Atomistic Simulation of Ceramic/Metal Interfaces

Ceramic/metal interfaces are prominent in such applications as metal/matrix composites, electronic packaging, catalytic systems, and high-temperature alloy coatings. An understanding of interface structure and chemistry on an atomic scale would provide valuable guidance for optimizing performance and lifetime of the material. Owing to the complexity of ceramic/metal interfaces, their atomistic modeling has been limited. This report summarizes our recent progress in the development of realistic atomistic simulations for ceramic/metal interfaces.

Interatomic Potentials for Ceramic/Metal Interfaces: Interatomic potential models that describe either bulk metals (e.g., the embedded-atom method) or ionic crystals (e.g., the Born model, or the shell model) are reasonably accurate for many materials and have been employed to simulate grain boundaries in homogeneous (metallic or ionic) systems. The lack of a suitable model for the interatomic forces at ceramic/metal interfaces, however, has been a significant obstacle to atomistic simulations for such heterophase systems. Before such force models can be devised, the microscopic nature of the adhesion mechanism must be known. The results of ab initio local-density-functional-theory electronic structure calculations, as well as experiments, indicate that even for relatively weakly bonded ceramic/metal interfaces, such as MgO/Ag (100), chemical bonding at the interface dominates over weaker van der Waals and image-force contributions to adhesion. Our efforts have focused on the ``polar'' interface MgO/Cu (111), in which the ceramic consists of purely anion and purely cation layers parallel to the interface, and for which chemical bonding is even more dominant than for the MgO/Ag (100) [or MgO/Cu (100)] interface. An important implication of the dominance of chemical bonding is that forces are relatively short range, a feature advantageous to atomistic simulations.

MgO/Cu (111) Interface: MgO/Cu (111) was selected as an initial target system for our simulations for several reasons. This interface is well characterized experimentally by both atom-probe-field-ion microscopy (APFIM) and high-resolution electron microscopy (HREM) measurements. The APFIM measurements show chemically sharp interfaces between MgO precipitates and the matrix in internally oxidized Cu specimens; this means that essentially no atomic intermixing occurs between the MgO (bi)layers on one side of the interface and the Cu layers on the other. The HREM measurements show ``coherent interface'' regions (where there is a one-to-one relation between the Cu atoms on one side of the interface and O [or Mg] atoms on the other) interrupted by misfit dislocations. Misfit dislocations are a characteristic feature of ceramic/metal interfaces and result from the mismatch between the ceramic and metal lattice constants. Since the mismatch for MgOCu (111) is large (about 14%), the misfit dislocations are relatively dense, with approximately one dislocation for every seven atoms in a row. This high dislocation density is favorable for simulation, since it reduces the cell size required to encompass the characteristic dislocation structures in molecular dynamics or Monte Carlo simulations. MgO/Cu (111) is the only orientation that is observed in the APFIM observations of internally oxidized Cu(Mg) specimens, which suggests that this orientation is thermodynamically the most stable.

Approach: The most reliable framework for the calculation of cohesive energies in condensed matter is local-density-functional theory (LDFT), within which single-electron orbitals are determined self-consistently, and then employed to calculate the total electronic density and the total internal energy. Within this framework, the predominance of chemical bonding at some prototype ceramic/metal interfaces was established. The large numerical effort in LDFT calculations, however, restricts their application to cells with at most a few dozen atoms. Even systems with relatively small spacing of misfit dislocations require hundreds (or thousands) of atoms, for which LDFT calculations would not currently be feasible. Since misfit is an important feature of ceramic/metal interfaces, we pursue a different approach that will enable atomistic simulations on a sufficiently large scale to treat misfit dislocations. Specifically, we employ LDFT total-energy calculations for selected interface configurations (without misfit) to establish a database from which effective interface potentials may be determined. The resultant interface potentials, in conjunction with appropriate potentials for the bulk metal and bulk ceramic, will then be employed in large scale molecular dynamics or Monte Carlo simulations.

