Influence of silver nanoparticle addition, porosity, and processing technique on the mechanical properties of Ba_0.3Co₄Sb₁₂ skutterudites

Abstract

The thermoelectric skutterudite Ba_0.3Co₄Sb₁₂ is a promising candidate for waste heat recovery applications. Recently, it was demonstrated that the addition of silver nanoparticles (Ag_NP) to Ba_0.3Co₄Sb₁₂ increases both the thermoelectric figure of merit and electrical conductivity. This study is the first to examine the effect of Ag_NP addition on the material’s mechanical properties. This study also found that the Young’s modulus, E, shear modulus, G, and bulk modulus, B, decreased linearly with increasing volume fraction porosity, P. Resonant ultrasound spectroscopy was employed to measure the elastic moduli, and Vickers indentation was used to determine the hardness, H, and fracture toughness, K _C. Trends in the mechanical properties as a function of grain size, porosity, and the Ag_NP are discussed in terms of the pertinent literature. While K _C was independent of Ag_NP addition, porosity, and grain size, both E and H decreased linearly with increasing porosity. In addition, this study is the first to identify (i) the Ag₃Sb phase formed and (ii) the enhanced densification that occurs when the Ag_NP is sintered with Ba_0.3Co₄Sb₁₂ powders, where both effects are consistent with the eutectic and peritectic reactions observed in the binary phase diagram Ag–Sb. These eutectic/peritectic reactions may also be linked to the enhancement of electrical conductivity previously observed when Ag is added to Ba_0.3Co₄Sb₁₂. Also, similar beneficial eutectic/peritectic reactions may be available for other systems where conductive particles are added to other antimonides or other thermoelectric systems.

Appendix A: Effect of nanoparticle addition on the elastic modulus of a composite material

The effect of the nanoparticle additions on the Young’s modulus, E _C, of a nanocomposites material can be predicted from numerous models. In this Appendix, we list relationships for four composite models, namely rule of mixtures (ROM), Reuss constant strain (RCS), Hashin particulate (HP), and Halpin–Tsai (HT) [90]. For each model, the Young’s modulus of the composite, E _C, is the based on E _r, the elastic modulus of the nanoparticle reinforcement phase, V _r, the volume fraction reinforcement phase, E _m, the Young’s modulus of the matrix phase, and, V _m, the volume fraction matrix phase. Expressions for the four models can be written as

$$ {\text{ROM}}: E_{\text{C}} = V_{\text{m}} E_{\text{m}} + V_{\text{r}} E_{\text{r}} $$

(8)

$$ {\text{RCS}}:\frac{1}{{E_{\text{C}} }} = \frac{{V_{\text{m}} }}{{E_{\text{m}} }} + \frac{{V_{\text{r}} }}{{E_{\text{r}} }} $$

(9)

$$ {\text{HP}}:E_{\text{C}} = E_{\text{m}} \left( {\frac{{E_{\text{m}} V_{\text{m}} + E_{\text{r}} \left\{ {V_{\text{f}} + 1} \right\}}}{{E_{\text{r}} V_{\text{m}} + E_{\text{m}} \left\{ {V_{\text{r}} + 1} \right\}}}} \right) $$

(10)

$$ {\text{HT}}:E_{\text{C}} = E_{\text{m}} \left( {\frac{{1 + 2(a/b)qV_{\text{r}} }}{{E_{\text{r}} V_{\text{m}} + E_{\text{m}} \left\{ {V_{\text{r}} + 1} \right\}}}} \right) $$

(11)

In the HT model, a/b is the aspect ratio (length/thickness) for the reinforcing phase and q is a boundary condition parameter given by

$$ q = \frac{{\left( {\frac{{E_{\text{r}} }}{{E_{\text{m}} }}} \right) - 1}}{{\left( {\frac{{E_{\text{r}} }}{{E_{\text{m}} }}} \right) + 2\left( \frac{a}{b} \right)}} $$

(12)

Table 8 summarizes the Young’s modulus change due to the addition of both micron-sized and nanosized-metallic particles to brittle matrices in studies by Hasselman [91] and by Fujieda et al. [64]. Table 8 gives the measured composite modulus, E _C, for the addition of 0.10, 0.20, 0.30, and 0.40 volume fraction of tungsten particles with diameters of approximately 30 µm to a borosilicate glass [91], along with the predicted values of modulus calculated by the ROM, RCS, HP, HT models and the modulus of tungsten [92]. In addition, Table 8 lists the measured E _C, for composite specimens from Fujieda et al. [64], who measured the elastic modulus change induced by adding either 26 wt % platinum nanoparticles (Pt_NP) [93] or 26 wt % Ag_NP [94, 95] to a dental porcelain, where the mean diameters of the Pt_NP and Ag_NP nanoparticles were 5 nm and 10 nm, respectively. The measured composite moduli, E _C, (Table 8) [64, 91] agree quite well with the moduli calculated in this study using the Halpin–Tsai model (HT). Since the metal particles were spherical in both the Hasselman [91] and Fujieda et al. [64] studies, for the purposes of the calculations, we set a/b = 1 in Eq. (11), where a/b is the particle aspect ratio.

The amounts of particle addition in the studies by Fujieda et al. [64] and Hasselman [91] were significantly greater than the 0.0068 volume fraction (0.5 wt %) Ag_NP added in this study. The four composite models given in this Appendix predict a decrease in E _C of about 0.39 % with the 0.5 wt % Ag_NP addition to the Ba-skutterudite in this study. In recent research by Schmidt et al. [90] applied the four modulus-composite models to a thermoelectric system consisting of a brittle matrix and a brittle reinforcing phase, namely with 0.00, 0.01, 0.02, 0.03, and 0.04 volume fraction of added SiC nanoparticles (SiC_NP) in the brittle thermoelectric matrix SnTe_1+X , (where x = 0.0 or 0.016), Hashin and the Halpin–Tsai models best described the elastic modulus data. Thus, for the Hasselman [91] and Fujieda et al. [64] studies in which the volume percentage of micro- and nano-particles added was relatively high (from 0.10 to 0.40 volume fraction), as well as the SnTe_1+X (with 0.00 to 0.04 volume fraction SiC_NP added), the Haplin–Tsai model agrees with the experimental modulus data relatively well. In particular, for 0.5 wt % Ag_NP in this study, the Haplin–Tsai model predicts a change in E of only 0.35 %, which is consistent with the E values measured in this study for the Ba-skutterudite with and without added Ag_NP.