The Negative Thermal Expansion Property of NdMnO_(3) Based on Pores Effect and Phase Transition

A novel negative thermal expansion(NTE) material NdMnO_(3) was synthesized by solid-state method at 1 523 K. The crystal structure, phase transition, pores effect and negative expansion properties of NdMnO_(3) were investigated by variable temperature X-ray diffraction(XRD), scanning electron microscope(SEM) and variable temperature Raman spectra. The compound exhibits NTE properties in the orderly O' phase crystal structure. When the temperature is from 293 to 759 K, the ceramic NdMnO_(3) shows negative thermal expansion of-4.7×10^(-6)/K. As temperature increases, the ceramic NdMnO_(3) presents NTE property range from 759 to 1 007 K. The average linear expansion coefficient is-18.88×10^(-6)/K. The physical mechanism of NTE is discussed and clarified through experiments.

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.

Tailoring of thermal expansion and phase transition temperature of ZrW_(2)O_8 with phosphorus and enhancement of negative thermal expansion of ZrW_(1.5)P_(0.5)O_(7.75)

ZrW_(2)O_(8)is a typical isotropic negative thermal expansion material with cubic structure.However,quenching preparation,pressure phase transition and metastable structure influence its practical applications.Adopting P to part-substitute W for ZrW_(2-x)P_(x)O_(8-0.5x)has decreased the sintering temperature and avoided the quenching process.When x=0.1,ZrW_(1.9)P_(0.1)O_(7.95)with a stable cubic structure can be obtained at 1150℃.The thermal expansion coefficient is tailored with the P content,and phase transition temperature is lowered.When x=0.5,thermal expansion coefficient attains-13.6×10^(-6)℃^(-1),ZrW_(1.5)P_(0.5)O_(7.75)exhibits enhance negative thermal expansion property.The difference of electronegativity leads to the decrease of phase transition temperature with the increase of P content.The different radii of ions lead to new structure of materials when P substitutes more.The results suggest that the P atom plays the stabilization role in the crystal structure of ZrW_(2-x)P_(x)O_(8-0.5x).

Negative thermal expansion and phase transition of low-temperature Mg_(2)NiH_(4)

The negative thermal expansion(NTE) phenomenon is of great significance in fabricating zero thermal expansion(ZTE) materials to avoid thermal shock during heating and cooling. NTE is observed in limited groups of materials, e.g., metal cyanides, oxometallates, and metalorganic frameworks, but has not been reported in the family of metal hydrides. Herein, a colossal and continuous negative thermal expansion is firstly developed in the low-temperature phases of LT1-and LT2-Mg_(2)NiH_(4) between 488 K and 733 K from in-situ transmission electron microscope(TEM) video, with the volume contraction reaching 18.7% and 11.3%, respectively. The mechanisms for volume contraction of LT1 and LT2 phases are elucidated from the viewpoints of phase transformation, magnetic transition, and dehydrogenation, which is different from common NTE materials containing flexible polyhedra units in the structure. The linear volume shrinkage of LT2 in the temperature of 488-553 K corresponds to the phase transition of LT2→HT with a thermal expansion coefficient of -799.7 × 10^(-6) K^(-1) revealed by in-situ synchrotron powder X-ray diffraction. The sudden volume contraction in LT1 between 488 and 493 K may be caused by the rapid dehydrogenation of LT1 to Mg_(2)Ni. The revealed phenomenon in single composite material with different structures would be significant for preparing zero thermal expansion materials by tuning the fraction of LT1 and LT2 phases.

