We have devised an isotropic interaction potential that gives rise to negative thermal expansion (NTE) behavior in equilibrium many-particle systems in both two and three dimensions over a wide temperature and pressure range (including zero pressure). An optimization procedure is used in order to find a potential that yields a strong NTE effect. A key feature of the potential that gives rise to this behavior is the softened interior of its basin of attraction. Although such anomalous behavior is well known in material systems with directional interactions (e.g., zirconium tungstate), to our knowledge this is the first time that NTE behavior has been established to occur in single-component many-particle systems for isotropic interactions. Using constant-pressure Monte Carlo simulations, we show that as the temperature is increased, the system exhibits negative, zero and then positive thermal expansion before melting (for both two- and three-dimensional systems). The behavior is explicitly compared to that of a Lennard-Jones system, which exhibits typical expansion upon heating for all temperatures and pressures.
We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.
electromagnetic field distributions are found for frequencies slightly under one hundred giga Hertz, using a left handed substrate in a microstrip guided wave structure
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve negative thermal expansion via a metamaterial approach. The metamaterial is constructed with unit cells that combine bi-material strips and anti-chiral structures. Both experimental and simulation results display isotropic negative thermal expansion properties. The coefficient of negative thermal expansion of the metamaterials is d…
The properties of artificial isotropic microwave composites which would possess simultaneously negative permittivity and permeability are studied theoretically. Four kinds of composites are considered. Two of them concern media with split-ring resonator particles with different particle arrangements. The other two are realized with Omega particles. An analytical antenna model of the electromagnetic behavior of a split-ring resonator (SRR) is suggested and verified by numerical simulations. Next, material parameters of composite media made with SRR or Omega particles are calculated. It is shown…
We investigate three-dimensional left-handed and related meta-materials based on a fully symmetric multi-gap single-ring SRR design and crossing continuous wires. We demonstrate isotropic transmission properties of a SRR-only meta-material and the corresponding left-handed material which possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity. Minor deviations from complete isotropy are due to the finite thickness of the meta-material.
We present a novel approach to efficiently implement thermal expansion in the quasi-harmonic approximation (QHA) for both isotropic and more importantly, anisotropic expansion. In this approach, we rapidly determine a crystal's equilibrium volume and shape at a given temperature by integrating along the gradient of expansion from zero Kelvin up to the desired temperature. We compare our approach to previous isotropic methods that rely on a brute-force grid search to determine the free energy minimum, which is infeasible to carry out for anisotropic expansion, as well as quasi-anisotropic appro…
A simulation study of negative thermal expansion in Y2W3O12 was carried out using calculations of phonon dispersion curves through the application of density functional perturbation theory. The mode eigenvectors were mapped onto flexibility models and results compared with calculations of the mode Gruneisen parameters. It was found that many lower-frequency phonons contribute to negative thermal expansion in Y2W3O12, all of which can be described in terms of rotations of effectively rigid WO4 tetrahedra and Y-O rods. The results are strikingly different from previous phonon studies of higher-s…
Results of a series of molecular dynamics simulations of cubic siliceous zeolites suggest that pressure-induced softening -- the phenomenon in which a material becomes progressively more compressible under pressure -- is likely to be a common feature of framework materials that show negative thermal expansion. The correlation between the negative thermal expansion and the pressure-induced softening is investigated on the basis of thermodynamics.
We have investigated temperature dependence of the lattice parameters and the unit cell volume of ZnF$_2$ by neutron diffraction and have discovered negative thermal expansion (NTE) at low temperature. To understand why this simple compound exhibits NTE we performed first principle calculations. These calculations reproduce qualitatively the experimental temperature dependence of volume.
