Mechanism Of Negative Thermal Expansion Research Articles

Negative thermal expansion in hexagonal VF3 predicted by first-principles calculation

Abstract Searching negative thermal expansion (NTE) materials is challenging. Herein, hexagonal VF3 is predicted as a new NTE material for the first time. VF3 displays NTE property in the temperature range from 0 to 380 K, and the minimum NTE coefficient(α) is approximately −4.68 × 10−6 K−1 at 120 K. The NTE mechanism was ascribed to the vibrations of F atom with larger atomic displacement parameters, which dominates the negative Grüneisen parameters. The difference of minimum NTE coefficient between VF3 and TiF3 might be caused by their different chemical bond strength between Ti–F and V–F. This research provides a deeper understanding between NTE and crystal structure.

Local Structure and Dynamics in MPt(CN)6 Prussian Blue Analogues.

We use a combination of X-ray pair distribution function (PDF) measurements, lattice dynamical calculations, and ab initio density functional theory (DFT) calculations to study the local structure and dynamics in various MPt(CN)6 Prussian blue analogues. In order to link directly the local distortions captured by the PDF with the lattice dynamics of this family, we develop and apply a new "interaction-space" PDF refinement approach. This approach yields effective harmonic force constants, from which the (experiment-derived) low-energy phonon dispersion relations can be approximated. Calculation of the corresponding Grüneisen parameters allows us to identify the key modes responsible for negative thermal expansion (NTE) as arising from correlated tilts of coordination octahedra. We compare our results against the phonon dispersion relations determined using DFT calculations, which identify the same NTE mechanism.

Pressure‐Induced Volumetric Negative Thermal Expansion in CoZr2 Superconductor

AbstractThe study investigates the thermal expansion and superconducting properties of a CuAl2‐type (tetragonal) superconductor CoZr2 under high pressures. High‐pressure synchrotron X‐ray diffraction is performed in a pressure range of 2.9 GPa < P < 10.4 GPa, and it is discovered that CoZr2 exhibits volumetric negative thermal expansion (NTE) under high pressures. Although uniaxial positive thermal expansion (PTE) along the a‐axis is observed under ambient pressure, it is suppressed by pressure, whereas a large uniaxial NTE along the c‐axis is maintained under the pressure regime. Because of the combination of the suppressed uniaxial PTE along the a‐axis and uniaxial NTE along the c‐axis, volumetric NTE is achieved under high pressure in CoZr2. The volumetric NTE mechanism is based on the flexible crystal structure caused by the soft Co–Co bond, as observed in the isostructural compound FeZr2, which exhibits a uniaxial NTE along the c‐axis. High‐pressure electrical resistance measurements of CoZr2 are performed and confirm superconductivity at 0.03 GPa < P < 41.9 GPa. Because of the coexistence of the two phenomena, volumetric NTE and superconductivity, in CoZr2 under high pressure, coexistence can be achieved under ambient pressure by tuning the chemical composition after the present observation.

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.

High configurational entropy for low phase transition temperature and thermal expansion of A2M3O12 oxide ceramics

Transverse vibrations of bridging atoms in framework structure oxides contribute to negative thermal expansion (NTE), increasing the configurational entropy. Herein, the configurational entropy of NTE (Al1/3Fe1/3Cr1/3)2Mo3O12 (AFCM) is tuned by introducing ZrMg and W to AlFeCr and Mo sites to lower NTE. The NTE of ((Zr1/2Mg1/2)x(Al1/3Fe1/3Cr1/3)(1-x))2Mo3O12 (ZMAFCM) reduce obviously with increasing the content of ZrMg and also the phase transition temperatures (PTTs) (x = 0∼0.5). For ((Zr1/2Mg1/2)x(Al1/3Fe1/3Cr1/3)(1-x))2(Mo1/2W1/2)3O12 (ZMAFCMW), the NTE and PTTs reduce at a faster rate than that of ZMAFM. The configurational entropy increases with the content of ZrMg firstly (x = 0∼0.4) and then decreases. The possible mechanism of thermal expansion change is related to the enhanced lattice configuration, high entropy. The inconsistent transverse vibrations of bridging oxygen atoms could reduce their contribution to NTE, especially for high entropy. The PTT of high configurational entropy oxides is reduced obviously due to the influenced on the effective electronegativity. The investigation paves a high entropy way to lower thermal expansion and PTT of A2M3O12 oxide ceramics and explores the further mechanism of NTE.

Crystal growth and negative thermal expansion properties of a Y2Mo4O15 single crystal.

A bulk-size single crystal of Y2Mo4O15 with 20 × 11 × 8 mm3 was successfully grown by the top-seed solution growth (TSSG) method. The full-width at half maximum of (100) and (010) crystal faces is 37 and 27 arcsec, respectively. The thermal conductivity coefficients κ 11, κ 22, κ 33, and κ 13 are determined to be 1.519, 2.097, 0.445, and 0.997 W m-1 K-1, respectively. It is worth noting that the Y2Mo4O15 crystal shows significant anisotropy thermal expansion properties, which exhibits a negative thermal expansion along the b-axis (α 22 = -5.11 × 10-6 K-1). The crystal structure analysis shows that the shrinking of Mo-O bond lengths along the b-axis with the increasing temperature would be the main origin of the negative thermal expansion properties for Y2Mo4O15 crystal, which does not comply with the current mechanism.

