J. Mater. Sci. Technol. ›› 2018, Vol. 34 ›› Issue (9): 1592-1601.DOI: 10.1016/j.jmst.2018.01.004
• Orginal Article • Previous Articles Next Articles
Qun Luoa, Kang Lia, Qian Liabc*()
Received:
2017-07-19
Revised:
2017-11-15
Accepted:
2017-12-06
Online:
2018-09-20
Published:
2018-09-25
Contact:
Li Qian
Qun Luo, Kang Li, Qian Li. Thermodynamic investigation of phase equilibria in Al-Si-V system[J]. J. Mater. Sci. Technol., 2018, 34(9): 1592-1601.
Fig. 2. SEM images of samples #1 and #2: (a) sample #1 annealed at 500 °C for 1080 h, (b) sample #1 annealed at 500 °C for 3000 h, (c) sample #1 annealed at 654 °C for 480 h and then annealed at 500 °C for 840 h, (d) sample #2 annealed at 500 °C for 1080 h, (e) sample #2 annealed at 500 °C for 3000 h, and (f) sample #2 annealed at 654 °C for 480 h and then annealed at 500 °C for 840 h.
Samples | As cast | 654 °C/480 h → 500 °C/840 h | 600 °C/144-1080 h | 654 °C/72-720 h | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
XRD | EDS | XRD | EDS | XRD | EDS | XRD | EDS | |||||||||
Al | Si | V | Al | Si | V | Al | Si | V | Al | Si | V | |||||
#1 Al58.5Si18.3V23.2 | Fcc(Al) | 98.7 | 1.1 | 0.2 | Al3V | 72.7 | 2.0 | 25.3 | Al3V | 72.8 | 2.8 | 24.4 | Al3V | 72.9 | 1.6 | 25.4 |
Al45V7 | 83.2 | 3.5 | 13.3 | Al45V7 | 83.3 | 2.7 | 14.0 | Al45V7 | 82.8 | 3.3 | 13.9 | Al45V7 | 83.1 | 3.5 | 13.4 | |
Si3V5 | 1.8 | 38.2 | 60.0 | Si2V | 8.9 | 58.9 | 32.2 | Si2V | 7.9 | 59.4 | 32.7 | Si2V | 9.0 | 59.1 | 31.9 | |
#2 Al64.7Si20.2V15.1 | Fcc(Al) | 98.6 | 1.2 | 0.2 | Fcc(Al) | 99.2 | 0.3 | 0.5 | Fcc(Al) | 99.4 | 0.4 | 0.2 | Fcc(Al) | 98.8 | 0.7 | 0.5 |
Al45V7 | 81.5 | 4.5 | 14.1 | Al45V7 | 82.5 | 3.9 | 13.6 | Al45V7 | 82.0 | 4.3 | 13.7 | Al45V7 | 82.1 | 4.1 | 13.7 | |
Si3V5 | 5.3 | 37.3 | 57.4 | Si2V | 7.5 | 62.3 | 30.2 | Si2V | 4.8 | 63.2 | 32.0 | Si2V | 7.0 | 60.7 | 32.3 | |
Si2V | 9.0 | 58.3 | 32.7 | / | / | / | / | / | / | / | / | / | / | / | / | |
#3 Al73.0Si18.3V8.7 | Fcc(Al) | 97.7 | 1.8 | 0.5 | Fcc(Al) | 99.1 | 0.8 | 0.1 | Fcc(Al) | 98.5 | 1.4 | 0.1 | L | 98.8 | 0.8 | 0.4 |
Si2V | 11.5 | 56.1 | 32.4 | Si2V | 6.9 | 62.6 | 30.5 | Si2V | 6.7 | 60.7 | 32.6 | Al45V7 | 82.4 | 4.0 | 13.6 | |
/ | / | / | / | / | / | / | / | / | / | / | / | Si2V | 7.8 | 59.7 | 32.5 | |
#4 Al29.2Si57.6V13.2 | Fcc(Al) | 81.6 | 18.3 | 0.1 | Fcc(Al) | 99.0 | 0.8 | 0.2 | L | 85.1 | 14.7 | 0.2 | L | 97.5 | 2.5 | 0.0 |
Si | 0.2 | 99.6 | 0.2 | Si | 0.0 | 100.0 | 0.0 | Si | 0.1 | 99.8 | 0.1 | Si | 0.5 | 99.4 | 0.1 | |
Si2V | 2.4 | 65.3 | 32.3 | Si2V | 5.8 | 63.8 | 30.4 | Si2V | 2.6 | 64.5 | 32.9 | Si2V | 2.6 | 64.0 | 33.4 |
Table 1 XRD and EDS (in at.%) results of cast samples and annealed samples at 654, 600 and 500 °C.