The effect of pressure on the thermal expansion of solid CH$_4$ is calculated for the low temperature region where the contributions from phonons and librons can be neglected and only the rotational tunnelling modes are essential. The effect of pressure is shown to increase the magnitude of the peaks of the negative thermal expansion and shifts the positions of the peaks to the low-temperature region, which goes asymptotically to zero temperature with increasing pressure. The Gruneisen thermodynamical parameter for the rotational tunnelling modes is calculated. It is large, negative, and incre…
Recent experimental work has revealed that the unusually strong, isotropic structural negative thermal expansion in cubic perovskite ionic insulator ScF3 occurs in excited states above a ground state tuned very near a structural quantum phase transition, posing a question of fundamental interest as to whether this special circumstance is related to the anomalous behavior. To test this hypothesis, we report an elastic and inelastic X-ray scattering study of a second system Hg2I2 also tuned near a structural quantum phase transition while retaining stoichiometric composition and high crystallini…
Thermal expansion is a problem in many technological applications and its control represents a challenge in materials design. In this Letter, after studying the correlation between thermal expansion, cubic-to-rhombohedral transition and lattice parameter of ReO3-type structures, I show how in the different methods for controlling thermal expansion the key element is actually the lattice parameter. By varying the lattice parameter through external pressure, chemical modifications or other methods, the single-well potential energy of the octahedral rotation, responsible for Negative Thermal Expa…
We use first-principles theory to show that the ingredients assumed to be essential to the occurrence of negative thermal expansion (NTE) -- rigid unit phonon modes with negative Grüneisen parameters -- are neither sufficient nor necessary for a material to undergo NTE. Instead, we find that NTE in PbTiO$_3$ involves a delicate interplay between the phonon properties of a material (Grüneisen parameters) and its anisotropic elasticity. These unique insights open new avenues in our fundamental understanding of the thermal properties of materials, and in the search for NTE in new materials classe…
Time-of-flight neutron powder diffraction and specific heat measurements were used to study the nature of thermal expansion in rhenium trioxide, an electrically conducting oxide with cubic symmetry. The temperature evolution of the lattice parameters show that ReO3 can exhibit negative thermal expansion at low temperatures and that the transition from negative to positive thermal expansion depends on sample preparation; the single crystal sample demonstrated the highest transition temperature, 300 K, and largest negative value for the coefficient of thermal expansion, alpha = -1.1(1)x 10^-6 K^…
Negative thermal expansion in ZrW2O8 was investigated using a flexibility analysis of ab-initio phonons. It was shown that no previously proposed mechanism adequately describes the atomic-scale origin of negative thermal expansion in this material. Instead it was found that NTE in ZrW2O8 is driven, not by a single mechanism, but by wide bands of phonons that resemble vibrations of near-rigid WO4 units and Zr-O bonds at low frequency, with deformation of O-W-O and O-Zr-O bond angles steadily increasing with increasing NTE phonon frequency. It is asserted that this phenomenon is likely to provid…
Pressure and temperature dependence of the negative thermal expansion in Zn(CN)$_2$ is fully investigated using molecular dynamics simulations with a built potential model. The advantage of this study allows us to reproduce all the exotic behaviours of the material, including the negative thermal expansion (NTE), the reduction of NTE with elevated temperature, the pressure enhancement of NTE and the pressure-induced softening. Results of the study provide us detailed data to link the properties in the energy space and the real space, giving us insights to understand the properties and the conn…
The thermal expansion at constant pressure of solid CD$_4$ III is calculated for the low temperature region where only the rotational tunneling modes are essential and the effect of phonons and librons can be neglected. It is found that in mK region there is a giant peak of the negative thermal expansion. The height of this peak is comparable or even exceeds the thermal expansion of solid N$_2$, CO, O$_2$ or CH$_4$ in their triple points. It is shown that like in the case of light methane, the effect of pressure is quite unusual: as evidenced from the pressure dependence of the thermodynamic G…
Controlling the thermal expansion of materials is of great technological importance. Uncontrolled thermal expansion can lead to failure or irreversible destruction of structures and devices. In ordinary crystals, thermal expansion is governed by the asymmetry of the microscopic binding potential, which cannot be adjusted easily. In artificial crystals called metamaterials, thermal expansion can be controlled by structure. Here, following previous theoretical work, we fabricate three-dimensional two-component polymer microlattices by using gray-tone laser lithography. We perform cross-correlati…
Thermally-densified hafnium terephthalate UiO-66(Hf) is shown to exhibit the strongest isotropic negative thermal expansion (NTE) effect yet reported for a metal-organic framework (MOF). Incorporation of correlated vacancy defects within the framework affects both the extent of thermal densification and the magnitude of NTE observed in the densified product. We thus demonstrate that defect inclusion can be used to tune systematically the physical behaviour of a MOF.
