Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Heat and mass transfer taking place during growth of Y₃Al₅O₁₂ (YAG) crystals by the Czochralski method, including inner radiation, is analyzed numerically using a Finite Element Method. For inner radiative heat transfer through the crystal the band approximation model and real transmission characteristics, measured from obtained crystals, are used. The results reveal significant differences in temperature and melt flow for YAG crystals doped with different dopands influencing the optical properties of the crystals. When radiative heat transport through the crystal is taken into account the melt‐crystal interface shape is different from that when the radiative transport is not included. Its deflection remains constant over a wide range of crystal rotation rates until it finally rapidly changes in a narrow range of rotation rates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Einfluß der Transportkinetik auf die Kristallisation von AIIBIVC-Verbindungen beim Gasphasentransport

The reported investigation intended to find tendencies in the influence of thermal and chemical conditions of chemical transport reactions on the growth of ZnSiP₂ and ZnSiAs₂ crystals. A more favourable crystallisation with less intergrowth is proved, if transport gases of the same system — as e.g. ZnCl₂ or SiCl₄ — is used instead of PbCl₂ and TeCl₄. — Depending on the concentration of the transporting medium the largest amount of crystals with lengths of more than 5 mm coincides with the point of lowest transport rate. The number of crystal defects increases with the dimensions of the crystals. — From the experimental results a hypothesis for explaining the locally different growth of crystals of ternary compounds is presented.     

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.     

Growth of several quantum crystals: CD4, 4He and 3He

Large single crystals of CD₄, ⁴He, and ³He have been grown from the melt at low temperatures. These “quantum” crystals were characterized with X-ray diffraction techniques which allow excellent determinations of crystal quality. The crystal CD₄ was grown from its melt at saturated vapor pressure. Over 100 helium crystals were grown at constant pressures between 2.9 and 13.8 MPa. It has been found that the hcp and bcc crystals grow in preferred directions, and that growth rates of about 0.3 mm/ min are appropriate for hcp ⁴He, while bcc ³He requires the slower rate of 0.06 mm/min for good quality crystals. There is some indication that it is the isotope, and not the crystal structure, which is the cause of the fact that the hcp ⁴He crystals are much more stable than the bcc ³He crystals. Comparison of several theoretical crystal growth parameters for many substances leads to the conclusion that methane is basically a normal material, while helium is abnormal, having very different growth parameters from most substances. Helium is interesting in that its crystal growth parameters can be changed by very large amounts while keeping the chemistry constant.     

Effects of ammonium citrate additive on crystal morphology of aluminum phosphate ammonium taranakite

In this communication, we demonstrated the growth of aluminum phosphate ammonium taranakite (NH₄-AlPO₄) crystals from regular hexagonal form into the disk-like form could be controlled by ammonium citrate (AMC) as the effective crystal growth modifier at 90 °C. Prepared crystals were characterized by field emission scanning electron microscopy (SEM) and X-ray diffraction (XRD). The effects of AMC's concentration on the crystal form and morphology of NH₄-AlPO₄ were studied. The results showed that the AMC's concentration is an important parameter to control the size and morphology of NH₄-AlPO₄ crystal. The formation mechanism of the special morphology of NH₄-AlPO₄ crystals was also analyzed.     

Results of crystal growth of bismuth-antimony alloys (Bi100–xSbx) in a microgravity environment

Results of two experiments are presented for growth of crystals from (Bi_100–xSb_x) alloys in a microgravity environment. In the growth experiments different variants of the Bridgman technique were used. It was shown that in crystal growth from the melt in closed ampoules under microgravity conditions convection can be prevented completely. Therefore it is possible to grow crystals from melts of some components under diffusion controlled conditions of mass transfer. In microgravity a reduced interaction between the melt and the confining walls was observed even if they have large contact with each other. The investigation of surface morphology corroborated the importance of surface effects for crystal growth from the melt under microgravity conditions. Measurements of electronic properties of crystals grown in microgravity showed a good quality in comparison to earth grown crystals. Because under microgravity conditions in closed ampoules the diffusion controlled mass transfer can be realized and the interaction between the melt and confining wall is reduced, homogeneous crystals with high perfection can be grown melts of some components.     

Experimental Verification of the Numerical Model for a CaF2 Crystal Growth Process

Large calcium fluoride (CaF₂) single crystals are required for the fabrication of lenses in so‐called wafer‐steppers of future IC‐lithography technologies operating at 193 nm and 157 nm. Numerical simulation plays an important role to design an adequate growth setup and processing conditions for the growth of high quality crystals. An important issue is the consideration of the internal heat transfer by radiation in the semitransparent CaF₂ during the crystal growth process. Results of the numerical modeling of the heat transport are presented, which are obtained by using the software package CrysVUn++ with different models considering the internal heat transport in CaF₂. To improve the availability of experimental data on CaF₂ bulk growth, an especially designed R&D‐facility was built. This growth system is equipped with a variety of in‐situ measurement systems to detect the temperature distributions in the crystal and melt region. Calculated temperature distributions are compared with experimental data. Also first results on single crystal growth will be reported.     

