The basic growth parameters of ZnS single crystals grown by sublimation

The application of the crystal growth dislocation theory [11] to ZnS single-crystal growth is discussed. The experimental material, above all for determining the actual supersaturation in the growth region and the mechanism of ZnS transport (diffusion, transport gas, chemical transport) was found to be insufficient. An expression for the growth rate of the ZnS crystal plane (the dependence on the supersaturation is not linear) is derived and two different stages in growing ZnS crystals are described.     

Morphological phase diagram of a spherical crystal growing under nonequilibrium conditions at the growth rate as a quadratic function of supersaturation

The complete morphological diagram of a spherical nucleus growing from a solution under nonequilibrium conditions at a local growth rate as a quadratic function of supersaturation is calculated for the first time on the basis of a linear analysis for morphological stability and the principle of maximum entropy production. The results of calculations are compared with those obtained previously for a spherical particle in the case of a linear dependence of the growth rate on the supersaturation.     

用激光偏振干涉技术测量KDP晶体柱面生长速度

 采用激光偏振干涉技术实现了KDP晶体柱面生长速度的实时测量,精度可达0.01 μm/min。研究了不同的过饱和度控制方式对柱面死区实时测量的影响。发现晶体双折射率随温度的变化是导致光强-时间曲线中死区直线斜率不为零的原因。认为晶体生长速度与杂质离子的吸附时间有关。研究了杂质离子含量不同的两种原料在不同的溶液饱和点下的柱面生长速度和死区随过饱和度的变化关系,结合C-V模型和K-M理论讨论了其中的动力学规律。讨论了晶体光学质量与生长过饱和度的关系,认为利用激光偏振干涉系统进行溶液鉴定,将传统降温法的过饱和度控制在死区范围内和将点籽晶快速生长技术的过饱和度控制在线性区是保证晶体光学质量的关键。     

The influence of a magnetic field on the mosaic spread and growth rate of small Rochelle salt crystals

The growth rates of small (length <1 mm) crystals of Rochelle salt grown with and without a magnetic field have been measured at constant supersaturation (4%). It has been shown that some crystals grown in the presence of a magnetic field exhibit a decrease in the linear growth rate in the [010] direction relative to that shown under normal conditions. It was further noticed that a few crystals of the total number showed slight increases in growth rate. The fact that a majority of crystals showed a decrease in growth rate has given rise to speculations that this should be caused by an increase of strain (mosaic spread), resulting from a change of the mode of incorporation of the growth units into the crystal surface brought about by the applied magnetic field. The results show that most of crystals grown in the magnetic field have a higher mosaic spread and lower growth rate than observed during growth without an applied field. An increase in growth rate in the presence of the magnetic field, observed for a few crystals, might be explained by the relaxation of this strain by formation of dislocations, which in turn enhance the growth rate.     

Calculations of the complete morphological phase diagram for nonequilibrium growth of a spherical crystal under arbitrary surface kinetics

Complete morphological diagrams (with stable, metastable, and absolutely unstable regions) were calculated for the problem of morphology selection under the conditions of nonequilibrium growth of a spherical crystal taking into account arbitrary kinetic process rates at the boundary and a linear dependence of the growth rate on supersaturation. The consideration was performed by jointly using linear stability analysis and the principle of maximum entropy production. The principal difference between kinetically and diffusion-controlled crystal growth is the possibility of the coexistence of three or more morphological phases under the same conditions in the former case. It was shown that, at the transition point, the rate of accretion of the growing crystal mass increased in a jump. The jump value was studied as a function of the parameters of the problem.     

Influence of supersaturation on the growth of gallium arsenide films in chloride gas-transport systems

An experimental investigation was made into the growth kinetics and relief of the growth surface for the (111)A, (111)B, (110), and (001) planes of gallium arsenide for different degrees of supersaturation determined by the difference between the temperatures of the source and the substrate. The obtained dependences are interpreted on the basis of the basic conclusions of the theory of the growth of crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89–93, March, 1981.We are grateful to G. M. Ikonnikovaya for assistance in the experiments.     

