engleski

The oscillating growth rate of 111 facets of partly faceted single crystal of superionic cuprous selenide during the nearly-equilibrium growth at a low constant volume growth rate

The time dependence of a slow free-space growth of the nearly-equilibrium crystal shape (n-ECS) of superionic cuprous selenide Cu_2-xSe (x=0.25) has been investigated. The growth has been performed using Ohachi's method, developed for ionic-electronic mixed conductors ((Cu,Ag)_2ąx(S,Se,Te)). The growth of Cu_2-xSe at constant temperature T=800 K and at constant Se vapour pressure (constant nonstoichiometry x=0.25) is controlled by the high diffussion of mobile Cu atoms driven by constant chemical potential difference (Delta mu=0.48 eV). During the growth (150-250 hours) at constant volume rate (0.2-0.1 mm^3/h, respectively ), single crystal exhibits a spherical shape with well developed macroscopic 111 facets. The growth rate of the average sphere radius (dR/dt) is therefore a rapidly decreasing function of time, and for the most of the growth time (except for its beginning) is between 10 and 1 molecular layers per second. With these rates we approach the range of rates declared for the growth of the hcp ^4He of ECS, which is by far the most extensively investigated system. A certain (single) crystal, in thermodynamic equilibrium with its liquid or vapour phase, will in time spontaneously achieve history independent equilibrium shape as the result of the balance between crystal forces and surface tension at any point of its surface. The ECS criteria require also the size independent shape. By restricting our spherical grown crystal to the part of thermodynamic space (T_growth,x) in which there is a stable coexistance of macroscopic 111 facets (smooth phase) and curved parts (rough phase), the size independent shape is equivalent to the request that the ratio of facet (L) and sphere (R) diameters should be independent of the radius of the sphere. Monitoring the time dependence of L/R ratio we are able to study the macroscopic aspect of the growth process, as well as the ECS features, both slightly out of and in the thermodynamic equilibrium. An impressive fact is that although the hcp ^4He crystal are grown at below 1.30 K (p=25 bars) in equilibrium with superfluid He, the time dependence of the n-ECS and the ECS itself of Cu_2-xSe exhibit during the growth a close similarity to hcp ^4He up to the scaling factor related to the magnitude of interatomic forces. We may see that during the growth L/R ratio shows a relaxation toward its equilibrium value at (T_g, x) point. This behaviour may be described by three parameters: equilibrium ratios (L/R) of the initial (fully faceted crystal in this very case) and final (800 K, equilibrium presure of Se for x=0.25) phase points and the unique relaxation time (tau = 1000 min.). There is a new effect, superimposed on the relaxation behaviour, observed as the winking of the facet size (up to 30 percent) which suggests repeatedly enhanced lateral growth of the facet at the expense of the curved parts of the sphere. Experiments also exhibit a corresponding correlated behaviour of the modulus of facet radial vector, which is almost pinned down during the enhanced lateral growth. The single oscillation period is of the same order of magnitude as the relaxation time mentioned above. The results are dicussed within the framework of current ECS growth models.

cuprous selenide; superionic conductor; equilibrium crystal shape; crystal growth; Ohachi's method; constant volume growth rate; facet oscillating growth

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