Luminescent Piezoelectric CdSiP2: Normal Probability Plot Analysis, Crystal Structure, and Generalized Structure of the AIIBIVC2V Family

CdSiP₂ is a typical member of the A^IIB^IVC₂^V family with chalcopyrite structure. The x‐ray scattering for luminescent and nonluminescent material is essentially identical: The atomic order at the Cd and Si sites is at least 99.8% complete. The lattice constants of this tetragonal crystal are $\text{a\hspace{0.17em}=\hspace{0.17em}5.680\hspace{0.17em}±\hspace{0.17em}0.001}$ and $\text{c\hspace{0.17em}=\hspace{0.17em}10.431\hspace{0.17em}±\hspace{0.17em}0.003 Å}$ at 298°K. The space group is $\text{I4̄2d}$ , and there are four formulas per unit cell. A total of 2370 reflections from a nonluminescent crystal, and 2156 from a luminescent CdSiP₂ crystal, were measured with PEXRAD. Least squares refinement, based on 320 symmetry‐independent reflections from both crystals, led to a final agreement factor of 0.047. Normal probability plot analysis shows the least squares derived standard deviations to be underestimated by a factor of 3.0, and the two sets of measured structure factors to possess a small parallel bias. The bond angles about the Si atom do not differ significantly from the regular tetrahedral angle of 109.47°. Regular tetrahedral bond angles about Si were previously observed in ZnSiP₂. The assumption that the B^IV atom in all members of the A^IIB^IVC₂^V family maintains a regular tetrahedral valence angles leads to the relation: ${\text{x\hspace{0.17em}=\hspace{0.17em}0.5\hspace{0.17em}−\hspace{0.17em}(c}}^2{\text{\hspace{0.17em}/\hspace{0.17em}32a}}^2\mathrm{\hspace{0.17em}-\hspace{0.17em}}\frac{1}{\text{1 6}}{)}^{\text{1/2}}$ , where $x$ is the atomic coordinate of the C^V atom at position $x\frac{1}{4}\frac{1}{8}$ . The predicted interatomic distances for a wide group of family members are both internally consistent and in excellent agreement with measurement on ZnSiP₂ and CdSiP₂. The experimental Cd–P distance is 2.561 ± 0.002 Å, and Si–P is 2.247 ± 0.002 Å. The CdSiP₂ characteristic temperature $\theta$ is 282°K, and representation is $\text{ΠPP(4̄2m)}$ .