Negative Thermal Expansion Behavior Research Articles

Low frequency bandgap and high stiffness of innovative auxetic metamaterial with negative thermal expansion

Achieving multifunctional integration is crucial in mechanical metamaterials to meet the requirements of structures and equipment serving in complex environments across various engineering fields. In this study, we propose two novel bi-material and tri-material metamaterials based on the original edge-shared quadrangle (EQ/EQO) metamaterial, which exhibit negative thermal expansion (NTE), negative Poisson's ratio (NPR), and bandgap characteristics. The effective thermoelastic properties, including coefficient of thermal expansion (CTE), Poisson's ratio (PR), and Young's modulus, are compared and analyzed through theoretical formulation based on Timoshenko beam theory and numerical simulation using continuum elements with Abaqus. Additionally, finite element analysis is employed to calculate the energy band structures of these metamaterials based on Bloch's theorem, while the transmission characteristic curve verifies the validity of the obtained band structure. We systematically discuss the bandgap characteristics, coupling relationship between bandgaps and thermoelastic properties, as well as the influence of geometrical parameters on both bandgaps and thermoelastic properties. Our results demonstrate that the effective thermoelastic properties of these metamaterials are primarily determined by their frame structure's geometrical parameters, particularly the incline angle. Furthermore, for bi-material metamaterials, their specific stiffness closely relates to their bandgaps; however, for tri-material metamaterials, only the central local resonant unit determines their bandgap behavior. Notably, planar and 3D tri-material metamaterials can concurrently achieve a low-frequency bandgap along with high stiffness as well as NTE/NPR behavior. This work presents a new design strategy for optimizing multifunctional metamaterials' bandgaps while incorporating NTE behavior.

Zero thermal expansion high-strength metallic glass-based composites

Materials with zero thermal expansion (ZTE) properties demonstrate remarkable dimensional stability, making them crucial in aerospace, electronics, and various industrial sectors. However, these materials face challenges such as weak mechanical properties and narrow ZTE temperature range. In this study, a novel ZTE metallic glass-based composite (Cu2P2O7/La65Al14Cu9.17Ag1.83Ni5Co5) with negative thermal expansion (NTE) reinforcement was prepared using gas pressure infiltration and water quenching. SEM and 3D CT results revealed the dense structure and the non-reactive interface structure. The NTE behaviors resulting from the coupling of CuO5 and PO4 polyhedra within the NTE Cu2P2O7 are demonstrated to counterbalance the positive thermal expansion in metallic glass. Consequently, the resulting composites exhibit a wide range of zero thermal expansion and high strength properties, presenting a novel approach for creating high-performance ZTE metallic glass-based composites.

High‐Entropy Anti‐Perovskites with Enhanced Negative Thermal Expansion Behavior

AbstractThe negative thermal expansion (NTE) materials, which can act as thermal‐expansion compensators to counteract the positive thermal expansion, have great applications merit in precision engineering. However, the exploration of NTE behavior with a wide temperature range has reached its upper ceiling through traditional doping strategies due to composition limitations. In this paper, the unique sluggish characteristics and extended optimization space in empirically screened high‐entropy anti‐perovskite (HEAP) are utilized to broaden the NTE temperature range. Typically, the NTE temperature range in Mn3Cu0.2Zn0.2Ga0.2Ge0.2Mn0.2N is broadened to ΔT = 235 K (5 K ≤ T ≤ 240 K), which is two or three times wider than that of traditional low‐entropy doping systems. The neutron diffraction analysis reveals a unique sluggish characteristic in magnetic phase transition which survives in an ultra‐wide temperature range of 5 K ≤ T ≤ 350 K (ΔT = 345 K). The sluggish characteristic is further experimentally proved to come from disturbed phase transition dynamics due to distortion in atomic spacing and chemical environmental fluctuation observed by the spherical aberration‐corrected electron microscope. The demonstration provides a unique paradigm for broadening the temperature range of NTE materials through entropy engineering.

