Metal/ceramics interfaces are object of extensive study, due to their broad technological applications in electronics, catalysis, medicine and engineering.
The definition and prediction of the physical-chemical properties of such a system is a complex problem which has its fundaments in "common" challenges in materials science: the ability to join ceramic parts to metallic alloys is conditioned by the knowledge of the microscopic processes that take place at the interface as a function of the experimental conditions.
In order to properly engineer a metal/ceramic interface, bridging between different approaches in materials science is needed to realize a multiscale approach which combines different
modeling techniques, namely atomistic, thermodynamic and kinetic modeling, as well as continuum mechanics/FEM, and stochastic-kinematic modeling.
The goal is to simulate the interaction between structure and composition of e.g. brazed cBN grains on a micro and nano scale on one hand, and the mechanical performance and long term stability under complex loading conditions on the other.
The problem of metal/ceramic interface is complex and characterized by the ability of a molten alloy to wet the ceramic substrate. The wetting depends on the bonding characteristics of the liquid and the ceramic as well as on the magnitude of interactive forces at the interface.
Moreover, the reactions at molten alloy/ceramic substrate interface involve the formation and subsequent growth of many reaction products whose layering and morphology are the result of the interplay of the thermodynamics and kinetics of the whole system.
A complex metal/ceramic interface is characterized by the coexistence of different phases (e.g. in the case of Ti/cBN, at the interface the TiB TiN and TiB2 phases coexists) so that thermodynamic approaches that allow to compute the different phase equilibria are needed.
How far can we go with ab initio simulations in a realistic description of a metal/ceramic interface?
What information can we get from the electronic structure at the interface in terms of nature of the bonding and its strength?
For this class of systems is it possible to set up a series of ab initio calculations aimed at defining the basic ingredients for a phenomenological (e.g. classical atomistic force fields and mesoscopic coarse graining) large scale approach?
Which kind of physical outcome can we expect from a large scale simulation? Which kind of failures?
At which point an atomistic description has to be abandoned in favor of thermodynamic phase field ap-proaches or continuum models?
Answering these questions should be the starting point for a multiscale approach to the simulation of a complex metal/ceramic interface. During the workshop, experts in different fields of materials science will discuss all these points, from ab initio simulations and large scale molecular dynamics simulations based on empirical potentials up to thermodynamic approaches and continuum models.
State of the art
The realistic simulation of a metal ceramic interface is a challenging problem, a pure ab initio approach would imply unaffordable large size systems. On the other end, ab initio tecniques are mandatory for a correct description of the complex pattern of interactions at the interface.
Large scale systems (several thousands of atoms) are needed to accommodate, without artifacts, all the geometric features (e.g. defects,dislocations,..) that characterize the interface. Only empirical potentials allow for a treatment of large size systems through classical MD based methods or through Monte Carlo methods.
To go beyond the simulation of a model with a geometry fixed by experimental data, it is necessary to combine classical molecular dynamics with methods that allow for enhancing statistical sampling.
We here give a brief summary of the status of the art of computational techniques related to the subject.
The survey is divided in three parts.
Ab initio simulation of interfaces
The microscopic characterization of interfaces with the help of ab initio simulations has reached a considerable level of accuracy and complexity.
With the increase of computational power and the development of new algorithms, realistic modeling of extended systems has become possible in physics, chemistry, and biology (see, e.g., (Allen 2001)); in materials science, phenomenological and semiempirical calculations have gradually left the stage to accurate electronic structure models based on density functional theory (DFT).
Metal/ceramics interfaces, for example, due to the broad technological applications in electronics, catalysis, medicine, engineering, have been object of extensive study (see, e.g., (Finnis 1995) (Finnis 1996)).
Quantities directly accessible to experiments, like the work of adhesion and the work of separation could be computed for systems like metal/sapphire (Kruse 1996), metal/ceramics in presence of Titanium (Lee 1995; Yamazaki 1996; Kostlmeier 2000; Dudiy 2001; Christensen 2002; Dudiy 2004), and several authors developed a theoretical framework to include entropic effects and partial pressure of other elements in the model (Zhang 2000; Xiao-Gang 2002; Wang 2003; Wei-Xue 2003; Chatterjee 2006; Feng 2007; Neurock 2007), or of different orientation of the interface constituents (Dudiy 2004).
Ab initio simulations combined with microscopic statistical mechanics models allowed to extract quantitative predictions concerning the growth of metallic films on insulating substrates (Fuks 2000, Fuks 2002); more recently, the enhancement of metallic wetting at CaF2 surfaces was explained with a detailed inspection to the interfacial electronic structure (Barzilai 2008).
Another very active field of research concerns the interfaces between semiconductors and oxides and their structural properties (Bongiorno 2000; Bongiorno 2002; Bongiorno 2003; Giustino 2005; Fischer 2006; Devynck 2007); here the additional problem being the presence of an amorphous phase like silica, resulting in a complex modelization.
All these studies usually start from models of the interface in the slab geometry with the supercell approach: a suitable number of elementary crystal cells is explicitly included. The electronic degrees of freedom are part of the description, and the structure of the interface is optimized with respect to the total energy of the system.
