Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain boundaries play an essential role in defining the effective properties of materials across multiple scales. In this paper we derive a Fokker–Planck model for the evolution of the planar grain boundary network. The proposed model considers anisotropic grain boundary energy which depends on lattice misorientation and takes into account mobility of the triple junctions, as well as independent dynamics of the misorientations. We establish long time asymptotics of the Fokker–Planck solution, namely the joint probability density function of misorientations and triple junctions, and closely related the marginal probability density of misorientations. Moreover, for an equilibrium configuration of a boundary network, we derive explicit local algebraic relations, a generalized Herring Condition formula, as well as formula that connects grain boundary energy density with the geometry of the grain boundaries that share a triple junction. Although the stochastic model neglects the explicit interactions and correlations among triple junctions, the considered specific form of the noise, under the fluctuation–dissipation assumption, provides partial information about evolution of a grain boundary network, and is consistent with presented results of extensive grain growth simulations.
more »
« less
This content will become publicly available on December 1, 2024
Point process microstructural model of metallic thin films with implications for coarsening
Abstract We develop a thin-film microstructural model that represents structural markers (i.e., triple junctions in the two-dimensional projections of the structure of films with columnar grains) in terms of a stochastic, marked point process and the microstructure itself in terms of a grain-boundary network. The advantage of this representation is that it is conveniently applicable to the characterization of microstructures obtained from crystal orientation mapping, leading to a picture of an ensemble of interacting triple junctions, while providing results that inform grain-growth models with experimental data. More specifically, calculated quantities such as pair, partial pair and mark correlation functions, along with the microstructural mutual information (entropy), highlight effective triple junction interactions that dictate microstructural evolution. To validate this approach, we characterize microstructures from Al thin films via crystal orientation mapping and formulate an approach, akin to classical density functional theory, to describe grain growth that embodies triple-junction interactions.
more »
« less
- NSF-PAR ID:
- 10431546
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 9
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Atom probe tomography (APT) of a nanocrystalline Cu–7 at.% V thin film annealed at 400°C for 1 h revealed chemical partitioning in the form of solute segregation. The vanadium precipitated along high angle grain boundaries and at triple junctions, determined by cross-correlative precession electron diffraction of the APT specimen. Upon field evaporation, the V 2+ /(V 1+ + VH 1+ ) ratio from the decomposed ions was ~3 within the matrix grains and ~16 within the vanadium precipitates. It was found that the VH 1+ complex was prevalent in the matrix, with its presence explained in terms of hydrogen's ability to assist in field evaporation. The change in the V 2+ /(V 1+ + VH 1+ ) charge-state ratio (CSR) was studied as a function of base temperature (25–90 K), laser pulse energy (50–200 pJ), and grain orientation. The strongest influence on changing the CSR was with the varied pulse laser, which made the CSR between the precipitates and the matrix equivalent at the higher laser pulse energies. However, at these conditions, the precipitates began to coarsen. The collective results of the CSRs are discussed in terms of field strengths related to the chemical coordination.more » « less
-
Español, M ; Lewicka, M ; Scardia, L ; Schlömerkemper, A (Ed.)Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a crucial role in determining the grain structure and defining the materials properties across multiple scales. In this work, we consider two models for the motion of grain boundaries with the dynamic lattice misorientations and the triple junctions drag, and we conduct extensive numerical study of the models, as well as present relevant experimental results of grain growth in thin films.more » « less
-
more » « less
AlN thin films are enabling significant progress in modern optoelectronics, power electronics, and microelectromechanical systems. The various AlN growth methods and conditions lead to different film microstructures. In this report, phonon scattering mechanisms that impact the cross-plane (κz; along the c-axis) and in-plane (κr; parallel to the c-plane) thermal conductivities of AlN thin films prepared by various synthesis techniques are investigated. In contrast to bulk single crystal AlN with an isotropic thermal conductivity of ∼330 W/m K, a strong anisotropy in the thermal conductivity is observed in the thin films. The κz shows a strong film thickness dependence due to phonon-boundary scattering. Electron microscopy reveals the presence of grain boundaries and dislocations that limit the κr. For instance, oriented films prepared by reactive sputtering possess lateral crystalline grain sizes ranging from 20 to 40 nm that significantly lower the κr to ∼30 W/m K. Simulation results suggest that the self-heating in AlN film bulk acoustic resonators can significantly impact the power handling capability of RF filters. A device employing an oriented film as the active piezoelectric layer shows an ∼2.5× higher device peak temperature as compared to a device based on an epitaxial film.
-
more » « less
Abstract A multistep deposition technique is developed to produce highly oriented diamond films by hot filament chemical vapor deposition (HFCVD) on Si (111) substrates. The orientation is produced by use of a thin, 5–20 nm, Ni interlayer. Annealing studies demonstrate diffusion of Ni into Si to form nickel silicides with crystal structure depending on temperature. The HFCVD diamond film with Ni interlayer results in reduced non-diamond carbon, low surface roughness, high diamond crystal quality, and increased texturing relative to growth on bare silicon wafers. X-ray diffraction results show that the diamond film grown with 10 nm Ni interlayer yielded 92.5% of the diamond grains oriented along the (110) crystal planes with ~ 2.5 µm thickness and large average grain size ~ 1.45 µm based on scanning electron microscopy. Texture is also observed to develop for ~ 300 nm thick diamond films with ~ 89.0% of the grains oriented along the (110) crystal plane direction. These results are significantly better than diamond grown on Si (111) without Ni layer with the same HFCVD conditions. The oriented growth of diamond film on Ni interlayers is explained by a proposed model wherein the nano-diamond seeds becoming oriented relative to the β1-Ni3Si that forms during the diamond nucleation period. The model also explains the silicidation and diamond growth processes.
Article Highlights High quality diamond film with minimum surface roughness and ~93% oriented grains along (110) crystallographic direction is grown on Si substrate using a thin 5 to 20 nm nickel layer.
A detailed report on the formation of different phases of nickel silicide, its stability with different temperature, and its role for diamond film texturing at HFCVD growth condition is presented.
A diamond growth model on Si substrate with Ni interlayer to grow high quality-oriented diamond film is established.
