Diffusion bonding of ceramics with a metallic interlayer can deliver a variety of joint microstructures including a seamless bond.  When applied to ZrC with Ti interlayer such procedure can deliver the seamless joint, depending on the parameters of the process, of which the thickness of the interlayer is particularly relevant.  Experiments indicate existence of the critical interlayer thickness, below which the seamless homogeneous joint is obtained, and above which the joint does not homogenize.
 
We analyze the thermodynamics and kinetics of the diffusion bonding process with metallic interlayer, uncover the driving forces for the diffusion and phase transformations, and, explain the critical thickness of the interlayer.  We begin with the sharp interface thermodynamics, then develop the phase field model which predicts the observed behavior.
 
During the bonding procedure (heating-hold-cooling), Ti first undergoes phase transformation from hcp to bcc.  This and the thermal expansion mismatch between Ti and ZrC results in the compressive stresses in Ti.  At hold temperature, the key process is the diffusion of carbon from ZrC into Ti, which, when the critical carbon concentration is reached, initiates the phase transformation of bcc Ti (with interstitial C) to B1 structure (TiC) identical to ZrC structure.  The binary Zr/Ti diffusion is then driven by entropy and results in a seamless Zr(Ti)C joint.
 
Analysis of phase diagrams of Zr-C and Ti-C systems and elastic strain energies indicate that the changes bulk free energies resulting from small changes in carbon concentrations oppose the diffusion of carbon.We show that the only component of the total system energy that decreases with carbon transfer from ZrC to Ti is the interface energy.Specifically, the interface energy must depend on the jump in the carbon concentration across the interface, in such a way that a lower concentration jump produces a lower interface energy.
 
The critical film thickness is then estimated as the ratio of the change in interface energy with the concentration jump to the change in bulk energy density (elastic and/or chemical). The sharp interface model yields an estimate for the critical thickness of 10 microns, while the phase field simulations of the diffusion bonding process with a range of film thicknesses predicts the value of 32 microns, both in good agreement with experimental findings (10-50 microns).
 
The analysis and methods are applicable to the broad range of transition metal carbides.
 
References:
 
[1]        R. Pan, H. Wei, T. Lin, P. He, D.P. Sekulic, Q. Wang, X. Duan, 2016 Homogenization of the zirconium carbide_titanium interface domain. Scripta Mater. 112, 42–45.
[2]        Kovacevic, S., Pan, R., Sekulic, D.P. & Mesarovic, S.D.  2020. Interfacial energy as the driving force for diffusion bonding of ceramics.  Acta Mater. 186, 405–414.