Effect of Ti4+ and Pb2+ on negative thermal expansion and polarization behaviors of KSr2Nb5O15: First-principles investigation

The utilization of both negative and positive thermal expansion coefficients presents a potential means of mitigating internal stress in high-temperature materials, hence offering a novel approach to enhance the impact strength of those materials. The investigation of the thermal expansion coefficient and polarization characteristics of KSr2Nb5O15 doped with Ti4+ and Pb2+ was conducted by the utilization of first-principles calculations. The introduction of Ti4+ and Pb2+ into the KSr2Nb5O15 lattice resulted in an increase in lattice distortion. This effect was particularly pronounced when Ti4+ and Pb2+ were co-doped, leading to the largest lattice distortion observed in KSr2Nb5O15. Furthermore, the negative thermal expansion coefficient of KSr2Nb5O15 was also found to be the highest under these co-doping conditions, with a value of −0.560×10−5 K−1 compared to the original value of −0.011×10−5 K−1. Conversely, when Ti4+ was doped individually, the lattice distortion and negative thermal expansion coefficient of KSr2Nb5O15 were found to be the smallest. Furthermore, the inclusion of Ti4+ and Pb2+ leads to an enhancement in the dielectric constant. This effect is particularly pronounced when Ti4+ and Pb2+ are simultaneously incorporated into the KSr2Nb5O15 lattice. Consequently, the dielectric constant of the material exhibits a substantial improvement. The greatest polarization intensity is achieved when KSr2Nb5O15 is co-doped with Ti4+ and Pb2+, resulting in a polarization intensity of 38.61 μC/cm2. The dense ceramics comprising of KSr2Nb5O15, with the addition of Ti4+ and Pb2+ dopants, were synthesized using the solid-state reaction method. Subsequently, the thermal expansion coefficients and dielectric characteristics of these ceramics were evaluated. The experimental results are not in good agreement with the calculated results, but qualitatively, the trend predicted by the theory is confirmed by experiment. This study establishes the groundwork for the synthesis of KSr2Nb5O15 materials exhibiting pronounced negative thermal expansion characteristics.

Mechanism of Negative Thermal Expansion in Monoclinic Cu2P2O7 from First Principles.

Negative thermal expansion (NTE) materials generally have high-symmetry space groups, large average atomic volumes, and corner-sharing octahedral and tetrahedral coordination structures. By contrast, monoclinic α-Cu2P2O7, which has a small average atomic volume and edge-sharing structure, has been reported to exhibit NTE, the detailed mechanism of which is unclear. In this study, we investigate the A2B2O7 polymorphs and analyze the NTE behavior of α-Cu2P2O7 using first-principles lattice-dynamics calculations. From the polymorphism investigation in 20 A2B2O7 compounds using 6 representative crystal structures, small A and B cationic radii are found to stabilize the α-Cu2P2O7-type structure. We then analyze the NTE behavior of α-Cu2P2O7 using quasi-harmonic approximation. Our calculated thermal expansion coefficients and anisotropic atomic displacement parameters were in good agreement with those of the experimental reports at low temperatures. From the mode-Grüneisen parameter distribution plotted over the entire first-Brillouin zone, we found that the phonon contributing most significantly to NTE emerges not into the special points but between them. In this phonon mode, the O connecting two PO4 tetrahedra rotates, and the Cu and O vibrate perpendicular to the bottom of the CuO5 pyramidal unit, which folds the ac lattice plane. This vibration behavior can explain the experimentally reported anisotropic NTE behavior of α-Cu2P2O7. Our results demonstrate that the most negative mode-Grüneisen parameter contributing to NTE behavior is not always located on high-symmetry special points, indicating the importance of lattice vibration analyses for the entire first-Brillouin zone.

Influence of A/B Element Substitution on Negative Thermal Expansion in AB(CN)6 (A = Al, Ga, In; B = Co, Fe, Mn, Cr, V, Ti): A Density Functional Theory Study.

Negative thermal expansion as an abnormal physical behavior of materials has promising applications in a high sophisticated equipment field, but the materials are rare. Here, we use the first-principles calculations based on density functional theory combined with the recently developed average atomic volume (AAV = V/N, where V is unit cell volume and N is the number of atoms in the unit) rule to predict the large isotropic negative thermal expansion materials of Prussian blue analogues AB(CN)6 (A = Al, Ga, In; B = Co, Fe, Mn, Cr, V, Ti) in a wide temperature range. Our results clearly show that the coefficient of negative thermal expansion has a near-linear relationship with the average atomic volume of the systems and is also influenced by the element substitution at the A or B site. Lattice dynamic simulations indicate that the main contribution to the negative thermal expansion comes from the low-frequency transverse vibration of the (B)-C≡N-(A) groups, especially the transverse vibration of the N atoms. Thus, the element substitution at the A site (binding to N) can tune the negative thermal expansion behavior of the systems more effectively than that at the B site (binding to C), indicating the different roles of bonds on the negative thermal expansion. Our present work not only expands the kinds of isotropic materials but also gives some insights into the relationship between the average atomic volume and negative thermal expansion.