Samples | As cast | 654 °C/480 h → 500 °C/840 h | 600 °C/144-1080 h | 654 °C/72-720 h | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
XRD | EDS | XRD | EDS | XRD | EDS | XRD | EDS | |||||||||
Al | Si | V | Al | Si | V | Al | Si | V | Al | Si | V | |||||
#1 Al58.5Si18.3V23.2 | Fcc(Al) | 98.7 | 1.1 | 0.2 | Al3V | 72.7 | 2.0 | 25.3 | Al3V | 72.8 | 2.8 | 24.4 | Al3V | 72.9 | 1.6 | 25.4 |
Al45V7 | 83.2 | 3.5 | 13.3 | Al45V7 | 83.3 | 2.7 | 14.0 | Al45V7 | 82.8 | 3.3 | 13.9 | Al45V7 | 83.1 | 3.5 | 13.4 | |
Si3V5 | 1.8 | 38.2 | 60.0 | Si2V | 8.9 | 58.9 | 32.2 | Si2V | 7.9 | 59.4 | 32.7 | Si2V | 9.0 | 59.1 | 31.9 | |
#2 Al64.7Si20.2V15.1 | Fcc(Al) | 98.6 | 1.2 | 0.2 | Fcc(Al) | 99.2 | 0.3 | 0.5 | Fcc(Al) | 99.4 | 0.4 | 0.2 | Fcc(Al) | 98.8 | 0.7 | 0.5 |
Al45V7 | 81.5 | 4.5 | 14.1 | Al45V7 | 82.5 | 3.9 | 13.6 | Al45V7 | 82.0 | 4.3 | 13.7 | Al45V7 | 82.1 | 4.1 | 13.7 | |
Si3V5 | 5.3 | 37.3 | 57.4 | Si2V | 7.5 | 62.3 | 30.2 | Si2V | 4.8 | 63.2 | 32.0 | Si2V | 7.0 | 60.7 | 32.3 | |
Si2V | 9.0 | 58.3 | 32.7 | / | / | / | / | / | / | / | / | / | / | / | / | |
#3 Al73.0Si18.3V8.7 | Fcc(Al) | 97.7 | 1.8 | 0.5 | Fcc(Al) | 99.1 | 0.8 | 0.1 | Fcc(Al) | 98.5 | 1.4 | 0.1 | L | 98.8 | 0.8 | 0.4 |
Si2V | 11.5 | 56.1 | 32.4 | Si2V | 6.9 | 62.6 | 30.5 | Si2V | 6.7 | 60.7 | 32.6 | Al45V7 | 82.4 | 4.0 | 13.6 | |
/ | / | / | / | / | / | / | / | / | / | / | / | Si2V | 7.8 | 59.7 | 32.5 | |
#4 Al29.2Si57.6V13.2 | Fcc(Al) | 81.6 | 18.3 | 0.1 | Fcc(Al) | 99.0 | 0.8 | 0.2 | L | 85.1 | 14.7 | 0.2 | L | 97.5 | 2.5 | 0.0 |
Si | 0.2 | 99.6 | 0.2 | Si | 0.0 | 100.0 | 0.0 | Si | 0.1 | 99.8 | 0.1 | Si | 0.5 | 99.4 | 0.1 | |
Si2V | 2.4 | 65.3 | 32.3 | Si2V | 5.8 | 63.8 | 30.4 | Si2V | 2.6 | 64.5 | 32.9 | Si2V | 2.6 | 64.0 | 33.4 |
Fig. 5. (a) DSC curve of alloys #1-#4 annealed at 500 °C for 840 h with the heating rate of 5 °C/min, (b) the DSC result with different heating rate of sample #1, and (c) the XRD patterns of sample #1 annealed at different temperature.