Raman Study of Lattice Vibration Modes and Growth Mechanism of KDP Single Crystals

The space group theoretical analyses and assignment of the lattice modes of the KDP crystal have been made, and the Raman spectra of their growth solution have been observed in different growth regions. The attention is focused on the analysis of the 912 cm^‐1 band arising from the H₂PO₄^‐ anions in the interface between the KDP crystals and their growth solution. This has been assigned to the asymmetrical stretching mode of the deformation P(OH)₂ . From these results, the growth units of KDP crystal has been concluded to be the dimers of H₂PO₄^‐ anions. We consider that the result presented here is an important step towards the development of more complete crystal growth theories.     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10⁻³ cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.     

Optimization of the crystallization rate in growing Bi4Ge3O12 crystals by the LTG CZ technique

The influence of the growth rate on the shaping and quality of Bi₄Ge₃O₁₂ (BGO) crystals during their growth by the low-thermal-gradient Czochralski technique has been studied. Several series of BGO crystals have been grown with the rate varying from 0.3 to 15 mm/h. The limited growing rates at which the crystal quality is not deteriorated are established. The results of the study make it possible to increase the growth rate in commercial systems by a factor of 1.5–2 and thus significantly increase the growth efficiency.     

Morphology of β-BaB2O4 (BBO) Crystals in Relation to its Structure and Growth Conditions

β-BaB₂O₄ (BBO) crystals with well-defined morphology have been grown from Na₂O solutions using the top seeded solution growth (TSSG) method. The crystal morphology in relation to its structure and growth conditions has been studied in detail on the basis of crystallography and crystal chemistry. It is found that the morphological characteristics are related to the orientations of structural unit (B₃O₆)^3— anion rings in the crystal. On the other hand, the growth parameters may greatly affect the appearance of faces of the crystal, but the crystals still generally take trigonal in outline and have a diagnostic character of point group 3m. The observed morphology is in disagreement with BFDH and PBC analyses and is explained from the incorporation of the growth units on the faces and facets. Since the incorporation rates of the growth units are different on different faces, the boule habits with well-defined morphology are formed.     

Surface morphology and growth mechanisms of argyrodite-type Cu6PS5 hal crystals

Single crystals of Cu₆PS₅Hal (Hal = Cl, Br, I) have been grown by dissociative sublimation and by chemical vapour transport with P, S, Hal, CuHal and combinations thereof as transporting agents in the temperature range 800 to 1000 K. Microscopic observation of the tetrahedral faces revealed several growth features. Macrosteps, closed loop steps and surface protuberances are always accompanied with the presence of liquid CuHal/Cu₂S droplets on the growing crystal surface. The phenomena are characteristic for a two-dimensional Vapour-Liquid-Solid growth mechanism. In the absence of CuHal/Cu₂S liquid phase, direct growth from the gas phase (VS growth) takes place leading to hillocks and growth spirals with low step heights (∼ 5–10 Å).     

Electron Microscopy and X-ray Study of the Growth of FeCr2S4 Spinel Single Crystals by Chemical Vapour Transport

The growth features of FeCr₂S₄ spinel single crystals prepared by chemical vapour transport were studied by means of scanning electron microscopy, transmission electron microscopy, high resolution electron microscopy, electron diffraction and X-ray analysis. Our results indicate that the epitaxial growth of the new phases FeCr₇S₁₂ and FeCr₈S₁₂, both based on the NiAs structure, can essentially inhibit the growth of large FeCr₂S₄ spinel single crystals in the octahedral habit. The new phases are fully characterised and the effects of defect ordering in these new phases are also reported.     

Growth parameters for large diameter float zone silicon crystals

Factors that directly affect the ability to grow dislocation free float zone silicon crystals up to 80 mm in diameter have been experimentally determined. The highest yield is obtained for 80 mm diameter crystals by starting with 68 mm to 74 mm diameter poly crystal rod stock. Lower transport speeds for crystal growth of (111) orientation crystals were 3 to 4 mm/min and for (100), 2 to 3 mm/min. Rotation rates of both upper and lower shafts were found to have an effect on growth at the solid-liquid interface. Rates established for lower shaft were 6 to 8 rpm for the (111) crystals and 3 to 4 rpm for (100), counter-clock-wise. Upper rotation rates were 2 rpm on (111) crystals and 3 to 5 rpm on (100), clockwise. Seed orientation, which is critical, was held to within plus or minus $\text{1}\text{2}\text{°}$ of perfect orientation. The minimum seed growth length was 50 to 70 mm. To assist in reducing the side lobes on (111) dislocation free crystals, a cooling ring with a flow or argon was used. For best (100) growth the shape of the lower side of a one turn copper rf work coil was made conical. Six to ten dislocation free crystals in each orientation group were produced using these parameters.     

