Ag–Ti system
71 accepted literature values from 2 paper(s) (experimental 26, model 14, unspecified 31); 4 calculated phase diagram(s). 7 further extracted value(s) not accepted by the reader-agreement checks are only in the JSON/CSV.
Data: JSON · CSV · interactive explorer · interactive phase diagram · phases (6) · papers (bibliography) · Markdown
| Evidence class | Values |
|---|---|
| experimental | 26 |
| model | 14 |
| unspecified | 31 |
| Property group | Values |
|---|---|
| invariant reaction | 35 |
| phase equilibrium | 7 |
| crystal structure | 29 |
Calculated phase diagrams
Binary phase diagrams calculated with pycalphad 0.11.2 from the SGTE binary collection (Hallstedt 2025, CC BY 4.0). Evidence class: model.
| TDB file | Assessment | SHA-256 | Links |
|---|---|---|---|
| AgTi-04Arr.tdb | R. Arroyave, PhD Thesis, MIT, 2004. | a954cc84f5226307c3aa58c238ade54dd6ae59f149e0d98fb778baf35353e595 | viewer · TDB · JSON |
| AgTi-05Li.tdb | M. Li, C. Li, F. Wang, W. Zhang, Calphad, 29, 269-75(2005). doi:10.1016/j.calphad.2005.09.002 | 794cf6fa270dac1a9406eb12800bc684e4b482c65466b97a9996dd47e9916946 | viewer · TDB · JSON |
| AgTi-23Gie.tdb | W. Gierlotka, A. Debski, W. Gasior, M. Polanski, Comput. Mater. Sci., 230, 112519(2023). doi:10.1016/j.commatsci.2023.112519 | 563e78d8083b3c21a22f07bdb910162d746b75820f9fd8cfd1fbe136bc33730c | viewer · TDB · JSON |
| AgTi-98Spe-LB.tdb | P.J. Spencer, unpublished work, 1998. | 9edb83ec276622eb91055d1d085af65c5db7e89d9e61ebdf853fe3920afc61e7 | viewer · TDB · JSON |
| TDB file | T (K) | Phases at the invariant |
|---|---|---|
| AgTi-04Arr.tdb | 1297.11 | LIQUID (x(Ti) 0.08892) + AGTI_B11 (x(Ti) 0.49776) + BCC_A2 (x(Ti) 0.83654) |
| AgTi-04Arr.tdb | 1231.78 | FCC_A1 (x(Ti) 0.05716) + LIQUID (x(Ti) 0.06133) + AGTI_B11 (x(Ti) 0.49158) |
| AgTi-04Arr.tdb | 1216.16 | AGTI_B11 (x(Ti) 0.50278) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88416) |
| AgTi-04Arr.tdb | 1216.16 | AGTI_B11 (x(Ti) 0.50278) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88422) |
| AgTi-04Arr.tdb | 1125.89 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.93391) + HCP_A3 (x(Ti) 0.95797) |
| AgTi-05Li.tdb | 1293.15 | LIQUID (x(Ti) 0.0604) + AGTI_B11 (x(Ti) 0.50167) + BCC_A2 (x(Ti) 0.83461) |
| AgTi-05Li.tdb | 1233.48 | FCC_A1 (x(Ti) 0.03756) + LIQUID (x(Ti) 0.04126) + AGTI_B11 (x(Ti) 0.49324) |
| AgTi-05Li.tdb | 1213.16 | AGTI_B11 (x(Ti) 0.51) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88578) |
| AgTi-05Li.tdb | 1213.16 | AGTI_B11 (x(Ti) 0.51002) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88586) |
| AgTi-05Li.tdb | 1126.89 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.92551) + HCP_A3 (x(Ti) 0.93246) |
| AgTi-05Li.tdb | 1126.89 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.92593) + HCP_A3 (x(Ti) 0.93289) |
| AgTi-23Gie.tdb | 1294.84 | LIQUID (x(Ti) 0.05858) + AGTI_B11 (x(Ti) 0.5) + BCC_A2 (x(Ti) 0.84524) |
| AgTi-23Gie.tdb | 1294.84 | LIQUID (x(Ti) 0.05863) + AGTI_B11 (x(Ti) 0.5) + BCC_A2 (x(Ti) 0.84521) |