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.

Spatial Modulation and Thermal-Induced Spin Phase Transition on the Negative Thermal Expansion of ScF3 with Metal Dopants

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is often related to the lattice, phonons, charges, and spin. However, most of the studies are mainly focused on the phonons, and the spin-related mechanism in open framework compounds remains unclear owing to the lack of more experimental pieces of evidence. Here, based on the first-principles calculations combined with the quasi-harmonic approximation, we carried out studies of the NTE properties of ScF3 with metal dopants to reveal the roles in NTE of both the spatial effects and spin states. For most of the dopants, the NTE coefficient decreases with the decrease of ionic radius, obeying a linear scaling relationship. Interestingly, for magnetic impurities with a spin phase transition from a high spin state to a low spin state, we show that they will exhibit a Jahn–Teller distortion behavior and enhance the longitudinal vibration mode. In turn, the longitudinal vibration mode has a large positive Grüneisen parameter, which can offset the NTE obviously. This work not only proposes a new insight into the NTE mechanism about impurities in ScF3 but also provides an approach to tailor the NTE properties for fluorides with magnetic impurities as well as oxides.

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.

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, electronic 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 synchrotron X-ray diffraction measurements. 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 YN6 triangular prism (tri-prism) units. The optical branches with low frequencies are mainly related to the distortion and twisting modes of the YN6 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 GdFe(CN)6 (αv = −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 GdFe(CN)6 comes from the strong tension effect induced by the transverse vibrations of the atomic –Fe–CN–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 GdN6 trigonal prisms in the framework structure of GdFe(CN)6.

Two-Dimensional Negative Thermal Expansion in a Crystal of LiBO2

Negative thermal expansion (NTE), violating the common sense of “thermal expansion and cold contraction” effects, is a novel temperature-responding behavior of great scientific and technical significance. Herein, we report a two-dimensional (2D) NTE behavior in a crystal of LiBO2, which is constructed by graphite-like [LiBO2]∞ layers. This intriguing thermal property originates from the synergistic effect of the distortion of in-plane [LiO3] bases in [LiO4] tetrahedra and the rotation of [BO3] triangles in the [LiBO2]∞ layer, driven by the force perpendicular to the layer owing to the large interlayer separation as temperature increases. Remarkably, the in-plane and out-of-plane Li–O bonds within the [LiO4] tetrahedra have nearly the same bond strength and exhibit the similar variation with respect to temperature, and this is quite different from the common sense on the 2D NTE behavior in layered structures that the intralayer atomic interaction must be much stronger than the interlayer ones. Our study deepens the understanding of the 2D NTE mechanism and would promote the exploration for NTE materials.

Effect of magnetic field on thermal strain, thermal expansion and negative thermal expansion property in a polycrystalline Ni55Mn18Ga27 alloy

The magnetic field effect on phase transition and thermal expansion properties were investigated in Ni55Mn18Ga27 alloy. The results show that the alloy has an excellent isotropy, reproducibility and thermostability in thermal strain and exhibits a large negative thermal expansion (NTE) effect in the direct and reverse martensitic transformations (MTs). For the direct MT, the average linear expansion coefficient α is about −225.21 ppm/K and the corresponding temperature span is around 8.2 K. Additionally, the sensitivities of the transformation strain and peak temperatures to field are about 88.5 ppm/T and 1.31 K/T, respectively. The rates of α and temperature spans of NTE to magnetic field are about 8.88 ppm/K T and 0.82 K/T, indicating that the magnetic field can improve the NTE property of the Ni–Mn-Ga alloy. Finally, the NTE mechanism has also been discussed. Our findings are beneficial to improving the thermal expansion and NTE properties of Ni–Mn-Ga alloys.

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 cubic-structure 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.

Pressure enhanced negative thermal expansion in 2H CuScO2 from first-principles calculations.

Finding materials with negative thermal expansion (NTE) property is challenging. Tuning NTE is of fundamental and technological importance. Pressure enhanced negative thermal expansion behavior in 2H CuScO2 is found and expounded using density functional theory (DFT) and quasi-harmonious approximation (QHA). The frequencies of low energy modes and Grüneisen parameters decrease under pressure, but the bulk modulus increases with pressure. The transverse vibration of Cu atoms becomes stronger under pressure and the materials undergo thermal softening. These factors including thermal softening, pressure induced decrease of Grüneisen parameters and pressure induced strengthening of transverse vibration of Cu atoms all contribute to the enhanced negative thermal expansion property in 2H CuScO2 in view of the thermodynamic relationship , Grüneisen's theory of thermal expansion and the mechanism of NTE, respectively.

