On the significance of surface tension driven flow in floating zone melting experiments

The predominance of the surface tension driven (Marangoni) flow over the buoyancy driven free convection for small zone lengths in electron beam floating zone melting of doped molybdenum rods is pointed out. The observed different patterns of microsegregation and the critical conditions of their occurrence, i.e. B-cores below a critical zone length of l_c = 3.5 mm and B-striations above this value, are shown to be in qualitative agreements with theoretical predictions made from convection models.     

On the surface diffusion during growth of a crystal on a substrate

Some of the possibilities of the method of investigating the growth kinetics of crystals from the vapour phase are discussed. The diffusion problem for the growth of non-singular cylindrical crystal surface is investigated, considering as example a cylindrical crystal model lying on a foreign substrate and taking into account the direct impact of molecules from the vapour as well as diffusion along the surface of the substrate. An expression is derived for the growth rate at the edge of the crystal face in contact with the substrate. It is established that for small crystals the growth rate does not depend on their size. In this case it is possible to measure from the experimental data the product of the kinetic coefficient and the concentration of the molecules in the adsorption layer at the surface of the crystal. The author's experimental estimate in the case of growth of diphenyl from the vapour phase shows that such measurements can be performed with crystals smaller than about 30 microns.     

On the internal nucleation of melting

Crystals of quartz have been superheated by some 450°C and crystals of albite by some 185°C above their respective melting points. In all cases, melting took place by the nucleation of liquid at the external surfaces (and internal boundaries as well in the case of albite). No evidence for the internal nucleation of liquid was found at any superheat for either material.The results of quartz indicate an exceptionallu large barrier to the internal nucleation of liquid. It is suggested that this large nucleation barrier is associated with the strain energy of forming a liquid nucleus within the crystalline phase.It is also indicated that the nucleation of liquid at the external surfaces of crystals at negligible superheats suggests that the free surfaces of liquids do not per se serve as preferred nucleating sites for crystallization — and that the crystal nucleation often observed at external surfaces or internal surfaces is in fact associated with condensed second-phase impurities.     

On the theory of crystal growth from impure solution using monolayer adsorption mechanism

Assuming the lateral interaction energy of the adsorbed molecules of solvent, solute and impurity in an adlayer of crystal-impure solution interface, the partition function and its partial derivatives are calculated using the Bragg-William monolayer model with empty sites. The condition for ideality and deviations from ideality in the adlayer are discussed. The effects of impurity on the generalized form of the BCF differential equation for surface diffusion is established and the crystal growth rate as a function of supersaturation is calculated from numerical intergration. The applicability of this model for crystal growth from impure solution is discussed.     

Investigation on the crystal growth process of spherical Si single crystals by melting

Spherical Si single crystals with a diameter of approximately 1 mm were grown by melting for solar cell applications. The start sources were spherical Si multicrystals fabricated by a dropping method, which had various irregular shapes. Spherical Si multicrystals were melted into droplets and recrystallized on a quartz plate sample holder that was coated with Si₃N₄. It was found that a surface coating of SiO₂ layer on the start sources and oxygen atmosphere during melting and recrystallization were essential to achieve almost perfect spherical shape. Defect-free single crystalline spherical Si could be obtained at recrystallization temperature ranging from 1400 to 1330 °C, corresponding to an undercooling ranging from 14 to 84 °C, with a yield of nearly 100%. At recrystallization temperatures higher than 1380 °C, the recrystallized spherical Si crystals were almost perfect spheres, whereas small protuberances were formed when the recrystallization temperature was lower than 1360 °C. It was also found that that melting at a temperature close to the melting point of Si (at ~1414 °C), a slow cooling rate of ~1 °C/min before recrystallization and relatively fast cooling rate of ~20 °C/min after recrystallization were important for achieving high carrier lifetime. The average carrier lifetime was greatly improved from lower than 2.5 μs of start sources up to ~7.5 μs by melting at optimized conditions. The influences of residual oxygen on the carrier lifetime of recrystallized spherical Si are discussed based on the measurement results with Fourier transform infrared spectrometer.     

In-situ observation of crystal growth and the mechanism

The spatial and time resolution in the measurements of growth rates and the observation of surface morphologies and the associated transport phenomena reflecting their growth mechanism have been developed because advanced microscopes and interferometers have attained nano-scale resolution. The first part covers the historical background how in-situ observation of crystal growth at molecular-level by optical and other scanning methods had been developed for understanding of crystal growth by measuring crystal growth rates and by observing surface nano-topographies, such as growth steps and spiral hillocks, with the same vertical resolutions comparable to that of the scanning probe microscopic techniques. The potential of recently developed interferometric techniques, such as Phase-Shift Interferometry (PSI) is then reviewed with the principle of the optics. Capability of measuring growth rates of crystals as low as 10⁻⁵ nm/s (1 µm/year) is introduced. Second part of the article emphasizes basic interferometric technique for the understanding of crystal growth mechanism by measuring growth rate vs supersaturation. Utilization of these techniques not only in fundamental crystal growth fields but also in environmental sciences, space sciences and crystallization in microgravity would briefly be introduced. At the end, we select a few examples how growth mechanism was analyzed based on these kinetic measurements.     

