This study reveals a previously unreported phenomenon: elastic softening of synthetic diamonds at temperatures below 1 K. We present ultrasonic measurements on single-crystalline, non-irradiated synthetic diamonds--namely, type-IIa (colorless) and type-Ib (yellow) diamonds grown by high-pressure high-temperature (HPHT) synthesis, as well as type-IIa diamond grown by chemical vapor deposition (CVD). A pronounced, divergent decrease in the elastic stiffness constant $C_{44}$ was observed in all samples down to 20 mK. We attribute this softening to electric quadrupolar degrees of freedom with irreducible representation $T_2$ in diamond. The microscopic origin of this effect, however, remains unresolved. By analogy with similar behavior observed in silicon, we suggest the presence of an as-yet-unidentified, defect-derived quantum ground state with $T_1$ or $T_2$ symmetry at ppb-level concentrations in all three diamonds studied.
Ultra-nanocrystalline diamond is a polycrystalline material, having crystalline diamond grains of sizes in the nanometer regime. We study the structure and mechanical properties of this material as a function of the average grain size, employing atomistic simulations. From the calculated elastic constants and the estimated hardness, we observe softening of the material as the size of its grains decreases. We attribute the observed softening to the enhanced fraction of interfacial atoms as the average grain size becomes smaller. We provide a fitting formula for the scaling of the cohesive energ…
Cobalt pyrochlore fluoride NaCaCo$_2$F$_7$ is a disordered frustrated magnet composed of Co$^{2+}$ ions with an effective spin-$\frac{1}{2}$ magnetic moment and exhibits spin freezing below $T_f \sim$2.4 K. We perform ultrasound velocity measurements on a single crystal of the cubic NaCaCo$_2$F$_7$. The temperature dependence of the bulk modulus (the breathing elastic mode) exhibits Curie-type softening upon cooling below $\sim$20 K down to $T_f$, which is suppressed by the magnetic field. This Curie-type softening should be a precursor to the enhancement of the strength of exchange disorder v…
A combined experimental and numerical study on the variation of the elastic properties of defective single-crystal diamond is presented for the first time, by comparing nano-indentation measurements on MeV-ion-implanted samples with multi-scale modeling consisting of both ab initio atomistic calculations and meso-scale Finite Element Method (FEM) simulations. It is found that by locally introducing defects in the 2x10^18 - 5x10^21 cm-3 density range, a significant reduction of, as well as of density, can be induced in the diamond crystal structure without incurring in the graphitization of the…
The structural and elastic properties of diamond nanocomposites and ultrananocrystalline diamond films (UNCD) are investigated using both empirical potentials and tight binding schemes. We find that both materials are extremely hard, but their superb diamondlike properties are limited by their sp^2 component. In diamond composites, the sp^2 atoms are found in the matrix and far from the interface with the inclusion, and they are responsible for the softening of the material. In UNCD, the sp^2 atoms are located in the grain boundaries. They offer relaxation mechanisms which relieve the strain b…
Many proper and improper ferroelastic materials display (at sufficiently low measurement frequencies) a huge elastic softening below Tc. This giant elastic softening, which can be suppressed with uniaxial stress, is caused by domain wall motion. Here we shortly review our results on frequency and temperature dependent elastic measurements of some perovskites which exhibit improper ferroelastic phase transitions. We also present a new model - based on Landau-Ginzburg theory including long range interaction of needle shaped ferroelastic domains - which describes superelastic softening observed i…
In this paper we present a theoretical analysis of the effect of magnetostriction on quantum oscillations of elastic constants in metals under strong magnetic fields. It is shown that at low temperatures a significant softening of some acoustic modes could occur near peaks of quantum oscillations of the electron density of states (DOS) at the Fermi surface (FS). This effect is caused by a magnetic instability of a special kind, and it can give rise to a lattice instability. We also show that the most favorable conditions for this instability to be revealed occur in metals whose Fermi surfaces …