Crystal structure and negative thermal expansion of solid solution Lu_2W_(3-x)Mo_xO_(12)

A new series of solid solutions Lu2W3-xMoxO12 （0.5≤r≤2.5） were successfully synthesized by the solid-state method. Their crystal structure and negative thermal expansion properties were studied using high-temperature X-ray powder diffraction and the Rietveld method. All samples of rare-earth ttmgstates and molybdates are found to crystallize in the same orthorhombic structure with space group Pnca and show the negative thermal expansion phenomena related to transverse vibration of bridging oxygen atoms in the structure. Thermal expansion coefficients （TEC） of Lu2W3_xMoxO12 are determined as -20.0× 10^-6 K^-1 for x=0.5 and -16.1×10^-6 K^-1 for x=2.5 but -18.6× 10^-6 and -16.9× 10^-6K^-1 for unsubstituted Lu2W3012 and Lu2M03012 in the identical temperature range of 200 to 800℃. High-temperature X-ray diffraction （XRD） data and bond length analysis suggest that the difference between W-O and Mo-O bond is responsible for the change of TECs after the element substitution in this series of solid solutions.

Negative thermal expansion of Ca2RuO4 with oxygen vacancies

Oxygen vacancies have a profound effect on the magnetic,electronic,and transport properties of transition metal oxides but little is known about their effect on thermal expansion.Herein we report the effect of oxygen defects on the structure formation and thermal expansion properties of the layered perovskite Ca2RuO4(CRO).It is shown that the CRO containing excess oxygen crystallizes in a metallic L-CRO phase without structure transition from 100 K to 500 K and displays a normal thermal expansion behavior,whereas those with oxygen vacancies adopt at room temperature an insulating S-CRO phase and exhibit an enormous negative thermal expansion(NTE)from 100 K to about 360 K,from where they undergo a structure transition to a high temperature metallic L-CRO phase.Compared to the L-CRO containing excess oxygen,the S-CRO structure has increasingly large orthorhombic strain and distinctive in-plane distortion upon cooling.The in-plane distortion of the RuO6 octahedra reaches a maximum across 260 K and then relaxes monotonically,providing a structure evidence for the appearance of an antiferromagnetic orbital ordering in the paramagnetic phase and the A_g phonon mode suppression and phase flip across the same temperature found recently.Both the L-and S-CRO display an antiferromagnetic ordering at about 150-110 K,with ferromagnetic ordering components at lower temperature.The NTE in S-CRO is a result of a complex interplay among the spin,orbital,and lattice.

Characterization of the negative thermal expansion material Zr_(1-x)Hf_xW_2O_8

The oxide ZrW_2O_8 displays unusual property of isotropic negative thermalexpansion in a large wide temperature range, which makes it have a number of important potentialapplications. The cubic Zr_(1-x)Hf_xW_2O_8 (x velence 0,0.3, 0.5, 0.7, and 1.0) were synthesized bystandard solid state reaction technique. The high and low temperature X-ray diffraction analysisindicate that the substitution of the Hf^(4+) for Zr^(4+) only leads to reducing the latticeconstants, and the changes of negative thermal expansion coefficients are not obvious. The linearexpansion coefficients of Zr_(1-x)Hf_xW_2O_8 (x velence 0,0.3, 0.5, 0.7, and 1.0) are about -6 X 10^(-6) K^(-1) in the temperature range of 298 to 973 K, while that of Zr_(0.5)Hf_(0.5)W_2O_8 is -9.6X 10^(-6) K_(-1) from 83 to 298 K. The phase transition temperatures from alpha-ZrW_2O_8 tobeta-ZrW_2O_8 structure were also determined by X-ray diffraction method. Thermogravimetric analysis(TGA) exhibits that Zr_(1-x)Hf_xW_2O_8 is not hygroscopic in air.

Semi-empirical estimation for enhancing negative thermal expansion in PbTiO_(3)-based perovskites

Generally,most materials expand when heated and contract when cooled,whereas negative thermal expansion(NTE)materials are very rare.As a typical NTE material,PbTiO_(3) and related compounds have drawn particular interest in recent years.The discovery of an enhanced NTE system in PbTiO_(3) is beneficial to deepen our understanding of its mechanism and regulate its properties.At present,the method of discriminating an enhanced NTE material based on PbTiO_(3) is not universal.Here,we propose a semi-empirical method through evaluating the average lattice distortion in related systems to estimate the relative coefficient of thermal expansion conveniently.The rationality of the method was verified by the analysis of the 0.6PbTiO_(3)-0.4Bi(Ga_(x)Fe_(1-x))O_(3) system.So far,all PbTiO_(3)-based compounds with enhanced NTE conform well to this method.This method provides the possibility to find more enhanced NTE PbTiO_(3)-based materials.