Samples | 760 °C/144 h | 850 °C/43 h | 930 °C/40 h | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
XRD | EDS | XRD | EDS | XRD | EDS | |||||||
Al | Si | V | Al | Si | V | Al | Si | V | ||||
#1 Al58.5Si18.3V23.2 | Al3V | 72.2 | 2.8 | 25.0 | Al3V | 72.9 | 1.9 | 25.2 | Al3V | 72.7 | 2.4 | 24.9 |
L | 97.9 | 1.0 | 1.1 | L | 96.2 | 2.3 | 1.5 | L | 95.5 | 1.9 | 2.6 | |
Si2V | 10.7 | 56.9 | 32.4 | Si2V | 9.1 | 58.5 | 32.4 | τ | 19.6 | 47.5 | 32.9 |
Table 2 XRD and EDS (in at.%) results of samples #1 annealed at 760, 850 and 930 °C.
Samples | 760 °C/144 h | 850 °C/43 h | 930 °C/40 h | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
XRD | EDS | XRD | EDS | XRD | EDS | |||||||
Al | Si | V | Al | Si | V | Al | Si | V | ||||
#1 Al58.5Si18.3V23.2 | Al3V | 72.2 | 2.8 | 25.0 | Al3V | 72.9 | 1.9 | 25.2 | Al3V | 72.7 | 2.4 | 24.9 |
L | 97.9 | 1.0 | 1.1 | L | 96.2 | 2.3 | 1.5 | L | 95.5 | 1.9 | 2.6 | |
Si2V | 10.7 | 56.9 | 32.4 | Si2V | 9.1 | 58.5 | 32.4 | τ | 19.6 | 47.5 | 32.9 |
Phases | Models and end-members | a (?) | b (?) | c (?) | ΔfH (kJ/mol atom) | Temperature (K) | Ref. |
---|---|---|---|---|---|---|---|
Al45V7 | (Al,Si)0.865385(V)0.134615 | ||||||
Al: V | 11.105 | 7.611 | 11.084 | -13.94 | 298 | DFT [ | |
-12.9 | 298 | Calphad [ | |||||
Si: V | 10.265 | 11.310 | 3.4272 | 0 | This work | ||
Al8V5 | (Al,Si)0.461539(Al,V,Si)0.153846(V,Al) 0.230769(V)0.153846 | ||||||
Al: Al: Al: V | 9.343 | -12.65 | 298 | DFT [ | |||
Al: V: Al: V | 9.295 | -19.39 | 298 | DFT [ | |||
Al: Al: V: V | 9.165 | -18.19 | 298 | DFT [ | |||
-34 | 298 | Exp [ | |||||
Al: V: V: V | 9.137 | -18.18 | 298 | DFT [ | |||
Al: Si: V: V | 9.145 | -19.030 | 0 | This work | |||
Si: Al: V: V | 8.902 | -22.557 | 0 | This work | |||
Si: Si: V: V | 8.834 | -20.269 | 0 | This work | |||
Al3V | (Al,Si)0.75(V)0.25 | ||||||
Al: V | 3.769 | 8.313 | -26.91 | 298 | DFT [ | ||
-27.8 | 298 | Exp [ | |||||
Si: V | 3.641 | 7.921 | 1.194 | 0 | This work | ||
Si3V5 | (Si,Al)0.125(Si,Al)0.25(V)0.125(V)0.5 | ||||||
Si: Si: V: V | 9.383 | 4.760 | -55.4 | 0 | Calphad [ | ||
9.395 | 4.731 | -57.6 | 0 | DFT [ | |||
-59.0 ± 2 | 298 | Exp [ | |||||
Al: Si: V: V | 9.490 | 4.860 | -43.584 | 0 | This work | ||
Si: Al: V: V | 9.864 | 4.682 | -17.465 | 0 | This work | ||
Al: Al: V: V | 9.864 | 4.812 | -10.955 | 0 | This work | ||
Si2V | (Si,Al)0.6666(V)0.3334 | ||||||
Si: V | 4.573 | 6.374 | -54.1 | 0 | Calphad [ | ||
4.563 | 6.364 | -47.0 | 0 | DFT [ | |||
4.578 | 6.367 | -54.674 | 0 | This work | |||
-44.4 ± 1 | 298 | Exp [ | |||||
Al: V | 4.872 | 6.736 | -8.285 | 0 | This work | ||
τ | (Si,Al)0.6666(V)0.3334 | ||||||
Si: V | 4.551 | 8.039 | 8.426 | -52.409 | 0 | This work | |
Al: V | 4.961 | 8.284 | 8.961 | -10.083 | 0 | This work |
Table 3 Calculated enthalpies of formation of Al-Si-V compounds.