A cobalt(II) hydrogen-bonded organic framework exhibiting uniaxial negative thermal expansion and field-induced slow magnetic relaxation

The magnetic and thermal expansion properties of a cobalt(II) hydrogen-bonded organic framework (CoHOF), [Co(H2O)6](NPS)2 (1, HNPS = naphthalene-2-sulphonic acid), constructed by hexaaquacobalt(II) and organsulfonate were reported. Single-crystal X-ray diffraction reveals a porous 2D hydrogen-bonded framework of 1 sustained by multiple and charge-assisted intermolecular hydrogen bonding interactions. Variable-temperature single-crystal combined with powder X-ray diffraction and thermal gravimetric analyses confirms the high thermal stability of the CoHOF. The dynamic changes of the crystal lattice indicate uniaxial negative thermal expansion (NTE) behavior along the c-axis direction through a possible slippage motion. Magnetic measurements indicate the Co2+ ions show uniaxial magnetic anisotropy with D = −92.5 cm−1. A.C. susceptibility measurements reveal field-driven slow magnetic relaxation of 1. These results provide a rare cobalt(II) hydrogen-bonded organic framework showing single-ion magnetism and negative thermal expansion properties.

B-direction anomalous thermal expansion behavior in SmCrO3

The ceramic composites of Sm1-xBixCrO3 (x = 0, 0.1, 0.2, 0.3) have been prepared by solid state reaction. X-ray diffraction patterns demonstrate that Bi-doped polycrystalline samples match with standard pattern of SmCrO3. After Bi doping, the lattice constants in three directions increase slightly. The thermal expansion properties were studied by X-ray powder diffraction over the temperature range from 100 to 400 K. The results showed that the compound SmCrO3 exhibits positive thermal expansion behavior in the a and c directions in the whole measurement temperature range. The anomaly is that in the b direction the lattice exhibits positive thermal expansion behavior at low temperatures, while above 200 K it exhibits near zero thermal expansion behavior. The thermal expansion behaviors of all Bi-doped SmCrO3 are similar to that of SmCrO3, but unexpectedly, negative thermal expansion behaviors were observed in the b direction above 200 K in the highly Bi doped samples. The dielectric measurement shows that there are two thermal activation processes in all Sm1-xBixCrO3 (x = 0, 0.1, 0.2, 0.3) respectively, with the low-temperature activation corresponding to the grain itself, while the high-temperature activation comes from the grain boundary. After low-temperature thermal activation, with increasing temperature, the enhanced vibration of the corner oxygen atoms of the CrO6 octahedron is mainly perpendicular to the b axis, which leads to the near zero thermal expansion behavior in the b direction. Moreover, after high-temperature thermal activation, as the temperature increases, the enhanced interaction between Bi3+ and the free oxygen atom (space oxygen atom) at the grain boundary will further lead to the negative thermal expansion behavior in the b-direction of the high concentration doped samples.

Preparation of In0.5Sc1.5Mo3O12 nanofibers and its negative thermal expansion property

Orthorhombic In0.5Sc1.5Mo3O12 nanofibers were prepared by electrospinning followed by a heat treatment. The effects of post-annealing temperatures on the phase composition, microstructure and morphology were investigated by XRD, SEM, HRTEM and XPS. Negative thermal expansion (NTE) behaviors of the In0.5Sc1.5Mo3O12 nanofibers were analyzed by high-temperature XRD. Results indicate that the as-prepared In0.5Sc1.5Mo3O12 nanofibers show an amorphous structure with smooth and homogeneous shape. The average diameter of the as-prepared In0.5Sc1.5Mo3O12 nanofibers is around 515 nm. Well crystallized orthorhombic In0.5Sc1.5Mo3O12 nanofibers could be prepared after post-annealing at 550 °C for 2 h with an average diameter of about 192 nm. The crystallinity of In0.5Sc1.5Mo3O12 nanofibers gradually improved with the increase of annealing temperature. However, too high post-annealing temperature leads to a damage of sample's fiber structure. The high-temperature XRD results reveal that In0.5Sc1.5Mo3O12 nanofibers show an anisotropic NTE, and the coefficients of thermal expansion (CTEs) along a-axis and c-axis were −5.95 × 10−6 °C−1 and -3.54 × 10−6 °C−1, while the one along b-axis is 5.61 × 10−6 °C−1. The volumetric CTE of In0.5Sc1.5Mo3O12 nanofibers is −3.90 × 10−6 °C−1 and the linear one is 1.3 × 10−6 °C−1 in 25–700 °C.

