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Register a new userOrder and randomness in dopant distributions: exploring the thermodynamics of solid solutions from atomically resolved imaging
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Exploration of structure-property relationships as a function of dopant concentration is commonly based on mean field theories for solid solutions. However, such theories that work well for semiconductors tend to fail in materials with strong correlations, either in electronic behavior or chemical segregation. In these cases, the details of atomic arrangements are generally not explored and analyzed. The knowledge of the generative physics and chemistry of the material can obviate this problem, since defect configuration libraries as stochastic representation of atomic level structures can be generated, or parameters of mesoscopic thermodynamic models can be derived. To obtain such information for improved predictions, we use data from atomically resolved microscopic images that visualize complex structural correlations within the system and translate them into statistical mechanical models of structure formation. Given the significant uncertainties about the microscopic aspects of the materials processing history along with the limited number of available images, we combine model optimization techniques with the principles of statistical hypothesis testing. We demonstrate the approach on data from a series of atomically-resolved scanning transmission electron microscopy images of Mo$_x$Re$_{1-x}$S$_2$ at varying ratios of Mo/Re stoichiometries, for which we propose an effective interaction model that is then used to generate atomic configurations and make testable predictions at a range of concentrations and formation temperatures.
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Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. Here we develop a workflow based on a machine learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow is universal and can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.
Molybdenum disulfide (MoS$_2$) nanosheet is a two-dimensional material with high electron mobility and with high potential for applications in catalysis and electronics. We synthesized MoS$_2$ nanosheets using a one-pot wet-chemical synthesis route with and without Re-doping. Atom probe tomography revealed that 3.8 at.% Re is homogeneously distributed within the Re-doped sheets. Other impurities are found also integrated within the material: light elements including C, N, O, and Na, locally enriched up to 0.1 at.%, as well as heavy elements such as V and W. Analysis of the non-doped sample reveals that the W and V likely originate from the Mo precursor.
The development of high-resolution imaging methods such as electron and scanning probe microscopy and atomic probe tomography have provided a wealth of information on structure and functionalities of solids. The availability of this data in turn necessitates development of approaches to derive quantitative physical information, much like the development of scattering methods in the early XX century which have given one of the most powerful tools in condensed matter physics arsenal. Here, we argue that this transition requires adapting classical macroscopic definitions, that can in turn enable fundamentally new opportunities in understanding physics and chemistry. For example, many macroscopic definitions such as symmetry can be introduced locally only in a Bayesian sense, balancing the prior knowledge of materials physics and experimental data to yield posterior probability distributions. At the same time, a wealth of local data allows fundamentally new approaches for the description of solids based on construction of statistical and physical generative models, akin to Ginzburg-Landau thermodynamic models. Finally, we note that availability of observational data opens pathways towards exploring causal mechanisms underpinning solid structure and functionality.
The kinetics of intrinsic and dopant-enhanced solid phase epitaxy (SPE) is stud- ied in amorphous germanium (a-Ge) layers formed by ion implantation on <100> Ge substrates. The SPE rates were measured with a time-resolved reflectivity (TRR) system between 300 and 540 degC and found to have an activation energy of (2.15 +/- 0.04) eV. To interpret the TRR measurements the refractive indices of the a-Ge layers were measured at the two wavelengths used, 1.152 and 1.532 {mu}m. For the first time, SPE rate measurements on thick a-Ge layers (>3 {mu}m) have also been performed to distinguish between bulk and near-surface SPE growth rate behavior. Possible effects of explosive crystallization on thick a-Ge layers are considered. When H is present in a-Ge it is found to have a considerably greater retarding affect on the SPE rate than for similar concentrations in a-Si layers. Hydrogen is found to reduce the pre-exponential SPE velocity factor but not the activation energy of SPE. However, the extent of H indiffusion into a-Ge surface layers during SPE is about one order of magnitude less that that observed for a-Si layers. This is thought to be due to the lack of a stable surface oxide on a-Ge. Dopant enhanced kinetics were measured in a-Ge layers containing uniform concentration profiles of implanted As or Al spanning the concentration regime 1-10 x1019 /cm-3. Dopant compensation effects are also observed in a-Ge layers containing equal concentrations of As and Al, where the SPE rate is similar to the intrinsic rate. Various SPE models are considered in light of these data.
Atom probe tomography (APT) helps elucidate the link between the nanoscale chemical variations and physical properties, but it has limited structural resolution. Field ion microscopy (FIM), a predecessor technique to APT, is capable of attaining atomic resolution along certain sets of crystallographic planes albeit at the expense of elemental identification. We demonstrate how two commercially-available atom probe instruments, one with a straight flight path and one fitted with a reflectron-lens, can be used to acquire time-of-flight mass spectrometry data concomitant with a FIM experiment. We outline various experimental protocols making use of temporal and spatial correlations to best discriminate field evaporated signals from the large field ionised background signal, demonstrating an unsophisticated yet efficient data mining strategy to provide this discrimination. We discuss the remaining experimental challenges that need be addressed, notably concerned with accurate detection and identification of individual field evaporated ions contained within the high field ionised flux that contributes to a FIM image. Our hybrid experimental approach can, in principle, exhibit true atomic resolution with elemental discrimination capabilities, neither of which atom probe nor field ion microscopy can individually fully deliver - thereby making this new approach, here broadly termed analytical field ion microscope (aFIM), unique.
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