A crowdion mechanism of crystal twinning

The processes of plastic deformation of crystals via mechanical twinning are considered. Models of nucleation and motion of twin boundaries leading to formation of twin interlayers are proposed. These models are based on the crowdion mechanism of deformation in crystals and are considered by an example of close-packed structures. Good agreement between the predictions of the models proposed and the experimental results for crystals deformed by a concentrated load is demonstrated.     

Growth of PbI2 single crystal by the top seed vertical zone melting method

PbI₂ is a type of syntectic compound, and its single crystal is one of the room temperature semiconductor nuclear radiation detector materials. A new method for the growth of the PbI₂ single crystal is proposed in this article, which was named the top seed vertical zone melting method (TSVZMM), directly from the synthesis of polycrystal with analytically pure lead and iodine, by controlling the decomposition and stratification of the melt and the stoichiometry of the PbI₂ crystal. Impurities in the crystal and the coagulating droplets of lead were eliminated during the PbI₂ crystal growth process from the top to bottom by TSVZMM. The PbI₂ single crystal was successfully grown with the size of Φ15 mm×15 mm, an infrared transmittance of more than 40%, a resistivity of 2×10¹² Ω cm magnitude and stoichiometry close to its theoretical value.     

Physico-chemical processes in single crystal growing of calcium aluminates by zone melting

The growing of single crystals of calcium aluminates of compositions 12 CaO · 7 Al₂O₂, CaO · Al₂O₃, and CaO · 2 Al₂O₃ by zone melting under vacuum of 10⁻⁵ mm Hg permitted to establish that some of the Al³⁺ ions in octahedral coordination have been driven back by the moving crystallization front. Energetically, this process can be represented on the basis of the viscous flow model with the activation energy of −45 kcal/mole. The possible mathematical models have been considered for the processes of preparation of single phase crystals of the aluminates mentioned above which take account of incongruent vaporization of the component oxides and refining of the melt from structural impurities by the moving crystallization front.     

Structural contribution to the roughness of supersmooth crystal surface

Technological advances in processing crystals (Si, sapphire α-Al₂O₃, SiC, GaN, LiNbO₃, SrTiO₃, etc.) of substrate materials and X-ray optics elements make it possible to obtain supersmooth surfaces with a periodicity characteristic of the crystal structure. These periodic structures are formed by atomically smooth terraces and steps of nano- and subnanometer sizes, respectively. A model surface with such nanostructures is proposed, and the relations between its roughness parameters and the height of atomic steps are determined. The roughness parameters calculated from these relations almost coincide with the experimental atomic force microscopy (AFM) data obtained from 1 × 1 and 10 × 10 μm areas on the surface of sapphire plates with steps. The minimum roughness parameters for vicinal crystal surfaces, which are due to the structural contribution, are calculated based on the approach proposed. A comparative analysis of the relief and roughness parameters of sapphire plate surfaces with different degrees of polishing is performed. A size effect is established: the relief height distribution changes from stochastic to regular with a decrease in the surface roughness.     

On the thermodynamics of homogeneous crystal nucleation

A correct phenomenological consideration is given to the change in the Gibbs thermodynamic potential in the course of crystal nucleation. It is proved that this process is described by two activation barriers.     

On the growth mechanism of an A-B crystal: II. effect of dissociative adsorption of B2 molecules

In a previous treatment, the BCF theory which applies to a monatomic crystal has been extended to the case of an A-B crystal growing from the vapour according to a scheme A(g) + B(g) ? AB(cr).The effect of dissociative adsorption of diatomic gas molecules according to a scheme A(g) + 1/2 B₂(g)?AB(cr) is incorporated in the present work. The results obtained are as follows. (i) The growth rate for a constant driving force Δg = kT ln[P_A(P_B2)^1/2/P_A0(P_B201/2] varies with the partial pressures P_A and P_B2. (ii) In the limiting cases, P_A å P_B2 or P_A å P_B2, the major component is nearly under saturation and the growth rate is me$\text{r}$ely controlled by the minor component, which works as the so-called “growth unit”. (iii) Because of the associative desorption of B adatoms, the mean migration distance $\text{x}$_sB depends on the partial pressure P_B2. (iv) The theory is in good agreement with an experiment on the vapour growth of CdTe under controlled partial pressure of the constituent element.     