Self-consistent diffusion-controlled growth of nuclei from eutectic solutions

A study is made of the dynamics of self-consistent motion and growth of spherical new-phase nuclei from a eutectic melt. The growth rate of nuclei is shown to be proportional to supersaturation in both components. Motion of a single nucleus in a concentration-gradient field and of a pair of nuclei in a self-consistent concentration field is investigated. The velocity of motion of the nucleus as a whole has been established to depend on the key parameters of the problem, namely, supersaturation, radii of the nuclei, and their separation. The force of mutual attraction between nuclei is estimated, and it is shown to be inversely proportional to the fifth power of their separation. Fiz. Tverd. Tela (St. Petersburg) 40, 1615–1618 (September 1998)     

Weakly nonlinear analysis of the morphological stability of a two-dimensional cylindrical crystal

We present the first weakly nonlinear analysis of the morphological stability of a two-dimensional cylindrical crystal growing from solution in an arbitrary regime (with the growth rate proportional to supersaturation). A quadratic (with respect to the perturbation amplitude) correction to the critical radius of a stable crystal determined in the linear theory is obtained in an analytical form and studied as a function of the per-turbation frequency and the growth regime. It is established that an increase in the perturbation amplitude vir-tually always leads to a decrease in the critical radius. Factors accounting for this nontrivial effect are consid-ered.     

The mass transfer process and the growth rate of NaCl crystal growth by evaporation based on temporal phase evaluation

The mass transfer process and the crystal growth rate have been proved to be very important in the study of crystal growth kinetics, which influence the crystal quality and morphological stability. In this paper, a new method based on temporal phase evaluation was presented to characterize the mass transfer process in situ and determine the crystal growth rate. The crystallization process of NaCl crystal growth by evaporation was monitored in situ by a Mach-Zehnder interferometer, and the absolute concentration evolution, the evaporation rate and the real-time supersaturation of solution were obtained using temporal phase analysis, which acted as a novel technique to extract phase variation along time axis recently. Based on the evaporation rate and the absolution concentration, a new method to calculate mass transfer flux during the crystal growth without the knowledge of the mass transfer coefficient was proposed, and then the crystal growth rate could also be retrieved under the hypothesis of cubic crystals. The results show that the crystal growth rate increases with the supersaturation linearly. It is in agreement with the diffusion theories, which presume that matter is deposited continuously on a crystal face at a rate proportional to the difference in concentration between the points of deposition and the bulk of solution. The method is applicable to the research of crystallization process based on evaporation or vapor diffusion of which the precise conditions of nucleation and supersaturation are usually unknown because of the complexity of the evaporation rate and crystal growth rate.     

High-temperature diamond-like Si-based ferromagnet with self-organized superlattice distribution of Mn impurity

The crystal structure of nanofilms of a Si:Mn dilute magnetic semiconductor with the Curie temperature of about 500 K obtained by the pulsed deposition from a laser plasma has been studied by high-resolution electron microscopy and diffraction. The ferromagnetism of Si:Mn characterized by high electrical and complete magnetic activities of Mn manifests itself in the ferromagnetic resonance, anomalous Hall effect, and magneto-optic Kerr effect. It is shown that the nonequilibrium laser technique allows achieving a pronounced supersaturation of the Mn solid solution as high as 15%. In such solutions, Mn substitutes silicon, leaving unchanged the diamond-like crystal structure and does not prevent the epitaxial growth of Si:Mn films. At the same time, there occurs a self-organized formation of the superlattice structure with the period equal to triple the distance between the nearest (110) atomic layers, where (110) layers doped with Mn are oriented along the growth direction of the Si:Mn film.     

Kinetic frustration of Ostwald ripening in Ge/Si(100) hut ensembles

We show that low area density Ge/Si(100) island ensembles comprised solely of hut and pyramid clusters do not undergo Ostwald ripening during days-long growth temperature anneals. In contrast, a very low density of large, low chemical potential Ge islands reduce the supersaturation causing the huts and pyramids to ripen. By assuming that huts lengthen by adding single {105} planes that grow from apex-to-base, we use a mean-field facet nucleation model to interpret these experimental observations. We find that each newly completed plane replenishes the nucleation site at the hut apex and depletes the Ge supersaturation by a fixed amount. This provides a feedback mechanism that reduces the island growth rate. As long as the supersaturation remains high enough to support nucleation of additional planes on the narrowest hut cluster, Ostwald ripening is suppressed on an experimental time scale.     

