β'-AuCd ($B19$) Structure: AB_oP4_51_e_f-001
| Prototype | AuCd |
| AFLOW prototype label | AB_oP4_51_e_f-001 |
| Strukturbericht designation | $B19$ |
| ICSD | 58409 |
| Pearson symbol | oP4 |
| Space group number | 51 |
| Space group symbol | $Pmma$ |
| AFLOW prototype command |
aflow --proto=AB_oP4_51_e_f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}$ |
Other compounds with this structure
AuTi (H.T.), CdMg, IrMo, IrW, MoPt (H.T.), NbPt, NbRh, PbTi, PtTi, PtV (L.T.)
- When $a=b=c$, $z_{1}=1/4$, and $z_{2}=3/4$ the atoms are on the sites of a face-centered cubic lattice.
- When $a=c$, $z_{1}=1/4$, and $z_{2}=3/4$ the system reduces to the $L1_{0}$ (AuCu) structure.
- When $a/b=(8/3)^{2/3}$, $c/b=3^{1/2}$, $z_{1}=1/3$, and $z_{2}=5/6$, the atoms are on the sites of the hcp structure.
- Finally, when $z_{2}=1/2+z_{1}$ the atoms are at the positions of the $\alpha$–U ($A20$) structure.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{1} \,\mathbf{\hat{z}}$ | (2e) | Au I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{1} \,\mathbf{\hat{z}}$ | (2e) | Au I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2f) | Cd I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2f) | Cd I |
References
- \begin{thebibliography}{1}\expandafter\ifx\csname urlstyle\endcsname\relax \providecommand{\doi}[1]{doi:\discretionary{}{}{}#1}\else \providecommand{\doi}{doi:\discretionary{}{}{}\begingroup \urlstyle{rm}\Url}\fi\providecommand{\selectlanguage}[1]{\relax}\providecommand{\bibAnnoteFile}[1]{% \IfFileExists{#1}{\begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} \input{#1}\end{quotation}}{}}\providecommand{\bibAnnote}[2]{% \begin{quotation}\noindent\textsc{Key:} #1\ \textsc{Annotation:} #2\end{quotation}}\bibitem{chang51:b19}L.-C. Chang, Atomic displacements and crystallographic mechanisms in diffusionless transformation of gold-cadium single crystals containing 47.5 atomic per cent cadmium}, Acta Cryst. 4, 320–324 (1951), doi:10.1107/S0365110X51001057.\bibAnnoteFile{chang51:b19
Found in
- W. B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys (Wiley Interscience, New York, London, Sydney, Tornoto, 1972), chap. 7, pp. 313–314.
Prototype Generator
aflow --proto=AB_oP4_51_e_f --params=$a,b/a,c/a,z_{1},z_{2}$