Growth kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing Co(II) and Ni(II) impurities

The growth kinetics of different faces of ammonium oxalate monohydrate (AO) single crystals from aqueous solutions containing different concentrations of Co(II) and Ni(II) ions at a constant temperature are described and discussed. It was found that: (1) at a given supersaturation σ, both Co(II) and Ni(II) ions lead to a decrease in the growth rates R of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d, but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, and (3) the values of σ_d and σ* increase with increasing concentration c_i of the impurity. The experimental R(σ) data for different concentrations c_i of the impurities were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. Analysis of the data showed that: (1) adsorption of Co(II) and Ni(II) impurities occurs on the surface terrace of AO crystals, (2) there is a simple relationship between Langmuir constant K and the impurity concentration c_i* corresponding to maximum surface coverage, and (3) the ratio σ_d/σ* of the supersaturation barriers observed in the presence of both impurities increases with an increase in impurity concentration c_i, and may be explained from the standpoint of the mechanism of adsorption of impurity particles at kinks and ledges. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: II. Growth kinetics

The experimental results of the effect of concentration of Mn(II) ions on the growth kinetics of different faces of ammonium oxalate monohydrate single crystals from aqueous solutions at a constant temperature and different predefined supersaturations are described and discussed. It was observed that: (1) at a given supersaturation σ, Mn(II) ions lead to a decrease in the growth rates of different faces of AO crystals, (2) the growth of a particular face of the crystals occurs above a critical supersaturation σ_d but there is also another supersaturation barrier σ* when the rate abruptly increases with σ, (3) the values of σ_d and σ* increase with increasing concentration of the impurity, and (4) the values of σ_d depend on the growth kinetics of a face but those of σ* are independent of face growth kinetics. The experimental R(σ) data for different Mn(II) concentrations c_i were analysed according to the model involving complex source of cooperating screw dislocations and concepts of instantaneous and time‐dependent impurity adsorption. It was found that: (1) for a given face the differential heat of adsorption Q_diff is higher during instantaneous impurity adsorption than that during time‐dependent adsorption, and (2) the values of Q_diff involved during instantaneous adsorption are related with face growth kinetics but those during time‐dependent adsorption are independent of face growth kinetics.     

In situ measurement of growth kinetics of {100} KDP crystal faces in the presence of polyphosphate impurities

The face growth rate and critical supersaturation of {100} face were in situ measured using the laser‐polarization‐interference technique in the presence of potassium pyrophosphate, trimetric sodium phosphate and sodium hexametaphosphate impurities. The polyphosphate impurities inhibit the growth rate of prismatic faces. The face growth rate as a function of supersaturation at different impurity concentrations, as well as critical supersaturation as a function of impurity concentrations, was found in good agreement with a two‐dimensional nucleation model in the pure system and Kubota and Mullin's model in the presence of impurities. The average distance L between active sites available for impurity adsorption as well as the edge free energy was calculated. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

In situ study of growth and dissolution kinetics of ammonium oxalate monohydrate single crystals from aqueous solutions containing cationic impurities

The results of an in situ investigation of the effect of four different bi‐ and trivalent cations (Fe(III), Cu(II), Mn(II) and Cr(III)) on the displacement velocity of individual growth steps on the (110) face of ammonium oxalate monohydrate crystals as a function of supersaturation are described and discussed. It was observed that: (1) at a particular temperature of pure solutions and solutions containing impurities, the velocity v of movement of the [110] growth steps is always greater than that of the [111] steps, (2) fluctuations in the velocity of individual growth steps occur in all solutions containing similar concentrations of different impurities, (3) the value of kinetic coefficient β for growth steps decreases with an increase in the concentration c_i of Cu(II) impurity, but that for dissolution steps does not depend on c_i; moreover, the value of kinetic coefficient β for growth steps is higher than that of dissolution steps, and (4) in the presence of Mn(II) and Cr(III) impurities, the kinetic coefficient β for dissolution steps is several times greater than that for growth steps. The results are explained from the standpoint of Kubota‐Mullin model of adsorption of impurities at kinks in the steps and the stability of dominating complexes present in solutions. Analysis of the results revealed that: (1) the effectiveness of different impurities in inhibiting growth increases in the order: Fe(III), Cu(II), Mn(II), and Cr(III), and this behavior is directly connected with the stability and chemical constitution of dominating complexes in saturated solutions, (2) fluctuations in the velocity of growth steps is associated with the effectiveness of an impurity for adsorption; the stronger the adsorption of an impurity, the higher is the fluctuation in step velocity v, and (3) depending on the nature of the impurity, the kinetic coefficient for the dissolution steps can remain unchanged or can be higher than that of the growth steps. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of cationic impurities on solubility and crystal growth processes of ammonium oxalate monohydrate: Role of formation of metal‐oxalate complexes

