. Umklapping can also be initiated by favourably oriented dislocations, is G′ would approach to G′_crit in their neighbourhood: G′_critG′(xM8), with xM8  Umklapp-concentration. This is possible by variation of x during isothermal reactions, in the course of whicht he β₁-matrix will heterogenize itself into Zn-poorer and -richer districts β and β (pre-diffusion by means of quenchy vacancies). Both kinds of districts, among which the latter ones will enhance their degree of stability, are joint together coherently. They build up a so called β /β -parquet. The parquet-bricks can reach a critical size, which is necessary that sufficient large atom-collectives can simultaneously be caused to an Umklapp-motion and to occupate new equilibrium positions by thermo-acoustic shear-waves (comparison with a sin-wave beeing changed to a zigzag-line). Only at higher temperatures the bricks come up to the critical size. Umklapping comes about only in the β -bricks, which turn by it to a transition lattice (β₂) with a structure similary to that of the lowtemperature-martensite β′′. After that β₂ changes to α-phase. The way β ⇒ α is marked by the following steps: prediffusion, Umklapping + dislocation, leading to β₂, and a further dislocation dissoziation, leading the atoms to the equilibrium positions in the α-lattice. The so stepped mechanism acts an nucleationmechanism of the α-phase. After the nucleation the α-nuclei grow at the cost of too much formed β (postdiffusion). By isothermal reactions at too low temperatures a mini-herterogenized state of the β₁-matrix will be caused comparable with coldhardening states of other alloys (Guinier-Preston-zones). A β₁-matrix in such a state is unable to isothermal Umklapping, so that α-crystals can be formed – provided that the mini-heterogenities are resolved by increasing of the reaction temperature.