Stretched Non-negative Matrix Factorization

An algorithm is described and tested that carries out a non negative matrix factorization (NMF) ignoring any stretching of the signal along the axis of the independent variable. This extended NMF model is called StretchedNMF. Variability in a set of signals due to this stretching is then ignored in the decomposition. This can be used, for example, to study sets of powder diffraction data collected at different temperatures where the materials are undergoing thermal expansion. It gives a more meaningful decomposition in this case where the component signals resemble signals from chemical components in the sample. The StretchedNMF model introduces a new variable, the stretching factor, to describe any expansion of the signal. To solve StretchedNMF, we discretize it and employ Block Coordinate Descent framework algorithms. The initial experimental results indicate that StretchedNMF model outperforms the conventional NMF for sets of data with such an expansion. A further enhancement to StretchedNMF for the case of powder diffraction data from crystalline materials called Sparse-StretchedNMF, which makes use of the sparsity of the powder diffraction signals, allows correct extractions even for very small stretches where StretchedNMF struggles. As well as demonstrating the model performance on simulated PXRD patterns and atomic pair distribution functions (PDFs), it also proved successful when applied to real data taken from an in situ chemical reaction experiment.Comment: 39 pages, 16 figure

A thermal‐gradient approach to variable‐temperature measurements resolved in space

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155923/1/jcr2te5056.pd

Site Dependency of the High Conductivity of Ga₂In₆Sn₂O₁₆: The Role of the 7‑Coordinate Site

The 6-coordinated cation site is the fundamental building block of the most effective transparent conducting oxides. Ga₂In₆Sn₂O₁₆, however, maintains 4-, 6-, 7-, and 8-coordinated cation sites and still exhibits desirable transparency and high conductivity. To investigate the potential impact of these alternative sites, we partially replace the Sn in Ga₂In₆Sn₂O₁₆ with Ti, Zr, or Hf and use a combined approach of density functional theory-based calculations, X-ray diffraction, and neutron diffraction to establish that the substitution occurs preferentially on the 7-coordinate site. In contrast to Sn, the empty d orbitals of Ti, Zr, and Hf promote spd covalency with the surrounding oxygen, which decreases the conductivity. Pairing the substitutional site preference with the magnitude of this decrease demonstrates that the 7-coordinate site is the major contributor to conductivity. The optical band gaps, in contrast, are shown to be site-independent and composition-dependent. After all 7-coordinate Sn has been replaced, the continued substitution of Sn results in the formation of a 7-coordinate In antisite or replacement of 6-coordinate Sn, depending on the identity of the d⁰ substitute

nmfMapping : a cloud-based web application for non-negative matrix factorization of powder diffraction and pair distribution function datasets

A cloud-hosted web-based software application, nmfMapping, for carrying out a non-negative matrix factorization of a set of powder diffraction or atomic pair distribution function datasets is described. This application allows structure scientists to find trends rapidly in sets of related data such as from in situ and operando diffraction experiments. The application is easy to use and does not require any programming expertise. It is available at https://pdfitc.org/

Synthesis and Characterization of MgCr₂S₄ Thiospinel as a Potential Magnesium Cathode

Magnesium-ion batteries are a promising energy storage technology because of their higher theoretical energy density and lower cost of raw materials. Among the major challenges has been the identification of cathode materials that demonstrate capacities and voltages similar to lithium-ion systems. Thiospinels represent an attractive choice for new Mg-ion cathode materials owing to their interconnected diffusion pathways and demonstrated high cation mobility in numerous systems. Reported magnesium thiospinels, however, contain redox inactive metals such as scandium or indium, or have low voltages, such as MgTi₂S₄. This article describes the direct synthesis and structural and electrochemical characterization of MgCr₂S₄, a new thiospinel containing the redox active metal chromium and discusses its physical properties and potential as a magnesium battery cathode. However, as chromium­(III) is quite stable against oxidation in sulfides, removing magnesium from the material remains a significant challenge. Early attempts at both chemical and electrochemical demagnesiation are discussed

Defect-Accommodating Intermediates Yield Selective Low-Temperature Synthesis of YMnO3 Polymorphs.

In the synthesis of complex oxides, solid-state metathesis provides low-temperature reactions where product selectivity can be achieved through simple changes in precursor composition. The influence of precursor structure, however, is less understood in solid-state synthesis. Here we present the ternary metathesis reaction (LiMnO2 + YOCl → YMnO3 + LiCl) to target two yttrium manganese oxide products, hexagonal and orthorhombic YMnO3, when starting from three different LiMnO2 precursors. Using temperature-dependent synchrotron X-ray and neutron diffraction, we identify the relevant intermediates and temperature regimes of reactions along the pathway to YMnO3. Manganese-containing intermediates undergo a charge disproportionation into a reduced Mn(II,III) tetragonal spinel and oxidized Mn(III,IV) cubic spinel, which lead to hexagonal and orthorhombic YMnO3, respectively. Density functional theory calculations confirm that the presence of Mn(IV) caused by a small concentration of cation vacancies (∼2.2%) in YMnO3 stabilizes the orthorhombic polymorph over the hexagonal. Reactions over the course of 2 weeks yield o-YMnO3 as the majority product at temperatures below 600 °C, which supports an equilibration of cation defects over time. Controlling the composition and structure of these defect-accommodating intermediates provides new strategies for selective synthesis of complex oxides at low temperatures

Defect-Accommodating Intermediates Yield Selective Low-Temperature Synthesis of YMnO3 Polymorphs.

In the synthesis of complex oxides, solid-state metathesis provides low-temperature reactions where product selectivity can be achieved through simple changes in precursor composition. The influence of precursor structure, however, is less understood in solid-state synthesis. Here we present the ternary metathesis reaction (LiMnO2 + YOCl → YMnO3 + LiCl) to target two yttrium manganese oxide products, hexagonal and orthorhombic YMnO3, when starting from three different LiMnO2 precursors. Using temperature-dependent synchrotron X-ray and neutron diffraction, we identify the relevant intermediates and temperature regimes of reactions along the pathway to YMnO3. Manganese-containing intermediates undergo a charge disproportionation into a reduced Mn(II,III) tetragonal spinel and oxidized Mn(III,IV) cubic spinel, which lead to hexagonal and orthorhombic YMnO3, respectively. Density functional theory calculations confirm that the presence of Mn(IV) caused by a small concentration of cation vacancies (∼2.2%) in YMnO3 stabilizes the orthorhombic polymorph over the hexagonal. Reactions over the course of 2 weeks yield o-YMnO3 as the majority product at temperatures below 600 °C, which supports an equilibration of cation defects over time. Controlling the composition and structure of these defect-accommodating intermediates provides new strategies for selective synthesis of complex oxides at low temperatures