The empty perovskite ScF3 exhibits negative thermal expansion up to 1100 K. We demonstrate that ab-initio calculations of temperature-dependent effective phonon spectra allow to quantitatively describe the behavior of this compound and the suppression of negative thermal expansion. Based on this result, we predict an anomalous temperature dependence of the thermal conductivity and interpret it as a general feature of the perovskite class. Finally, we comment on the fact that the suppression of negative thermal expansion at such a high temperature is beyond the reach of the quasi-harmonic appro…
We use a combination of X-ray diffraction, total scattering and quantum mechanical calculations to determine the mechanism responsible for hydration-driven contraction in ZrW$_2$O$_8$. Inclusion of H$_2$O molecules within the ZrW$_2$O$_8$ network drives the concerted formation of new W--O bonds to give one-dimensional (--W--O--)$_n$ strings. The topology of the ZrW$_2$O$_8$ network is such that there is no unique choice for the string trajectories: the same local changes in coordination can propagate with a large number of different periodicities. Consequently, ZrW$_2$O$_8$ is heavily disorder…
An infrared study of the phonon spectra of ZrW2O8 as a function of temperature which includes the low energy (2-10 meV) region relevant to negative thermal expansion is reported and discussed in the context of specific heat and neutron density of states results. The prevalence of infrared active phonons at low energy and their observed temperature dependence are highly unusual and indicative of exotic low-energy lattice dynamics. Eigenvector calculations indicate a mixing of librational and translational motion within each low-frequency IR mode. The role of the underconstrained structure in es…
Additive manufacturing (AM) could be a novel method of fabricating composite and porous materials having various effective performances based on mechanisms of their internal geometries. Materials fabricated by AM could rapidly be used in industrial application since they could easily be embedded in the target part employing the same AM process used for the bulk material. Furthermore, multi-material AM has greater potential than usual single-material AM in producing materials with effective properties. Negative thermal expansion is a representative effective material property realized by design…
DFT calculations have been used to provide insights into the origin of the colossal positive and negative thermal expansion in Ag$_3$[Co(CN)$_6]$. The results confirm that the positive expansion within the trigonal basal plane and the negative expansion in the orthogonal direction are coupled due to the existence of a network defined by nearly-rigid bonds within the chains of Co--C--N--Ag--N--C--Co linkages. The origin of the colossal values of the coefficients of thermal expansion arise from an extremely shallow energy surface that allows a flexing of the structure with small energy cost. The…
In the paper we report the modeling and design of material which has a negative thermal expansion (NTE). The basic assumption is a potential between the atoms in the material can be approximated by a Lennard-Jones potential (6-12) and the dominant interaction is only between nearest neighbors. We show that the material formed by alternating atomic layers wherein each layer contains a type of atom, and geometry of the arrangement of atoms is triangular, may experience an NTE when sigma_AA = sigma_BB = sigma_AB, epsilon_AA = epsilon_BB < epsilon_AB/4 are satisfied, where sigma_ij and epsilon_ij …
The thermal expansion behavior of metal fluorides can be tuned by choosing appropriate metal cation. We present ab-initio lattice dynamical studies on the metal fluorides (CaZrF6, MgZrF6 and SrZrF6) and identify the anharmonic phonon modes responsible for the negative thermal expansion in these materials. These phonons involve ZrF6 polyhedral rotational motion, which leads to large transverse amplitude of the vibrations of the fluorine atom in the Zr-F-Zr bond. The compounds with larger anisotropy in the thermal amplitude of the fluorine atoms show larger NTE behaviour. This has enabled to und…
