Interfaces

Given a data set consisting of a large number of pre- dictors plus a response, the problem addressed in this work is to select a minimal model which correctly predicts the response. Methods for achieving this subsetting of the predictors have been the topic of a considerable amount of study within the statistics community. Unfortunately, current methods often fail when

Diffusion bonding of ceramics with a metallic interlayer can give a variety of very complex joint microstruc-tures, which are highly influenced by ceramic compositions, the material and thickness of the interlayer, bonding temperature as well as time at the peak bonding temperature. Experiments with a diffusion bonding of ZrC using a Ti interlayer clearly show that under a certain bonding condition, a seamless joint with the total dissolution of the interlayer can be obtained. They also indicate the existence of the critical interlayer thickness, below which the seamless homogeneous joint domain is obtained, and above which the joint does not homogenize. The key process leading to these outcomes is the diffusion of carbon from ZrC into Ti, which, when the critical carbon concentration is reached, initiates the phase transformation of bcc Ti to TiC, while the binary Zr/Ti diffusion is then driven by entropy and results in a seamless Zr(Ti)C joint. We first show that the dependence of ZrC/Ti interfacial energy on the carbon concentration jump across the interface is the main thermodynamic driving force of the diffusion of carbon from ZrC to the Ti interlayer. Then, we show that the characteristic length (critical thickness of the interlayer) arises as the ratio of this driving force (energy/area) and the bulk energy densities, which oppose the carbon diffusion. Finally, we develop a diffuse interface (phase-field) model to simulate the process. The novelty in the phase-field model is the introduction of a dependence of the interfacial energy on the carbon concentrations on the two sides of the interface. The critical thickness of the interlayer is estimated employing both models and good agreement with experimental findings is obtained.