Entropic elasticity and negative thermal expansion in a simple cubic crystal

Regulating the thermal expansion of a [FePt(CN)4] layer by axial coordination and dimensional reduction

Thermal expansion regulation by chemical decoration at a molecular level is of great technological value for materials science. Herein, we show that the spin crossover active compound Fe(pyz)Pt(CN)4 (pyz = pyrazine) shows a rare 2D negative thermal expansion (NTE) in the ab-plane. By introducing axial coordination iodine ions or reducing the framework dimension from 3D to 2D, the NTE behavior can be effectively switched to positive thermal expansion (PTE) or even zero thermal expansion (ZTE). Moreover, it is found that different spin states of Fe2+ also influence the magnitude of NTE. Compared with the low-spin (LS) sate, the high-spin (HS) state tends to enhance the magnitude of NTE. Combined in situ structural and Raman spectral analyses revealed that the NTE mainly originates from the transverse vibration of a bridging cyano group and the tailorable thermal expansion is closely related to the state of the Fe-CN-Pt linkage. The present study shows how the rational regulation of the building unit and framework dimensions can effectively control thermal expansion behaviors. This insight can serve as guidance for designing and synthesizing novel NTE materials.

Exploring negative thermal expansion materials with bulk framework structures and their relevant scaling relationships through multi-step machine learning

Discovering new negative thermal expansion (NTE) materials is a great challenge in experiment. Meanwhile, the machine learning (ML) method can be another approach to explore NTE materials using the existing material databases. Herein, we adopt the multi-step ML method with efficient data augmentation and cross-validation to identify around 1000 materials, including oxides, fluorides, and cyanides, with bulk framework structures as new potential NTE candidate materials from ICSD and other databases. Their corresponding coefficients of negative thermal expansion (CNTE) and temperature ranges are also well predicted. Among them, about 57 materials are predicted to have an NTE probability of 100%. Some predicted NTE materials were tested by the first-principles calculations with quasi-harmonic approximation (QHA), which indicates that the ML results are in good agreement with the first principles calculation results. Based on the comprehensive analysis of the existing and predicted NTE materials, we established three universal relationships of CNTE with an average electronegativity, porosity, and temperature range. From these, we also identified some important critical values characterizing the NTE property, which can serve as an important criterion for designing new NTE materials.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Equation of state predictions for ScF3 and CaZrF6 with neural network-driven molecular dynamics

In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

Switch of Thermal Expansions Triggered by Itinerant Electrons in Isostructural Metal Trifluorides

Manageable thermal expansion (MTE) of metal trifluorides can be achieved by introducing local structure distortion (LSD) in the negative thermal expansion ScF₃. However, an open issue is why isostructural TiF₃, free of LSD, exhibits positive thermal expansion. Herein, a combined analysis of synchrotron X-ray diffraction, X-ray pair distribution function, and rigorous first-principles calculations was performed to reveal the important role of itinerant electrons in mediating soft phonons and lattice dynamics. Metallic TiF₃ demonstrates itinerant electrons and a suppressed Grüneisen parameter γ ≈ -20, while insulating ScF₃ absence of itinerant electrons has a considerable γ ≈ -120. With increasing electron doping concentrations in ScF₃, soft phonons become hardened and the γ is repressed significantly, identical to TiF₃. The presented results update the thermal expansion transition mechanism in framework structure analogues and provide a practical approach to obtaining MTE without inducing sizable structure distortion.

Inherent Anharmonicity of Harmonic Solids

Atomic vibrations, in the form of phonons, are foundational in describing the thermal behavior of materials. The possible frequencies of phonons in materials are governed by the complex bonding between atoms, which is physically represented by a spring-mass model that can account for interactions (spring forces) between the atoms (masses). The lowest-order, harmonic, approximation only considers linear forces between atoms and is thought incapable of explaining phenomena like thermal expansion and thermal conductivity, which are attributed to nonlinear, anharmonic, interactions. Here, we show that the kinetic energy of atoms in a solid produces a pressure much like the kinetic energy of atoms in a gas does. This vibrational or phonon pressure naturally increases with temperature, as it does in a gas and therefore results in a thermal expansion. Because thermal expansion thermodynamically defines a Grüneisen parameter γ , which is a typical metric of anharmonicity, we show that even a harmonic solid will necessarily have some anharmonicity. A consequence of this phonon pressure model is a harmonic estimation of the Grüneisen parameter as γ ≈ 3 / 2 3 - 4 x 2 / 1 + 2 x 2 , where x = v t / v l is the ratio of the transverse and longitudinal speeds of sound. We demonstrate the immediate utility of this model by developing a high-throughput harmonic estimate of lattice thermal conductivity that is comparable to other state-of-the-art estimations. By linking harmonic and anharmonic properties explicitly, this study provokes new ideas about the fundamental nature of anharmonicity, while also providing a basis for new material engineering design metrics.

Chemical Diversity for Tailoring Negative Thermal Expansion

Negative thermal expansion (NTE), referring to the lattice contraction upon heating, has been an attractive topic of solid-state chemistry and functional materials. The response of a lattice to the temperature field is deeply rooted in its structural features and is inseparable from the physical properties. For the past 30 years, great efforts have been made to search for NTE compounds and control NTE performance. The demands of different applications give rise to the prominent development of new NTE systems covering multifarious chemical substances and many preparation routes. Even so, the intelligent design of NTE structures and efficient tailoring for lattice thermal expansion are still challenging. However, the diverse chemical routes to synthesize target compounds with featured structures provide a large number of strategies to achieve the desirable NTE behaviors with related properties. The chemical diversity is reflected in the wide regulating scale, flexible ways of introduction, and abundant structure-function insights. It inspires the rapid growth of new functional NTE compounds and understanding of the physical origins. In this review, we provide a systematic overview of the recent progress of chemical diversity in the tailoring of NTE. The efficient control of lattice and deep structural deciphering are carefully discussed. This comprehensive summary and perspective for chemical diversity are helpful to promote the creation of functional zero-thermal-expansion (ZTE) compounds and the practical utilization of NTE.

Symmetry-adapted pair distribution function analysis (SAPA): a novel approach to evaluating lattice dynamics and local distortions from total scattering data

A novel symmetry-adapted pair distribution function analysis (SAPA) method for extracting information on local distortions from pair distribution function data is introduced. The implementation of SAPA is demonstrated in the TOPAS-Academic software using the freely available online software ISODISTORT, and scripts for converting the output from ISODISTORT to a SAPA input file for TOPAS are provided. Finally, two examples are provided to show how SAPA can evaluate the nature of both dynamic distortions in ScF3 and the distortions which act as an order parameter for the phase transitions in BaTiO3.

Colossal Pressure-Induced Softening in Scandium Fluoride

The counterintuitive phenomenon of pressure-induced softening in materials is likely to be caused by the same dynamical behavior that produces negative thermal expansion. Through a combination of molecular dynamics simulation on an idealized model and neutron diffraction at variable temperature and pressure, we show the existence of extraordinary and unprecedented pressure-induced softening in the negative thermal expansion material scandium fluoride ScF_{3}. The pressure derivative of the bulk modulus B, B^{'}=(∂B/∂P)_{P=0}, reaches values as low as -220±30 at 50 K, and is constant at -50 between 150 and 250 K.