Page 134 - Read Online

Chong et al. J Mater Inf 2023;3:21 https://dx.doi.org/10.20517/jmi.2023.17 Page 3 of 18

where s, l, and g indicate the solid, liquid, and gas phases, respectively. Here, (i) ay > bx, indicating the
oxidation is from M O to M O ; (ii) the oxygen gas species O is selected due to its extreme dominance in
b
a
x
2
y
[17]
comparison with the other oxygen species of O and O ; and (iii) the reactions are under the total pressure
1
3
of 1 atm with 1 mole of O . Under the assumptions of (a) ideal gas with O being the dominant gas species
2
2
and (b) the activities of liquids and solids as unity, the ΔG of equation (1) or (2) at equilibrium can be
o
determined by the activity of oxygen (a ) , as described by the equation:
[18]
o2
where R is the gas constant, and T is the absolute temperature. By setting the reference pressure and the
5
total pressure P = P = 1 atm (10 Pa), then, a = P /P with P being the partial pressure of O . Note that
o2
ref
tot
ref
o2
2
o2
(a) only the stable or metastable oxides at 1 atm are considered in the present work; and (b) the reactions in
equations (1) and (2) only involve the phases that are able to be in equilibrium with each other, i.e., only the
phases involving neighboring oxidation states are allowed in a reaction. For example, the oxidation in the
Cr-O system is from Cr to Cr O and then to Cr O with increasing oxygen content, x(O). For the ternary
12
5
3
2
oxide of AlTaO with x(O) = 0.667, only the reaction from the oxide with x(O) = 0.6 (i.e., Al O ) is
4
2
3
considered. Table 1 summarizes all the possible reactions to form oxides in the present Al-Cr-Hf-Pt-Ta-O
system, including seven binary oxides (Al O , Cr O , Cr O , HfO , PtO, PtO , and Ta O ) and 1 ternary
2
3
2
12
5
5
2
2
3
2
oxide (AlTaO ). Note that the listed reaction to form NiO is for reference only, and four polymorphs of
4
Al O (α-Al O , δ-Al O , γ-Al O , and κ-Al O ) were included in the SGTE substance database (i.e., the
2
2
3
3
2
3
2
3
3
2
SSUB5) but only α-Al O is stable.
[19]
2
3
Thermodynamic database and thermodynamic calculations
Calculating Ellingham diagrams requires a thermodynamic database (TDB) for the present
Al-Cr-Hf-Pt-Ta-O system, which was created by a combination of the metal system Al-Cr-Hf-Pt modeled
[19]
by Kim with a thermodynamic description of the binary oxides from the SSUB5 database . The missing
[20]
thermodynamic properties of the Pt-O compounds (PtO, PtO , and Pt O ) were added to SSUB5 using the
4
2
3
[4]
reported enthalpies and entropies of formation at room temperature . The missing thermodynamic
properties of AlTaO were estimated with the reference states being the binary oxides in SSUB5,
4
The enthalpy of formation (ΔH) of equation (4) was predicted by the density functional theory (DFT)-based
first-principles calculations using the Vienna Ab initio Simulation Package (VASP) . The ion-electron
[21]
[22]
interaction was described by the projector augmented wave (PAW) method , and the exchange-
correlation (X-C) functionals were described by the local density approximation (LDA) and the
[23]
generalized gradient approximation (GGA) improved for densely packed solids and their surfaces
[24]
(PBEsol) . Other details of first-principles calculations are given in Table 2, as well as the default settings
used by the software DFT Tool Kits (DFTTK) , including crystal structures of the three oxides, the used k-
[25]
point meshes, the employed plane-wave cutoff energy, and the selected potentials for elements Al, Ta,
and O. In addition, Table 2 also lists the DFT results reported by the Materials Project (MP) and
[26]