Optimizing Thermoelectric Properties of In Situ Plasma-Spray-Synthesized Sub-stoichiometric TiO_2−x Deposits

Abstract

In this article, an attempt has been made to relate the thermoelectric properties of thermal spray deposits of sub-stoichiometric titania to process-induced phase and microstructural variances. The TiO_2−x deposits were formed through the in situ reaction of the TiO_1.9 or TiO_1.7 feedstock within the high-temperature plasma flame and manipulated via varying the amounts of hydrogen fed into in the thermal plasma. Changes in the flow rates of H₂ in the plasma plume greatly affected the in-flight particle behavior and composition of the deposits. For reference, a high-velocity oxy-fuel spray torch was also used to deposit the two varieties of feedstocks. Refinements to the representation of the in-flight particle characteristics derived via single particle and ensemble diagnostic methods are proposed using the group parameters (melting index and kinetic energy). The results show that depending on the value of the melting index, there is an inverse proportional relationship between electrical conductivity and Seebeck coefficient, whereas thermal conductivity has a directly proportional relationship with the electrical conductivity. Retention of the original phase and reduced decomposition is beneficial to retain the high Seebeck coefficient or the high electrical conductivity in the TiO₂ system.

Appendix

The earlier work by Vaidya et al. (Ref 21) has shown that the melting state of ceramic particles can be described through group parameter referred to as melting index. This is expressed as:

$${\text{M}} . {\text{I}} .= \frac{{T_{\text{s}} \Delta t_{\text{fly}} }}{D},$$

(2)

where T_s is the measured particle surface temperature (K), Δt_fly is the particle in-flight time assuming the constant acceleration of particles (s), and D is the particle size (m), which has the following expression:

$$\Delta t_{\text{fly}} = \frac{2L}{v},$$

(3)

where L is the spray distance (m) and v is the particle velocity (m s⁻¹). More comprehensive formulations have been derived by Zhang et al. (Ref 35) redefined as

$${\text{M}} . {\text{I}} .= \frac{{\Delta t_{\text{fly}} }}{{\Delta t_{\text{melt}} }} \approx \alpha \frac{{\left( {T_{\text{s}} - T_{\text{m}} } \right) \Delta t_{\text{fly}} }}{D}\quad {\text{where}}\,\alpha = A\frac{6h}{{\rho h_{fg} }}\quad {\text{for}}\,{\text{Bi}}{<<}\,1$$

(4)

$$A = \frac{{T_{\text{f}} - T_{\text{m}} }}{{T_{\text{s}} - T_{\text{m}} }}$$

(5)

$${\text{Bi}} = \frac{hD}{{k_{\text{l}} }},$$

(6)

where ΔT_melt is the total melting time (s), T_m is particle melting temperature (K), A is dimensionless factor, h is heat transfer coefficient (W m⁻² k⁻¹), ρ is particle density (kg m⁻³), h_fg is enthalpy of fusion (kJ kg⁻¹), Bi is Biot number, T_f is flame temperature (K), and k_l is thermal conductivity of liquid material (W m⁻¹ k⁻¹), respectively.

Another group parameter Reynolds number refers to

$$Re = \frac{\rho vD}{\mu } = \frac{vD}{\upsilon },$$

(7)

where µ is dynamic viscosity (Ns m⁻² or kg m⁻¹ s⁻¹) and υ is kinematic viscosity (m² s⁻¹). In this paper, the assumption was made for T_f = T_s since flame temperature around particles is not constant during the time of flight and it is not possible to measure it accurately. For TiO_1.9 and TiO_1.7 feedstock, the density and particle melting index were measured to be 3.973 and 3.917 kg m⁻³, and 1942 and 1868 K, respectively. The heat transfer coefficient h was assumed constant for all calculations. Thermophysical properties used in the calculations are summarized in Table 3.

Table 3 Thermophysical properties of TiO_2−x used in the calculations