Kinetics and intimate mechanism of protein crystal nucleation

Experimental and theoretical investigations on protein crystal nucleation are reviewed. Various experimental applications of the classical principle, which requires separation of the nucleation and growth stages of the crystallization process, are described. Temperature control is used most frequently, hypergravity and concentration changes being auxiliary techniques. Nucleation time-lags are measured by imposing temperature evoked supersaturation gradients. Application perspectives are revealed. Nucleation rates are measured according to the classical principle mentioned above, and energy barriers for crystal nucleation and numbers of molecules constituting the critical nuclei are calculated. Surprisingly, although requiring unusually high supersaturation, protein crystal nucleation occurs much more slowly than that with small molecule substances. On this basis novel notions are suggested for the elementary mechanism of protein crystal bond formation. Due to the selection of the crystalline bonding patches a successful collision between protein molecules, resulting in the formation of a crystalline connection, requires not only sufficiently close approach of the species, but also their proper spatial orientation. Imposing a rigid steric constraint, the latter requirement postpones the crystal nucleus formation. Besides, it was shown that cluster coalescence is not a factor, hampering the protein crystal nucleation. The comparison of the model predictions with experimental results proved that nucleation kinetics is governed by kinetic (not by energetic) factors.     

Numerical investigation of carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth

Carbon contamination in single crystalline silicon is detrimental to the minority carrier lifetime, one of the critical parameters for electronic wafers. In order to study the generation and accumulation of carbon contamination, transient global modeling of heat and mass transport was performed for the melting process of the Czochralski silicon crystal growth. Carbon contamination, caused by the presence of carbon monoxide in argon gas and silicon carbide in the silicon feedstock, was predicted by the fully coupled chemical model; the model included six reactions taking place in the chamber. A simplified model for silicon carbide generation by the reaction between carbon monoxide and solid silicon was proposed using the closest packing assumption for the blocky silicon feedstock. The accumulation of carbon in the melted silicon feedstock during the melting and stabilization stages was predicted. Owing to this initial carbon content in the melt, controlling carbon contamination before the growth stage becomes crucial for reducing the carbon incorporation in a growing crystal.     

On the mechanisms of modulation of crystal structures

Based on the assumption that crystal structures of a number of sulfides are the result of modulation of cationic lattices by anionic lattices, the versions of their conjugation in direct and reciprocal spaces have been analyzed using common translational lattices. The concept of this phenomenon, developed within the superspace formalism, is supplemented by a proposed interpretation of the real modulation of the structures.     

On the initial stages of skeletal crystal growth

The transition from isometric into skeletal form of a crystal growing under diffusion control is explained as a result of the transition from a global compensation of the super-saturation nonhomogeneity, i.e. in the framework of the whole crystal face, to a spatially limited one. The said compensation is now possible only in the region of the macroscopically flat margin surrounding the gross morphological defect (in the form of a depression) which is the immediate result of the uneven, and unsufficient matter supply.     

On the crystal structure stability of calcite-type carbonates

The preparation of carbonates of the bivalent metals (Mg, Ca, Ba, Sr, Mn, Fe, Co, Ni, Cu and Zn) by two methods under ordinary conditions has been investigated. The stability of calcite type carbonates has been discussed. The shortest O—O distance (d*_O—O) between two neighbouring octahedra has been proposed as a criterion for the formation of stable calcite type carbonates. The lower stereochemical boundary of the calcite carbonate stability has been found to be d*_O−O ∼ 2.9 Å. The relative stability of carbonates with d_O−O* < 2.9 Å (Zn, Co and Ni) has been studied with respect to their isomorphous incorporation into MnCO₃.     

On the bindings in the crystal phases of Mn

The heterotypism of Mn may be interpreted energetically when a temperature dependent valence electron concentration is supposed which takes on values between 2.2 and 0.6 electrons per atom. The room temperature phase Mn.r (= αMn) belongs to a series of structural types: Cr₃Si, U.h₁ (= βU), Mn.r, which occur in alloy systems such as MoRe_M (M = undetermined mole number) at certain values of the averaged group number (AGN) of the perodic system of chemical elements (rule of Raub). An interpretation of the series by means of the plural-correlations model becomes possible when instead of the (Ekmanian) AGN count another (non-Ekmanian) electron count is used. The phase Mo₃Re (Cr₃Si-type) yields a simple bonding type (binding) which undergoes moderate transformations to form the phases Mo₂Re₃(U.h₁) and MoRe₃(Mn.r) and the binding of MoRe₃ may be taken to be valid also for Mn.r; it corresponds to the valence electron concentration N′^A_b = 2.16. For the high temperature phases Mn.h₁ (= βMn) and Mn.h₂ (= γMn) the values N′^A_b = 1.6 and 1.0 are probable and allow the brass-like structures Mn.h₁ (C20) and Cu(Fl). The binding of Mn.h₂, incidentally, explains the occurrence of the tetragonal metastable phase Mn.m. finally Mn.h₃ (= δMn) crystallizing in the W-type is isodesmic to Fe.h₂ (= δFe), i.e. of the same binding.