Phases | Models and end-members | a (?) | b (?) | c (?) | ΔfH (kJ/mol atom) | Temperature (K) | Ref. |
---|---|---|---|---|---|---|---|
Al45V7 | (Al,Si)0.865385(V)0.134615 | ||||||
Al: V | 11.105 | 7.611 | 11.084 | -13.94 | 298 | DFT [ | |
-12.9 | 298 | Calphad [ | |||||
Si: V | 10.265 | 11.310 | 3.4272 | 0 | This work | ||
Al8V5 | (Al,Si)0.461539(Al,V,Si)0.153846(V,Al) 0.230769(V)0.153846 | ||||||
Al: Al: Al: V | 9.343 | -12.65 | 298 | DFT [ | |||
Al: V: Al: V | 9.295 | -19.39 | 298 | DFT [ | |||
Al: Al: V: V | 9.165 | -18.19 | 298 | DFT [ | |||
-34 | 298 | Exp [ | |||||
Al: V: V: V | 9.137 | -18.18 | 298 | DFT [ | |||
Al: Si: V: V | 9.145 | -19.030 | 0 | This work | |||
Si: Al: V: V | 8.902 | -22.557 | 0 | This work | |||
Si: Si: V: V | 8.834 | -20.269 | 0 | This work | |||
Al3V | (Al,Si)0.75(V)0.25 | ||||||
Al: V | 3.769 | 8.313 | -26.91 | 298 | DFT [ | ||
-27.8 | 298 | Exp [ | |||||
Si: V | 3.641 | 7.921 | 1.194 | 0 | This work | ||
Si3V5 | (Si,Al)0.125(Si,Al)0.25(V)0.125(V)0.5 | ||||||
Si: Si: V: V | 9.383 | 4.760 | -55.4 | 0 | Calphad [ | ||
9.395 | 4.731 | -57.6 | 0 | DFT [ | |||
-59.0 ± 2 | 298 | Exp [ | |||||
Al: Si: V: V | 9.490 | 4.860 | -43.584 | 0 | This work | ||
Si: Al: V: V | 9.864 | 4.682 | -17.465 | 0 | This work | ||
Al: Al: V: V | 9.864 | 4.812 | -10.955 | 0 | This work | ||
Si2V | (Si,Al)0.6666(V)0.3334 | ||||||
Si: V | 4.573 | 6.374 | -54.1 | 0 | Calphad [ | ||
4.563 | 6.364 | -47.0 | 0 | DFT [ | |||
4.578 | 6.367 | -54.674 | 0 | This work | |||
-44.4 ± 1 | 298 | Exp [ | |||||
Al: V | 4.872 | 6.736 | -8.285 | 0 | This work | ||
τ | (Si,Al)0.6666(V)0.3334 | ||||||
Si: V | 4.551 | 8.039 | 8.426 | -52.409 | 0 | This work | |
Al: V | 4.961 | 8.284 | 8.961 | -10.083 | 0 | This work |
Fig. 6. (a) Calculated enthalpy of mixing of liquid for Si-V system at 1702 °C (2000 K) with the reference states of liquid(Si) and liquid(V), (b) the calculated enthalpy of formation of Si-V system at 25 °C with the reference states of Diamond(Si) and Bcc(V), (c) the calculated phase diagram of Si-V system.
Fig. 7. Calculated isothermal sections of Al-Si-V system at (a) 500 °C, (b)600 °C, (c) 654 °C, (d) 850 °C, and the vertical sections of Al-Si-V system at (e) 10 at.% and (f) 20 at.%.
Invariant reaction | Calculation (°C) | DSC results (°C) |
---|---|---|
L+Si2V → fcc(Al)+Si | 577 | 570-572 |
L+Al45V7 → fcc(Al)+Si2V | 642 | 620-639 |
L+Al21V2 → Al45V7+fcc(Al) | 652 | / |
L+Al3V → Al23V4+Al45V7 | 735 | / |
L+Al3V+Si2V → Al45V7 | 743 | 731-750 |
L+τ → Al3V+Si2V | 868 | 865-874 |
L+Si3V5 → Al3V+τ | 974 | 962-979 |
Table 4 Invariant reactions between 500 and 1100 °C of the Al-Si-V system.
