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Inaug.-Diss.--Leipzig. / Vita.

Proefschrift (D. Agr.)--Landbouwhoogeschool te Wageningen. / "Literatuur": p. 211-216.

Inaug.-diss.--Erlangen. / Lebenslauf. "Literaturübersicht": p. [5]-8.

Geometric models of the pyroxenes have been developed that allow the calculation of pyroxene crystal chemical properties as a function of pressure, temperature, and composition. The set of all closest-packed stacking sequence labels of length N using the standard A, B, and C notation is partitioned into equivalence classes using the generalized symmetry group, Q ≅ D(N) x S₃. Representatives of each equivalence class are used to derive crystal structure data sets for all of the possible ideal pyroxenes based on stacking sequences of length 12 or less. Stacking sequences of observed pyroxenes are identified, crystallographic settings of the pyroxenes and transformations between them are systematically derived, and the M2-T interatomic distance is identified as an important crystal chemical parameter. The constraint of closest-packing is removed and models of the commonly observed polytypes are derived that have regular M1 and T. These models are parameterized in terms of the O3-O3-O3 angle and the model oxygen radius. M2 is allowed to distort. Crystallographic parameters such as interatomic distances, unit cell volume, and packing distortion are determined as a function of the O3-O3-O3 angle. Results are compared with observed pyroxenes, providing insight into which interatomic interactions are important in determining pyroxene topology and behavior. Temperature is shown to favor polyhedral regularity in orthopyroxene and protopyroxene. Compression and expansion strain ellipsoids for observed and model pyroxenes are compared, demonstrating that a combination of tetrahedral rotation and isotropic compression approximately reproduces the compression ellipsoids of pyroxenes, but not the expansion ellipsoids. Ambient cell volumes of the C2/c pyroxenes are strongly correlated with M1 cation radius. Integrating the relationship between volume and M1 radius with the model provides a means to model volume changes with P, T, and x in the C2/ c pyroxenes.

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