Acta Metallurgica Sinica (English Letters) ›› 2015, Vol. 28 ›› Issue (11): 1326-1331.DOI: 10.1007/s40195-015-0329-2
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Na Wang1(), Wei-Bing Zhang2, Bi-Yu Tang3, En-Jie He1, Mao-Lian Zhang1
Received:
2015-06-26
Revised:
2015-09-23
Online:
2015-11-12
Published:
2015-11-20
Na Wang, Wei-Bing Zhang, Bi-Yu Tang, En-Jie He, Mao-Lian Zhang. First-Principle Calculations of the MgYA4 (A = Co and Ni) Phase with AuBe5-Type Structure[J]. Acta Metallurgica Sinica (English Letters), 2015, 28(11): 1326-1331.
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Fig. 1 Crystal structure of AuBe5-type for MgYNi4 (MgYCo4) phase, where the yellow, red and blue balls represent Mg, Y and Ni (Co) atoms, respectively
Phase | Multiplicity, Wyckoff letter | x | y | z | |
---|---|---|---|---|---|
MgYCo4 | Y, 4a | Relaxed | 0 | 0 | 0 |
Expt. | 0 | 0 | 0 | ||
Mg, 4c | Relaxed | 0.2500 | 0.2500 | 0.2500 | |
Expt. | 0.2500 | 0.2500 | 0.2500 | ||
Ni, 16e | Relaxed | 0.6243 | 0.6243 | 0.6243 | |
Expt. | 0.6250 | 0.6250 | 0.6250 | ||
MgYNi4 | Y, 4a | Relaxed | 0 | 0 | 0 |
Expt. | 0 | 0 | 0 | ||
Mg, 4c | Relaxed | 0.2500 | 0.2500 | 0.2500 | |
Expt. | 0.2500 | 0.2500 | 0.2500 | ||
Co, 16e | Relaxed | 0.6237 | 0.6237 | 0.6237 | |
Expt. | 0.6250 | 0.6250 | 0.6250 |
Table 1 Calculated crystallographic parameters of MgYCo4 and MgYNi4 phases, and compared with experimental data, the coordinates are (0, 0, 0) + (0.0, 0.5, 0.5) + (0.5, 0.0, 0.5) + (0.5, 0.5, 0.0)
Phase | Multiplicity, Wyckoff letter | x | y | z | |
---|---|---|---|---|---|
MgYCo4 | Y, 4a | Relaxed | 0 | 0 | 0 |
Expt. | 0 | 0 | 0 | ||
Mg, 4c | Relaxed | 0.2500 | 0.2500 | 0.2500 | |
Expt. | 0.2500 | 0.2500 | 0.2500 | ||
Ni, 16e | Relaxed | 0.6243 | 0.6243 | 0.6243 | |
Expt. | 0.6250 | 0.6250 | 0.6250 | ||
MgYNi4 | Y, 4a | Relaxed | 0 | 0 | 0 |
Expt. | 0 | 0 | 0 | ||
Mg, 4c | Relaxed | 0.2500 | 0.2500 | 0.2500 | |
Expt. | 0.2500 | 0.2500 | 0.2500 | ||
Co, 16e | Relaxed | 0.6237 | 0.6237 | 0.6237 | |
Expt. | 0.6250 | 0.6250 | 0.6250 |
Phase | a (Å) | V 0 (Å3) | B 0 (GPa) | E c (eV/atom) | ∆H (eV/atom) | M (µB/cell) | |
---|---|---|---|---|---|---|---|
MgYCo4 | Present. | 7.02 | 346 | 127 | -4.82 | -0.13 | 19.65 |
Expt [ | 7.07 | 353 | - | - | - | - | |
MgYNi4 | Present. | 7.01 | 344 | 129 | -4.62 | -0.39 | 0 |
Expt [ | 7.01 | 344 | - | - | - | - |
Table 2 Structural parameters for MgYNi4 and MgYCo4 phases
Phase | a (Å) | V 0 (Å3) | B 0 (GPa) | E c (eV/atom) | ∆H (eV/atom) | M (µB/cell) | |
---|---|---|---|---|---|---|---|
MgYCo4 | Present. | 7.02 | 346 | 127 | -4.82 | -0.13 | 19.65 |
Expt [ | 7.07 | 353 | - | - | - | - | |
MgYNi4 | Present. | 7.01 | 344 | 129 | -4.62 | -0.39 | 0 |
Expt [ | 7.01 | 344 | - | - | - | - |
Strain | Parameters (unlisted e i = 0) | ∆E/V 0-0 (δ 2 ) |
---|---|---|
\(\varepsilon^{(1)}\) | \(e_{1} = e_{2} = \delta ,\;e_{3} = { [}(1 + \delta )^{ - 2} - 1 ]\) | \(3(C_{11} - C_{12} )\delta^{2}\) |
\(\varepsilon^{(2)}\) | \(e_{1} = e_{2} = e_{3} = \delta\) | \(3(C_{11} + 2C_{12} )\delta^{2} /2\) |
\(\varepsilon^{(3)}\) | \(e_{6} = \delta /2,\quad e_{3} = \delta^{2} (1 - \delta )^{ - 1}\) | \(\left( {C_{44} \delta^{2} } \right)/2\) |
Table 3 Three kinds of strain used for unit cell in present work
Strain | Parameters (unlisted e i = 0) | ∆E/V 0-0 (δ 2 ) |
---|---|---|
\(\varepsilon^{(1)}\) | \(e_{1} = e_{2} = \delta ,\;e_{3} = { [}(1 + \delta )^{ - 2} - 1 ]\) | \(3(C_{11} - C_{12} )\delta^{2}\) |
\(\varepsilon^{(2)}\) | \(e_{1} = e_{2} = e_{3} = \delta\) | \(3(C_{11} + 2C_{12} )\delta^{2} /2\) |
\(\varepsilon^{(3)}\) | \(e_{6} = \delta /2,\quad e_{3} = \delta^{2} (1 - \delta )^{ - 1}\) | \(\left( {C_{44} \delta^{2} } \right)/2\) |
Phase | C 11 | C 12 | C 44 | B | G | G/B | E | ν |
---|---|---|---|---|---|---|---|---|
MgYCo4 | 158 | 104 | 48 | 122 | 38 | 0.31 | 103 | 0.36 |
MgYNi4 | 184 | 91 | 65 | 122 | 56 | 0.46 | 146 | 0.30 |
Table 4 Single-crystal and polycrystalline elastic constants
Phase | C 11 | C 12 | C 44 | B | G | G/B | E | ν |
---|---|---|---|---|---|---|---|---|
MgYCo4 | 158 | 104 | 48 | 122 | 38 | 0.31 | 103 | 0.36 |
MgYNi4 | 184 | 91 | 65 | 122 | 56 | 0.46 | 146 | 0.30 |
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