| AgTi-23Gie.tdb | 1236.2 | LIQUID (x(Ti) 0.0393) + FCC_A1 (x(Ti) 0.04298) + AGTI_B11 (x(Ti) 0.5) |
| AgTi-23Gie.tdb | 1211.82 | AGTI_B11 (x(Ti) 0.5) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.89081) |
| AgTi-23Gie.tdb | 1211.82 | AGTI_B11 (x(Ti) 0.5) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.89084) |
| AgTi-23Gie.tdb | 1126.85 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.93365) + HCP_A3 (x(Ti) 0.94624) |
| AgTi-23Gie.tdb | 1126.85 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.93399) + HCP_A3 (x(Ti) 0.94653) |
| AgTi-98Spe-LB.tdb | 1287.81 | LIQUID (x(Ti) 0.079) + AGTI_B11 (x(Ti) 0.5) + BCC_A2 (x(Ti) 0.82203) |
| AgTi-98Spe-LB.tdb | 1287.81 | LIQUID (x(Ti) 0.07905) + AGTI_B11 (x(Ti) 0.5) + BCC_A2 (x(Ti) 0.82199) |
| AgTi-98Spe-LB.tdb | 1232.96 | FCC_A1 (x(Ti) 0.054) + LIQUID (x(Ti) 0.05735) + AGTI_B11 (x(Ti) 0.5) |
| AgTi-98Spe-LB.tdb | 1232.96 | FCC_A1 (x(Ti) 0.05358) + LIQUID (x(Ti) 0.05688) + AGTI_B11 (x(Ti) 0.5) |
| AgTi-98Spe-LB.tdb | 1200.48 | AGTI_B11 (x(Ti) 0.5) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88863) |
| AgTi-98Spe-LB.tdb | 1200.48 | AGTI_B11 (x(Ti) 0.5) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88877) |
| AgTi-98Spe-LB.tdb | 1200.48 | AGTI_B11 (x(Ti) 0.5) + AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.88858) |
| AgTi-98Spe-LB.tdb | 1127.56 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.92871) + HCP_A3 (x(Ti) 0.94124) |
| AgTi-98Spe-LB.tdb | 1127.56 | AGTI2 (x(Ti) 0.66667) + BCC_A2 (x(Ti) 0.92911) + HCP_A3 (x(Ti) 0.94156) |
Convex hulls: Materials Project DFT hull · OQMD DFT hull · CALPHAD hull AgTi-04Arr · CALPHAD hull AgTi-05Li · CALPHAD hull AgTi-98Spe-LB
Invariant reactions (literature)
| T (K) | Reaction / phases | Compositions (mole fraction) | Class | Source | Location | Quote |
|---|---|---|---|---|---|---|
| 1311 | (β-Ti) + L = AgTi | (β-Ti): Ti 0.163; AgTi: Ti 0.5 | experimental | [1] Gierlotka 2023 cites Adenstedt 1953 doi | Table 1, p. 2, row 2 report | |
| 1297 | L + (β Ti) = AgTi | L: Ti 0.085; (β Ti): Ti 0.836; AgTi: Ti 0.5 | model | [1] Gierlotka 2023 cites Arroyave 2004 | Table 5, p. 5, row 3 report | |
| 1294.8 | L + (β Ti) = AgTi | L: Ti 0.058; (β Ti): Ti 0.845; AgTi: Ti 0.5 | model | [1] Gierlotka 2023 | Table 5, p. 5, row 1 report | |
| 1293 | peritectic: L -> (Ag) + (AgTi) | L: Ti 0.0116; (Ag): Ti 0.0465; (AgTi): Ti 0.52 | experimental | [2] Li 2005 cites McQuillan 1960 | Table 3, p. 4, row 3 report | |
| 1293 | peritectic: L + β(Ti) -> (AgTi) | L: Ti 0.06; β(Ti): Ti 0.847; (AgTi): Ti 0.5 | experimental | [2] Li 2005 cites Eremenko 1969 | Table 3, p. 4, row 5 report | |
| 1293 | (β-Ti) + L = AgTi | L: Ti 0.94; AgTi: Ti 0.5 | experimental | [1] Gierlotka 2023 cites Eremenko 1969 doi | Table 1, p. 2, row 4 report | |
| 1293 | peritectic: L + β(Ti) -> (AgTi) | L: Ti 0.06; β(Ti): Ti 0.835; (AgTi): Ti 0.501 | model | [2] Li 2005 | Table 3, p. 4, row 4 report | |