Negative Thermal Expansion Caused by the Antiferroelectric Phase Transition in Lead-Free Perovskite Ceramics

Due to the structural stability and high adjustability of perovskite, lead-free perovskite ceramics are widely thought to be one of the most promising functional materials. In this work, an abnormal negative thermal expansion behavior with a linear expansion coefficient of −54.95 ppm/K is achieved in the (1-x)NaNbO3-xCaZrO3 system by driving the antiferroelectric phase transition from orthorhombic phase and tetragonal phase. The NTE mechanism is verified by temperature-dependent high-energy synchrotron X-ray diffraction, dielectric spectra, and Raman scattering spectroscopy. The relationship between the antiferroelectric phase transition and negative thermal expansion behavior is systematically revealed by analyzing the evolution of the phase structure with temperature. This novel negative thermal expansion feature caused by the antiferroelectric phase transition provides new guidance for designing more negative thermal expansion materials.

Hydrothermal synthesis of flower-like Sc2Mo3O12 and its investigation into negative thermal expansion property

Orthorhombic Sc2Mo3O12 samples have been synthesized using ethylene glycol (EG)-assisted hydrothermal reaction. The influences of hydrothermal temperature, hydrothermal time and additive content of EG on the preparation and negative thermal expansion (NTE) behavior of Sc2Mo3O12 samples were characterized using XRD, SEM, HRTEM, EDX, TMA and HTXRD. Results indicate that flower-like Sc2Mo3O12 with a uniform particle size of 1–2 μm can be synthesized at 120 °C for 2 h by adding 60 ml EG. Hydrothermal temperature, time and additive content of EG have strong influences on the growth and morphology of the Sc2Mo3O12. The average coefficients of thermal expansion (CTEs) of the Sc2Mo3O12 prepared at 120 °C for 2 h and 200 °C for 24 h are tested to be −6.94 × 10−6 °C−1 and -7.18 × 10−6 °C−1 in 25–700 °C using TMA. HTXRD results indicate that the flower-like Sc2Mo3O12 exhibits anisotropic NTE, and the corresponding CTEs along the a, b and c axes are −6.73 × 10−6 °C−1, 4.98 × 10−6 °C−1 and -4.78 × 10−6 °C−1 in 25–700 °C, respectively, and the corresponding linear CTE is −2.21 × 10−6 °C−1.

Effects of Fe doping on structure, negative thermal expansion, and magnetic properties of antiperovskite Mn3GaN compounds

AbstractWe synthesized antiperovskite Mn3Ga1−xFexN (0 ≤ x ≤ 0.30) compounds and investigated their negative thermal expansion (NTE) behavior, structure, and magnetic properties. A high‐resolution transmission electron microscopy analysis and a selected‐area electron diffraction (SAED) pattern indicate that the samples have high crystallinity with a single‐phase cubic structure. Tunable NTE behavior appears below room temperature, and the NTE operation temperature range (△T) is broadened while increasing the Fe doping. Furthermore, introducing Fe in Mn3Ga1−xFexN can efficiently adjust the NTE coefficient from −232.57 × 10−6/K (x = 0) to −12.57 × 10−6/K (x = 0.20), and the corresponding △T can be broadened from △T = 22 K to 51 K. Besides, the total entropy change (ΔStotal) at the phase transitions continuously decreases from 9.2 to 4.7 J/(kg K) while increasing the Fe content from x = 0.05 to 0.10. With increasing Fe into Ga sites, the magnetic ordering varies from antiferromagnetic (AFM) to ferromagnetic (FM), the AFM to paramagnetic (PM) phase transition temperature decreases, whereas the FM to PM transition temperature increases when increasing the Fe content. The present study indicates that magnetic element doping can efficiently tune the NTE and the correlated physical features of the antiperovskite compounds.

Anisotropic thermal expansion of silicon monolayer in biphenylene network.

Materials with a negative thermal expansion property are of great importance in the emerging family of two-dimensional materials. For example, mixing two materials with negative and positive coefficients of thermal expansion avoids volume changing with temperature. In this work, based on first-principles calculations and Grüneisen's theory, we investigated the thermal expansion properties of a silicon monolayer in biphenylene networks. Our results show that the thermal expansion is greatly negative and anisotropic, as the linear thermal expansion coefficient along the a-direction is significantly smaller than the one along the b-direction, even at high temperatures. At 300 K, the thermal expansion coefficients along the two lattice directions are -17.010 × 10-6 K-1 and -2.907 × 10-6 K-1, respectively. By analyzing the Grüneisen parameters and the elastic compliance, we obtained an understanding of the giant negative thermal expansion of the material. Rigid unit modes are also responsible for the negative thermal expansion behavior. Our work provides fundamental insights into the thermal expansion of silicon monolayer in biphenylene networks and should stimulate the further exploration of the possible thermoelectric and thermal management applications of the material.

