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Materials Data on Fe3Pt by Materials Project

Fe3Pt is Uranium Silicide structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are two inequivalent Fe sites. In the first Fe site, Fe is bonded to eight Fe and four equivalent Pt atoms to form distorted FeFe8Pt4 cuboctahedra that share corners with twelve equivalent FeFe8Pt4 cuboctahedra, edges with eight equivalent PtFe12 cuboctahedra, edges with sixteen FeFe8Pt4 cuboctahedra, faces with four equivalent PtFe12 cuboctahedra, and faces with fourteen FeFe8Pt4 cuboctahedra. There are four shorter (2.62 Å) and four longer (2.71 Å) Fe–Fe bond lengths. All Fe–Pt bond lengths are 2.62 Å. In the second Fe site, Fe is bonded to eight equivalent Fe and four equivalent Pt atoms to form FeFe8Pt4 cuboctahedra that share corners with twelve equivalent FeFe8Pt4 cuboctahedra, edges with eight equivalent PtFe12 cuboctahedra, edges with sixteen equivalent FeFe8Pt4 cuboctahedra, faces with four equivalent PtFe12 cuboctahedra, and faces with fourteen FeFe8Pt4 cuboctahedra. All Fe–Pt bond lengths are 2.71 Å. Pt is bonded to twelve Fe atoms to form PtFe12 cuboctahedra that share corners with twelve equivalent PtFe12 cuboctahedra, edges with twenty-four FeFe8Pt4 cuboctahedra, faces with six equivalent PtFe12 cuboctahedra, and faces with twelve FeFe8Pt4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Fe3Pt by Materials Project

Fe3Pt is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. Fe is bonded to eight equivalent Fe and four equivalent Pt atoms to form distorted FeFe8Pt4 cuboctahedra that share corners with twelve equivalent FeFe8Pt4 cuboctahedra, edges with eight equivalent PtFe12 cuboctahedra, edges with sixteen equivalent FeFe8Pt4 cuboctahedra, faces with four equivalent PtFe12 cuboctahedra, and faces with fourteen equivalent FeFe8Pt4 cuboctahedra. All Fe–Fe bond lengths are 2.65 Å. All Fe–Pt bond lengths are 2.65 Å. Pt is bonded to twelve equivalent Fe atoms to form PtFe12 cuboctahedra that share corners with twelve equivalent PtFe12 cuboctahedra, edges with twenty-four equivalent FeFe8Pt4 cuboctahedra, faces with six equivalent PtFe12 cuboctahedra, and faces with twelve equivalent FeFe8Pt4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Fe3Pt by Materials Project

Fe3Pt crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are five inequivalent Fe sites. In the first Fe site, Fe is bonded to nine Fe and three equivalent Pt atoms to form distorted FeFe9Pt3 cuboctahedra that share corners with twelve equivalent FeFe9Pt3 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with eighteen FeFe9Pt3 cuboctahedra, faces with six equivalent PtFe6Pt6 cuboctahedra, and faces with twelve FeFe9Pt3 cuboctahedra. There are three shorter (2.50 Å) and six longer (2.72 Å) Fe–Fe bond lengths. All Fe–Pt bond lengths are 2.69 Å. In the second Fe site, Fe is bonded to twelve Fe atoms to form FeFe12 cuboctahedra that share corners with six equivalent FeFe12 cuboctahedra, corners with six equivalent PtFe6Pt6 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with eighteen FeFe9Pt3 cuboctahedra, and faces with eighteen FeFe9Pt3 cuboctahedra. All Fe–Fe bond lengths are 2.72 Å. In the third Fe site, Fe is bonded to nine Fe and three equivalent Pt atoms to form distorted FeFe9Pt3 cuboctahedra that share corners with seventeen FeFe9Pt3 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with sixteen FeFe9Pt3 cuboctahedra, faces with six equivalent PtFe6Pt6 cuboctahedra, and faces with fifteen FeFe9Pt3 cuboctahedra. There are three shorter (2.50 Å) and six longer (2.72 Å) Fe–Fe bond lengths. All Fe–Pt bond lengths are 2.69 Å. In the fourth Fe site, Fe is bonded to sixteen Fe atoms to form FeFe16 cuboctahedra that share corners with six equivalent PtFe6Pt6 cuboctahedra, corners with sixteen FeFe9Pt3 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with eighteen FeFe9Pt3 cuboctahedra, and faces with thirty-four FeFe9Pt3 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.50–5.45 Å. In the fifth Fe site, Fe is bonded to nine Fe and three equivalent Pt atoms to form distorted FeFe9Pt3 cuboctahedra that share corners with seventeen FeFe9Pt3 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with sixteen FeFe9Pt3 cuboctahedra, faces with six equivalent PtFe6Pt6 cuboctahedra, and faces with fifteen FeFe9Pt3 cuboctahedra. All Fe–Fe bond lengths are 2.72 Å. All Fe–Pt bond lengths are 2.69 Å. Pt is bonded to six equivalent Fe and six equivalent Pt atoms to form distorted PtFe6Pt6 cuboctahedra that share corners with six equivalent FeFe12 cuboctahedra, corners with six equivalent PtFe6Pt6 cuboctahedra, edges with six equivalent PtFe6Pt6 cuboctahedra, edges with eighteen FeFe9Pt3 cuboctahedra, faces with six equivalent PtFe6Pt6 cuboctahedra, and faces with twelve equivalent FeFe9Pt3 cuboctahedra. All Pt–Pt bond lengths are 2.72 Å.