Negative thermal expansion and photoluminescence in solid solution(HfSc)_(0.83)W_(2.25)P_(0.83)O_(12-δ)

A solid solution of （HfSc）0.83W2.25P0.83O12-δ is synthesized by the high-temperature, solid-state reaction and fast-quenching method. It is shown that it possesses an orthorhombic structure with space group Pmmm （47） and exhibits negative thermal expansion （NTE） property with low anisotropy in thermal expansion. The coefficients of thermal expansion （CTEs） for a, b, and c axes are -1.41×10^-6 K^-1, -2.23×10^-6 K^-1, and -1.87×10^-6 K^-1, respectively. This gives rise to volume and linear CTEs of -3.10×10^-6 K^-1 and -1.03×10^-6 K^-1, respectively. Besides, it exhibits also intense photoluminescence from 360 nm to about 600 nm. The mechanism of NTE and the correlation of the PL with axial thermal expansion property are discussed.

Phase Transition and Negative Thermal Expansion Property of ZrMnMo_3O_(12)

A novel material of ZrMnMo3012 with negative thermal expansion is presented. The phase transition temperature and coemcient of thermal expansion （CTE） are investigated by temperature-dependent x-ray diffraction and Raman spectra. It is shown that ZrMnMo3012 adopts monoclinic structure with space group P21/a （No. 14） from 298 to 358K and transforms to orthorhombic with space group Pnma （No. 62） above 363K. The linear CTE obtained from the results of XRD refinement is -2.80 × 10-6 K-1 from 363 to 873 K. The CTE of the bulk cylinder ceramic measured by a thermal dilatometer is -4.7× 10-6 K-1 from 373 to 773K approximatively.

Negative thermal expansion in NbF_(3)and NbOF_(2):A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field.Here,the negative thermal expansion of NbF_(3)and NbOF_(2)was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA).We studied the total charge density,thermal vibration,and lattice dynamic to investigate the thermal expansion mechanism.We found that the presence of O induced the relatively strong covalent bond in NbOF_(2),thus weakening the transverse vibration of F and O in NbOF_(2),compared with the case of NbF_(3).In this study,we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds,but also provides an insight on thermal expansion control by designing chemical bond type.

Isotropic negative thermal expansion and its mechanism in tetracyanidoborate salt CuB(CN)_(4)

The control of thermal expansion is essential in applications where thermal stability is required from fiber optics coatings,high performance fuel cell cathodes to tooth fillings.Negative thermal expansion(NTE)materials,although rare,are fundamental for this purpose.This work focuses on studying tetracyanidoborate salt CuB(CN)_(4),an interesting cubicstructure material that displays large isotropic NTE.A joint study of synchrotron x-ray diffraction,temperature-dependent Raman spectroscopy,and lattice dynamics calculations was conducted,showing that not only low-frequency optical modes(transverse thermal vibrations of N and C atoms)but also the acoustic modes(the vibrations of Cu atoms as a collective torsion of the neighboring atoms),contribute to NTE.As a result,new insights were gained into the NTE mechanism of CuB(CN)_(4) and related framework materials.

Simple chemical synthesis and isotropic negative thermal expansion in MHfF_(6)(M=Ca,Mn,Fe,and Co)

The rapid progress of modern technologies has accelerated the prominence of thermal expansion mismatch between materials,and tunable thermal expansion materials will be a powerful safeguard against this challenge.Here,isotropic MHfF_(6)(M=Ca,Mn,Fe,and Co)compounds with tunable thermal expansion have been produced via a low-cost synthetic method and investigated.By utilizing temperature dependent X-ray diffraction(XRD)and Raman spectroscopy,combined with first principles calculations,it was revealed that the transverse thermal vibrations of the F atoms are dominated by low-frequency phonons with negative Grüneisen parameters and are therefore the origin of the negative thermal expansion(NTE).Very interestingly,with the increase of the M atomic number,the metal…F atomic linkages become stiffer,reducing the number of vibrational modes with negative Grüneisen parameters,so that the strong NTE can be gradually adjusted to moderate NTE and to near zero thermal expansion.The present study achieves the tunable thermal expansion in a new compound family and shed light on the internal mechanism from the perspective of lattice vibrational dynamics.