Invariant reaction | Calculation (°C) | DSC results (°C) |
---|---|---|
L+Si2V → fcc(Al)+Si | 577 | 570-572 |
L+Al45V7 → fcc(Al)+Si2V | 642 | 620-639 |
L+Al21V2 → Al45V7+fcc(Al) | 652 | / |
L+Al3V → Al23V4+Al45V7 | 735 | / |
L+Al3V+Si2V → Al45V7 | 743 | 731-750 |
L+τ → Al3V+Si2V | 868 | 865-874 |
L+Si3V5 → Al3V+τ | 974 | 962-979 |
Parameters | Ref. |
---|---|
Liquid: substitutional-solution, (Al, Si, V) | |
$^{0}L^{L}_{Al,Si}=-11655.93-0.92934T$ | [ |
$^{1}L^{L}_{Al,Si}=-2873.45+0.2945T$ | [ |
$^{2}L^{L}_{Al,Si}=2520$ | [ |
$^{0}L^{L}_{Al,V}=-78540+10.07T$ | [ |
$^{1}L^{L}_{Al,V}=17594$ | [ |
$^{0}L^{L}_{Si,V}=-198326.8+44.563T$ | This work |
$^{1}L^{L}_{Si,V}=8265.4$ | This work |
$^{2}L^{L}_{Si,V}=43546.5$ | This work |
fcc: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Fcc}_{Al,Si}=-3423.91-0.09584T$ | [ |
$^{0}L^{Fcc}_{Al,V}=-64732$ | [ |
Hcp: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Hcp}_{Al,V}=-95000+20T$ | [ |
$^{1}L^{Hcp}_{Al,V}=-6000$ | [ |
Bcc: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Bcc}_{Al,V}=-79106+0.654T$ | [ |
$^{1}L^{Bcc}_{Al,V}=6645$ | [ |
$^{0}L^{Bcc}_{Al,V}=-210573.1+61.02211T$ | [ |
Diamond_Si: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Diamond}_{Al,Si}=111417.7-46.1392T$ | [ |
Al21V2: stoichiometric, (Al)0.913043(V)0.086957 | |
$G^{Al_{21}V_{2}}_{Al:V}=0.913043°G^{Fcc}_{Al}+0.086957°G^{Bcc}_{V}-10729+2.13T$ | [ |
Al23V4: stoichiometric, (Al)0.851852(V)0.148148 | |
$G^{Al_{23}V_{4}}_{Al:V}=0.851852°G^{Fcc}_{Al}+0.148148°G^{Bcc}_{V}-18028+3.68T$ | [ |
Al8V5: CEF, (Al,Si)0.461539(Al,V,Si)0.153846(Al,V)0.230769(V)0.153846 | |
$G^{Al_{8}V_{5}}_{Al:Al:Al:V}=0.846154°G^{Fcc}_{Al}+0.153846°G^{Bcc}_{V}-12854$ | [ |
$G^{Al_{8}V_{5}}_{Al:V:Al:V}=0.692308°G^{Fcc}_{Al}+0.307692°G^{Bcc}_{V}-19309$ | [ |
$G^{Al_{8}V_{5}}_{Al:Al:V:V}=0.615385°G^{Fcc}_{Al}+0.384615°G^{Bcc}_{V}-19309$ | [ |
$G^{Al_{8}V_{5}}_{Al:V:V:V}=0.461538°G^{Fcc}_{Al}+0.538462°G^{Bcc}_{V}-18258$ | [ |
$G^{Al_{8}V_{5}}_{Si:V:V:V}=0.461538°G^{Diamond}_{Si}+0.153846°G^{Fcc}_{Al}+0.384615°G^{Bcc}_{V}-22557$ | This work |
$G^{Al_{8}V_{5}}_{Al:Si:V:V}=0.461538°G^{Fcc}_{Al} +0.153846°G^{Diamond}_{Si}+0.384615°G^{Bcc}_{V}-19030$ | This work |
$G^{Al_{8}V_{5}}_{Si:Si:V:V}=0.615385°G^{Diamond}_{Si}+0.384615°G^{Bcc}_{V}-20269$ | This work |
$^{0}L^{Al_{8}V_{5}}_{Al:Al,Si:V:V}=-11040.86-9T$ | This work |