Node Distortion as a Tunable Mechanism for Negative Thermal Expansion in Metal–Organic Frameworks

Chemically functionalized series of metal-organic frameworks (MOFs), with subtle differences in local structure but divergent properties, provide a valuable opportunity to explore how local chemistry can be coupled to long-range structure and functionality. Using in situ synchrotron X-ray total scattering, with powder diffraction and pair distribution function (PDF) analysis, we investigate the temperature dependence of the local- and long-range structure of MOFs based on NU-1000, in which Zr6O8 nodes are coordinated by different capping ligands (H2O/OH, Cl- ions, formate, acetylacetonate, and hexafluoroacetylacetonate). We show that the local distortion of the Zr6 nodes depends on the lability of the ligand and contributes to a negative thermal expansion (NTE) of the extended framework. Using multivariate data analyses, involving non-negative matrix factorization (NMF), we demonstrate a new mechanism for NTE: progressive increase in the population of a smaller, distorted node state with increasing temperature leads to global contraction of the framework. The transformation between discrete node states is noncooperative and not ordered within the lattice, i.e., a solid solution of regular and distorted nodes. Density functional theory calculations show that removal of ligands from the node can lead to distortions consistent with the Zr···Zr distances observed in the experiment PDF data. Control of the node distortion imparted by the nonlinker ligand in turn controls the NTE behavior. These results reveal a mechanism to control the dynamic structure of MOFs based on local chemistry.

Lightweight 3D Graphene Metamaterials with Tunable Negative Thermal Expansion.

In this study, a 3D graphene metamaterial (GM) showing negative thermal expansion is prepared using a strategy of hyperbolically oriented freezing under a dual temperature gradient along orthogonal directions after the π-π stacking-derived assembly of 2D graphene sheets. As the fundamental construction element of the 3D GM, the graphene sheet displays anomalous shrinking deformation with a thermal expansion coefficient of (-6.12 ± 0.28) × 10-6 that is triggered by thermally induced out-of-plane vibrations of the CC bonds. A combination of numerical simulations and experimental investigations validates that anomalous negative thermal expansion (NTE) behavior can be effectively delivered to scalable 3D GM candidates at larger dimensions beyond the basic 2D graphene sheets at the microscale. The multiscale design and optimization of the structural characterization of the 3D GM further realize the desirable regulation of the NTE performance with the NTE coefficient ranging from negative ((-7.5± 0.65) × 10-6 K-1 ) to near-zero values ((-0.8 ± 0.25) × 10-6 K-1 ). This is attributed to the NTE-derived release regulation of the primary stress/strain of the microstructure, and the 3D GM exhibits high thermal stability while preserving the desirable structural robustness and fatigue resistance under thermo-mechanical coupling conditions. Therefore, this 3D GM offers promising potential for applications as protective skin, thermal actuator, smart switcher, and packing filler.

Negative thermal expansion behaviour of graphdiyne

Negative thermal expansion (NTE) is an effect of a material contracting upon heating, and NTE materials are useful for the preparation of zero thermal expansion (ZTE) composite materials for applications in energy conversion and electronic devices. In this work, the NTE behaviour of graphdiyne (GDY) was observed and studied by temperature-dependent Raman spectroscopy. The characteristic Y mode in Raman spectra of GDY film exhibit blueshift with increasing temperature, in contrast to the redshift of positive thermal expansion materials. Our theoretical calculations show that the dimension of GDY decreases when the temperature is elevated, and the blueshift of the Y mode is due to the contraction of GDY. The thermal expansion coefficient (TEC) of GDY in the temperature range of 180–420 K was found to be negative, − 7.18 × 10−6 K−1 at room temperature. Our results provide a measure of the thermal property of GDY and indicate promising applications of GDY in NTE composite materials.

