DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds
Abstract
:1. Introduction
2. Methodology
2.1. DFT Calculations
2.2. Thermodynamic Modeling
3. Results
3.1. Structural Stability at 0 K for Al And Ni
3.2. Phase Stability and Molar Volumes of Binary Phases at 0 K
3.2.1. Enthalpies of Formation of Ordered Compounds
3.2.2. Molar Volumes of Ordered Compounds
3.3. Thermodynamic Properties of Individual Phases at Finite Temperature
3.4. Phase Stability at Finite Temperature—The Phase Diagram
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
ATAT | Alloy Theoretic Automated Toolkit |
BWG | Bragg–Williams–Gorsky |
Calphad | CALculation of PHAse Diagrams |
CE | Cluster Expansion |
CEF | Compound Energy Formalism |
CVM | Cluster Variation Method |
DFT | Density Functional Theory |
FP | First Principles |
FPLMTO | Full-Potential Linear Muffin-Tin Orbital |
GGA | Generalized Gradient Approximation |
LMTO | Linear Muffin-Tin Orbital |
MC | Monte Carlo Simulations |
MD | Molecular Dynamics |
PAW | Projector Augmented Wave |
PBE | Perdew-Burke-Ernzerhof |
SL | Sublattice(-s) |
SGTE | Scientific Group Thermodata Europe |
TCP | Topologically Closed Packed |
TDB | Thermodynamic Database |
VASP | Vienna Ab initio Simulation Package |
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Reference | Entropy Model | TDB Available | Approach |
---|---|---|---|
This work | BWG | yes | DFT-CEF + no excess parameters reference state at 0 K |
Al–Ni [9] | CE/MC | no | DFT 0 K |
ATAT [13] | CE/CVM/MD | yes | DFT + finite temperature |
Co-Ta [14] | BWG + excess | yes | DFT-CEF + excess parameters reference state at 298.15 K (SGTE) |
Aluminium | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Ref. | A1 | A2 | A3 | A15 | A12() | D8() | C36 | C14 | C15 | D5 | D0 | |
H (kJ/mol) | ||||||||||||
This work | 0.0 | 9.3 | 3.2 | 7.7 | 5.1 | 6.3 | 10.0 | 15.0 | 14.3 | 15.6 | 17.1 | 1.4 |
PAW-PW91 [24] | 0.0 | 9.7 | - | 7.5 | 4.9 | 6.5 | 9.7 | - | 13.9 | 15.1 | - | - |
PAW-PW91 [25] | 0.0 | 9.21 | 2.85 | - | - | - | - | - | - | - | - | - |
SGTE [26] | 0.0 | 10.1 | 5.5 | - | - | - | - | - | - | - | - | - |
V (Å/at) | ||||||||||||
This work | 16.48 | 16.91 | 16.64 | 16.93 | 17.13 | 16.91 | 17.31 | 17.45 | 17.45 | 17.43 | 18.78 | 16.59 |
PAW-PBE [27] | 16.71 | - | - | - | - | - | - | - | - | - | - | - |
FPLMTO-GGA [28] | 16.63 | - | - | - | - | - | - | - | - | - | - | - |
LMTO-LDA [29] | 15.93 | 16.17 | - | - | - | - | - | - | - | - | - | - |
Calphad [30] | - | 17.13 | 16.85 | - | - | - | - | - | - | - | - | - |
Calphad [31] | 16.30 | 15.50 | 15.50 | - | - | - | - | - | - | - | - | - |
B (GPa) | ||||||||||||
This work | 77.6 | 69.8 | 73.3 | 64.7 | 69.4 | 74.0 | 70.1 | 65.7 | 66.3 | 66.5 | 67.4 | 76.0 |
PAW-PBE [27] | 72.5 | - | - | - | - | - | - | - | - | - | - | - |
FPLMTO-GGA [28] | 74.4 | - | - | - | - | - | - | - | - | - | - | - |