The effect of different bi‐ and trivalent cationic impurities on the solubility of ammonium oxalate and the composition and distribution of chemical complexes formed in saturated ammonium oxalate aqueous solutions as a function of impurity concentration are investigated. The knowledge of the composition and stability of complexes formed in saturated aqueous solutions is then employed to explain the appearance of dead zones of supersaturation for growth and the difference in the effective segregation coefficient of the impurities. Analysis of the experimental results revealed that: (1) at a constant temperature, the dependence of concentration of complex species formed in saturated solutions on the concentration of different impurities can be described by an equation similar to that of the concentration dependence of density of solutions, (2) the dominant metal‐containing species present in saturated solutions are negatively‐charged, most stable oxalato complexes like Cu(C₂O₄)₂²⁻, Mn(C₂O₄)₃⁴⁻, Zn(C₂O₄)₃⁴⁻, Cr(C₂O₄)₃³⁻ and Fe(C₂O₄)₃³⁻, (3) in the investigated range of impurity concentration, the solubility of ammonium oxalates increases linearly with the concentration of all impurities and the increase is associated with the stability of dominant complexes, (4) appearance of dead supersaturation zones in the presence of impurities is associated with instantaneous adsorption of all growth sites by dominant oxalato complexes in relatively short adsorption time, and (5) the segregation coefficient of an impurity cation M of charge z + increases with a decrease in the solubility product constant K_sp for the hydrolysis products of reactions of the type: M^{z +} ↔ M₁^{(z −1)+} + H⁺ (where the cation M has z + charge, and H⁺ is hydrogen ion). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Influence of Impurities on Crystallization Kinetics of Sodium Chloride

The influence of impurities on the crystallization kinetics of NaCl was investigated in a fluidized bed crystallizer. The growth and dissolution rates were related to the supersaturation and impurity concentrations. The effect of different impurities on the growth rate of NaCl crystals can be divided into thermodynamic effects where the impurities influence the solubility and kinetic effects where the impurities will suppress the growth rate compared to the pure NaCl. A mathematical model describing crystal growth rates from aqueous solution as a function of impurity concentration is presented. The model explains impurity concentration effects on the crystal growth rate in terms of an impurity effectiveness factor and a Langmuir adsorption isotherm for the impurity.     

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.     

The role of hydration and complexing in the mechanism of impurity influence on crystal growth

The influence of impurities of chlorides and nitrates of divalent Ca²⁺ and Ba²⁺ cations on the kinetic growth of potassium dihydrophosphate KH₂PO₄ crystals at a saturation temperature of 323 K and relative supersaturation of 0.03 has been investigated experimentally. It is established that the impurity acts differently, depending on the face index, the impurity concentration, cation hydration, and the stability of the complexes formed in the solution by impurity salt ions. A model is proposed to explain the different influence of impurity ions on the growth of crystal faces. This influence is determined by the different hydration of cations and enhanced association of cations and anions of impurity salts in the surface layer with a lower dielectric constant.     