The enhanced negative thermal expansion in less-oxygen-vacancies copper pyrophosphate

For oxides,controlling the concentration of oxygen vacancy is a useful way to optimize their functional properties.However,when it comes to the field of negative thermal expansion(NTE),much less attention has been paid to the effect of oxygen vacancy on NTE,though oxide-typed NTE materials account for more than 40%of the total NTE materials.Here,we report that the linear coefficient of thermal expansion at 250–350 K of copper pyrophosphate(i.e.,Cu_(2)P_(2)O_(7))can be significantly improved from–13.88 to–36.60 ppm/K when the synthesis temperature is raised from 1073 to 1373 K.The combined study including X-ray absorption near edge structure,neutron powder diffraction,and X-ray diffraction has confirmed the selective vacancies in the O1 site for low-temperature synthesized samples,which suppress both the phase-transition and framework-structure driven NTE simultaneously.Our result proposes a new approach for optimizing the NTE effect of oxides.

A new isotropic negative thermal expansion material of CaSnF_(6)with facile and low-cost synthesis

Double ReO_(3)-type fluorides have a great interest in the field of negative thermal expansion(NTE)and luminescent materials.However,their application is limited by the scarcity of quantity,expensive raw materials,and harsh preparation conditions.In this work we have found a new NTE material,CaSnF_(6),by applying the concept of the average atomic volume.More importantly,different from the previous solid-phase sintering and direct fluorination methods,the nano CaSnF6 has been synthesized for the first time by solvothermal method.The results of X-ray diffraction(XRD)and Raman spectroscopy show that a phase transition occurs from rhombohedral(R3)to cubic(Fm3m)structure at about 200 K,and a strong isotropic NTE(αv=−15.78×10^(−6)K^(−1))appears in the cubic phase.Lattice dynamics calculations from first-principles illustrate that the NTE is due to the transverse vibration of fluorine atoms excited by low-frequency phonons.This work not only broadens the NTE family of fluorides,but also provides a new facile and low-cost fabricati on method for the preparation of NTE fluorides.

Illuminating the negative thermal expansion mechanism of YFe(CN)_(6)via electronic structure and unusual phonon modes

Understanding the negative thermal expansion(NTE)mechanism remains an important and challenging thing.In this work,we selected the case of YFe(CN)_(6)to investigate the structure-mechanism relation on the base of crystal structure,electro nic structure and lattice dynamics.We expanded the NTE of YFe(CN)_(6)to 150 K,and the temperature dependence of volume and lattice constants was determined by temperature-variable synchrotro n X-ray diffraction measure ments.A large NTE was found in the system.Our theoretical calculations indicate that the Y-N bond exhibits a strong ionic feature through the calculated electron localization function(ELF),which has a strong influence on the anisotropic vibration of the N atom.The detailed lattice dynamics simulations suggest that the NTE of YFe(CN)_(6)may be related to the presence of the unusual low-frequency modes of the YN_(6)triangular prism(tri-prism)units.The optical branches with low frequencies are mainly related to the distortion and twisting modes of the YN_(6)tri-prism units,which contribute most to the NTE effect in the crystal.