Elastic softening in the paraelastic phases of Ba$_{1-x}$Sr$_{x}$TiO$_{3}$ is largest near the transition temperatures and decreases on heating smoothly over extended temperature ranges. Softening extends to the highest measured temperature(850~K) for Ba-rich compounds. The temperature evolution of the excess compliance of the precursor softening follows a power law $δS\propto |T-T_{\mathrm{C}}|^{-κ}$\ with a characteristic exponent $κ$\ ranging between 1.5 in SrTiO$_{3}$\ and 0.2 in BaTiO$_{3}$. The latter value is below the estimated lower bounds of displacive systems with three orthogonal s…
The effect of pressure on the zone-center optical phonon modes and the elastic properties of hafnium has been studied by both experimental (Raman scattering) and theoretical (DFT) approaches. It was found an anomaly dependence of the phonon frequency of E$_{2g}$ mode in the pressure range from 0 to 67 GPa. The calculated electronic structure of hafnium shows significant changes under pressure, which have a pronounced spatial anisotropy similar to the anisotropy of the observed phonon properties. The dependencies of the elastic properties on pressure including the components of the elasticity t…
The cubic-to-orthorhombic structural transition occurring in CsH at a pressure of about 17 GPa is studied by ab initio calculations. The relative stability of the competing structures and the transition pressure are correctly predicted. We show that this pressure-induced first-order transition is intimately related to a displacive second-order transition which would occur upon application of a shear strain to the (110) planes. The resulting instability is rationalized in terms of the pressure-induced modifications of the electronic structure.
Niobium does not show any structure transition up to very high pressures. Nonetheless, by using density functional theory, we demonstrate in this work that it exhibits striking softening in elastic moduli C44 and C' at a pressure from 20 to 150 GPa. A novel anomaly softening in C44 from 275 to 400 GPa is also predicted. The physics behind these two anomalies is elaborated by electronic structure calculations, which revealed that they are actually different, with the first one directly relates to an underlying rhombohedral distortion whereas the latter originates in an electronic topological tr…
We combine density functional theory within the local density approximation, the quasiharmonic approximation, and vibrational density of states to calculate single crystal elastic constants, and bulk and shear moduli of diamond at simultaneous high pressures and temperatures in the ranges of 0-500 GPa and 0-4800 K. Comparison with experimental values at ambient pressure and high temperature shows an excellent agreement for the first time with our first-principles results validating our method. We show that the anisotropy factor of diamond increases to 40% at high pressures and becomes temperat…
We present results of ultrasonic measurements on a single crystal of the distorted diamond-chain compound azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$. Pronounced elastic anomalies are observed in the temperature dependence of the longitudinal elastic mode $c_{22}$ which can be assigned to the relevant magnetic interactions in the system and their couplings to the lattice degrees of freedom. From a quantitative analysis of the magnetic contribution to $c_{22}$ the magneto-elastic coupling $G$ = $\partial J_2$/$\partial ε_b$ can be determined, where $J_2$ is the intra-dimer coupling constant and $ε_b$ th…
In this letter, we study the higher-order effect on the third-order elastic constants (TOECs) of diamond using longitudinal stress-uniaxial strain (LSUS) approach based on density functional theory. The result shows that the higher-order effect on TOECs is not negligible in the shock wave experiments and similar calculations. By taking the higher-order elastic response (up to fifth order) into consideration, the convergence of TOECs against maximum stain gets improved significantly and resolves the discrepancy of several different theoretical methods and experiments.