Poly(vinyl pyrrolidone)-assisted hydrothermal synthesis of erythrocyte-like Sc2W3O12 with negative thermal expansion

In this study, orthorhombic Sc2W3O12 with an erythrocyte structure has been successfully prepared by poly(vinyl pyrrolidone) (PVP)-assisted hydrothermal method. The effects of PVP additive on the phase composition, morphology and negative thermal expansion (NTE) behavior of Sc2W3O12 were studied. Results indicate that pure orthorhombic Sc2W3O12 can be synthesized at 220 °C via the hydrothermal method with 0.25–0.6 g PVP additives. PVP additive has great influences on the synthesis of Sc2W3O12. It can inhabit the formation of impurity during hydrothermal reaction. With the increase of PVP contents, the flake Sc2W3O12 started to aggregate and transformed into the uniform erythrocyte-like Sc2W3O12 with a size of 2 × 4 μm. Erythrocyte-like Sc2W3O12 shows anisotropic NTE in 25–700 °C. The coefficients of thermal expansion (CTE) along a, b and c-axes directions are −6.10 × 10−6, 3.10 × 10−6 and −4.96 × 10−6 K−1, and the corresponding linear CTE is −2.65 × 10−6 K−1.

Penta-graphene and phagraphene: thermal expansion, linear compressibility, and Poisson’s ratio

Nonplanar penta-graphene and planar phagraphene, which are connected by carbon pentagons and penta–hexa–hepta carbon rings, respectively, are two allotropes of graphene. Graphene as a star material in two-dimensional materials has been widely studied. However, the studies around penta-graphene and phagraphene are still insufficient. We are interested in both materials’ response to temperature, hydrostatic pressure, and stress. In this work, the thermal expansion, linear compressibility, and Poisson’s ratio of penta-graphene and phagraphene have been investigated systematically. It is found that both materials can exhibit abnormal negative thermal expansion behavior, while their linear compressibility behavior is normal. The negative Poisson’s ratio behavior only occurs in penta-graphene, which is consistent with other work. Through an analysis of the lattice vibrations and associated mode Grüneisen parameters, it is found that there are anomalies in the phonon spectra of both penta-graphene and phagraphene. It is noted that acoustic phonons contribute most to their respective anomalies, especially the transverse acoustic mode. The librational motion of the lowest-frequency optical phonon of both materials is identified and also associated with their novel properties. In general, the unique topological arrangement of carbon atoms can play a decisive role in determining the performances of penta-graphene and phagraphene.

Anharmonic Interaction in Negative Thermal Expansion Material CaTiF6.

Although the quasi-harmonic approximation (QHA) method applies to many materials, it is necessary to study the anharmonic interaction for extremely anharmonic materials. In this work, the unusual negative thermal expansion (NTE) property of CaTiF6 is studied by combing QHA and anharmonic interaction. The improved self-consistent phonon approximation (ISCPA), which treats anharmonic effects in solids nonperturbatively, is employed. The agreement of NTE behavior between the calculation and the experiment can be further promoted from qualitative consistency by QHA to quantitative consistency by the ISCPA. From mode Grüneisen parameters, it is found that the low-frequency phonons, especially acoustic phonons, contribute greatly to the NTE behavior of CaTiF6. The rigid unit modes (RUMs) of low-frequency optical phonons can be identified. The phonon lifetime of CaTiF6 is calculated from three-phonon interactions; thereby, the NTE mechanism can be further explored by phonon lifetimes of phonons with different frequencies on heating. The anomalous lattice thermal conductivity (LTC) is predicted using the Boltzmann transport equation within the relaxation time approximation. The glasslike LTC can occur in crystal CaTiF6.

The negative thermal expansion behavior in Prussian blue analogue Zn3[Fe(CN)6]2: A first-principles study

We have studied the electronic and thermal expansion properties in Prussian blue analogue (PBA) Zn3[Fe(CN)6]2 by first-principles calculation. The results show that Zn3[Fe(CN)6]2 is an insulator with an indirect band gap. The composition of valence band maximum (VBM) and conduction band minimum (CBM) can be obtained. It is demonstrated that Fe-C and Zn-N are strong ionic bonds and C-N is a strong covalent bond combining qualitative and quantitative analysis. The negative thermal expansion (NTE) behavior has been confirmed. It is found that low-frequency phonons play a significant role. Especially, acoustic phonons have the most negative mode/total Grüneisen parameter, suggesting their greatest contribution to the NTE behavior. From the mode analysis of low-frequency optical phonons, we can know that the NTE behavior is closely associated with transverse vibration in the same direction of bridge atoms (C and N atoms) as well as polyhedral movements and distortions (FeC6 octahedron and ZnN4 tetrahedron).