ICMCTF 2023 Session B6-MoA: Computationally-aided Materials Design

Sustainable energy strategies, particularly solar-to-hydrogen production, are anticipated to overcome the global reliance on fossil fuels. Thereby, materials enabling the production of green hydrogen from water and sunlight are continuously designed, e.g., ZnO nanostructures coated by gold sea-urchin-like nanoparticles, which employ the light-to-plasmon resonance to realize photoelectrochemical water splitting. Due to the complex growth of Gold sea-urchin-like nanoparticles (GSNPs) and the need for a precise prediction of their surface plasmon wavelength, genetic-algorithm-based artificial neural networks (GANNs) are used to determine the relationship between synthesis parameters and the surface plasmon wavelength of GSNPs grown via seed-mediated growth assisted by machine learning. Herein, a low-data test is trained by varying the ratio and concentration of gold seeds, sodium citrate, hydroquinone, and HAuCl₄. Then, a big data confirmation is conducted through massive parameter collection from over 684 samples. The well-trained GANN can guide parameter selection for seed-mediated growth to obtain the desired surface plasmon wavelength. In additions, such light-to-plasmon resonance is strongly impacted by the size, the species, and the concentration of the metal nanoparticles coating on the ZnO nanoflower surfaces. Therefore, a precise prediction of the surface plasmon resonance is crucial to achieving an optimized nanoparticle fabrication of the desired light-to-plasmon resonance. To this end, we synthesized a substantial amount of metal (gold) nanoparticles of different sizes and species, which are further coated on ZnO nanoflowers. Subsequently, we utilized a genetic algorithm neural network (GANN) to obtain the synergistically trained model by considering the light-to-plasmon conversion efficiencies and fabrication parameters, such as multiple metal species, precursor concentrations, surfactant concentrations, linker concentrations, and coating times. In addition, we integrated into the model's training the data of nanoparticles due to their inherent complexity, which manifests the light-to-plasmon conversion efficiency far from the coupling state. Therefore, the trained model can guide us to obtain a rapid and automatic selection of fabrication parameters of the nanoparticles with the anticipated light-to-plasmon resonance, which is more efficient than an empirical selection. The capability of the method achieved in this work furthermore demonstrates a successful projection of the light-to-plasmon conversion efficiency and contributes to an efficient selection of the fabrication parameters leading to the anticipated properties.

We introduce a Bayesian optimization (BayesOpt) based approach to guide the sputter deposition of molybdenum (Mo) thin films with desired residual stress and electrical resistivity. Thin films are of key importance in various technologies, including, e.g., semiconductor and optical devices. In thin film sputter deposition, process parameters, such as deposition power, vacuum chamber pressure, and working distance, can affect film physical properties, such as residual stress and resistivity. Excessive film residual stress as well as high resistivity can negatively affect the performance of devices; hence, choosing the optimum combination of process parameters that produce thin films with residual stress and resistivity within a desired range is essential. However, considering that the experiment is the available black-box "function" to evaluate these physical properties from process parameters, it is clear that the associated expense of full exploration of the design space for process optimization purposes is prohibitively expensive. BayesOpt is ideal for optimizing black-box functions without reliance on gradient information, and can find optimal process parameters with minimal evaluations.

In this work, we seek a combination of two primary process parameters (deposition power and pressure) such that 1) residual stress and resistivity of Mo thin films are within a specified range, and 2) the variations in the stress are least susceptible to stochastic fluctuations in the deposition process parameters. To achieve this, we use BayesOpt to optimize an objective function, custom-built using observed stress and resistivity data, targeting both criteria. This involves incorporation of knowledge of stress dependence on pressure obtained from existing experimental observations into a stress-pressure surrogate, whose gradients are employed in the objective function. This surrogate, and thus the objective function, are updated based after each new measurement, ahead of the next BayesOpt step. We illustrate the performance of BayesOpt in the exploration of the Mo thin film deposition design space (power and pressure), arriving at optimal conditions that meet desired constraints on stress and resistivity.