The main aim of the present work is to estimate the effective elastic stiffnesses of a two-phase diamond/$β$-SiC composite thin film that is fabricated by chemical vapor deposition. The parameters of linear elasticity are determined by numerical homogenization. The database is sparse since for the 3D volume of interest only two micrographs displaying the phase distributions in perpendicular planes are available; micrographs each of a cross-section and the surface of the thin film. A representative volume element (RVE) is reconstructed by an optimization software and by means of identified mate…
The classical motion of gliding dislocation lines in slip planes of crystalline solid helium leads to plastic deformation even at temperatures far below the Debye temperature and can affect elastic properties. In this work we argue that the gliding of dislocations and plasticity may be the origin of many observed elastic anomalies in solid He-4, which have been argued to be connected to supersolidity. We present a dislocation motion model that describes the stress-strain $τ$-$ε$ curves and work hardening rate $dτ/dε$ of a shear experiment performed at constant strain rate $\dotε$ in solid heli…
Experimental phonon imaging in diamond anvils cell is demonstrated to be an adequate tool to extract the complete set of elastic constants of single-crystalline silicon up to the ZB$\rightarrow β-$Sn transition (10 GPa). Contrary to what was commonly admitted, we demonstrate that the development of the strain-energy density in terms of strains cannot be stopped, for silicon, after the terms containing the third-order elastic constants. Nonlinear elasticity, degree of anisotropy and pressure-induced mechanical stability of the cubic silicon structure are thus revisited and investigated in more …
Reports published in the last 25 years on the synthesis of carbon-based materials significantly superior to diamond in hardness and elastic properties have been critically examined, and three groups of recently appearing myths have been analyzed. The first group concerns the possibility of producing materials with bulk moduli much higher than that of diamond. The second group regards to "experimentally measured" hardness significantly higher than that of diamond. Myths of the third group state that quantum confinement effects supposedly provide "theoretical" foundations for a several-fold (!) …
We study the geometrically nonlinear behavior of uniformly compressed tensegrity prisms, through fully elastic and rigid--elastic models. The presented models predict a variety of mechanical behaviors in the regime of large displacements, including an extreme stiffening-type response, already known in the literature, and a newly discovered, extreme softening behavior. The latter may lead to a snap buckling event producing an axial collapse of the structure. The switching from one mechanical regime to another depends on the aspect ratio of the structure, the magnitude of the applied prestress, …
This work focuses on the thermodynamics of pseudo-elastic models which represent the Mullins effect. Two established models are analyzed theoretically, their thermomechanical properties are derived, and certain critical points are identified. These findings are used to deduce an alternative approach to deviate pseudo-elasticity. This is achieved by defining a suitable free energy which imposes conditions on the stress tensor and the dissipation using the Clausius-Duhem inequality. The concept of pseudo-elasticity is then generalized to extend arbitrary thermomechanical, even inelastic, materia…
The atomic structure and physical properties of few-layered <111> oriented diamond nanocrystals (diamanes), covered by hydrogen atoms from both sides are studied using electronic band structure calculations. It was shown that energy stability linear increases upon increasing of the thickness of proposed structures. All 2D carbon films display direct dielectric band gaps with nonlinear quantum confinement response upon the thickness. Elastic properties of diamanes reveal complex dependence upon increasing of the number of <111> layers. All theoretical results were compared with available experi…
Anisotropic Electrostatic-Elastic Softening and Stability in Charged Colloidal Crystals
Zhejiang Key Laboratory of Soft Matter Biomedical Materials, Wenzhou Institute, University of Chinese Academy of Sciences（温州研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Inelastic and elastic neutron scattering have been used to study a single crystal of the Ni$_{54}$Mn$_{23}$Al$_{23}$ Heusler alloy over a broad temperature range. The paper reports the first experimental determination of the low-lying phonon dispersion curves for this alloy system. We find that the frequencies of the TA$_2$ modes are relatively low. This branch exhibits an anomaly (dip) at a wave number $ξ_{0} ={1/3}\approx 0.33$, which softens with decreasing temperature. Associated with this anomalous dip at $ξ_{0}$, an elastic central peak scattering is also present. We have also observed s…
