The Effect of Undercooling on Solidification of YSZ Splats

Abstract

We consider the rapid solidification of a molten YSZ particle, by solving the so-called hyperbolic equations for heat and mass transfer. The hyperbolic model predicts the interface undercooling (due to thermal and solutal effects) and velocity as a function of time, as well as the yttria redistribution within the solid phase. Results are then compared to corresponding ones that we obtained from a parabolic model, to assess the extent to which YSZ solidification is influenced by nonequilibrium effects. Results indicate that these effects are limited to the early part of the solidification process when undercooling is most significant. At this stage, the interface velocity is unsteady, and solute redistribution is most evident. As solidification decelerates, the nonequilibrium effects wane and solidification can then be properly modeled as an equilibrium process.

Experiments and modeling of rapid solidification of plasma-sprayed yttria-stabilized zirconia

“…The physical properties of YSZ [15] used for the simulations are given in Table 2. Results were calculated for a 10 lm thick splat, admittedly thicker than the splat of Fig.…”

“…At the splat/ substrate interface, we prescribed a value of the heat transfer coefficient in the range h ¼ 5:0 Â 10 5 to 1:0 Â 10 7 Wm À2 K À1 , that is usually associated with thermal spray splat solidification. The equilibrium melting temperature of YSZ is 2950 K [15]; we specified an initial undercooling of either 150 or 700 K, leading to the onset of grain growth when the temperature at the splat/substrate interface initially reached 2800 or 2250 K, respectively. The 150 K undercooling was also specified by Wang [11]; the 700 K undercooling comes from Fig.…”

“…Yet YSZ has a low diffusive speed V D $ 1 m s À1 [11]. As a result, use of the traditional Fourier's and Fick's laws is questionable, because they assume an infinite velocity of heat and mass propagation [15]. A more general approach is a hyperbolic model obtained by adding a relaxation term (proportional to a relaxation time s D ) to the standard parabolic diffusion equations.…”

“…Combining these laws with equations for conservation of energy and concentration yields the following hyperbolic equations [15]:…”

“…When h is high, the results vary little with undercooling, because regardless of its value, T i drops very rapidly from the initial liquid temperature Table 2 Physical properties of YSZ used in the calculations [15].…”