Proposals for the Optimization of Crystal Growth in Gels

Crystal growth in gels is viewed under the aspect of diffusion and factors governing this. From simple diffusion experiments proposals for the modification of growth apparatus and growth regime are made to minimize quality decreasing effects. The application of diffusion measurement results on crystal growth in gels is shown by optaining NaHC₂O₄ × × H₂O crystals in silica gel (sodium metasilica gel respectively).     

Temperature gradient controlled growth and optical properties of Er:BaY2F8 crystals

Single crystals of Erbium (Er) doped BaY₂F₈ have been obtained by the temperature gradient technique (TGT). No‐seed‐grown crystal of Er:BaY₂F₈, with the dimensions up to several centimeters, was obtained by self‐crystallization. The optimizations of various growth parameters were systemically investigated. The results indicated that the temperature gradient of 6‐7 K/mm and the cooling velocity less than 6 K/h were suitable for the crystal growth. The XRD data and the investigations on the growth striations by a stereo polarization microscope displayed that the [001] direction is the dominating direction for the crystal growth. The crystal grown by TGT often cracks along with the (100) plane, which is caused by the excessive decrease of the temperature during the crystal growth, for there is a rapid change in the thermal expansion curve of the BaY₂F₈ crystal in the temperature range from 800 °C to 900 °C. The spectral properties of Er:BaY₂F₈ single crystals have been studied and the effects of frequency up‐conversion of the crystals are reported. Spectral data suggest that the quality of Er:BaY₂F₈ crystal obtained by TGT method is good and the crystal has the potential application in laser devices. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydrothermal crystal growth of fresnoite

The growth of fresnoite, Ba₂TiSi₂O₈, by hydrothermal synthesis has led to spontaneous generation of large, (4-5 mm) optically clear crystals from 6 M KF mineralizer solutions. Growth was achieved at relatively low synthesis temperatures (575 °C) comparative to fresnoite synthesis by Czochralski or flux methods. Bulk crystal growth possibilities were explored by transport reactions performed in both fluoride and hydroxide mineralizers with 25-45 °C temperature gradients. Growth rates of 0.14×0.19×0.22 mm³/week were established in 6 M KOH, which is significantly slower than standard hydrothermal rates of 1 mm/week. Although relatively slow, the hydrothermal method has been demonstrated as a synthesis route to high quality single crystals of fresnoite.     

Morphology of BBO Crystals and their Inclusions

This paper reports on the morphology and inclusions in the low temperature phase barium metaborate BaB₂O₄(BBO) crystal grown by an improved flux pulling method. The morphology of ideal BBO crystals and the relationship between the faces and the growth rate are given. The result that BBO has the symmetry L₃3P and belongs to the space group C_3v−3m can therefore be concluded. It is found that the polarity of the BBO crystal along the Z (or c) axis has a visible influence on the morphology. The investigation of the inclusions in BBO crystals shows that these have a six-fold symmetry which corresponds to the extension of flute-like facets. It is also found that most of the inclusions have a regular geometric figure and can be regarded as the negative-crystal structure which is due to the internal growth mechanism.     

Effect of impurity adsorption on the growth of Rochelle salt crystals

The influence of impurities of copper compounds on the growth of Rochelle salt crystals of the composition KNaC₄H₄O₄ · 4H₂O is studied. The growth rates of the faces of various simple forms experimentally measured as functions of the CuCO₃ concentration in solution at a constant supersaturation and temperature are compared with the theoretical models of impurity adsorption on the faces of a growing crystal. Deceleration of the growth of various faces of a Rochelle salt crystal is satisfactorily described by the Bliznakov equation with the use of the Langmuir, Frumkin-Fowler, and de Boor adsorption isotherms for all the faces except for {010}. However, such a comparison does not allow one to reveal the cause of adsorption or its type on different faces. Photometric scanning of Rochelle salt solutions with copper-compound impurity showed that a small addition of alkali (0.06–0.4 g/l) to the solution results in the appearance in the absorption spectra of both the solution nd the crystal grown from it of a maximum at the wavelength 660–670 nm. The intensity of this maximum increases with an increase in the copper concentration. The EPR data, the absorption spectra of the solution and the crystal, and the modified crystal shape showed that the addition of alkali to the solution results in the formation of new copper complexes that more actively decelerate the growth of Rochelle salt faces.     

Effect of Carbamide Adsorption on the Growth Kinetics of the NH4Cl Crystals

This work supplements the adsorption model of 2D-isomorphism proposed earlier for the NH₄Cl-CO(NH₂)₂ system and reveals the correspondence between the growth rates of the NH₄Cl crystals in the presence of carbamide and the co-crystallization of carbamide with ammonium chloride. It follows from the kinetic data that the NH₄Cl · CO(NH₂)₂ impurity capture becomes significant when the carbamide concentration in solution is sufficient for almost monolayer adsorption of the impurity on the crystal surface and the onset of multilayer adsorption. The concentration of the guest phase intergrowths falls with the increase in the host crystal growth rate.