We substantiate by calculations that the recently discovered superconductivity below 4 K in 3% boron-doped diamond is caused by electron-phonon coupling of the same type as in MgB$_2$, albeit in 3 dimensions. Holes at the top of the zone-centered, degenerate $σ$-bonding valence band couple strongly to the optical bond-stretching modes. The increase from 2 to 3 dimensions reduces the mode-softening crucial for $T_{c}$ reaching 40 K in MgB$_{2}.$ Even if diamond had the same \emph{bare} coupling constant as MgB$_{2},$ which could be achieved with 10% doping, $T_{c}$ would only be 25 K. Supercond…
In this work, we address the issue of peaking of piezoelectric response at a particular composition in the morphotropic phase boundary (MPB) region of (Pb0.940Sr0.06)(ZrxTi1-x)O3 (PSZT) piezoelectric ceramics. We present results of synchrotron x-ray powder diffraction, dielectric, piezoelectric and sound velocity studies to critically examine the applicability of various models for the peaking of physical properties. It is shown that the models based on the concepts of phase coexistence, polarization rotation due to monoclinic structure, tricritical point and temperature dependent softening of…
Using a valence force field model based on that introduced by Martin, we present three related methods through which we analytically determine valence force field parameters. The methods introduced allow easy derivation of valence force field parameters in terms of the Kleinman parameter $ζ$ and bulk properties of zincblende and diamond crystals. We start with a model suited for covalent and weakly ionic materials, where the valence force field parameters are derived in terms of $ζ$ and the bulk elastic constants $C_{11}$, $C_{12}$, and $C_{44}$. We show that this model breaks down as the mate…
Electrostatic-Elastic Softening and Ultraviolet Instability Driven by Non-DLVO Interactions in Charged Colloidal Crystals
Wenzhou Institute, University of Chinese Academy of Sciences（温州研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Silicon is an important material and many empirical interatomic potentials have been developed for atomistic simulations of it. Among them, the Tersoff potential and its variants are the most popular ones. However, all the existing Tersoff-like potentials fail to reproduce the experimentally measured thermal conductivity of diamond silicon. Here we propose a modified Tersoff potential and develop an efficient open source code called GPUGA (graphics processing units genetic algorithm) based on the genetic algorithm and use it to fit the potential parameters against energy, virial and force data…
The precise measurement of mechanical stress at the nanoscale is of fundamental and technological importance. In principle, all six independent variables of the stress tensor, which describe the direction and magnitude of compression/tension and shear stress in a solid, can be exploited to tune or enhance the properties of materials and devices. However, existing techniques to probe the local stress are generally incapable of measuring the entire stress tensor. Here, we make use of an ensemble of atomic-sized in-situ strain sensors in diamond (nitrogen-vacancy defects) to achieve spatial mappi…
Density functional perturbation theory calculations of alpha-quartz using extended norm conserving pseudopotentials have been used to study the elastic properties and phonon dispersion relations along various high symmetry directions as a function of bulk, uniaxial and non-hydrostatic pressure. The computed equation of state, elastic constants and phonon frequencies are found to be in good agreement with available experimental data. A zone boundary (1/3, 1/3, 0) K-point phonon mode becomes soft for pressures above P=32 GPa. Around the same pressure, studies of the Born stability criteria revea…
Diamond-like carbon (DLC) films are synthesized on Si using plasma enhanced chemical vapor deposition. The role of substrate bias and nitrogen doping on the structural evolution and local elastic modulus of DLC films are systematically investigated. Raman spectroscopic studies reveal that the amount of graphitic C=C sp2 bonding increases with substrate bias and nitrogen doping. The density and hydrogen concentration in the films are found to vary from 0.7 to 2.2 g/cm3 and 16 to 38 atomic %, respectively, depending upon the substrate bias and nitrogen concentration in the DLC films. Atomic forc…
