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.

Negative Thermal Expansion of (ZrMg)xY2-2xMo3O12 Ceramics with Low Hygroscopicity

(ZrMg)xY2-2xMo3O12(x=0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,and 1)ceramics have been synthesized to obtain less hygroscopicity and negative thermal expansion.With increasing the substitution of(ZrMg)^6+(ion radius 7.2×10^-11 m)for Y3+(ion radius 9×10^-11 m),the crystal water are reduced obviously.The linear thermal expansion coefficient is improved with increasing the content of(ZrMg)^6+.The material shows near zero thermal expansion(-0.12×10^-6 K^-1,430-870 K)with x=0.7.Meanwhile,ZrMgMo3O12 shows low non-hygroscopicity and negative thermal expansion,but low softening temperature.After substituting amount of Y^3+for(ZrMg)^6+in ZrMgMo3O12(x=0.8),the softening temperature increases remarkably(750 K to 830 K)and it presents near zero thermal expansion.

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.

Negative Thermal Expansion of GaFe(CN)_6 and Effect of Na Insertion by First-Principles Calculations

We study the negative thermal expansion(NTE) properties and effect of Na insertion on the NTE of the framework material GaFe(CN)_6 by first-principles calculations based on density functional theory within the quasi-harmonic approximation. The calculated results show that the material exhibits NTE due to the low transverse vibrational modes of the CN groups. The modes demonstrate larger negative values of the mode Grüneisen parameters. Once Na is introduced in the framework of the material, it prefers to locate at the center of the quadrates of the framework material and binds to the four N anions nearby. As a consequence, the transverse vibrational mode of the CN group is clearly hindered and the NTE of the material is weakened. Our theoretical calculations have clarified the mechanisms of NTE and the effect of the guest Na on the NTE of the framework material.

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.

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.

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.

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.

Negative Thermal Expansion of the Dy_2Fe_(16)Cr Compound

Structural, thermal expansion, and magnetic properties of the Dy_2Fe_(16)Cr compound are investigated by means of x-ray diffraction and magnetization measurements. The Dy_2Fe_(16)Cr compound has a hexagonal Th_2Ni_(17)-type structure. There exists a negative thermal expansion resulting from a strong spontaneous magnetostriction in the magnetic state of the Dy_2Fe_(16)Cr compound. The average thermal expansion coefficient is-0.794 × 10^(-5)/K in the temperature range 292–407 K. The spontaneous magnetostrictive deformation and the Curie temperature are discussed.

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.

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.

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.

On Thermodynamic Analysis of Substances with Negative Coefficient of Thermal Expansion

There are reports in the literature on the discovery of novel materials that were observed to shrink upon heating. Treatment of these materials in the same manner as the materials with positive coefficient of thermal expansion can lead to the misinterpretation of the laws of thermodynamics. This is because volume expansivity is usually defined at constant pressure. Negative values for volume expansivity can be shown using Maxwell’s reciprocity relations to lead to negative values for absolute temperature for ideal gas. For real systems, using Helmholz free energy analysis at equilibrium an expression for the volume expansivity was derived. It can be seen that this expression would be always positive for real physical changes, either heating or cooling. Isentropic volume expansivity is proposed as better suited for analysis of materials with negative thermal expansion, NTE and composites used in space such as Hubble telescope and Chandra telescope with zero coefficient of thermal expansion. This kind of a switch from isobaric to isentropic has precedence in the history of development of speed of sound.

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 phase transition, hygroscopicity, and thermal expansion properties of Yb_(2-x)Al_xMo_3O_(12)

Materials with the formula Yb2-xAlxMo3O12 （x = 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 0.9, 1.0, 1.1, 1.3, 1.5, and 1.8） were synthesized and their structures, phase transitions, and hygroscopicity investigated using X-ray powder diffraction, Raman spectroscopy, and thermal analysis. It is shown that Yb2-xAlxMo3012 solid solutions crystallize in a single monoclinic phase for 1.7 〈 x 〈 2.0 and in a single orthorhombic phase for 0.0 〈 x 〈 0,4, and exhibit the characteristics of both monoclinic and orthorhombic structures outside these compositional ranges. The monoclinic to orthorhonlbic phase transition temperature of A12Mo3012 can be reduced by partial substitution of A13＋ by Yb3＋, and the Yb2-zAlxMo3012 （0.0 〈 x 〈 2.0） materials are hydrated at room temperature and contain two kinds of water species. One of these interacts strongly with and hinders the motions of the polyhedra, while the other does not. The partial substitution of A13＋ for Yb3＋ in Yb2Mo3012 decreases its hygroscopicity, and the linear thermal expansion coefficients after complete removal of water species are measured to be -9.1 x 10-6/K, -5.5 x 10-6/K, 5.74 x 10-6/K, and 9.5 x 10 6/K for Ybl.sAlo.2（MoO4）3, Yb1.6Alo.4（MoO4）3, Ybo.4All.6（Mo04）3, and Ybo.2Al1.8（MoO4）3, respectively.

Synthesis and thermal expansion of 4J36/ZrW_2O_8 composites

Gas atomized 4J36 alloy powder was milled for 72 h then mixed with ZrW2O8 powder and sintered at 600℃ for 4 h under argon atmosphere. 4J36/ZrW2O8 composites containing 10 vol.%, 20 vol.%, 30 vol.%, and 40 vol.% ZrW2Os were fabricated, the relative density of which ranged from 70% to 80%. Thermal expansion coefficients of the composites decreased as the amount of ZrW2O8 increased, in agreement with the rule of the mixture. The coefficient of thermal expansion of the 4J36/40 vol.%ZrW2O8 composite in 25-100℃ is 0.55 × 10^＋6/℃.