| 1290 | peritectic | experimental | [2] Li 2005 cites McQuillan 1960 | p. 5 report | The type of the invariant reaction involving (Ag), liquid and (AgTi) was questionable. McQuillan [9] reported that the reaction is of peritectic type and occurs at 1290 K. | |
| 1290 | peritectic: L + β(Ti) -> (AgTi) | L: Ti 0.1; β(Ti): Ti 0.85; (AgTi): Ti 0.5 | experimental | [2] Li 2005 cites McQuillan 1960 | Table 3, p. 4, row 6 report | |
| 1290 | (β-Ti) + L = AgTi | (β-Ti): Ti 0.15; L: Ti 0.9; AgTi: Ti 0.5 | experimental | [1] Gierlotka 2023 cites McQuilian 1960 | Table 1, p. 2, row 3 report | |
| 1289 | L + (β Ti) = AgTi | L: Ti 0.059; (β Ti): Ti 0.835; AgTi: Ti 0.5 | model | [1] Gierlotka 2023 cites Li 2005 doi | Table 5, p. 5, row 2 report | |
| 1273 | (β-Ti) + L = AgTi | AgTi: Ti 0.5 | experimental | [1] Gierlotka 2023 cites Deccecco 1953 | Table 1, p. 2, row 1 report | |
| 1237 | L + AgTi = (Ag) | L: Ti 0.042; AgTi: Ti 0.5; (Ag): Ti 0.047 | model | [1] Gierlotka 2023 cites Li 2005 doi | Table 5, p. 5, row 11 report | |
| 1235 | L + AgTi = (Ag) | L: Ti 0.039; AgTi: Ti 0.5; (Ag): Ti 0.043 | model | [1] Gierlotka 2023 | Table 5, p. 5, row 10 report | |
| 1233 | eutectic: L -> (Ag) + (AgTi) | L: Ti 0.0413; (Ag): Ti 0.0376; (AgTi): Ti 0.493 | model | [2] Li 2005 | Table 3, p. 4, row 1 report | |
| 1232 | L = AgTi + (Ag) | L: Ti 0.95; AgTi: Ti 0.5; (Ag): Ti 0.95 | unspecified | [1] Gierlotka 2023 cites Murray 1983 doi | Table 1, p. 2, row 5 report | |
| 1232 | eutectic: L -> (Ag) + (AgTi) | L: Ti 0.05; (Ag): Ti 0.05; (AgTi): Ti 0.5 | experimental | [2] Li 2005 cites Eremenko 1969 | Table 3, p. 4, row 2 report | |
| 1232 | L = (Ag) + AgTi | L: Ti 0.061; (Ag): Ti 0.057; AgTi: Ti 0.5 | model | [1] Gierlotka 2023 cites Arroyave 2004 | Table 5, p. 5, row 12 report | |
| 1218 | (β-Ti) + AgTi = AgTi2 | AgTi: Ti 0.5; AgTi2: Ti 0.66 | experimental | [1] Gierlotka 2023 cites Eremenko 1969 doi | Table 1, p. 2, row 9 report | |
| 1218 | peritectoid: β(Ti) + (AgTi) -> AgTi2 | β(Ti): Ti 0.872; (AgTi): Ti 0.51; AgTi2: Ti 0.667 | experimental | [2] Li 2005 cites Eremenko 1969 | Table 3, p. 4, row 8 report | |
| 1216 | AgTi + (β Ti) = AgTi2 | AgTi: Ti 0.5; (β Ti): Ti 0.885; AgTi2: Ti 0.667 | model | [1] Gierlotka 2023 cites Arroyave 2004 | Table 5, p. 5, row 6 report | |
| 1213 | (β-Ti) + AgTi = AgTi2 | (β-Ti): Ti 0.117; AgTi: Ti 0.5; AgTi2: Ti 0.66 | experimental | [1] Gierlotka 2023 cites Plichta 1977 | Table 1, p. 2, row 6 report | |
| 1213 | peritectoid: β(Ti) + (AgTi) -> AgTi2 | β(Ti): Ti 0.886; (AgTi): Ti 0.51; AgTi2: Ti 0.667 | model | [2] Li 2005 | Table 3, p. 4, row 7 report | |
| 1212 | AgTi + (β Ti) = AgTi2 | AgTi: Ti 0.5; (β Ti): Ti 0.889; AgTi2: Ti 0.667 | model | [1] Gierlotka 2023 | Table 5, p. 5, row 4 report | |
| 1203 | (β-Ti) + AgTi = AgTi2 | (β-Ti): Ti 0.12; AgTi: Ti 0.5; AgTi2: Ti 0.66 | experimental | [1] Gierlotka 2023 cites McQuilian 1960 | Table 1, p. 2, row 8 report | |
| 1203 | peritectoid: β(Ti) + (AgTi) -> AgTi2 | β(Ti): Ti 0.88; (AgTi): Ti 0.52; AgTi2: Ti 0.667 | experimental | [2] Li 2005 cites McQuillan 1960 | Table 3, p. 4, row 9 report | |