Using a 1,8-diamino naphthalene–copper (II) system as a turn-on fluorescence probe for detecting Sudan I

An easy-to-use fluorescence probe for detecting Sudan I was developed. The probe detects Sudan I because Sudan I and 1,8-diamino naphthalene competitively interact with copper (II). Copper (II) effectively quenches the fluorescence of 1,8-diamino naphthalene because the 1,8-diamino naphthalene interacts with copper (II) and forms a 1,8-diamino naphthalene–copper (II) complex. Adding Sudan I causes the fluorescence of the system to be recovered because the Sudan I removes copper (II) from the 1,8-diamino naphthalene–copper (II) complex, liberating the 1,8-diamino naphthalene. The displacement of 1,8-diamino naphthalene by Sudan I gives a high fluorescence recovery efficiency. Under optimal conditions, the fluorescence intensity F achieved when Sudan I was added had a good linear relationship (R²?=?0.999) with the Sudan I concentration over the range 0–4.6?µM. The Sudan I detection limit was 0.032?µM. The method offers a new way of quantitatively determining Sudan I.     

Melt crystalfization and crystal morphology of two low molecular weight linear polyethylene fractions

Melt-crystallization behavior and single-crystal morphology of two low molecular weight (LMW) linear polyethylene (PE) fractions of 3900 and 5800 have been investigated. Linear growth rates along the b axis (G _b) of these fractions were measured via polarized light microscopy (PLM). The two fractions show a growth rate change at an undercooling of 17°C (at 117°C and 120°C, respectively, for these two fractions), which may be identified as the regime I/II transition. This transition does not correspond to a single-crystal morphological change from a truncated lozenge with curved (200) and (110) planes to a lenticular crystal as proposed previously. However, this morphological change can be observed at a temperature higher than the regime transition (at 122°C and 124°C), at which the cusps of the G _b data can be observed for these two fractions. Based on our morphological study via PLM, transmission electron microscopy, electron diffraction, small-angle x-ray scattering (SAXS), and differential scanning calorimetry (DSC) experiments, it is found that within a 2°C temperature region, the G _b change is accompanied by a sharp long period increase and a drastic change in single-crystal morphology from a truncated lozenge with curved (200) and (110) planes to a lenticular-shape crystal. The morphological change may result from a sudden increase in the G _b coupled with a smaller change in the growth rate along the a axis with undercooling. This implies that, within this temperature region (2°C), the crystals may undergo substantial changes in the geometry of the (110) and (200) crystal growth fronts and chain folding behavior.     

Dilution wave and negative-order crystallization kinetics of chain molecules

We show that the crystal growth rate of a very long-chain n-alkane C C(198)H(398) from solution can decrease with increasing supersaturation and follow strongly negative order kinetics. The experimental behavior can be well represented by a theoretical model which allows the molecule to attach and detach as either extended or folded in two. The obstruction of extended-chain growth by unstable folded depositions increases disproportionately with increasing concentration. As a consequence of this abnormal kinetics, a "dilution wave" can propagate and trigger a folded-to-extended-chain transformation on its way.     

New developments on size-dependent growth applied to the crystallization of sucrose

The effect of crystal size on the growth rate of sucrose (C₁₂H₂₂O₁₁) at 40 °C is investigated from a theoretical and an experimental point of view. Based on new perspectives resulting from the recently introduced spiral nucleation model [P.M. Martins, F. Rocha, Surf. Sci. 601 (2007) 3400], crystal growth rates are expressed in terms of mass deposition per time and crystal volume units. This alternative definition is demonstrated to be size-independent over the considered supersaturation range. The conventional overall growth rate expressed per surface area units is found to be linearly dependent on crystal size. The advantages of the “volumetric” growth rate concept are discussed. Sucrose dissolution rates were measured under reciprocal conditions of the growth experiments in order to investigate the two-way effect of crystal size on mass transfer rates and on the integration kinetics. Both effects are adequately described by combining a well-established diffusion-integration model and the spiral nucleation mechanism.     

Surface electronic structure of SnO2(110)

We report theoretical investigations on the surface electronic structure of the (110)-face of SnO₂, a semiconductor of rutile bulk structure. Starting with a tight binding Hamiltonian for the bulk, we determine the surface electronic structure using the scattering theoretic method. As results we obtain the surface bound states, the surface resonances and the wave-vector resolved surface layer densities of states. The dominant features are two backbond states in the stomach gap of the main valence band and two Sn-s derived states in the lower conduction band region. In the upper valence band region, only weak resonances occur, like in other materials with relatively strong ionicity.     

A microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation

The morphological stability of a growing faceted crystal is discussed. We argue that the interplay between nonuniformity in supersaturation on a growing facet and anisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted instability. Qualitatively speaking, as long as the nonuniformity in supersaturation on the facet is not too large, it can be compensated for by a variation of step density along the facet, and the faceted crystal can grow in a stable manner. The problem can be modeled as a Hamilton-Jacobi equation for height of the crystal surface. The notion of a maximal stable region of a growing facet is introduced for microscopic time scale approximation of the original Hamilton-Jacobi equation. It is shown that the maximal stable region keeps its shape, determined by profile of the surface supersaturation, with constant growth rate by studying large time behavior of solution of macroscopic time scale approximation. A quantitative criterion for the facet stability is given.     

Modified growth theory for high supersaturation

The classical BCF (Burton, Cabrera, Frank) growth theory assumes atomic step motion driven by the diffusion of adatoms toward the step acting as sinks. Stationary solutions of the diffusion equation have been obtained by BCF neglecting the movement of the coordinate system. By using a moving frame, as already done for a single-step flow model by Mullins and Hirth, we calculate the velocity of a periodic parallel sequence of steps, the distribution of adatoms, and the condensation coefficient as a function of the step distance for various supersaturations. This modification result in significant deviations from the original theory if a dimensionless normalized supersaturation parameterb which is proportional to the supersaturation exceeds one-half. Large values of this parameterb may occur for the high supersaturation found in Si-MBE (molecular beam epitaxy) for temperatures far below the melting point.     

Morphology,Crystallization, and Melting of Single Crystals and Thin Films of Star‐branched Polyesters with Poly(ϵ‐caprolactone) Arms as Revealed by Atomic Force Microscopy

The morphology and thermal stability of different sectors in solution‐ and melt‐grown crystals of star‐branched polyesters with poly(?‐caprolactone) (PCL) arms, and of a reference linear PCL, have been studied by tapping‐mode atomic‐force microscopy (AFM). Real‐time monitoring of melt‐crystallization in thin films of star‐branched and linear PCL has been performed using hot‐stage AFM. A striated fold surface was observed in both solution‐ and melt‐grown crystals of both star‐branched and linear PCL. The presence of striations in the melt‐grown crystals proved that this structure was genuine and not due to the collapse of tent‐shaped crystals. The crystals of the star‐branched polymers had smoother fold surfaces, which can be explained by the presence of dendritic cores close to the fold surfaces. The single crystals of linear PCL grown from solution showed earlier melting in the {100} sectors than in the {110} sectors, whereas no such sectorial dependence of the melting was found in the solution‐grown crystals of the star‐branched polymers. The proximity of the dendritic cores to the fold surface yields at least one amorphous PCL repeating unit next to the dendritic core and more nonadjacent and less sharp chain folding than in linear PCL single crystals; this evidently erased the difference in thermal stability between the {110} and {100} sectors. Melt‐crystallization in thin polymer films at 53–55°C showed 4 times faster crystal growth along b than along a, and more irregular crystals with niches on the lateral faces in star‐branched PCL than in linear PCL. Crystal growth rate was strictly constant with time. Multilayer crystals with central screw dislocation (growing with or without reorientation of the b–axis) and twisting were observed in both classes of polymers.     

Nanoscale anglesite growth on the celestite (0 0 1) face

In situ atomic force microscopy (AFM) was used to study the growth behaviour of anglesite (PbSO₄) monolayers on the celestite (0 0 1) face. Growth was promoted by exposing the celestite cleavage surfaces to aqueous solutions that were supersaturated with respect to anglesite. The solution supersaturation, β_ang, was varied from 1.05 to 3.09 (where β_ang = a(Pb²⁺) · a(SO₄²⁻)/K_sp,ang). In this range of supersaturation, two single anglesite monolayers (3.5 Å in height each) from pre-existent celestite steps were grown. However, for solution supersaturation β_ang < 1.89 ± 0.06, subsequent multilayer growth is strongly inhibited. AFM observations indicate that the inhibition of a continuous layer-by-layer growth of anglesite on the celestite (0 0 1) face is due to the in-plane strain generated by the slight difference between the anglesite and celestite lattice parameters (i.e. the linear misfits are lower than 1.1%). The minimum supersaturation required to overcome the energy barrier for multilayer growth gave an estimate of the in-plane strain energy: 11.4 ± 0.6 mJ/m²_. Once this energy barrier is overcome, a multilayer Frank–Van Der Merwe epitaxial growth was observed.