Metastable Au$_{5}$Zn$_{3}$ Structure: A5B3_oP16_26_a2c_a2b-001
| Prototype | Au$_{5}$Zn$_{3}$ |
| AFLOW prototype label | A5B3_oP16_26_a2c_a2b-001 |
| ICSD | 58629 |
| Pearson symbol | oP16 |
| Space group number | 26 |
| Space group symbol | $Pmc2_1$ |
| AFLOW prototype command |
aflow --proto=A5B3_oP16_26_a2c_a2b-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$ |
- (Iwasaki, 1965) found this structure to form metastably between 300° and 600°. Below 300° it transforms into the ordered Au$_{5}$Zn$_{3}$ structure.
- There is considerable disorder on most of the sites in this system, to wit:
- Site Au-I (2a) is 60% gold and 40 % zinc,
- Site Zn-I (2c) is 20% gold and 80 % zinc,
- Site Zn-II (2b) is 10% gold and 90 % zinc,
- Site Zn-III (2b) is 40% gold and 60 % zinc,
- Site Au-II (4c) is 85% gold and 15 % zinc, and
- Site Au-III (4c) is 100% gold with no zinc.
- We label each site by its dominant component.
- (Iwaskai, 1965) gave the lattice constants in kX units. We used the conversion factor 1 kX = 1.00202Å. (Wood, 1947).
- The ICSD entry is from (Iwasaki, 1962).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2a) | Au I |
| $\mathbf{B_{2}}$ | = | $- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Au I |
| $\mathbf{B_{3}}$ | = | $y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2a) | Zn I |
| $\mathbf{B_{4}}$ | = | $- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | Zn I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2b) | Zn II |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Zn II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2b) | Zn III |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | Zn III |
| $\mathbf{B_{9}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | Au II |
| $\mathbf{B_{10}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Au II |
| $\mathbf{B_{11}}$ | = | $x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Au II |
| $\mathbf{B_{12}}$ | = | $- x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4c) | Au II |
| $\mathbf{B_{13}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4c) | Au III |
| $\mathbf{B_{14}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Au III |
| $\mathbf{B_{15}}$ | = | $x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4c) | Au III |
| $\mathbf{B_{16}}$ | = | $- x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4c) | Au III |
References
- H. Iwasaki, The Crystal Structure and the Phase Transition of a Metastable Phase in the Au-37.8% Zn Alloy, J. Phys. Soc. Jpn. 20, 2129–2140 (1965), doi:10.1143/JPSJ.20.2129.
- E. A. Wood, The Conversion Factor for kX Units to Angström Units, J. Appl. Phys. 18, 929–930 (1947), doi:10.1063/1.1697570.
- H. Iwasaki, Study on the Ordered Phases with Long Period in the Gold-Zinc Alloy System II. Structure Analysis of Au$_{3}$Zn[R$_{1}$], Au$_{3}$Zn[R$_{2}$] and Au$_{3}+$Zn, J. Phys. Soc. Jpn. 17, 1620–1633 (1962), doi:10.1143/JPSJ.17.1620.
Prototype Generator
aflow --proto=A5B3_oP16_26_a2c_a2b --params=$a,b/a,c/a,y_{1},z_{1},y_{2},z_{2},y_{3},z_{3},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6}$