| 1173 | (β-Ti) + AgTi = AgTi2 | (β-Ti): Ti 0.1; AgTi: Ti 0.5; AgTi2: Ti 0.66 | experimental | [1] Gierlotka 2023 cites Adenstedt 1953 doi | Table 1, p. 2, row 7 report | |
| 1133 | eutectoid: β(Ti) -> AgTi2 + α(Ti) | β(Ti): Ti 0.924; AgTi2: Ti 0.667; α(Ti): Ti 0.953 | experimental | [2] Li 2005 cites Plichta 1978 doi | Table 3, p. 4, row 14 report | |
| 1129 | (β Ti) = AgTi2 + (α Ti) | (β Ti): Ti 0.924; AgTi2: Ti 0.667; (α Ti): Ti 0.931 | model | [1] Gierlotka 2023 cites Li 2005 doi | Table 5, p. 5, row 8 report | |
| 1128 | (β-Ti) = (α-Ti) + AgTi2 | (β-Ti): Ti 0.076; (α-Ti): Ti 0.047; AgTi2: Ti 0.66 | unspecified | [1] Gierlotka 2023 cites Murray 1983 doi | Table 1, p. 2, row 10 report | |
| 1128 | eutectoid: β(Ti) -> AgTi2 + α(Ti) | β(Ti): Ti 0.885; AgTi2: Ti 0.72; α(Ti): Ti 0.93 | experimental | [2] Li 2005 cites Worner 1953 | Table 3, p. 4, row 11 report | |
| 1127 | eutectoid: β(Ti) -> AgTi2 + α(Ti) | β(Ti): Ti 0.926; AgTi2: Ti 0.667; α(Ti): Ti 0.933 | model | [2] Li 2005 | Table 3, p. 4, row 10 report | |
| 1126 | (β Ti) = AgTi2 + (α Ti) | (β Ti): Ti 0.933; AgTi2: Ti 0.667; (α Ti): Ti 0.958 | model | [1] Gierlotka 2023 cites Arroyave 2004 | Table 5, p. 5, row 9 report | |
| 1124 | eutectoid: β(Ti) -> AgTi2 + α(Ti) | β(Ti): Ti 0.916; AgTi2: Ti 0.667; α(Ti): Ti 0.958 | experimental | [2] Li 2005 cites Eremenko 1969 | Table 3, p. 4, row 12 report | |
| 1122 | eutectoid: β(Ti) -> AgTi2 + α(Ti) | β(Ti): Ti 0.917; AgTi2: Ti 0.667; α(Ti): Ti 0.958 | experimental | [2] Li 2005 cites Adenstedt 1953 | Table 3, p. 4, row 13 report |
Other properties
Phase equilibrium (7)
| Property | Value | T (K) | Phases / composition | Class | Source | Location | Quote |
|---|---|---|---|---|---|---|---|
| Phase composition | 1023 | (Ag) + TiAg (Ag): Ag 0.9696, Ti 0.0304; TiAg: Ag 0.5117, Ti 0.4883 | experimental | [2] Li 2005 | Table 2, p. 3, row 1 report | ||
| Phase composition | 1023 | Ti2Ag + α(Ti) Ti2Ag: Ag 0.3307, Ti 0.6693; α(Ti): Ag 0.0234, Ti 0.9766 | experimental | [2] Li 2005 | Table 2, p. 3, row 3 report | ||
| Phase composition | 1023 | TiAg + Ti2Ag TiAg: Ag 0.4785, Ti 0.5215; Ti2Ag: Ag 0.3307, Ti 0.6693 | experimental | [2] Li 2005 | Table 2, p. 3, row 2 report | ||
| Phase composition | 1253 | L + TiAg L: Ag 0.9636, Ti 0.0364; TiAg: Ag 0.5021, Ti 0.4979 | experimental | [2] Li 2005 | Table 2, p. 3, row 4 report | ||
| Phase composition | 1253 | TiAg + β(Ti) TiAg: Ag 0.4986, Ti 0.5014; β(Ti): Ag 0.1516, Ti 0.8484 | experimental | [2] Li 2005 | Table 2, p. 3, row 5 report | ||
| Phase composition | 1373 | L + β(Ti) L: Ag 0.937, Ti 0.063; β(Ti): Ag 0.1665, Ti 0.8335 | experimental | [2] Li 2005 | Table 2, p. 3, row 6 report | ||
| Phase composition | 1473 | L + β(Ti) L: Ag 0.875, Ti 0.125; β(Ti): Ag 0.1923, Ti 0.8077 | experimental | [2] Li 2005 | Table 2, p. 3, row 7 report |
Crystal structure (29)
| Property | Value | T (K) | Phases / composition | Class | Source | Location | Quote |
|---|---|---|---|---|---|---|---|
| Lattice a | 2.889 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 9 report | |
