Phase diagram studies in n-CoSb 3 skutterudites
5.3 Soluble site other than the void .1 Solubility debate of In and Ga .1 Solubility debate of In and Ga
5.3.2 DFT calculations of In-doped CoSb 3 systems
Before taking on experimental study, DFT calculations were applied to help navigate the research direction. Two types of calculations were performed, the first being the band structures of CoSb3
and different Ga/In-doped systems. Due to the similarity between band structures of Ga- and In- doped systems, only the results on In-doped systems are shown in Figure 5.9. The second is the formation energies of possible defects as a function of both doping level and Fermi level. Results are shown in Figure 5.10 and 5.11.
-1.0 -0.5 0.0 0.5 1.0
Γ H N Γ P
Co32Sb96
Energy (eV)
-0.6 -0.3 0.0 0.3
0.6 Co32Sb95InSb
Γ H N Γ P
Energy (eV)
Figure 5.9 Band structures of CoSb3 and different In-doped systems. The dashed lines are the Fermi levels.
Figure 5.9 shows the band structures of pure CoSb3, Co32Sb95InSb, InVFCo32Sb95InSb, and (InVF)2Co32Sb95(InSb). Results show that In doping at different sites has different effect on band structures. Pure CoSb3 is a semiconductor with small band gap. One In atom at the Sb substitution site generates a deficiency of two electrons and one In atom at the void-filling position adds one extra electron compared to pure CoSb3. As a result, one In substituting for Sb leads to imbalanced charge and pushes up one Sb-based band above the Fermi level, which brings the system to an unstable state at no charge compensation. For the same reason InVFCo32Sb95InSb is also hardly stable whereas (InVF)2Co32Sb95(InSb) is charge-balanced and is thus a semiconductor. Intuitively InxCo4Sb12-x/3, equivalently (InVF)2x/3Co4Sb12-x/3(InSb)x/3, is expected to be a stable skutterudite phase.
Similar results are also observed in Ga-doped CoSb3, namely, (GaVF)2x/3Co4Sb12-x/3(GaSb)x/3, is expected to be a stable skutterudite phase as well.
The charged defects from In-containing CoSb3, such as InCo, InSb substitutions in the Co-Sb framework, InVF on the crystal void site, and their combinations, with different charge states q are calculated by ab initio methods. The defect formation Gibbs free energy per impurity can be written as follows:
(Eq. 5.1) where is the total energy of a 2×2×2 supercell InyCo32-wInwSb96-zInz. is the total energy of supercell of bulk CoSb3. y is the filling fraction of In in crystal voids, w is the substituting fraction at Co sites, and z is the substituting fraction at Sb sites.
is chemical potential for R (
)
, q is the charge state of the point defect, is the-0.4 0.0 0.4 0.8
Γ H N Γ P
InVFCo32Sb95InSb
Energy (eV)
-0.6 -0.3 0.0 0.3 0.6
Γ H N Γ P
(InVF)2Co32Sb95InSb
Energy (eV)
Fermi level, referring to the valence band maximum Ev in CoSb3, and ΔV is the correction term to align the reference potential in the defect supercell with that in the perfect supercell.
Figure 5.10(a) shows the calculated for (GaVF)xCo4Sb12-x/2(GaSb)x/2 at 923 K possesses the lowest values and stays negative at about x ≤0.25. The formation energy (-0.116 eV) of GaSb, a known secondary phase in Ga-contained CoSb3, is also shown in Figure 5.10(a), and it becomes lower than for (GaVF)xCo4Sb12-x/2(GaSb)x/2 after x ≥ 0.08, indicating that (GaVF)xCo4Sb12- x/2(GaSb)x/2 is the most stable phase when x is less than 0.08. In other words, the maximum filling fraction for Ga in Co4Sb12 should be around 0.08, and the total Ga atoms in a unit of Co4Sb12 should be around 0.12 (=1.5x) at 923 K. Similarly, a solubility of In in a unit of Co4Sb12 at around 0.27 (=1.5*0.18, x = 0.18 is the filling fraction limit) at 873K is predicted.
Figure 5.10 Calculated Gibbs free energy ( ) as a function of doping content x of (a) Ga in Ga- CoSb3 skutterudite at 923K and (b) In in In-CoSb3 skutterudite at 873K.
Figure 5.11 Formation energies of possible defects as a function of Fermi level at the Co-rich limit in Ga-containing (a) and In-containing (b) skutterudites. The zero Fermi level corresponds to the top of the valence band, and the width of shadowed area indicates the energy gap. The number for labeling is the charge state of the point defect.
0.0 0.2 0.4 0.6 0.8
-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6
∆G (eV)
InxCo4Sb12-x/2Inx/2 InxCo4Sb12 Co4Sb12-xInx
x
InSb 1100K873K
(a) (b)
(a) (b)
Figure 5.11 shows the defect formation energy as a function of Fermi level at the Co-rich limit, where the system is connected to a Co reservoir. Ga-containing skutterudites form stable charge- compensated compound defects (CCCD) (GaVF)2x/3Co4Sb12-x/3(GaSb)x/3 when the Fermi level falls in the gap area. The formation energy of the single filling defect (GaVF)xCo4Sb12 is always very high.
In contrast, In-containing skutterudite favors In-filling into the void at relatively low Fermi level instead, and dual-site In occupancy can form as the Fermi level increases. In the gap area 0~0.17eV (shadow in Figure 5.11), Ga always forms the charge compensated defect, and In forms either a single filling, or a dual-site defect with or without charge compensation, at different Fermi levels which likely corresponds to different experimental conditions such as the amount of indium impurity or the stoichiometric ratio of Co/Sb.
The results from theoretical study above can be summarized as follows. Firstly, unlike for other fillers, the void is NOT the only soluble site for both In and Ga. Secondly, Ga or In-doping in CoSb3 based skutterudites results in both void filling and Sb substituting, which leads to compound defects (charge-compensated in the Ga case and not fully charge-compensated in the In case).
Thirdly, the solubility limit is predicted to be 0.12 for Ga in a Co4Sb12 unit at 923K and 0.27 for In at 873K.
The solubility region can then be estimated to be mainly directed along the direction of (RVF)2x/3Co4Sb12-x/3(RSb)x/3 to CoSb3 (R = Ga, or In). This is different from the commonly known direction of (RVF)x Co4Sb12 to CoSb3 when the void is the only soluble site for alkali, alkaline earth, and rare earth element fillers. The experimental phase diagram study is accordingly designed as shown in Section 5.3.3 below.