R. Lacmann

Growth kinetics of ice from the vapour phase and its growth forms

A new interpretation of the habits of ice growing from vapour is proposed. The basic habits of ice alternate three times: plates (A) → -4°C → columns (B) → -10°C → plates (C) → between -20°C and -35°C → columns (D). The theory is based on a view- that the surface of ice just below 0°C is covered with a quasi-liquid layer, whose thickness ϑ or coverage δ decreases with falling temperature, and therefore the growth mechanism of a crystal face changes also as follows: (I) Vapour—Quasi-Liquid— Solid mechanism (δ > 1), (II) Adhesive Growth on a surface strongly adsorbed by H2O molecules (0.02 < δ < 1) and (III) Two- Dimensional Nucleation Growth on a surface with low eigen adsorption (δ < 0.02). The type of surface structure and consequently the growth mechanism depends on the surface orientation and the temperature. The complicated habit change is caused mainly by the combination of surface kinetics of the {0001} and {10110} face. The first and second conversion temperature (TAB, TBC) are expected to be independent of the absolute supersaturation δP as found in experiments. On the other hand, the third (TCD) is the temperature where the usual two-dimensional nucleation growth rate of the {0001} face reaches the one of the {1010} face, and exceeds it by the effect of diffusion field, so that the third conversion temperature falls with decreasing δP. The marked columnar crystals observed at -7°C can be explained only by taking into account the spherical volume diffusion field near the {0001} face and a cylindrical one near the {10110} face. For plate-like crystals between -10°C and -20°C to -35°C the surface diffusion from {0001} to {1010} and volume diffision with cylindrical symmetry near {10110} faces is very important.

Studies of the growth and dissolution kinetics of the CaCO3 polymorphs calcite and aragonite II. The influence of divalent cation additives on the growth and dissolution rates

The influence of the divalent cations Fe2+, Cu2+, Zn2+, Mg2+, Sr2+, and Ba2+ on the growth and dissolution rates of calcite and aragonite has been studied. In most cases the results can be interpreted by a reversible adsorption of the impurity ions at kinks sites according to the Langmuir-Volmer model. Ions of the transition metals show a stronger inhibition than earth alkaline ions. Mg2+ and Fe2+ have no influence on growth and dissolution of aragonite. Further, Cu2+ and Zn2+ have a stronger effect on calcite, while Sr2+ and Ba2+ are more effective on aragonite. Results are used to show consequences for the polymorphic precipitation of CaCO3.

Studies of the growth and dissolution kinetics of the CaCO3 polymorphs calcite and aragonite I. Growth and dissolution rates in water

Abstract Growth and dissolution rates of calcite and aragonite in water were measured by the pH-stat method as functions of the super- and undersaturation from ( S − 1) = −0.6 to 3, at temperatures T = 20–70°C, and for different calcium and carbonate concentrations. For calcite from fits of power laws r = p¦S − 1¦ n to the experimental growth and dissolution rates almost linear laws are obtained. From the high activation energy of the prefactor p it follows that for moderate deviations from saturation growth and dissolution are determined by processes at the surface and not by diffusion from the bulk of the solution. Measurements with constant (Ca 2+ )(HCO − 3 ) ion product and different (Ca 2+ ):(HCO − 3 ) ratios show that the growth and dissolution rates are independent of the individual concentrations but depend solely on the ion product. The results are interpreted by a new two-step growth model. The first, chemical step involves a formation of CaCO 3 molecules in the adsorption layer of the crystals possibly via CaHCO + 3 ion pairs, the second, surface kinetic one an incorporation of the formed CaCO 3 molecules into the crystal lattice by surface and step diffusion to kink sites. While the surface kinetics is rate determining at low deviations from equilibrium, the formation and decomposition of CaCO 3 dominate growth and dissolution at large super- and undersaturations. The same growth model can be applied to aragonite. The interpretation of the experimental results is, however, complicated because of the occurrence of different crystallographic faces, which allows only a description of the measured rates as overall rates. Results for growth may be interpreted by different power laws for different faces or by two-dimensional nucleation. For dissolution an influence of diffusion in the bulk of the solution is observed.