On the thermodynamic stability of disperse systems

Investigation has been carried out on the effect of the surface activity of capillary or surface active substances (impurities), called surfactants (i.e. the effect of the lowering (Δσ) of the specific surface energy after impurity adsorption at the solid/gas, solid/liquid, liquid/gas or liquid/liquid interface), on the thermodynamic equilibrium in a polydisperse system. Attention has been paid to the fact that the presence of a surfactant with an activity within the range 0 < Δσ < σ₀ (where σ₀ is the specific surface energy of an adsorption-free interface) reduces the thermodynamic driving force for the appearance of the Gibbs-Thomson effect and for the recondensation (recrystallization) processes in the heterogeneous polydisperse system. It is shown that with an impurity activity Δσ = σ₀, the supersaturation becomes zero and the condensed phase formations should be, irrespective of their size and shape, in equilibrium with one another because their vapour pressure becomes equal to that of an infinitely large phase. In this case the Gibbs-Thomson effect completely disappears, the system become thermodynamically stable and, regardless of its polydispersity, it can exist infinitely long. The behaviour of such a heterogeneous system, which is far from its critical point (the system temperature is T ≪ T_critical), is similar to the behaviour of a system in the region of its critical point: the surface tension becomes nearly equal to zero, and the fluctuations sharply increase. The case when the surfactant activity is so high (Δσ > σ₀) that σ_a = σ₀ − Δσ < 0 (σ_a, specific surface energy of the interface in the presence of a surfactant), is of special interest. It represents a paradox in the phase formation theory: as a result of the adsorption of an impurity with such a high activity, the condensed phase surface would be destabilized and the phase would be spontaneously dispersed.     

Effect of impurities on the metastable zone width of solute–solvent systems

The novel approach to interpret the metastable zone width obtained by the polythermal method using the classical theory of three-dimensional nucleation proposed recently [K. Sangwal, Cryst. Growth Des. 9 (2009) 942] is extended to describe the metastable zone width of solute–solvent systems in the presence of impurities. It is considered that impurity particles present in the solution can change the nucleation rate J by affecting both the kinetic factor A and the term B related with the solute–solvent interfacial energy γ. An expression relating metastable zone width, as defined by the maximum supercooling ΔT_max of a solution saturated at temperature T₀, with cooling rate R is proposed in the form: (T₀/ΔT_max)²=F(1−Z ln R), where F and Z are constants. The above relation can also be applied to describe the experimental data on maximum supercooling ΔT_max obtained at a given constant R as a function of impurity concentration c_i by the polythermal method and on maximum supersaturation σ_max as a function of impurity concentration c_i by the isothermal method. Experimental data on ΔT_max obtained as a function of cooling rate R for solutions containing various concentrations c_i of different impurities and as a function of concentration c_i of impurities at constant R by the polythermal method and on σ_max as a function of impurity concentration c_i by the isothermal method are analyzed satisfactorily using the above approach. The experimental data are also analyzed using the expression of the self-consistent Nývlt-like approach [K. Sangwal, Cryst. Res. Technol. 44 (2009) 231]: ln(ΔT_max/T₀)=Φ+β ln R, where Φ and β are constants. It was found that the trends of the dependences of Φ and β on impurity concentration c_i are similar to those observed in the trends of the dependences of constants F and Z on c_i predicted by the approach based on the classical nucleation theory.     

Impurity effect of iron(III) on the growth of potassium sulfate crystal in aqueous solution

Growth rates of the {1 1 0} faces of a potassium sulfate crystal were measured in a flow cell in the presence of traces of impurity Fe(III) (up to 2 ppm) over the range of pH=2.5–6.0. The growth rate was significantly suppressed by the impurity. The effect became stronger as the impurity concentration was increased and at pH<5. It became weaker with increasing supersaturation. It also became weaker as the pH was increased and at pH>5 it finally disappeared completely. The concentration and supersaturation effects on the impurity action were reasonably explained with a model proposed by Kubota and Mullin [J. Crystal Growth, 152 (1995) 203]. The surface coverage of the active sites by Fe(III) is estimated to increase linearly on increasing its concentration in solution in the range examined by growth experiments. The impurity effectiveness factor is confirmed to increase inversely proportional to the supersaturation as predicted by the model. Apart from the discussion based on the model, the pH effect on the impurity action is qualitatively explained by assuming that the first hydrolysis product of aqua Fe(III) complex compound, [Fe(H₂O)₅(OH)]²⁺, is both growth suppression and adsorption active, but the second hydrolysis product, [Fe(H₂O)₄(OH)₂]⁺, is only adsorption active.     

