Hollandite-type phases: Geometric consideration of unit-cell size and symmetry

Jinmin Zhang; Charles W. Burnham

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Other| February 01, 1994

Hollandite-type phases: Geometric consideration of unit-cell size and symmetry

Jinmin Zhang;

Jinmin Zhang

Harvard University, Department of Earth and Planetary Sciences, Cambridge, MA, United States

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Charles W. Burnham

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Author and Article Information

Jinmin Zhang

Harvard University, Department of Earth and Planetary Sciences, Cambridge, MA, United States

Charles W. Burnham

Publisher: Mineralogical Society of America

First Online: 02 Mar 2017

Online ISSN: 1945-3027

Print ISSN: 0003-004X

American Mineralogist (1994) 79 (1-2): 168–174.

Abstract

Equations are derived for predicting the lengths of unit-cell edges and the symmetry of hollandite-type compounds with the general formula A_0–2B₈(O,OH)₁₆. The unit-cell size of a hollandite-type compound is determined largely by the average B-O bond distance, and additionally by the charge of the B cation (Z_B), the excess size of the tunnel cation (A) relative to the BO₆ octahedral framework (δ_A), and the excess size of the B cation relative to the octahedral cavity (δ_B). These factors are incorporated in the following equations, which accurately estimate the unit-cell edge lengths:

\begin{matrix} a (Å) = 5.130 (r_{O} + r_{B}) - 0.0291 Z_{B} + 0.441 δ_{A} \\ a (Å) = \sqrt{2} (r_{O} + r_{B}) + 0.0366 Z_{B} + 0.552 δ_{B} . \end{matrix}

The symmetry of a hollandite-type compound is related to the size of the tunnel cation (A).If

r_{A} > \sqrt{2} (r_{O} + r_{B}) - r_{O}

⁠, the compound cannot be monoclinic, whereas if

r_{A} < \sqrt{2} (r_{O} + r_{B}) - r_{O} - 0.15

it cannot be tetragonal. These relationships make it possible to predict the symmetry and unit-cell size of a hollandite-type compound based on composition alone.