Many ferroelastic crystals display at sufficiently low measurement frequencies a huge elastic softening below Tc which is caused by domain wall motion. Materials range from perovskites to iron based superconductors and shape memory materials. We present a model - based on Landau-Ginzburg theory including long range elastic interaction between needle shaped ferroelastic domains - to describe the observed superelastic softening. The theory predicts that the domain wall contribution to the elastic susceptibility is different for improper and proper ferroelastic materials. A test of the theory aga…
To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary …
Calcium vanadate CaV$_2$O$_4$ has a crystal structure of quasi-one-dimensional zigzag chains composed of orbital-active V$^{3+}$ ions and undergoes successive structural and antiferromagnetic phase transitions at $T_s\sim 140$ K and $T_N \sim 70$ K, respectively. We perform ultrasound velocity measurements on a single crystal of CaV$_2$O$_4$. The temperature dependence of its shear elastic moduli exhibits huge Curie-type softening upon cooling that emerges above and below $T_s$ depending on the elastic mode. The softening above $T_s$ suggests the presence of either onsite Jahn-Teller-type or i…
Plutonium metal exhibits an anomalously large softening of its bulk modulus at elevated temperatures that is made all the more extraordinary by the finding that it occurs irrespective of whether the thermal expansion coefficient is positive, negative or zero --- representing an extreme departure from conventional Grüneisen scaling. We show here that the cause of this softening is the compressibility of plutonium's thermally excited electronic configurations, which has thus far not been considered in thermodynamic models. We show that when compressible electronic configurations are thermally ac…
Criteria of selecting strain and fitting schemes are proposed for the calculation of higher-order elastic constants more efficiently, robustly and accurately. As demonstrated by the third-order elastic constants (TOECs) of diamond, the proposed method is 3-5 times faster than existing methods, and the range of strain for getting correct TOECs is expanded. In addition, our result provides an evidence for the inaccuracy of some previous experiments caused by higher-order effect, and the difference among experiments and several different theoretical methods is resolved. Finally, we give the recom…
We study theoretically the equilibrium structure, as well as the response under external load, of characteristic carbon-based materials. The materials considered include diamond, amorphous carbon (a-C), ``amorphous diamond'' and nanocomposite amorphous carbon (na-C). A universal bulk-modulus versus density curve is obeyed by all structures we consider. We calculate the dependence of elastic constants on the density. The strength of a-C was found to increase in roughly a linear manner, with increasing concentration of four-fold atoms, with the maximum stress of the strongest a-C sample being ab…
Neutron scattering and ultrasonic methods have been used to study the lattice dynamics of two single crystals of Ni-Mn-In Heusler alloys close to Ni$_{50}$Mn$_{34}$In$_{16}$ magnetic superelastic composition. The paper reports the experimental determination of the low-lying phonon dispersion curves and the elastic constants for this alloy system. We found that the frequencies of the TA$_{2}$ branch are relatively low and it exhibits a small dip anomaly at a wave number $ξ_{0} \approx 1/3$, which softens with decreasing temperature. Associated with the softening of this phonon, we also observed…
The antipolar and antiferrodistortive (AFD) components of the antiferroelectric (AFE) transition in PbZr1-xTixO3 (x=0.054) can occur separately and with different kinetics, depending on the sample history, and are accompanied by elastic softening and stiffening, respectively. Together with the softening that accompanies octahedral tilting in the fraction of phase that is not yet transformed into AFE, they give rise to a variety of shapes of the curves of the elastic compliance versus temperature. All such anomalies found in samples with x=0.046 and 0.054, in addition to those already studied a…
Clear anomalies in the lattice thermal expansion (deviation from linear variation) and elastic properties (softening of the sound velocity) at the antiferromagnetic-to-paramagnetic transition are observed in the prototypical multiferroic BiFeO3 using a combination of picosecond acoustic pump-probe and high-temperature X-ray diffraction experiments. Similar anomalies are also evidenced using first-principles calculations supporting our experimental findings. Those calculations in addition to a simple Landau-like model we also developed allow to understand the elastic softening and lattice chang…
