Validity of Hartman–Perdok PBC theory in prediction of crystal morphology from solution and surface X-ray diffraction of potassium dihydrogen phosphate (KDP)

Abstract

Recent literature shows that the validity and capabilities of the Hartman–Perdok (HP) theory of crystal growth and morphology are in need of clarification. The HP theory can predict uniquely, growth layers and growth habits in terms of the crystal structure and the growth medium in energy-driven growth processes. An interpretation of the experimental results on the surfaces of potassium dihydrogen phosphate (KDP) (de Vries et al., Phys. Rev. Lett. 80 (1998) 2229), is open to fundamental challenge on the following claims. Prediction of which of the possible alternative surface terminations will control crystal growth in solution is supposed to be impossible, because the HP computation can deliver many theoretical growth layers. The theory is considered unable to account for the influence of the solution on the interface. The distinction of K + versus H 2PO 4 − pyramidal surface termination is seen as a long-standing issue that could not be resolved by theory. In ionic compounds like KDP, the atomic structure at the outermost boundary is believed to control the growth mechanism and morphology of the crystal, while the presence or absence of cation–anion alternation at that boundary is supposed to determine the role of polarity in step kinetics. The observed pyramidal surface cell of KDP is considered to generate a strongly polarized growth front. The present reassessment of the experimental results of the above work substantiates the following counterconclusions. The wide variety of computed growth layers is often diminished by conditions of space group symmetry; rather than being a theoretical artefact, it has physical significance, since in practice different theoretical growth layers ||(h k l) are activated by different growth environments such as vapour, melt or solutions. Surface electrostatics and the role of polarity on step kinetics cannot be inferred solely from the outermost ion array while ignoring the rest of the growth layer, including the step height. Cation–anion alternation at the surface termination is neither a necessary nor a sufficient condition for establishing surface polarity (cf. Strom, J. Phys. Chem. B 103 (1999) 11 339), and moreover it does not necessarily imply alternation of positive and negative atomic charges on that plane. Consequently, and consistently with the symmetry point located in the middle of the experimentally determined d 101 layer cell of KDP, the observed pyramidal surface is unpolarized. The occurrence of the K +-terminated, as opposed to the H 2PO 4 −-terminated, pyramidal surface of KDP grown out of an aqueous solution, as well as the role of ion impurities on the prismatic surface, have been anticipated on firm grounds in the past. Past HP predictions of solution-induced effects on other structures are outlined.