Growth Model of Whisker Controlled by Heterogeneous Chemical Reaction Considering the Size Effect

Abstract

Purpose. The subject of this study were whisker, which are quasi-one-dimensional single-crystal
objects with a high degree of sophistication and strength close to the theoretical model. The
transverse dimensions of whisker can be from hundreds of micrometres to tens of nanometres,
and their length is several orders of magnitude higher than the diameter. The study is devoted
to the investigation of the kinetics of fi lamentary crystal growth controlled by a heterogeneous
chemical reaction of crystallizing substance release. The goal of the study was the establishment
of kinetic laws of growth of whisker with transverse dimensions of less than 1 μm, when the size
effect associated with an increase in the pressure of saturated vapour over a solid or liquid surface
with an increase in its curvature becomes signifi cant.
Methods and methodology. Physical and computer modelling methods were used in the study.
Silicon whisker were obtained in an open fl ow system SiCl4 + H2. Metal particles (Cu, Au, Pt, Ni,
Ag, Sn) were deposited on the prepared single-crystal Si <111> substrates, which initiated crystal
growth by the vapour-liquid-crystal mechanism. Silicon substrates with metal particles were
placed in a horizontal reactor located in a furnace with radiation heating.
Results. The earlier proposed model of the growth of silicon whisker, controlled by a chemical
reaction at the liquid-gas interface, was supplemented by taking into account the pressure of
saturated silicon vapour in the melt at the top of the crystal. For crystals of suffi ciently small
sizes, the saturated vapour pressure of the crystallizing substance becomes so signifi cant that
crystal growth ceases. The model involves diffusion delivery of the starting substances, and the
removal of reaction products into a thin surface gas layer at the liquid-gas interface, where the
concentrations of the reagents remain constant. The concentration of reagents in this layer
determines the rate of the chemical reaction of the precipitation of the crystallizing substance.
The fl ow arising due to the pressure of saturated silicon vapour over the melt was taken into
account, providing that the evaporating atoms almost completely interact with the reactants in
the gas phase. The balance of diffusion, chemical and evaporation fl ows makes it possible to
determine the growth rate of a fi lamentary crystal depending on its radius and technological
parameters of the process. The dependence of the growth rate of a fi lamentary crystal on its
radius has a maximum value and for suffi ciently small transverse dimensions of the crystal it
becomes zero. With suffi ciently large radii, crystal growth ceases. The expression determining
the maximum radius of the crystal at which growth becomes impossible was obtained.
Conclusions. In the growth model of a fi lamentary crystal controlled by a heterogeneous
chemical reaction of crystallizing, the evaporation fl ow of the crystallizing substance from the
surface of the liquid phase and the dependence of the saturated vapour pressure on the transverse
size of the crystal were taken into account.
The dependence of the growth rate of nanocrystals on their radius and technological parameters
of the growth process was obtained, which has a maximum and is limited in the region of large
crystal radii. For suffi ciently small radii of nanocrystals, the growth rate becomes zero.
Expressions determining the maximum radius of nanocrystals at which growth ceases, and the
minimum radius at which the growth rate of nanocrystals becomes zero were obtained.
A growth model of nanocrystals controlled by a heterogeneous chemical reaction, taking into
account the size effect, yielded practical results explaining the known experimental data. The
simulation results can be used for the growth of nanocrystals of various substances under the
control of the heterogeneous chemical reaction of precipitation of crystallizing substance and
can be used for the control of the growth and optimization of the growth of nanocrystals.

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