L.J.P. Vogels

Morphology of synthetic and natural garnets: Theory and observations

Abstract The approach described in the previous paper is in this paper applied to the calculation of the advance velocities of steps in the (211) 1,2 slices and the (220) slice in different crystallographic directions for two synthetic garnets, YIG and YAG, and four natural garnets. Due to different chemical compositions, the anisotropy of the growth fronts depends on the chemical composition. Also, the relative growth rates of the slices (220) 1 and (211) 1,2 depend on the chemical composition of the garnets of the mother phase and the growth temperature. It is shown that the calculated habits of garnet crystals, concerning the relative morphological importance of faces {211} and {110} is in satisfactory agreement with a variety of observed growth forms of synthetic and natural garnets.

On the growth of ammonium nitrate(III) crystals.

The growth rate of NH4NO3 phase III crystals is measured and interpreted using two models. The first is a standard crystal growth model based on a spiral growth mechanism, the second outlines the concept of kinetical roughening. As the crystal becomes rough a critical supersaturation can be determined and from this the step free energy. The step free energy versus temperature turns out to be well represented by a Kosterlitz?Thouless type model. Further a phenomenological treatment of some peculiar growth observations is given.

Morphology of β phase monoacid triacyglycerol crystals: theory and observations

Abstract The morphology of β phase monoacid triacyglycerol crystals is derived schematically on a theoretical basis. The results of this theoretical morphology are compared with experimental growth forms. The theory used is based on the concepts of periodic bond chain (PBC), F-face and connected net, developed by Hartman and Perdok. The relative roughening transition temperature of F-faces is estimated using an Ising model. The theoretical morphologies are constructed using different criteria. The influence of the chain length of the hydrocarbon chains on the morphology is investigated. A flat needle-like habit with the needle axis parallel to the b -axis is predicted. This is in good agreement with the observed morphology.

On the morphology of β-K2SO4 type structures; theory and observation

Abstract In this paper we derive the theoretical morphology of the -K2SO4 type structure. The theories we use are the Hartman-Perdok theory combined with the theory of roughening transition. To predict the stability of faces at a certain temperature, we use calculated Ising temperatures. With these results we are able to construct the equilibrium and growth forms using a Gibbs-Wulff plot. The results of the theory are compared with morphological data from the literature, our own observations and sphere experiments. Three examples are investigated in more detail, namely -K2SO4, ((CH3)4N)2ZnBr4 and ((CH3)4N)2ZnCl4. A comparison of theory and observations yields satisfactory results.

Comprehensive computerized survey of the slice configurations of NH4H2PO4 (ADP) type structures

A thorough analysis of the surface configurations of NH4H2PO4 (ADP) at the atomic/molecular level has revealed a much larger number of PBCs and F-slices than obtained previously by Aquilo and Woensdregt (AW) in 1984 [J. Crystal Growth 69 (1984) 527] and 1987 [J. Crystal Growth 83 (1987) 549] by means of visual inspection of structure projections. The computational results of these relatively early applications of the Hartman-Perdok (HP) theory may be called into question insofar as they arise from an incomplete set of theoretical data. Specifically, the ADP forms {031} and {211}, {211} classified earlier by AW as S and K forms, respectively, are here demonstrated to be genuine F forms. The present theoretical results improve agreement with experiment: (i) The theoretical F character of {031}, a form thought by AW to be important in connection with tapering, is reconciled with the experimental observation by AW, according to which {031} grows as flat faces. (ii) The interpretation of an experimental observation by Dam et al. in 1986 [J. Crystal Growth 74 (1986) 118] of a series of small flat faces on zone [111] was dismissed by AW in 1987 as theoretically impossible, on the grounds that only one F face, the (022), was known to occur on that zone. The fact established here that (121) ≡ {211} is also an F face located on the same zone invalidates that objection. The theoretical F character of (121) agrees with the recent experimental observation of Verheijen et al., according to which (121) is located on the [111] flat face band. The aim of the present work is to (i) remove some degree of confusion currently in the literature as regards interpretation of experimental results, and (ii) provide a tool enabling a more accurate and adequate investigation of the growth mechanism and morphology of ADP type structures than has thus far been available.

Morphology of modulated crystals and quasicrystals

A survey is given of new types of crystallographic faces and forms occurring on modulated crystals which have to be indexed with four integers (hklm). These faces have so far been found on modulated crystals with an average beta -K2SO4 structure which can be grown from an aqueous solution and the mineral crystal calaverite (AuTe2) which can be grown from the melt. Interesting data on crystal growth obtained from in situ observations are presented. Among others, spiral-like patterns can be recognized. The occurrence on quasicrystals of crystal forms to be indexed with six integers (hklmno) is discussed and it is shown that these faces can in principle be explained by a generalization of the Hartman-Perdok theory. Crystal forms (hklm) and (hklmno) occurring on modulated and quasicrystals respectively can be explained by the higher than three-dimensional crystallography of de Wolff, Janner and Janssen (1977) where these crystals are considered as three-dimensional cuts out of a higher than three-dimensional truly translational invariant structure.

On the roughening transition of anisotropic and (pseudo) hexagonal lattices

In this paper the results of the calculations of the roughening transition temperatures of anisotropic and (pseudo) hexagonal lattices are presented. The calculations are based upon a so-called Ising lattice combined with a simple model for the representation of the lattice. The lattice has three different bonds of which for two the relative strengths are varied. The Ising transition temperatures have been calculated for different lattices and for the case of orthorhombic n-paraffin crystals they have been compared with experimental values obtained from vapour growth experiments.

A study on the morphology and stability of incommensurately modulated structures; a case study of ((CH3)4N)2ZnCl4−xBrx and AuTe2

In this paper we investigate the stability of crystal forms of modulated structures. First, in a classical analytical approach the forms on AuTe2 are investigated. Of the experimentally observed forms almost all important forms can be characterized as being stable. Secondly the forms on ((CH3)4N)2ZnCl4−xBrx are investigated, using a simple Ising model and various parameters to determine the stability of forms. Here we find that satellite forms {hklm} are clearly less stable than the main forms {hkl0}.

On the morphology of ammonium nitrate (III): theory and observation

The aim of this paper is to derive on a theoretical basis the morphology of crystals of ammonium nitrate, phase III, and to compare the results with experimental growth forms. The theory used is based on the concepts of periodic bond chain (PBC), F face and connected net, developed by Hartman and Perdok. Further an Ising model is used to determine roughening temperatures. Based on different criteria theoretical growth forms are predicted and compared with experiments.

On the hypomorphism of ADP crystals

The morphology and symmetry of spheres of ADP crystals has been studied. Faces as well as bands were observed. In contrast to the 42m symmetry as determined from X-ray and neutron diffraction studies, the bands on the spheres displayed a 222 symmetry. It is shown that this reduced symmetry either is the bulk symmetry or is induced by stereospecific interactions at the surface. The influence of several parameters on the stability of the bands and the symmetry of the spheres has been studied. At pH = 6.15 the symmetry reduction was found to be absent.