The influence of impurities on crystallization kinetics – a case study on ammonium sulfate

Abstract The influence of impurities on the crystallization kinetics of ammonium sulfate was investigated. MSMPR experiments were conducted with the impurities aluminum sulfate and the azo dyes amaranth and fuchsine. Nucleation and growth rates as well as mean crystal sizes were related to the supersaturation σ and-the width of the metastable zone. It was found that all impurity levels in the system reduce kinetic coefficients for crystal growth and suppress nucleation by adsorption on the crystal surfaces. An increase of supersaturation and metastable zone width compensates for this reduction at low impurity concentrations and allows the growth of larger crystals compared to the pure system. At high impurity concentrations and increasing surface coverage of the crystals, supersaturation rises faster than metastable zone width, causing an increase in nucleation rates and a higher fines content in the product compared to the pure system. A similar interdependence between impurity concentration, crystal size and supersaturation was found for other systems not reported here. The observations made can be explained in terms of adsorption equilibria of the impurities on the crystals. This seemingly general relationship allows the adjustment of crystal sizes in crystallization processes by control of impurity concentrations. A second paper will discuss the changes in crystal morphology in greater depth (Kuch et al., 2000).

Kinetics of nucleation and crystal growth

This paper deals with homogeneous and heterogeneous primary nucleation and the atomistic model of heterogeneous primary and secondary nucleation. Three aspects of crystal growth mechanisms will be taken into account: growth by two-dimensional nucleation, the so-called birth and spread model, spiral growth without and with consideration of the influence of diffusion, and finally adhesive growth. An equation for the estimation of the growth rate of imperfect crystals including dislocations, published by Mersmann [1], is discussed. The influence of additives on nucleation and crystal growth, respectively, will be exemplarily explained for several model systems. The effect of growth rate dispersion (GRD) is described. Therefore, some experimental results concerning growth rates and different ways to influence growth are represented and discussed. Furthermore, a model explaining the effect of GRD is represented.

Problems in temperature control performing in situ investigations with the scanning force microscope

Abstract Up to now, various publications dealing with in situ scanning force microscopy without any temperature control have been published. In this paper it is demonstrated that the temperature increase in the sample chamber due to the use of a diode laser in the detection unit cannot be neglected. The effect was quantified as 3–4 K per hour in the non-thermostatted SFM cell and by the recirculation of thermostatted liquid limited to 0.6 k.

The effect of additives on nucleation: A low cost automated apparatus

A transient technique for screening tests of the effects of additives on nucleation is introduced. The experiments are fast and simple, the system is automated by a microcomputer. First results are presented for the systems water/KCI and water/KNO 3 with a number of different additives. The results are in good agreement with already published data.

Methods and apparatus for in situ investigations with the scanning force microscope

Abstract Various methods of carrying out time resolved in situ monitoring of crystallization processes with the scanning force microscope (SFM) were tested and improved. First investigations, taking place in static liquids, were performed in a simple cup sample holder and in the liquid cell supplied by the manufacturers of the SFM. Continuous flow conditions were realized with a new recirculating flow system, which in addition allows temperature control. The different apparative approaches were tested with lab-grown crystals of L-ascorbic acid and lithium fluoride, as well as freshly cleaved fragments of the naturally occurring mineral calcite.

The dispersion of growth rate as a result of different crystal perfection

Abstract The aim of the cooperative work of the above mentioned institutes was to find out the reason for growth rate dispersion (GRD). Measurements of growth rate (overall or face-specific), microhardness (HV), etch pit density (EPD) and crystal perfection (X-ray topography and Laue X-ray method) were carried out using KAl(SO 4 ) 2 · 12H 2 O (PA) and KNO 3 (PN) crystals. The investigated crystals were grown under different conditions and treated in different ways. It is possible to influence the growth rate by well-directed alternations of supersaturation (σ 1 , σ 2 , σ 1 ), strain, mechanical stress, annealing and surface roughening. Depending on observation time, the constant crystal growth model (CCG model) (a few hours) as well as the random fluctuation model (RF model; a few days up to a month) describe the growth behaviour of PA. The growth of PN can only be described by the RF model. At constant supersaturation, the average growth rate of small particles in the subsieve size range (up to 60 μm) is considerably smaller than the average rate of larger crystals of the product size range (500 μm) in an MSMPR (mixed suspension mixed product removal) crystallizer.

Characterization of quantum structures by atomic-force microscopy

Abstract After a short discussion of errors incurred during atomic-force microscopy (AFM), we suggest methods for calibration. We describe specifically designed standards fabricated by metal organic vapor-phase epitaxy (MOVPE) which are utilized as a basis to calibrate the AFM microscope against a mechanical surface profiler and a scanning electron microscope (SEM). An important prerequisite is a well controlled technique to prepare the surface of the sample for AFM. This is demonstrated for the case of InGaAs/InP.