Si5V6: stoichiometric, (Si)0.454545(V)0.545455 | |
$G^{Si_{5}V_{6}}_{Si:V}=0.454545°G^{Diamond}_{Si}+0.545455°G^{Bcc}_{V}-55198.7+6.114T$ | This work |
SiV3: CEF, (V, Si)0.75(V,Si)0.25 | |
$G^{SiV_{3}}_{V:V}=°G^{Bcc}_{V}+5000$ | [ |
$G^{SiV_{3}}_{Si:Si}=°G^{Diamond}_{Si}+52000-20T$ | [ |
$G^{SiV_{3}}_{V:Si}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}-45534.8+6.47189T$ | This work |
$G^{SiV_{3}}_{Si:V}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}-54274.8-6.47189T$ | [ |
$^{0}L^{SiV_{3}}_{V,Si:V}=-38908.4$ | [ |
$^{0}L^{SiV_{3}}_{V,Si:Si}=-38908.4$ | [ |
$^{0}L^{SiV_{3}}_{V:V,Si}=16043.1-6.91487T$ | [ |
$^{0}L^{SiV_{3}}_{Si:V,Si}=16043.1-6.91487T$ | [ |
Si3V5: CEF, (Si,Al)0.125(Si,Al)0.25(V)0.125(V)0.5 | |
$G^{Si_{3}V_{5}}_{Si:Si:V:V}=0.375°G^{Diamond}_{Si}+0.625°G^{Bcc}_{V}-58417.1+7.07T$ | This work |
$G^{Si_{3}V_{5}}_{Al:Si:V:V}=0.125°G^{Fcc}_{Al}+0.25°G^{Diamond}_{Si}+0.625°G^{Bcc}_{V}-43584+4T$ | This work |
$G^{Si_{3}V_{5}}_{Si:Al:V:V}=0.125°G^{Diamond}_{Si}+0.25°G^{Fcc}_{Al}+0.625°G^{Bcc}_{V}-17465$ | This work |
$G^{Si_{3}V_{5}}_{Al:Al:V:V}=0.375°G^{Fcc}_{Al}+0.625°G{Bcc}_{V}-10955.2$ | This work |
$L^{Si_{3}V_{5}}_{Si,Al:Si:V:V}=-35370-8.56T$ | This work |
Si2V: CEF, (Si,Al)0.6666(V)0.3334 | |
$G^{Si_{2}V}_{Si:V}=-55302.8+136.13732T-226T ln T-0.0025T^{2}+110000/T$ | This work |
$G^{Si_{2}V}_{Al:V}=0.6666°G^{Fcc}_{Al}+0.3334°G^{Bcc}_{V}-8285$ | This work |
$^{1}L^{Si_{2}V}_{Al:V}=-26000$ | This work |
Al45V7: CEF, (Al,Si)0.865385(V)0.134615 | |
$G^{Al_{45}V_{7}}_{Al:V}=0.865385°G^{Fcc}_{Al}+0.134615°G^{Bcc}_{V}-16503+3.39T$ | [ |
$G^{Al_{45}V_{7}}_{Si:V}=0.865385°G^{Diamond}_{Si}+0.134615°G^{Bcc}_{V}+3427$ | This work |
$^{0}L^{Al_{45}V_{7}}_{Al,Si:V}=-31207.14+21.43T$ | This work |
Al3V: CEF, (Al,V,Si)0.75(V,Al)0.25 | |
$G^{Al_{3}V}_{Al:Al}=°G^{Fcc}_{Al}+20000$ | [ |
$G^{Al_{3}V}_{V:Al}=0.75°G^{Bcc}_{V}+0.25°G^{Fcc}_{Al}$ | [ |
$G^{Al_{3}V}_{Al:V}=0.75°G^{Fcc}_{Al}+0.25°G^{Bcc}_{V}-28114+4.52T$ | [ |
$G^{Al_{3}}_{V:V}=°G^{Bcc}_{V}+20000$ | [ |
$G^{Al_{3}V}_{Si:V}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}+1194$ | This work |
$^{0}L^{Al_{3}V}_{Al,Si:V}=-46656.25+31.25T$ | This work |
Si2V: CEF, (Si,Al)0.6666(V)0.3334 | |
$G^{Tau}_{Al:V}=0.6666° G^{Fcc}_{Al}+0.3334° G^{Bcc}_{V}-10083$ | This work |