Soft-mode anisotropy in the negative thermal expansion material ReO3

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the mechanism of negative thermal expansion (NTE) in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than the octahedra in the related compound ScF$_3$. These results support the idea that structural flexibility is an important factor in NTE materials, allowing the phonon modes that drive a volume contraction of the lattice to occupy a greater volume in reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. In addition, we investigate the thermal expansion properties of the material at high temperature and do not find the reported second NTE region. Finally, we show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that the motions associated with rigid unit modes are highly anisotropic in these systems.

Near-zero thermal expansion in β-CuZnV2O7 in a large temperature range

We report a new type of near-zero thermal expansion material β-CuZnV2O7 in a large temperature range from 173 K to 673 K. It belongs to a monoclinic structure (C2/c space group) in the whole temperature range. No structural phase transition is observed at atmospheric pressure based on the x-ray diffraction and Raman experiment. The high-pressure Raman experiment demonstrates that two structural phase transitions exist at 0.94 GPa and 6.53 GPa, respectively. The mechanism of negative thermal expansion in β-CuZnV2O7 is interpreted by the variations of the angles between atoms intuitively and the phonon anharmonicity intrinsically resorting to the negative Grüneisen parameter.

Uniaxial negative thermal expansion behavior of β -CuSCN

Negative thermal expansion (NTE) as an interesting physical behavior is promising for thermal expansion control engineering. β-CuSCN consists of linear chain units with NTE along the c-axis. The NTE mechanism of β-CuSCN is investigated by variable temperature x-ray diffraction, temperature- and pressure-dependent Raman spectra, and first-principles calculations. It is found that the quasi rigid unit modes associated with the rotations of S–C≡N–Cu chains driven by Cu and S antiphase transverse vibrations and longitudinal acoustic and transverse acoustic modes involving the collective motions of atoms have large negative Grüneisen parameters, contributing significantly to the NTE of c-axis. Translational and librational motions of C≡N units, in which C and N atoms vibrate in the same and opposite directions have much smaller negative Grüneisen parameters, contribute only a minor part to the NTE, which is different from the known NTE mechanism of cyanides and Prussian blue analogous.

Negative thermal expansion in YbMn2Ge2 induced by the dual effect of magnetism and valence transition

Negative thermal expansion (NTE) is an intriguing property, which is generally triggered by a single NTE mechanism. In this work, an enhanced NTE (αv = −32.9 × 10−6 K−1, ΔT = 175 K) is achieved in YbMn2Ge2 intermetallic compound to be caused by a dual effect of magnetism and valence transition. In YbMn2Ge2, the Mn sublattice that forms the antiferromagnetic structure induces the magnetovolume effect, which contributes to the NTE below the Néel temperature (525 K). Concomitantly, the valence state of Yb increases from 2.40 to 2.82 in the temperature range of 300–700 K, which simultaneously causes the contraction of the unit cell volume due to smaller volume of Yb3+ than that of Yb2+. As a result, such combined effect gives rise to an enhanced NTE. The present study not only sheds light on the peculiar NTE mechanism of YbMn2Ge2, but also indicates the dual effect as a possible promising method to produce enhanced NTE materials.

Negative thermal expansion in the Ruddlesden-Popper calcium titanates

Materials exhibiting negative thermal expansion (NTE) are important for the fabrication and operation of microelectronic devices and optical systems. As an important group of Ruddlesden-Popper (RP) perovskites, calcium titanates ${\mathrm{Ca}}_{n+1}{\mathrm{Ti}}_{n}{\mathrm{O}}_{3n+1}$ [(CTO), $n=1,2,...,\ensuremath{\infty}$] have layered structures and may exhibit quasi-two-dimensional (quasi-2D) NTE within their three-dimensional structural architectures. In this paper, combining density-functional-theory calculations and the self-consistent quasiharmonic approximation method, we investigate the variation of the quasi-2D character of the phonon spectra and thermal expansion in the ${\mathrm{Ca}}_{n+1}{\mathrm{Ti}}_{n}{\mathrm{O}}_{3n+1}$ family ($n=1--3$, and $\ensuremath{\infty}$) with respect to $n$. We find that a quasi-2D NTE mechanism is active in the RP-CTOs at $n$ of 1--3, whereas a quasi-rigid-unit mode mechanism is active at $n=\ensuremath{\infty}$ (i.e., the perovskite phase). We find a NTE trend with layer number for the orthorhombic materials comprising the RP series, but the monoclinic polymorph is an outlier. For the orthorhombic members, we find the critical pressure for NTE increases with increasing $n$, but the NTE critical temperature decreases (when materials are compared at the same pressure). Additionally, the elastic moduli can be used as effective descriptors for this layer-dependent behavior of the NTE, i.e., the stiffer the RP-CTO then the lower its NTE. We also propose the integrated NTE capacity to capture the correlation between the quasi-2D NTE and $n$, and it monotonically decreases with increasing $n$.