36 MATERIALS SCIENCE↗

Materials Data on Fe3PtN by Materials Project

Fe3PtN is (Cubic) Perovskite structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional and consists of one ammonia molecule and one Fe3Pt framework. In the Fe3Pt framework, Fe is bonded in a linear geometry to two equivalent Pt atoms. Both Fe–Pt bond lengths are 2.35 Å. Pt is bonded to six equivalent Fe atoms to form corner-sharing PtFe6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗

ZENN: A thermodynamics-inspired computational framework for heterogeneous data–driven modeling

Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.

36 MATERIALS SCIENCE↗

Quantifying the degree of disorder and associated phenomena in materials through zentropy: Illustrated with Invar Fe 3 Pt

Disorder exists in all materials at finite temperatures, implicating that the degree of disorder (ƒ DoD ) is a key parameter to tailor macroscopic functionalities of materials. Here, in this work, we propose to quantify ƒ DoD as a function of temperature using properties such as configurational entropy predicted by zentropy – a theory to represent total entropy of a system via a nested formula through the integration of quantum mechanics and statistical mechanics. Taking Invar Fe 3 Pt as an example through first-principles based calculations from 0 K to finite temperatures, we demonstrate the capability of the present approach in predicting ƒ DoD and associated phenomena in Fe 3 Pt such as Curie temperature and negative thermal expansion, showing a good agreement with experimental data.

36 MATERIALS SCIENCE↗

Chemical order-disorder nanodomains in Fe 3 Pt bulk alloy

Chemical ordering is a common phenomenon and highly correlated with the properties of solid materials. By means of the redistribution of atoms and chemical bonds, it invokes an effective lattice adjustment and tailors corresponding physical properties. To date, however, directly probing the 3D interfacial interactions of chemical ordering remains a big challenge. In this work, we deciphered the interlaced distribution of nanosized domains with chemical order/disorder in Fe 3 Pt bulk alloy. HAADF-STEM images evidence the existence of such nanodomains. The reverse Monte Carlo method with the X-ray pair distribution function data reveal the 3D distribution of local structures and the tensile effect in the disordered domains at the single-atomic level. The chemical bonding around the domain boundary changes the bonding feature in the disordered side and reduces the local magnetic moment of Fe atoms. This results in a suppressed negative thermal expansion and extended temperature range in Fe 3 Pt bulk alloy with nanodomains. Our study demonstrates a local revelation for the chemical order/disorder nanodomains in bulk alloy. The understanding gained from atomic short-range interactions within the domain boundaries provides useful insights with regard to designing new functional compounds.

36 MATERIALS SCIENCE↗