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Engineered Phase Inhomogeneity for CIS Device Optimization
Published in R D Tomlinson, A E Hill, R D Pilkington, Ternary and Multinary Compounds, 2020
B.J. Stanbery, C.-H. Chang, T.J. Anderson
The structural model reported by Hanada et al. [17] was represented as ABIn2Se4 where A and B correspond to atoms occupying the 2a and 2b lattice site subgroups in the P4¯2m space group. They suggest that correlated variations in the copper occupancy fraction of the 2a and indium occupancy fraction of the 2b sites enable the average valency to be maintained for each element within the same crystallographic structure as the overall composition changes. Within their model for example the composition CuIn3Se5 is equivalent to the ABIn2Se4 structure with A=Cu0.8 and B=In0.4. If one asks what composition corresponds to full occupancy of the 2a copper lattice sites (i.e. A=Cu1.0) and remains on the Cu2Se-In2Se3 pseudobinary tie-line (thus specifying the two degrees of freedom) the answer is Cu3InySe12 corresponding to the reaction: 3Cu2Se+7In2Se3→2Cu3In7Se12, a 70 mole% In2Se3 composition near the β phase boundary with B=In1/3. As the In2Se3 molar fraction increases to 5/6 (83.3%, approximate upper limit of the β phase) the 2a copper site occupancy linearly decreases from 1 to ½ while the 2b indium site occupancy linearly increases from 1/3 to ½, corresponding to the reaction: Cu2Se+5In2Se3→2CuIn5Se8.
A New Metatheorem and Subdirect Product Theorem for L-Subgroups
Published in Fuzzy Information and Engineering, 2018
In classical algebra, a generalized cyclic group can be characterized by the distributivity of its lattice of subgroups. Here we demonstrate that such groups can also be characterized in terms of the distributivity of its lattice of L-subgroups.