LMTO-LDA [29] | 87.0 | 88.0 | - | - | - | - | - | - | - | - | - | - |
Exp. [32] | 72.7 | - | - | - | - | - | - | - | - | - | - | - |
Nickel | ||||||||||||
Ref. | A1 | A2 | A3 | A15 | A12() | D8() | C36 | C14 | C15 | D5 | D0 | |
H (kJ/mol) | ||||||||||||
This work | 0.0 | 5.3 | 2.7 | 11.2 | 8.3 | 8.4 | 14.1 | 17.5 | 17.0 | 18.2 | 30.5 | 5.8 |
PAW-GGA [24] | 0.0 | 8.8 | - | 12.7 | 9.1 | 16.5 | 16.0 | - | 19.0 | 21.3 | - | - |
PAW-GGA [25] | 0.0 | 9.15 | 2.13 | - | - | - | - | - | - | - | - | - |
SGTE [26] | 0.0 | 8.7 | 2.9 | - | - | - | - | - | - | - | - | - |
V (Å/at) | ||||||||||||
This work | 10.88 | 10.94 | 10.92 | 11.11 | 11.07 | 11.08 | 11.30 | 11.40 | 11.39 | 11.43 | 12.20 | 11.08 |
PAW-PBE [27] | 10.90 | - | - | - | - | - | - | - | - | - | - | - |
PAW-PBE [33] | 10.94 | - | - | - | - | - | - | - | - | - | - | - |
LMTO-LDA [29] | 10.53 | 10.62 | - | - | - | - | - | - | - | - | - | - |
B (GPa) | ||||||||||||
This work | 199.3 | 193.7 | 189.7 | 185.3 | 202.1 | 189.5 | 177.2 | 188.5 | 198.5 | 183.5 | 165 | 145.2 |
PAW-PBE [27] | 190.5 | - | - | - | - | - | - | - | - | - | - | - |
PAW-PBE [33] | 193.0 | - | - | - | - | - | - | - | - | - | - | - |
LMTO-LDA [29] | 248.0 | 224.0 | - | - | - | - | - | - | - | - | - | - |
x(Ni) | Strukturbericht | Formation Energy [kJ/mol at] | Pearson Symbol | Space Group | Wyckoff Positions |
---|---|---|---|---|---|
fcc related | |||||
0.0 | A1-BB | 0.0 | cF4 (Cu) | Fmm (225) | 4a, 4b, 8c |
0.111 | Al8Ni-AB8 | −10.3 | tI18 (NbNi) | I4/mmm | 2a, 8h, 8i |
0.125 | D1D7-AB7 | −10.3 | cF32(CaGe) | Fmm (225) | 4a, 4b, 24d |
0.25 | D0-AB3 | −22.3 | tI8 (AlTi) | I4/mmm (139) | 2a, 2b, 4d |
0.25 | L1-AB3 | −22.3 | cP4 (CuAu) | Pmm (227) | 1a, 3c |
0.25 | D0-AB3 | −22.8 | tI16 (AlZr) | I4/mmm (139) | 4c, 4d, 4e |
0.25 | L6-AB3 | −22.3 | tP4 (CuTi) | P4/mmm (123) | 1a 1c 2e 2e |
0.333 | 12-AB2 | −38.5 | tI6 | I4/mmm (139) | - |
0.5 | CH40-AB | −58.2 | tI8(NbP) | I4/amd (141) | 2a, 2b |
0.5 | D4-AB | −31.0 | - | Fdm | - |
0.5 | L1-AB | −52.4 | tP2 (CuAu) | P4/mmm (123) | 1a, 1d |
0.5 | L1-AB | −43.0 | hR32 (CuPt) | Rm (166) | 1a, 1b |
0.5 | Z2-AB | −39.3 | tP8 | P4/nmm (129) | |
0.667 | 12-A2B | −45.6 | tI6 | I4/mmm (139) | |
0.75 | D0-A3B | −43.1 | tI8 (AlTi) | I4/mmm (139) | 2a, 2b, 4d |
0.75 | L1-A3B | −45.4 | cP4 (CuAu) | Pmm (227) | 1a, 3c |
0.75 | L6-A3B | −45.0 | tP4 (CuTi) | P4/mmm (123) | 1a 1c 2e 2e |
0.875 | D1D7-A7B | −23.2 | cF32(CaGe) | Fmm (225) | 4a, 4b, 24d |
0.889 | Al8Ni-A8B | −21.1 | tI18 (NbNi) | I4/mmm | 2a, 8h, 8i |
1.0 | A1-AA | 0.0 | cF4 (Cu) | Fmm (225) | 4a, 4b, 8c |
bcc related | |||||
0.0 | A2-BB | +9.3 | cI2 (W) | Imm (229) | 2a |
0.25 | D0-AB3 | −9.6 | cF16 (AlFe) | Fmm (225) | 4a, 4b, 8c |
0.333 | C11-AB2 | −39.6 | tl6 | I4/mmm (139) | 2a, 4e |
0.375 | PdTi-A3B5 | −47.0 | - | - | - |
0.4 | AlOs-A2B3 | −51.5 | - | - | - |
0.428571 | B11-A3B4 | −45.1 | tP4 (CuTi) | P4/nmm (129) | 2c |
