Marco Rubbo

Theoretical equilibrium and growth morphology of CaCO3 polymorphs. I. Aragonite

Abstract Periodic bond chain (PBC) analysis is performed using a potential function fitted to elastic, structural and vibrational properties of aragonite. The resulting equilibrium form of the crystal, bounded by six forms having F character, is dominated by {0 1 1}, {1 1 0} and {1 0 2}, other forms being {1 1 1}, {0 1 0} and {0 0 1}, the corresponding specific surface energy γ has a mean value of ≈940erg/cm 2 . The theoretical growth shape is defined by five F-forms: {1 1 0}, {0 1 0}, {0 1 1}, {0 0 1}, {1 0 2} and a stepped one, {0 2 1}. Its habit depends on what value of the attachment energy of {0 1 1} is considered. The agreement between the theoretical growth morphology and that of natural crystals is not fully satisfactory: as a matter of fact three out of the eight forms bounding the averaged natural morphology (i.e., {1 1 1}, {0 1 2} and {1 2 1}) are missing in the theoretical growth morphology. From the observation of the natural gypsum/aragonite epitaxy, a simple model is proposed to explain the striking morphological difference between the pseudo-symmetrical zones [0 1 0] and [1 1 0] in natural aragonite crystals. The variation on the attachment energy of {0 1 0}, induced by water adsorption, improves the fit between theory and observation around these zones, especially when the distribution of their vicinal faces is considered. The same reasoning on water adsorption is extended to the specific surface energy of the crystal: a theoretical value of 330 erg/cm 2 is calculated for γ erystal/water of the face (0 1 0).

Growth morphology of polar crystals: A comparison between theory and experiment in sucrose

Abstract The theoretical growth morphology of sucrose has been deduced by means of the theory of Hartman and Perdok. Only hydrogen bonds are considered to build up the periodic bond chains. The forms with F character are the following: {100}, {001}, {101}, {110} {110}, {011}, {011}, {111} and {111}. A comparison is made between theoretical and experimental morphology of sucrose crystals grown from pure aqueous solutions.

The competition between {} cleavage and {} steep rhombohedra in gel grown calcite crystals

Abstract Calcite crystals have been obtained from supersaturated solutions diffusing both in agarose and Na-metasilicate gels. Crystal morphology in agarose is characterized mainly by spherulites grown around solid gel impurities and terminated by the cleavage {1 0 1 4} rhombohedron. Grown from Na-metasilicate gel, {1 0 1 4} and {0 1 1 2} rhombohedra compete according to the influence of pH and of the acidifying agent, HCl or CH3COOH, the latter favouring the appearance of the {0 1 1 2} form.

Growth of sucrose crystals and tapering effect studied by holographic interferometry

Effects of dopant raffinose on the growth of sucrose crystals are studied by means of holographic interferometry. By the distribution of hologram fringes the selective doping effect is measured on {100}, {110}, and {110} forms. An interpretation is put forward for the tapering effect in wedge shaped crystals.

Equilibrium and growth forms of sucrose crystals in the {h0l} zone: 1. Theoretical treatment of {101}-d form

Abstract Observed {h0l} growth forms of the sucrose crystal are compared with calculated ones, on the basis of attachment energy plots. Agreement is found for all forms only if a modification of character of the {101}-d face is taken into consideration. Calculation of equilibrium and growth forms have been carried out using two potential for dispersion and hydrogen bond energy respectively. The same method is applied for studying the spiral growth shape on the (101) face and its field of validity is discussed: at low driving force values, the attachment energy at the steps is the relevant energy, determining the shape of spirals on the (101) face of sucrose.

Twin growth of sucrose crystals

Abstract A crystallographic and kinetic approach is given to understand twinning of sucrose crystals. The twin law is redefined and original composition planes for twinning (OCP) are found consistent with experiments. The elongation parameter Π is defined as a function of supersaturation and growth time. The calculated and measured Π values compare favourably both in pure solution growth and in the presence of low concentrations of raffinose. Experiments stress that the polar character of sucrose is determining both the crystallographic properties and kinetic behaviour of twins.

Theoretical equilibrium and growth morphology of anhydrite (CaSO4) crystals

Theoretical equilibrium and growth morphology of CaSO4 (anhydrite) are obtained by applying the Hartman-Perdok method and computing surface and attachment energies with a Born interatomic potential (electrostatic + dispersive + exponential repulsive terms). Dispersive coefficients derive from experimental refractivity data and the other parameters have been fitted to structural and elastic properties of the anhydrite crystal. A comparison is made with the morphology of natural samples, where the three fundamental pinacoids {100}, {010} and {001} prevail on other S forms. Finally the equilibrium shape of 2D nuclei which can form on F faces is calculated.

Equilibrium and growth forms of sucrose crystals in the {h0l} zone: II. Growth kinetics of the {101}-d form

The aim of the work is to assess the steady growth morphology of the {h0l} zone of sucrose crystals by measuring the growth rates of its individual faces. Experimental results on the kinetics of {101}-d form are presented and discussed in this paper. The novelty consists in the shape of the growth isotherms, which, at the moment, can be interpreted only qualitatively. Some possible parameters determining this shape are considered throughout.

Growth morphology of epsomite (MgSO4·7H2O)

Abstract A first approach to the study of the growth properties of epsomite (MgSO 4 ·7H 2 O) is presented. Particular attention is payed to the growth forms and to epitaxy relations between epsomite and some known habit modifiers. The starting point of the study is the Hartman and Perdok PBC analysis. It proves to be essential for knowing the actual surface profiles. Successively the theoretical growth morphology is given taking into account: the broken-bond model of Wolff and Broder, the energies associated to the hydrogen bonds only, and finally the attachment energies calculated on the basis of the Coulomb potential. Furthermore an analysis of 2D coincidence lattices leads us to the conclusion that a 2D epitaxy of both Na 2 B 4 O 7 ·lOH 2 O and/or Na 2 SO 4 ·lOH 2 O on {111} and/or forms of epsomite explains the effect of borax and Glaubers salt as habit modifiers.

Growth kinetics of epsomite (MgSO4·7H2O)

Abstract Growth isotherms of the most important F forms ({110}, {010}, {111}, { 1 1 1 } and {100}) of epsomite were measured on single crystals growing from pure aqueous solution at 30 and 40°C. The results are discussed and compared with previously reported data.