Large negative thermal expansion in GdFe(CN)_(6) driven by unusual low-frequency modes

Understanding the negative thermal expansion(NTE)mechanism is of great importance.In this work,we consider the new NTE compound Gd Fe(CN)_(6)(α_(v)=-34.2×10^(-6)K^(-1))as a case study to investigate the NTE mechanism from the perspective of the lattice vibrational dynamics.The atomic mean-square displacements suggest that the NTE of Gd Fe(CN)_(6)comes from the strong tension effect induced by the transverse vibrations of the atomic-Fe-C≡N-Gd-linkages,with the largest contribution given by N atoms.Lattice dynamics calculations show that three low-frequency optical modes at about 50 cm^(-1)show the largest negative Grüneisen parameters thus providing the largest contribution to the NTE.The existence of these unusual low-frequency vibrational modes can be ascribed to the presence of GdN_(6)trigonal prisms in the framework structure of Gd Fe(CN)_(6).

Negative thermal expansion: Mechanisms and materials

Negative thermal expansion(NTE)of materials is an intriguing phenomenon challenging the concept of traditional lattice dynamics and of importance for a variety of applications.Progresses in this field develop markedly and update continuously our knowledge on the NTE behavior of materials.In this article,we review the most recent understandings on the underlying mechanisms(anharmonic phonon vibration,magnetovolume effect,ferroelectrorestriction and charge transfer)of thermal shrinkage and the development of NTE materials under each mechanism from both the theoretical and experimental aspects.Besides the low frequency optical phonons which are usually accepted as the origins of NTE in framework structures,NTE driven by acoustic phonons and the interplay between anisotropic elasticity and phonons are stressed.Based on the data documented,some problems affecting applications of NTE materials are discussed and strategies for discovering and design novel framework structured NET materials are also presented.

Preparation of Negative Thermal Expansion ZrW_2O_8 Powders and Its Application in Polyimide/ZrW_2O_8 Composites

Negative thermal expansion （NTE） ZrW2O8 powders were prepared by step-by-step solid-state reaction with ZrO2 and WO3 powders. The coefficient of thermal expansion （CTE） of the as-prepared ZrW208 was around -5.08×10^-6 K^-1 at 20-700℃. Different amounts of ZrW208 powders were added in BTDA-ODA polyamic acid to form polyimide/ZrW2O8 composites （PI/ZrW2O8）. With the increment of ZrW2O8, experimental results show that ZrW2O8 powders can significantly enhance the thermal stability of the composites, and reduce the thermal expansion. A 50 wt pct ZrW2O8 addition can give rise to a 31% reduction of CTE. It is suggested that the PI/ZrW2O8 composites have potential applications in high performance microelectronic devices.

Evaluating thermal expansion in fluorides and oxides:Machine learning predictions with connectivity descriptors

Open framework structures(e.g.,ScF_(3),Sc_(2)W_(3O)_(12),etc.)exhibit significant potential for thermal expansion tailoring owing to their high atomic vibrational degrees of freedom and diverse connectivity between polyhedral units,displaying positive/negative thermal expansion(PTE/NTE)coefficients at a certain temperature.Despite the proposal of several physical mechanisms to explain the origin of NTE,an accurate mapping relationship between the structural–compositional properties and thermal expansion behavior is still lacking.This deficiency impedes the rapid evaluation of thermal expansion properties and hinders the design and development of such materials.We developed an algorithm for identifying and characterizing the connection patterns of structural units in open-framework structures and constructed a descriptor set for the thermal expansion properties of this system,which is composed of connectivity and elemental information.Our developed descriptor,aided by machine learning(ML)algorithms,can effectively learn the thermal expansion behavior in small sample datasets collected from literature-reported experimental data(246 samples).The trained model can accurately distinguish the thermal expansion behavior(PTE/NTE),achieving an accuracy of 92%.Additionally,our model predicted six new thermodynamically stable NTE materials,which were validated through first-principles calculations.Our results demonstrate that developing effective descriptors closely related to thermal expansion properties enables ML models to make accurate predictions even on small sample datasets,providing a new perspective for understanding the relationship between connectivity and thermal expansion properties in the open framework structure.The datasets that were used to support these results are available on Science Data Bank,accessible via the link https://doi.org/10.57760/sciencedb.j00113.00100.