Metastable Mo_1-xSi_x¹and Mo_1-xNi_x² alloy films with 0 ≤ x ≤ 1 were elaborated by magnetron co-sputtering. Amorphous or crystalline state were identified by x-ray diffraction while their mass density and atomic volume by x-ray reflectivity. Their elastic properties were investigated by combining the Brillouin light scattering (BLS) and the picoseconds ultrasonics (PU) techniques with additional conventional nanoindentation tests. A transition from bcc-crystalline to amorphous state is observed for a Si content, x_Si ~ 0.19 and Ni content, x_Ni ~ 0.26 while fcc-crystalline to amorphous state transition is observed for x_Ni ~ 0.73. These structural transitions are accompanied by modifications of physical and mechanical properties s, namely, longitudinal out-of-plane modulus C₃₃, and out-of-plane shear modulus C₄₄. In the crystalline regions, a pronounced softening of the shear elastic C₄₄ constant from 110 GPa to 60 GPa for MoSi and from 65 GPa to 45 GPa for MoNi, is observed. The longitudinal modulus C₃₃ has experienced a softening from 420 GPa to 300 GPa for MoSi and from 390 GPa to 280 GPa from both pure Mo and Ni. This behavior is an intrinsic consequence of the high Si and Ni supersaturation, leading to lattice instability. In the MoSi amorphous state, the evolution of the elastic properties exhibits two distinct behaviors depending on the electronic properties and metallic or covalent character of the amorphous alloys. For 0.19 ≤ x_Si ≤ 0.5, the metallic character of the solid solutions is maintained and the elastic properties are remarkably stable. For x_Si > 0.5, a reduction in the atomic density is progressively observed and the amorphous alloys acquire a covalent character. We are again witnessing a progressive softening of the elastic stiffness constants while, surprisingly, both the longitudinal and transverse acoustic velocities increase continuously. In general, the analysis of the evolutions generally highlights the interdependence between the structural and elastic properties of the non-equilibrium phases formed between Mo and Si or Ni. Inter-relationships are discussed with help of ab initio molecular dynamics (AIMD) and density functional theory calculations (DFT).Glassy solid state of alloys made of 256 atoms, was obtained from cooling down the melt from 3500 K to 300 K using the NVT ensemble and the Nose thermostat, followed by a relaxation of the cell with NPT ensemble and Langevin thermostat for at least 15 ps by steps of 1.5 fs. Special quasi-random structures were built to mimic the random crystalline alloys.

¹A Fillon et al., Phys.Rev.B 88, 174104(1-16) (2013)

²G. Abadias et al., Phys.Rev.B 65, pp. 212105(1-4) (2002)

Nitride-based ceramic materials serve high hardness and good thermal stability and have been attractive for high-temperature applications for decades. To improve these properties of materials in ceramics, the concept of alloying was revolutionized in multi-component or high-entropy alloys (HEAs), where five or more elements are distributed randomly on a crystalline lattice in equiatomic or near-equiatomic composition. One crucial form of these ceramics is high-entropy sublattice nitride (HESN), which is built upon the concept of HEAs. Four core effects have been postulated for such materials to stem from the configuration entropy: high configurational entropy, severe lattice distortion, sluggish diffusion, and cocktail effects.

Ab-initio calculations have proven an efficient tool for exploration of fundamental material properties. However, in the context of solid solutions, the required cell dimensions for accurate predictions still require significant computational expense, barring the progress in high-throughput exploration. We have remedied this weakness with machine-learning (ML) models that are trained on the results of density-functional theory calculations, thus guiding the computationally expensive ab-initio exploration by computationally cheap data science.
We investigated the phase space of all equimolar fcc solid solution nitrides of the group IVb-VIb nitrides + Al, with 1 to 5 metals in the compounds.

Using the DFT calculated energies of the multinary nitrides (published in [1]), we obtained the driving force for decomposition of the equiatomic multinary solid solutions into more stable phases for more than 16000 individual reactions. We trained different ML modelson this data and we developed some feature encoding strategies for the models to work on. The outcome is that a simple linear regression on a particular feature encoding is able to predict the driving force for decomposition quantitatively with an R² score of about 90%. This model is also capable of applying the concepts of entropy or strain stabilization [1] to predict stable phases beyond the current dataset.

The elastic constants of 230 nitrides have been iteratively calculated, starting from a base of ~30 compositions. ML regression models were trained and optimized to extrapolate the properties of these compositions and suggest points of interest for further ab-initio calculations, including Elastic Net, Random Forest, Gradient Boosting and Support Vector Regression. In the end, an aggregated model built on top of these four showed the best performance as measured by the R² score. This ML model was then fed more data in every iteration, increasing the prediction efficacy. After calculation of 230 alloys, the performance of the different models was cross-checked in a blind-test using the existing data. The best performing models reached correlation scores R² between 0.79-0.92 for different elastic properties such as bulk, shear, and Young’s modulus, and Cauchy pressure. Thus, the ab-initio trained ML model is able to make confident predictions on the mechanical properties within this chosen phase space of nitrides (~630 alloys), these properties were also validated on 12 magnetron sputtered nitride coatings.

[1] Kretschmer, A., et al. (2022). Strain-stabilized Al-containing high-entropy sublattice nitrides. Acta Materialia, 224, 117483. https://doi.org/10.1016/j.actamat.2021.117483

Silicon is a widely utilized semiconductor material with applications ranging from computer chips to solar panels. A realistic description of the surface of Si can improve the understanding of Si surface chemistry, especially in the presence of functional groups. In this study, the structural configuration of the Si (100) surface is studied for several terminating groups, including methyl, hydroxyl, fluoromethyl, and double-bonded oxygen. Relaxed surface geometries are calculated using density functional theory (DFT) structural optimization, along with bond dissociation energies and bond lengths at 0 K. This study provides a deeper understanding of the structure of functionalized silicon surfaces, leading to pathways to produce new advanced silicon-based materials.