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Growth Morphology and Atomic Surface Topology by Hartman-Perdok Analysis: Application to ABCO_{4} and YBa_{2}Cu_{3}O_{7-x}

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Woensdregt C. F.

Acta Physica Polonica A

1997

vol. 92

issue 1

35-46

The Hartman-Perdok theory explains the relation between crystal structure and morphology and provides the atomic surface topology of the crystal-melt interface. Hartman-Perdok theory has been applied to CaYAlO_{4} as model for all other ABCO_{4} compounds with a K_{2}NiF_{4} crystal structure. F forms are {002}, {101}, {103}, {110}, {112}, {200}, {211} and {213}. The strongly anisotropic shape caused by the perovskite-like AlO_{6} layers || {001} is very distinct in all theoretical growth forms. The form with formal charges is planar following {001} with {101} and {110} as lateral forms. Disordering of the boundary ions results in the disappearance of {110}. At lower effective charge on oxygen ions, q_{O}, the ordered forms are still tabular, while {110} and {112} are the only lateral faces. At still lesser negative q_{O} {112} appears as well. On the disordered models {112} replaces {110}. Crystals show often variations in colour parallel to the {110} interface due to the surface topology of {110}. YBa_{2}Cu_{3}O_{7-x} has, for x=1, the following F forms: {001}, {101}, {103}, {112} and {114}. The theoretical growth form of this tetragonal phase is tabular following {001} with {101} as lateral form. For x=0 the growth form shows important {101} and minor {103} and {001}. When the boundary ions on (001) are ordered, the outermost layer of {001} contains half of the Cu^{+} (x=1) or Cu^{3+} and O^{2-} (x=0) ions in a c(2×2) quadratic lattice which reduces the {001} growth rate significantly. An (1×2) reconstructed {010} surface can be traced for the orthorhombic polymorph which results into the appearance of {010} on the ordered growth form. Otherwise the presence of {010} on as-grown crystals must be due to external factors.

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1 Acta Physica Polonica A

1 1997

1 Woensdregt C. F.

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Growth Morphology and Atomic Surface Topology by Hartman-Perdok Analysis: Application to ABCO_{4} and YBa_{2}Cu_{3}O_{7-x}