0.444 | VZn-A4B5 | −31.5 | tI18 (VZn5) | I4/mmm (139) | 2a, 8h, 8i |
0.5 | B2-AB | −66.3 | cP2 (CsCl) | Pmm (221) | 1a, 1b |
0.5 | B32-AB | −35.6 | cF16 (NaTl) | Fdm (227) | 8a, 8b |
0.555556 | VZn-A5B4 | −43.7 | tI18 (VZn5) | I4/mmm (139) | 2a, 8h, 8i |
0.571429 | B11-A4B3 | −43.0 | tP4 (CuTi) | P4/nmm (129) | 2c |
0.6 | AlOs-A3B2 | −55.7 | - | - | - |
0.625 | PdTi-A5B3 | −52.3 | - | - | - |
0.667 | C11-A2B | −46.8 | tl6 | I4/mmm (139) | 2a, 4e |
0.75 | D0-A3B | −40.9 | cF16 (AlFe) | Fmm (225) | 4a, 4b, 8c |
1.0 | A2-AA | +5.3 | cI2 (W) | Imm (229) | 2a |
hcp related | |||||
0.0 | A3-BB | +3.2 | hP2 (Mg) | P6/mmc (194) | 2c |
0.25 | D0-AB3 | −21.2 | hP8 (NiSn) | P6/mmc (194) | 2c, 6h |
0.333 | B8-AB2 | −33.3 | hP6 (InNi) | P6/mmc (194) | 2a, 2c, 2d |
0.333 | B-AB2 | −41.0 | hP9 (AgZn) | P (147) | 1a, 2d, 6g |
0.5 | hcp-AB | −48.2 | hP2 | Pm2 (187) | 1a, 1f |
0.5 | B-AB | −44.5 | hP2 (WC) | Pm2 (187) | 1a, 1f |
0.5 | B-BA | −44.5 | hP2 (WC) | Pm2 (187) | 1a, 1f |
0.5 | B-AB | −19.0 | hP8 (AsTi) | P6/mmc (194) | 2a, 2d, 4f |
0.5 | B-BA | −49.8 | hP8 (AsTi) | P6/mmc (194) | 2a, 2d, 4f |
0.5 | B8-BA | −10.3 | hP4 (NiAs) | P6/mmc (194) | 2a, 2c |
0.5 | B35-BA | −2.2 | hP6 (CoSn) | P6/mmm (191) | 1a, 2d, 3f |
0.667 | B-A2B | −43.8 | hP9 (AgZn) | P (147) | 1a, 2d, 6g |
0.667 | B8-A2B | −50.0 | hP6 (InNi) | P6/mmc (194) | 2a, 2c, 2d |
0.75 | D0-A3B | −44.6 | hP8 (NiSn) | P6/mmc (194) | 2c, 6h |
1.0 | A3-AA | +2.7 | hP2 (Mg) | P6/mmc (194) | 2c |
Phase | Pearson Symbol | Space Group | Wyckoff Positions | Configurations |
---|---|---|---|---|
D5 (AlNi) | hP5 (AlNi) | Pm1 (164) | 1a 2d 2d | 8 |
D0 (AlNi) | oP16 (FeC) | Pmna (62) | 4c 4c 8d | 8 |
TCP | ||||
hR39 (FeW) | Rm (166) | 3a, 18h, 6c, 6c, 6c | 32 | |
D8() | tP30 (FeCr) | P4/mnm (136) | 2a, 4f, 8i, 8i, 8j | 32 |
A12() | cI58 ( Mg) | I3m (217) | 2a, 8c, 24g, 24g | 16 |
A15 | cP8 (CrSi) | Pmm (223) | 6c, 2a | 4 |
Laves | ||||
C14 | hP12 (MgZn) | P6/mmc (194) | 2a, 4f, 6h | 8 |
C15 | cF24 (MgCu) | Fdm (227) | 16d, 8a | 4 |
C36 | hP24 (MgNi) | P6/mmc (194) | 4e, 4f, 4f, 6g, 6h | 32 |
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Tumminello, S.; Palumbo, M.; Koßmann, J.; Hammerschmidt, T.; Alonso, P.R.; Sommadossi, S.; Fries, S.G. DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds. Metals 2020, 10, 1142. https://doi.org/10.3390/met10091142
Tumminello S, Palumbo M, Koßmann J, Hammerschmidt T, Alonso PR, Sommadossi S, Fries SG. DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds. Metals. 2020; 10(9):1142. https://doi.org/10.3390/met10091142
Chicago/Turabian StyleTumminello, Silvana, Mauro Palumbo, Jörg Koßmann, Thomas Hammerschmidt, Paula R. Alonso, Silvana Sommadossi, and Suzana G. Fries. 2020. "DFT-CEF Approach for the Thermodynamic Properties and Volume of Stable and Metastable Al–Ni Compounds" Metals 10, no. 9: 1142. https://doi.org/10.3390/met10091142