We have investigated the size effect of A1→L10 ordering of FePt nanoparticles in FePt–Al2O3 granular and FePt/SiO2 particulate films by transmission electron microscopy (TEM). The TEM results have shown convincingly that ordering does not progress when the particle size has a diameter of less than 4 nm. Calculation of the order parameter profile from the surface to the volume of the FePt nanoparticles based on diffuse-interface theory justified the experimentally observed size dependence of the ordering. The transition length from disorder to order depends on the interfacial energy, hence the critical particle size of ordering should vary depending on the type of matrix and substrate.

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Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA is now an accepted technique in various scientific fields. One key issue that remains controversial is the implementation of DA in massive simulation models under the constraints of limited computation time and resources. In this paper, we propose an adjoint-based DA method for massive autonomous models that produces optimum estimates and their uncertainties within reasonable computation time and resource constraints. The uncertainties are given as several diagonal elements of an inverse Hessian matrix, which is the covariance matrix of a normal distribution that approximates the target posterior probability density function in the neighborhood of the optimum. Conventional algorithms for deriving the inverse Hessian matrix require O(CN^{2}+N^{3}) computations and O(N^{2}) memory, where N is the number of degrees of freedom of a given autonomous system and C is the number of computations needed to simulate time series of suitable length. The proposed method using a second-order adjoint method allows us to directly evaluate the diagonal elements of the inverse Hessian matrix without computing all of its elements. This drastically reduces the number of computations to O(C) and the amount of memory to O(N) for each diagonal element. The proposed method is validated through numerical tests using a massive two-dimensional Kobayashi phase-field model. We confirm that the proposed method correctly reproduces the parameter and initial state assumed in advance, and successfully evaluates the uncertainty of the parameter. Such information regarding uncertainty is valuable, as it can be used to optimize the design of experiments.

The crystallization of amorphous Ge(a-Ge) in an Al (134 nm) and a-Ge (108 nm) thin-film bilayer deposited on a SiO2 substrate has been examined by a cross section transmission electron microscope technique. When crystallization of a-Ge begins at 125 °C, amorphous AlGe (a-AlGe) alloy is formed in the Ge layer. Then, the a-AlGe alloy layer also appeared at the surface of the bilayer. After complete crystallization, those amorphous layers disappeared and the bilayer film has been converted to a polycrystalline film. We discussed the crystallization of a-Ge and proposed the mechanism of the diffusion of Ge atoms from the inner a-Ge layer through the outer Al layer to the topmost surface that involves the formation of the metastable a-AlGe alloy in the Ge layer, followed by the crystallization of this alloy by the pseudo-eutectic reaction, leading to the decomposition into an equilibrium Al and Ge crystal mixture and a-Ge. Then, Ge atoms is released to the Al layer for the compensation of the Al diffusion down into the Ge layer and again forms the a-AlGe alloy in the Al layer. The a-AlGe alloy in the Al layer is also crystallized by the pseudo-eutectic reaction. Consequently, decomposed a-Ge is ejected from the inside to the surface of the bilayer, resulting in the surface Ge segregation.

Bayesian optimization (BO) is an effective tool for black-box optimization in which objective function evaluation is usually quite expensive. In practice, lower fidelity approximations of the objective function are often available. Recently, multi-fidelity Bayesian optimization (MFBO) has attracted considerable attention because it can dramatically accelerate the optimization process by using those cheaper observations. We propose a novel information theoretic approach to MFBO. Information-based approaches are popular and empirically successful in BO, but existing studies for information-based MFBO are plagued by difficulty for accurately estimating the information gain. Our approach is based on a variant of information-based BO called max-value entropy search (MES), which greatly facilitates evaluation of the information gain in MFBO. In fact, computations of our acquisition function is written analytically except for one dimensional integral and sampling, which can be calculated efficiently and accurately. We demonstrate effectiveness of our approach by using synthetic and benchmark datasets, and further we show a real-world application to materials science data.