$G^{Tau}_{Si:V}=G^{Si_{2}V}_{Si:V}+2200$ | This work |
$\frac{1}{C^{2}}=[\frac{2}{q\varepsilon\varepsilon _{0}N_{D}A^{2}}][E-E_{fb}-\frac{kT}{q}]$ | This work |
Parameters | Ref. |
---|---|
Liquid: substitutional-solution, (Al, Si, V) | |
$^{0}L^{L}_{Al,Si}=-11655.93-0.92934T$ | [ |
$^{1}L^{L}_{Al,Si}=-2873.45+0.2945T$ | [ |
$^{2}L^{L}_{Al,Si}=2520$ | [ |
$^{0}L^{L}_{Al,V}=-78540+10.07T$ | [ |
$^{1}L^{L}_{Al,V}=17594$ | [ |
$^{0}L^{L}_{Si,V}=-198326.8+44.563T$ | This work |
$^{1}L^{L}_{Si,V}=8265.4$ | This work |
$^{2}L^{L}_{Si,V}=43546.5$ | This work |
fcc: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Fcc}_{Al,Si}=-3423.91-0.09584T$ | [ |
$^{0}L^{Fcc}_{Al,V}=-64732$ | [ |
Hcp: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Hcp}_{Al,V}=-95000+20T$ | [ |
$^{1}L^{Hcp}_{Al,V}=-6000$ | [ |
Bcc: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Bcc}_{Al,V}=-79106+0.654T$ | [ |
$^{1}L^{Bcc}_{Al,V}=6645$ | [ |
$^{0}L^{Bcc}_{Al,V}=-210573.1+61.02211T$ | [ |
Diamond_Si: substitutional-solution, (Al, Si, V) | |
$^{0}L^{Diamond}_{Al,Si}=111417.7-46.1392T$ | [ |
Al21V2: stoichiometric, (Al)0.913043(V)0.086957 | |
$G^{Al_{21}V_{2}}_{Al:V}=0.913043°G^{Fcc}_{Al}+0.086957°G^{Bcc}_{V}-10729+2.13T$ | [ |
Al23V4: stoichiometric, (Al)0.851852(V)0.148148 | |
$G^{Al_{23}V_{4}}_{Al:V}=0.851852°G^{Fcc}_{Al}+0.148148°G^{Bcc}_{V}-18028+3.68T$ | [ |
Al8V5: CEF, (Al,Si)0.461539(Al,V,Si)0.153846(Al,V)0.230769(V)0.153846 | |
$G^{Al_{8}V_{5}}_{Al:Al:Al:V}=0.846154°G^{Fcc}_{Al}+0.153846°G^{Bcc}_{V}-12854$ | [ |
$G^{Al_{8}V_{5}}_{Al:V:Al:V}=0.692308°G^{Fcc}_{Al}+0.307692°G^{Bcc}_{V}-19309$ | [ |
$G^{Al_{8}V_{5}}_{Al:Al:V:V}=0.615385°G^{Fcc}_{Al}+0.384615°G^{Bcc}_{V}-19309$ | [ |
$G^{Al_{8}V_{5}}_{Al:V:V:V}=0.461538°G^{Fcc}_{Al}+0.538462°G^{Bcc}_{V}-18258$ | [ |
$G^{Al_{8}V_{5}}_{Si:V:V:V}=0.461538°G^{Diamond}_{Si}+0.153846°G^{Fcc}_{Al}+0.384615°G^{Bcc}_{V}-22557$ | This work |
$G^{Al_{8}V_{5}}_{Al:Si:V:V}=0.461538°G^{Fcc}_{Al} +0.153846°G^{Diamond}_{Si}+0.384615°G^{Bcc}_{V}-19030$ | This work |
$G^{Al_{8}V_{5}}_{Si:Si:V:V}=0.615385°G^{Diamond}_{Si}+0.384615°G^{Bcc}_{V}-20269$ | This work |
$^{0}L^{Al_{8}V_{5}}_{Al:Al,Si:V:V}=-11040.86-9T$ | This work |
Si5V6: stoichiometric, (Si)0.454545(V)0.545455 | |
$G^{Si_{5}V_{6}}_{Si:V}=0.454545°G^{Diamond}_{Si}+0.545455°G^{Bcc}_{V}-55198.7+6.114T$ | This work |