The interface formation energies and work of separation can be extracted from a series of analogous calculations, but they usually refer to solid phases with plasticity suppressed.
Ab initio thermodynamics or analogous approaches (Finnis 1998; Batyrev 2000; Wei-Xue 2003) can connect finite temperature quantities (free energies, works of adhesion) to the results of zero temperature DFT calculations.
Moreover, a DFT calculation allows to obtain a detailed description of the chemical bonding at the interface. For example, very useful tools for this analysis are the local density of electronic states projected onto the interface atoms or physical quantities related to the electron density like the electron localization function.
Dynamical properties like surface reactions and interfacial diffusion can be studied with DFT-based methods Examples include water/alpha alumina interface (Hass 1998) and again Si/SiO2 (Bongiorno 2005; Andreoni 2006; Fischer 2006; Godet 2006).
Large length and time scales: atomistic interface simulations.
Although ab initio simulations have reached a considerable level of complexity and can provide realistic predictions, most of the length and time scales pertinent to the experimentally accessible macroscopic quantities remain out of reach for "canonical" computational techniques like structural optimization and ab initio molecular dynamics.
One possibility is to include a continuum layer of description in the hierarchy of computational models for the interface. On the other hand, if one wants to stick to an atomistic description, different approaches can be used to overcome size and time limitations.
In order to increase the available system size (from nanometers to micrometers) and simulation times (from picoseconds to microseconds) a first logical step is the development of empirical potentials based on high level ab initio simulations.
Just to confine our analysis to the field of interface science a good example is the development of an augmented Tersoff potential for silicon oxynitride compounds, applied to their interfaces with silicon ((Billeter 2006) see also (Ackland) for a general discussion on empirical potentials).
Several thousands of atoms, different coordinations, defects and diffusive behavior can provide a model of the interface of realistic quality. It was recently shown that the contact angle of wetting can be obtained from classical molecular dynamics simulations with reasonable precision (Webb 2005).
When a time scale gap has to be overcome to describe a "rare event" that is fundamental for the physics of the system different methodologies are available to determine activation barriers (Elber 1987); (Henkelman 2000a; Henkelman 2000b; Galvan 2008), to overcome configurational barriers (Hansmann 1997; Sugita 1999; Bussi 2006) or to force a dynamical simulation to quickly sample the most relevant portion of the phase space (Montalenti 2001; Voter 2002); for a review of the different methods see (Christen 2008))
Thermodynamic calculations Phase-Field Models and continuum models
Computer simulations can provide useful information on the stable and metastable equilibrium phases at the metal/ceramic interface: once all possible reaction products are individually analyzed, the overall equilibrium conditions can be evaluated by CALPHAD method (Sundman 1985).
Recently, CALPHAD simulations have been interconnected with ab initio calculations to provide an even more powerful strategy (see, e.g., Kauf-man 2001). An interesting example of the application of CALPHAD in connection with phase field models (see below) for the evaluation of the equilibrium phases at the interface (together with heterogeneous nu-cleation) between immiscible metals can be found in (Toth 2007).
Another possible approach to characterize the the equilibrium phases at the interface relies on Phase Field Models: the sequence of reaction products is divided into separate steps which are individually analyzed and then coupled in a way to satisfy equilibrium and conservation conditions (2008 Moelans).
These models can incorporate physical effects such as interface kinetics and surface tension anisotropy in a natural manner, since the underlying formalism is based on a consistent thermodynamic description of the system (Visintin 1997).
Finally, to obtain a macroscopic description of the mechanical properties of the interface, continuum models have to be employed, cohesive models have been developed for several purposes (see Tvergaard 2003, Schwalbe 2003), mainly for the description of crack propagation and debonding between hard and ductile phases. In (Wegener 1995, 1999) constitutive equations for time dependent plasticity of metals have been derived and, in (Wegener 1996) the interrelationship between phenomenological modeling and physical principles of metals has been pointed out.
The experimental literature on the metal/ceramic interface is extremely wide and goes beyond the aim of this proposal. However we give a reference to the main experimental techniques that are commonly used to characterize metal/ceramic interfaces. We just give a reference to a review on sessile drop for wetting measurements (Eustathopoulos 1999, Eustathopoulos 2005) and we remind that different microscopic techniques are usually employed to characterize the interface composition: e.g. Scanning/Transmission Electron Microscopy, Electron Probe Micro-Analyzer, Focussed Ion Beam, (S)TEM + Energy Dispersive Xray analysis as well as x-ray diffraction and Raman spectroscopy. Moreover, sessile drop techniques allow to follow the reactive wetting in an efficient fashion (Hodaj 2007). The role of anisotropy in the wetting behavior has been recently reviewed by Chatain (Chatain 2008).
Finally, we cite the remarkable efforts to relate high temperature wetting experiments with thermodynamical models, done in the groups of D. Chatain, N. Eustathopoulos and A. Passerone (for an example concerning oxygen adsorption isotherms, see e.g., Ghetta 1996, Arato 2008, Giuranno 2006, Novakovic 2005a, Novakovic 2005b Passerone 2008, Muolo 2008)