We present atomistic simulations for the mechanical response of ultra nanocrystalline diamond, a polycrystalline form of diamond with grain diameters of the order of a few nm. We consider fully three-dimensional model structures, having several grains of random sizes and orientations, and employ state-of-the-art Monte Carlo simulations. We calculate structural properties, elastic constants and the hardness of the material; our results compare well with experimental observations for this material. Moreover, we verify that this material becomes softer at small grain sizes, in analogy to the obse…
We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific heat, and $^{119}$Sn Mössbauer spectroscopy measurements on SnTe and Sn$_{0.995}$Cr$_{0.005}$Te. Hall measurements at $T=77$ K indicate that our Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4 \times 10^{19}$ cm$^{-3}$ and that our Cr-doped crystals have an $n$-type concentration of $5.8 \times 10^{22}$ cm$^{-3}$. Although our SnTe crystals are diamagnetic over the temperature range $2\, \text{K} \leq T \leq 1100\, \text{K}$, the Cr-doped crysta…
The structural, dynamical, and thermodynamical properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory (DFT) total-energy calculations and density-functional perturbation theory (DFPT) lattice dynamics at the GGA-PBE level. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the associated elastic constants and phonon dispersions. Both the C_33 elastic constant and the Gamma to A phonon dispersions are brough…
In a recent Letter, Fujii et. al. [Phys. Rev. Lett. 125, 016001] predicted a new carbon allotrope, pentadiamond, with remarkable mechanical properties: elastic moduli comparable or larger than diamond, and negative Poisson's ratio $μ$ = -0.241. The estimated Vicker's hardness is 422 GPa, $\sim$4.6 times higher than in diamond($\sim$92 GPa), the hardest material known to date. Pentadiamond, however was not investigated. Motivated by this, we used different approaches to estimate the elastic properties of pentadiamond with different approximations based on Density Functional Theory. The tests we…
Ultrasound velocity measurements of magnesium chromite spinel MgCr$_2$O$_4$ reveal elastic anomalies in the paramagnetic phase that are characterized as due to geometrical frustration. The temperature dependence of the tetragonal shear modulus $(C_{11}-C_{12})/2$ exhibits huge Curie-type softening, which should be the precursor to spin Jahn-Teller distortion in the antiferromagnetic phase. The trigonal shear modulus $C_{44}$ exhibits nonmonotonic temperature dependence with a characteristic minimum at $\sim$50 K, indicating a coupling of the lattice to dynamical molecular spin state. These res…
We have studied the internal friction and the relative change in the speed of sound of amorphous diamond-like carbon films prepared by pulsed-laser deposition from 0.3 K to room temperature. Like the most of amorphous solids, the internal friction below 10 K exhibits a temperature independent plateau. The values of the internal friction plateau, however, are slightly below the universal ``glassy range'' where the internal frictions of almost all amorphous solids lie. Similar observations have been made in our earlier studies in the thin films of amorphous silicon and amorphous germanium, and t…
Adaptation of Wallace's Approach to the Specific Heat of Elemental Solids with Significant Intrinsic Anharmonicity, Particularly the Light Actinide Metals
By the combination of optical tweezer manipulation and digital video microscopy, the flexural rigidity of single glycolipid "nano" tubes has been measured below the transition temperature at which the lipid tubules are transformed into vesicles. Consequently, we have found a clear reduction of the rigidity obviously before the transition as temperature increasing. Further experiments of infrared spectroscopy (FT-IR) and differential scanning calorimetry (DSC) have suggested a microscopic change of the tube walls, synchronizing with the precursory softening of the nanotubes.
The possibility of propagation of second sound waves in diamond single crystals depending on their dimensions, concentrations of isotopes and temperature is studied. At this correct account of phonon scattering on boundaries is important. The calculation of phonon collision frequencies is carried out in the reduced isotropic crystal model using second and third modules of elasticity and in Callaway model on the basis of experimental data on diamond thermal conductivity. Both models give us the consistent values of parameters under which the propagation of SSW is possible. It is discovered that…