SiV3: CEF, (V, Si)0.75(V,Si)0.25 | |
$G^{SiV_{3}}_{V:V}=°G^{Bcc}_{V}+5000$ | [ |
$G^{SiV_{3}}_{Si:Si}=°G^{Diamond}_{Si}+52000-20T$ | [ |
$G^{SiV_{3}}_{V:Si}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}-45534.8+6.47189T$ | This work |
$G^{SiV_{3}}_{Si:V}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}-54274.8-6.47189T$ | [ |
$^{0}L^{SiV_{3}}_{V,Si:V}=-38908.4$ | [ |
$^{0}L^{SiV_{3}}_{V,Si:Si}=-38908.4$ | [ |
$^{0}L^{SiV_{3}}_{V:V,Si}=16043.1-6.91487T$ | [ |
$^{0}L^{SiV_{3}}_{Si:V,Si}=16043.1-6.91487T$ | [ |
Si3V5: CEF, (Si,Al)0.125(Si,Al)0.25(V)0.125(V)0.5 | |
$G^{Si_{3}V_{5}}_{Si:Si:V:V}=0.375°G^{Diamond}_{Si}+0.625°G^{Bcc}_{V}-58417.1+7.07T$ | This work |
$G^{Si_{3}V_{5}}_{Al:Si:V:V}=0.125°G^{Fcc}_{Al}+0.25°G^{Diamond}_{Si}+0.625°G^{Bcc}_{V}-43584+4T$ | This work |
$G^{Si_{3}V_{5}}_{Si:Al:V:V}=0.125°G^{Diamond}_{Si}+0.25°G^{Fcc}_{Al}+0.625°G^{Bcc}_{V}-17465$ | This work |
$G^{Si_{3}V_{5}}_{Al:Al:V:V}=0.375°G^{Fcc}_{Al}+0.625°G{Bcc}_{V}-10955.2$ | This work |
$L^{Si_{3}V_{5}}_{Si,Al:Si:V:V}=-35370-8.56T$ | This work |
Si2V: CEF, (Si,Al)0.6666(V)0.3334 | |
$G^{Si_{2}V}_{Si:V}=-55302.8+136.13732T-226T ln T-0.0025T^{2}+110000/T$ | This work |
$G^{Si_{2}V}_{Al:V}=0.6666°G^{Fcc}_{Al}+0.3334°G^{Bcc}_{V}-8285$ | This work |
$^{1}L^{Si_{2}V}_{Al:V}=-26000$ | This work |
Al45V7: CEF, (Al,Si)0.865385(V)0.134615 | |
$G^{Al_{45}V_{7}}_{Al:V}=0.865385°G^{Fcc}_{Al}+0.134615°G^{Bcc}_{V}-16503+3.39T$ | [ |
$G^{Al_{45}V_{7}}_{Si:V}=0.865385°G^{Diamond}_{Si}+0.134615°G^{Bcc}_{V}+3427$ | This work |
$^{0}L^{Al_{45}V_{7}}_{Al,Si:V}=-31207.14+21.43T$ | This work |
Al3V: CEF, (Al,V,Si)0.75(V,Al)0.25 | |
$G^{Al_{3}V}_{Al:Al}=°G^{Fcc}_{Al}+20000$ | [ |
$G^{Al_{3}V}_{V:Al}=0.75°G^{Bcc}_{V}+0.25°G^{Fcc}_{Al}$ | [ |
$G^{Al_{3}V}_{Al:V}=0.75°G^{Fcc}_{Al}+0.25°G^{Bcc}_{V}-28114+4.52T$ | [ |
$G^{Al_{3}}_{V:V}=°G^{Bcc}_{V}+20000$ | [ |
$G^{Al_{3}V}_{Si:V}=0.75°G^{Diamond}_{Si}+0.25°G^{Bcc}_{V}+1194$ | This work |
$^{0}L^{Al_{3}V}_{Al,Si:V}=-46656.25+31.25T$ | This work |
Si2V: CEF, (Si,Al)0.6666(V)0.3334 | |
$G^{Tau}_{Al:V}=0.6666° G^{Fcc}_{Al}+0.3334° G^{Bcc}_{V}-10083$ | This work |
$G^{Tau}_{Si:V}=G^{Si_{2}V}_{Si:V}+2200$ | This work |
$\frac{1}{C^{2}}=[\frac{2}{q\varepsilon\varepsilon _{0}N_{D}A^{2}}][E-E_{fb}-\frac{kT}{q}]$ | This work |
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