GeTe is a well-known ferroelectric and thermoelectric material that undergoes a structural phase transition from a rhombohedral to the rocksalt structure at $\sim 600-700$ K. We present a first principles approach to calculate the thermal expansion of GeTe in the rhombohedral phase up to the Curie temperature. We find the minimum of the Helmholtz free energy with respect to each structural parameter in a manner similar to the traditional Gr{ü}neisen theory, and account for the temperature dependence of elastic constants. We obtain the temperature variation of the structural parameters of rhomb…
The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of experiments and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and density of states (DOS) and their temperature dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the …
Using the Landau-de Gennes theory, the temperature, pressure and frequency dependence of the non-linear effect in the isotropic phase above the isotropic-cholesteric phase transition is calculated. The influence of pressure on the isotropic-cholesteric phase transition is discussed by varying the coupling between the orientational order parameter and the macroscopic polarization of polar cholesterics. Comparing the results of the calculations with existing data, we finally conclude that the model provides a description of the isotropic-cholesteric transition that takes all experimentally known…
The in-plane coefficient of thermal expansion (CTE) for CdSe nanoplatelets with the zinc-blende structure containing from two to five monolayers is calculated from first principles within the quasiharmonic approximation. A comparison of the obtained results with those for bulk CdSe with both the zinc-blende and wurtzite structures finds a significant increase in the magnitude of negative CTE and the temperature range of its observation in nanoplatelets. The main contribution to the negative thermal expansion in CdSe nanoplatelets is given by the out-of-plane flexural ZA mode and in-plane optic…
Dynamical disorder in negative thermal expansion compound Zn(CN)2 is investigated by quasielastic neutron scattering technique in the temperature range 170-320 K. Significant quasielastic broadening is observed above the phase transition temperature of about 250 K, however no broadening is observed at 220 K and below. Data at high temperatures are analyzed assuming the CN reorientation. Characteristic time associated with the CN orientation is estimated as 16 ps and 11 ps at 270 and 320 K respectively.
We investigated the temperature evolution of crystal structure of orthorhombic CoZr3, which is a superconductor with a transition temperature of 4.3 K, by synchrotron and laboratory (CuKα) X-ray diffraction. Uniaxial negative thermal expansion along the c-axis, which is similar to that observed in tetragonal CoZr2, has been observed at a wide temperature range of T = 90-800 K in CoZr3, while a-and b-axis exhibit positive thermal expansion.
Minimal models are developed to examine the origin of large negative thermal expansion (NTE) in under-constrained systems. The dynamics of these models reveals how underconstraint can organize a thermodynamically extensive manifold of low-energy modes which not only drives NTE but extends across the Brillioun zone. Mixing of twist and translation in the eigenvectors of these modes, for which in ZrW2O8 there is evidence from infrared and neutron scattering measurements, emerges naturally in our model as a signature of the dynamics of underconstraint.
The physical properties of the spinel LiGaCr4S8 have been studied with neutron diffraction, X-ray diffraction, magnetic susceptibility and heat capacity measurements. The neutron diffraction and synchrotron X-ray diffraction data reveal negative thermal expansion (NTE) below 111(4) K. The magnetic susceptibility deviates from Curie-Weiss behavior with the onset of NTE. At low temperature a broad peak in the magnetic susceptibility at 10.3(3) K is accompanied by the return of normal thermal expansion. First principles calculations find a strong coupling between the lattice and the simulated mag…
The existing controversy about the room temperature structure of multiferroic Pb(Fe_1/2Nb_1/2)O_3 is settled using synchrotron powder x-ray diffraction data. Results of Rietveld refinements in the temperature range 300 to 12K reveal that the structure remains monoclinic in the Cm space group down to 12K, but the lattice parameters show anomalies at the magnetic transition temperature (T_N) due to spin lattice coupling. The lattice volume exhibits negative thermal expansion behaviour, with Alpha = - 4.64 x 10^-6 K^-1, below T_N.