Study of growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions

Experimental results of the dependence of linear growth rates of ammonium oxalate monohydrate [(NH₄)₂C₂O₄ · H₂O; AO] single crystals on solution supersaturation are presented. The AO crystals were grown by constant-temperature, constant-supersaturation method at 30 and 40 °C in the supersaturation range of 1–9%. It was observed that the supersaturation dependence of growth rates follows the parabolic growth law. Analysis of the supersaturation dependence of linear growth rates of AO crystals showed (1) that growth models involving surface diffusion and direct incorporation of growth units give kinetic parameters similar to those reported for other compounds grown from solutions, and (2) that the the BCF model of cooperating screw dislocations is also applicable. An inverse relationship between the estimated values of the length, L, of the line containing the dislocations and growth rate, R, and a direct relationship between L and interplanar distance, d_hkl, of the face {hkl} were found. Both these relationships are associated with the process of generation of screw dislocations in the growing layer.     

Curved-face growth of NaNO<Subscript>3</Subscript> crystals

Curved-face growth of NaNO₃ crystals under the action of the (NH₄)₂Mo₂O₇ impurity is studied experimentally and possible causes of face bending are analyzed. Selective impurity adsorption on the basal pinacoid results in growth of platelike crystals with spherically bent faces. Growth-rate measurements show that the impurity decelerates pinacoid-face growth by the Bliznakov kink-poisoning mechanism. Face bending can be explained by gradual deceleration of step growth by the impurities accumulated before step fronts. A model of step deceleration is suggested that is based on the assumption of slow impurity adsorption resulting in the instability of a step train. The model allows one to qualitatively interpret the experimental data.     

Growth kinetics of zinc(tris)thiourea sulphate (ZTS) crystals

Growth kinetics of zinc (tris) thiourea sulphate (ZTS) crystals investigated as a function of supersaturation is reported in this communication. Crystal growth rates were investigated normal to the (100), (010) and (001) faces under growth conditions employed for bulk crystal growth. The growth rates normal to (010) and (100) were found to follow the continuous growth model (R_G = Cσ) with respect to the supersaturation whereas the growth rates normal to (001) was found to satisfy birth and spread (B+S) model (R_G = Aσ^5/6 exp(‐B/σ)). The growth rates observed normal to the studied face are in agreement with the growth mechanism predicted from the estimated α (Jackson) factor. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Impact of impurities on the α-LiIO3 crystal growth: Technique for measuring the “dead zone”

Lithium iodate (α-LiIO₃) single crystal is a promising nonlinear optical material, which used for efficient laser radiation conversion in the visible and near-IR regions. A technique for measuring the “dead zone” (ΔТ _dz) of LiIO₃ solutions has been developed; data on the impact of Fe(IO₃)₂, AgIO₃, CsOH, H₃PO₄, and methyl methacrylate on the growth of the (100) face of α-LiIO₃ crystals have been presented; and the dependences of the nucleation and motion of single steps on the degree of supersaturation have been measured. It is shown that the ΔТ _dz value makes it possible to estimate the validity of solutions for growing α-LiIO₃ crystals. The results of measuring the face growth rates and step velocities for KDP and α-LiIO₃ crystals are compared.

     

A statistical description of dislocation mobility at stresses close to the threshold of unlocking from the atmosphere of adsorbed impurities

A model is developed to describe the effect of impurities adsorbed by dislocation cores on the dislocation mobility in materials with a high potential relief (Peierls barriers). It is shown that the statistical fluctuations in the impurity distribution, which are due to the adsorption randomness, significantly change the conditions of dislocation kink formation. This model explains and describes the qualitative phenomenon experimentally found in semiconductor crystals: the immobilization of dislocations at stresses σ below a certain threshold value σ _unl (σ < σ _unl ). An analytical solution is obtained based on an analogy with the well-studied and urgent problem of calculating the ruin probability for insurance or other financial companies in the mathematical theory of mass service. A slight generalization of the methods developed in the theory made it possible to calculate the degree of “spread” of the threshold stress due to the random character of impurity distribution as well.     