Results: LDFT calculations for MgO/Cu (111) are performed for a unit cell with the Cu lattice parameter parallel to the interface stretched to the observed value for MgO, so that no misfit is present (this device is employed here for the purpose of determining the interatomic forces; however, one can also view these calculations as a representation of the coherent regions of the interface). The results presented here correspond to the oxygen ``termination'', which means that the (111) layer on the MgO side of the interface consists of O rather than Mg atoms. The equilibrium separation of the Cu and the O layers at the interface is that at which chemical bonding is maximized, which occurs when the total internal energy is minimized. The total energy as a function of the interface separation is referred to as the adhesive-energy curve. Besides the interface separation, two other significant degrees of freedom must be specified, namely the translation parallel to the interface of the Cu interface layer relative to the O interface layer. Thus a different adhesive-energy curve exists for each choice of the parallel translation vector. Two limiting cases are (1) the ``hollow'' position, in which the Cu atoms lie equidistant from three nearest-neighbor O atoms at the interface, and (2) the ``on top'' position where the Cu atoms are directly opposite the O atoms at the interface. Adhesive energy curves were performed for these two configurations, as well as several others, to establish the general pattern of behavior. The calculations were performed within the plane-wave-pseudopotential representation of LDFT, and the electron orbitals were obtained with a ``band-by-band'' conjugate gradient algorithm. Unit-cells with 9 atoms (3MgO and 3 Cu layers) were employed. A converged result for each configuration (specified by a given interface separation and parallel translation vector) required 10-20 CPU-hours on the NERSC C-90.

The results of these calculations are shown in figure 20. The inset to figure 20 shows the relative shift of the Cu interface layer relative to the O interface layer. The filled inverted triangle corresponds to the hollow site, and the open inverted triangle to the on-top position. An expected feature of the results is that at large enough interface separations, z, the adhesive energy curves essentially all coincide, and the results are insensitive to the parallel translation vector. For smaller values of z, the adhesive energy curve for the hollow position shows the largest binding and that for the on-top position the least. The adhesive energy for the hollow position can be regarded as defining a universal envelope curve, to which the others approach asymptotically at large z. This envelope curve can be fit accurately to an analytical form known as the ``Universal binding energy'' curve,

**Figure 20:** Results of local-density-function theory adhesive energy calculations for oxygen-terminated MgO/Cu (111) interface. The symbols represent the LDFT calculations and the continuous curves are the predictions of the model, E = E1 + E2 (see text), as a function of interface separation z. The inset shows relative position of interface Cu and O layers parallel to the interface. The triangular lattice of the (111) layers has six-fold rotational symmetry. Filled inverted triangle represents hollow site, and open inverted triangle represents on-top position.
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It is perhaps surprising that the bonding (i.e., negative) contributions to E, which occur only in E1, do not depend explicitly on CuO bond lengths and angles, as one would expect for ionic or covalent bonding, but only on the interface separation z. This may signify that the interface oxygen layer has become effectively ``metallized'' as a result of strong hybridization with the interface Cu layer, so that bond lengths and angles are less important than total ``volume'' (proportional to z).

The analytical expression given by (6) provides a tractable model for large-scale atomistic simulation, by either molecular dynamics or Monte Carlo, of the MgO/Cu (111) interface. Efforts are now underway to implement (6) into an existing parallel MD code, for processing on the T3D at NERSC. In our initial calculations, the MgO layers, which are elastically much more rigid than Cu, will be frozen, and only the metal atoms will be allowed to relax. Functionally, the interface simulation then reduces to the simulation of a metal (interacting via an embedded atom model potential), subject to the boundary condition specified by (6).

Utilizing the present approach, predictions of the atomistic structure of MgO/Cu(111) will be made, including lattice parameter misfit and the consequent misfit dislocation array. Results of these simulations will be compared with HREM observations, to test the validity of the model. Upon completing these preliminary tests, we will extend the simulations to address more detailed properties, such as the interactions and segregation of solutes to metal/ceramic interfaces, and mechanical properties.

NERSC 3 Greenbook

Atomistic Simulation of Ceramic/Metal Interfaces

NERSC 3 Greenbook