| Lattice a | 2.878 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 8 report | |
| Lattice a | 2.932 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 6 report | |
| Lattice a | 2.888 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 7 report | |
| Lattice a | 2.9 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 17 report | |
| Lattice a | 2.904 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 14 report | |
| Lattice a | 2.96 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 13 report | |
| Lattice a | 2.95 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 11 report | |
| Lattice a | 2.909 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 10 report | |
| Lattice b | 2.889 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 9 report | |
| Lattice b | 2.878 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 8 report | |
| Lattice b | 2.932 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 6 report | |
| Lattice b | 2.888 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 7 report | |
| Lattice b | 2.9 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 17 report | |
| Lattice b | 2.904 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 14 report | |
| Lattice b | 2.96 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 13 report | |
| Lattice b | 2.95 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 11 report | |
| Lattice b | 2.909 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 10 report | |
| Lattice c | 2.889 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 9 report | |
| Lattice c | 2.878 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 8 report | |
| Lattice c | 2.932 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 6 report | |
| Lattice c | 2.888 Å | 0 | (Ag) alloy: Ti 0 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 7 report | |
| Lattice c | 8.15 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 17 report | |
| Lattice c | 8.12 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 16 report | |
| Lattice c | 8.14 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 15 report | |
| Lattice c | 8.225 Å | 0 | AgTi alloy: Ti 0.5 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 14 report | |
| Lattice c | 11.85 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 13 report | |
| Lattice c | 12.183 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 10 report | |
| Lattice c | 11.82 Å | 0 | AgTi2 alloy: Ti 0.666667 | unspecified | [1] Gierlotka 2023 | Table 3, p. 3, row 12 report |
Sources
Reporting papers the values were read from (a value cited from another work names that work in its row).
- Wojciech Gierlotka, Adam Dębski, Władysław Gąsior, Marek Polański, Computational approach to the Ag-Ti system, Computational Materials Science 230, 112519 (2023). doi:10.1016/j.commatsci.2023.112519
- Mei Li, Changrong Li, Fuming Wang, Weijing Zhang, Experimental study and thermodynamic assessment of the Ag–Ti system, Calphad 29, 269-275 (2005). doi:10.1016/j.calphad.2005.09.002