In situ AFM investigation of 2D nucleation on the (100) face of KDP

Surface morphology of the (100) face of potassium dihydrogen phosphate (KDP) crystals which were grown at different supersaturations at 25 °C was investigated by in situ atomic force microscopy (AFM). Various AFM images of 2D nucleation under different growth conditions were presented. It is found that the growth of KDP is controlled by polynuclear nucleation mechanism at the high supersaturation. With reduction of the supersaturation, the growth velocity of 2D nuclei becomes very slow and shows typical anisotropy. It is found that the process of coalescence of 2D nuclei does not lead to defect. The experiments show that the growth mechanism for KDP at 25 °C changes between step flow and 2D nucleation in the supersaturation range of 4.5‐5%. The triangular nuclei which are close to equilateral triangle are observed in the experiment at the supersaturation σ = 6% for the first time, showing typical anisotropic growth. Through observing the dissolution of 2D nuclei, the dissolving process can be regarded as the reverse process of growth. We also find that the microcrystals landing on the surface at σ = 9% would grow and coalesce with each other and there is no observable defect in the coalescence. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth kinetics and adsorption trapping of impurity during crystallization of NH<Subscript>4</Subscript>Cl in the NH<Subscript>4</Subscript>Cl-CuCl<Subscript>2</Subscript>-H<Subscript>2</Subscript>O-CONH<Subscript>3</Subscript> system

The growth of NH₄Cl crystals and their trapping of copper impurity in the NH₄Cl-CuCl₂-H₂O-CONH₃ quaternary system have been experimentally studied. The epitaxial adsorption of copper complexes on (100) faces leads to a sharp decrease in the growth rate in good correspondence with the Bliznakov-Chernov equation. The copper impurity enters the crystal composition in amounts up to 6.5 mol %. The impurity distribution coefficient nonlinearly changes with the copper concentration in the solution: it is much larger than unity at low concentrations and sharply decreases with an increase in supersaturation. Such behavior is indicative of the adsorption mechanism of copper trapping by NH₄Cl crystals. Single-crystal X-ray study shows that the impurity is incorporated in NH₄Cl crystals in the form of oriented intergrowths of different complex coppercontaining compounds. The concentration and variety of impurity phases increase with an increase in the copper content in the solution and decrease with an increase in supersaturation. Heterogeneous 2D isomorphous trapping of copper impurity by NH₄Cl crystals induces high (up to 60 MPa) internal stresses in them, as a result of which anomalous birefringence and splitting of crystals occur.     

Effect of Mn(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: I. Growth habit and surface morphology

The effect of concentration of Mn(II) ions on the growth habit and the surface micromorphology of different as‐grown faces of ammonium oxalate monohydrate (AO) single crystals grown from aqueous solutions was studied at a constant temperature of 30 °C and predefined supersaturations up to 20%. It was observed that the growth habit and the surface morphology of the crystals strongly depend on the supersaturation used for growth and the impurity concentration in the solution. The experimental results were analysed in terms of connected nets determined from different projections of the structure of AO crystals. Analysis of the observations revealed that: (1) the directions of connected nets corresponding to basic growth units composed of single (NH₄)₂C₂O₄ · H₂O molecules are in excellent agreement with the low‐index crystallographic directions of the orientations of growth layers, (2) all faces appearing in the growth morphology of AO crystals are F faces, and (3) the {001} face growing from pure aqueous solutions is essentially a kinetically rough face but the presence of Mn(II) impurity leads to their appearance in the morphology due to increase in the strength of bonds of the connected nets composing the surface graph.     

Effect of organic impurities on the surface morphology and growth mechanism of KBP crystals (C8H5O4K)

The surface morphology of the (010) face of potassium biphthalate (KBP) crystals grown from aqueous solutions under the supersaturation ranging within 0.029–0.04 has been studied by the methods of optical and electron microscopies. It was revealed that the (010) surface has polygonal growth macrohills of the dislocation nature, small hillocks developing by the mechanism of successive two-dimensional nucleation, and numerous two-dimensional nuclei. The density of small hillocks (10⁴–10⁵ cm^?2) exceeds the dislocation density in KBP crystals by one to two orders of magnitude. It is shown that at low supersaturations, the (010) face grows simultaneously by the dislocation mechanism and the mechanism of successive two-dimensional nucleation. It is also established that the tangential velocity of growth-step motion on the (010) face increases in the presence of organic impurities. This effect can be used as one of the factors increasing the growth rates of crystal faces at low impurity concentrations (the so-called catalytic effect of impurities).