Lattice Elasticity Research Articles

Electrostatic-elastic coupling in colloidal crystals

Abstract Electrostatic-elastic coupling in colloidal crystals, composed of a mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloids, is studied on the continuum level in order to analyze the lattice-mediated interactions between mobile charges. The linearized, Debye-H{" u}ckel-like mean-field equations incorporating a minimal coupling between electrostatic and displacement fields imply an additional effective attractive interaction between mobile charges. For small screening lengths, the interactions between like mobile charges exhibit colloid lattice-mediated effective interaction, ranging from weak to strong attraction, while for large screening lengths the lattice mediated interaction is purely attractive. Continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges, augmented by the minimal electrostatic-elastic coupling terms, can serve as a baseline for more detailed microscopic models.

Multiscale topology optimization for the design of spatially-varying three-dimensional lattice structure

This paper introduces three dimensional (3D) topology optimization specifically tailored for designing spatially-varying primitive-cubic (CP) type lattice structures. The developed design process consists of three steps: pre-processing, main processing, and post-processing. In the pre-processing step, a surrogate model between lattice geometry variables and effective elasticity tensor is constructed using an artificial neural network. This surrogate model is essential because it enables the quick calculation of the effective elasticity tensor of lattice microstructure. In the subsequent main processing step, multiscale topology optimization is performed. During this step, lattice microstructure size and rotation design variables are optimized together with the macrostructure density design variables. Macrostructures are designed using a well-established three-field density scheme with a SIMP formulation. Formulations for spatially-varying 3D lattice microstructure are newly developed based on a unit quaternion rotation representation scheme. In the final post-processing step, a spatially-varying microstructure is restored using a de-homogenization scheme, newly developed particularly for the primitive-cubic (CP) type 3D lattice structures. The effectiveness and robustness of the proposed formulations are validated through three design examples for the compliance minimization problem. Moreover, a designed lattice structure is fabricated using an additive manufacturing machine.

On angular and surface interactions in two-dimensional elastic lattices

This paper deals with two-dimensional elastic lattices which asymptotically converge towards isotropic linear elastic continua. The square lattice composed of central and angular interactions, pioneered by Gazis et al. (1960) for 3D cubic lattices, allows the modelling of isotropic linear elastic continua (in the continuous asymptotic limit) with equivalent Poisson's ratios smaller than 1/3 in a plane stress assumption. This paper presents an alternative or complementary elastic model based on surface elastic interactions, which can be viewed as a complementary lattice model for values of Poisson's ratios greater than 1/3 in plane stress. The physical background of this non-central potential is discussed, basing on the existence of a dual surface pressure. The model can be also introduced from variational arguments. This surface model of Fuchs type is shown to be equivalent to a perimetric elastic model in the linear range. Additionally, this paper explores the possibility of coupling both surface and angular lattice elasticity for square lattices, with the potential to cover a large variety of elastic continua in the asymptotic limit. Gradient elasticity and lattice-based nonlocal elastic continua are constructed, starting from this simple square lattice composed of angular, surface and central interactions. The static behaviour of these square lattices (with central, angular and surface interaction) is investigated in pure compression and pure shear loading, with exact analytical solutions for the discrete displacement field.

Correlation between charge transport and lattice dynamics in La- and Y-doped Ca2MnO4 perovskites

Transition metal oxides exhibit fascinating physical phenomena and hold potential for next-generation electronic devices; therefore, fundamental understanding of their conduction mechanisms is of prime technological importance. We investigate charge transport kinetics and elastic behavior of bulk polycrystalline Ca2-xRxMnO4 oxides, where R = Y or La and 0.01 ≤ x ≤ 0.20. Analysis of temperature dependent electronic transport properties considering the nearest neighbor small polaron hopping model in combination with first-principles calculations of elastic properties indicates tight correlation between charge transport and lattice elasticity. We find that the polaron hopping energies of Y-doped compounds are lower than their La-doped counterparts, and attain minimum values of 60 and 73 meV, respectively. This is associated to softening of interatomic bonds, which is more pronounced for Y-doping compared to La-doping. This is corroborated by a fundamental model for elastically isotropic materials, indicating that the elastic energy induced by small polarons corresponds with the measured polaron hopping energies. Accordingly, the lattice shear and Young moduli, sound velocities and Debye temperatures calculated for Y-doped cells are smaller than for La-doped ones. The non-monotonous dependence of hopping energies on dopant concentration is explained in terms of polaron-polaron separation and mutual electrostatic interactions across the Mn+3-O-Mn+4 conduction path. Our study shows how charge carrier dynamics are strongly coupled with elastic properties, implying that the latter can be used to predict charge carrier mobility in oxide semiconductors.

A fractional nonlocal elastic model for lattice wave analysis

This paper investigates the link between lattice elasticity and nonlocal continuum mechanics from one-dimensional and multi-dimensional wave propagation problems. Eringen (1983) closed the bridge between one-dimensional linear lattice elasticity (called Lagrange lattice) and nonlocal elastic continuum. The Born-Kármán wave dispersive properties of the one-dimensional lattice are accurately fitted by Eringen's nonlocal differential elastic law using asymptotic or phenomenological arguments. A fractional version of Eringen's nonlocal model based on the introduction of a fractional Laplacian for the nonlocal differential operators can improve the accuracy in matching the wave dispersive curve of lattice dynamics. A multi-dimensional generalization of Lagrange lattice for cubic crystals is the lattice of Gazis et al. composed of central and angular interactions. We show in this paper that the differential Eringen's nonlocal elasticity differs from the lattice-based nonlocal elasticity continuum. In particular, Eringen's nonlocal elasticity preserves the isotropic property, whereas the cubic lattice is only isotropic in the low frequency regimes. The fractional generalization of Eringen's model accurately fitted the wave dispersive properties of the cubic crystal in the first Brillouin zone. The fractional generalization of Eringen's model highlights an isotropic response in the low frequency regimes and a cubic symmetry in the high frequency regime.

Explorations on properties of ε′ phase and new crystalline phase of Fe3Ge alloy under high pressures

We calculated the lattice dynamics, elasticity, electron spin polarizability P(EF), and electron specific heat coefficient γ of the L12-Fe3Ge crystalline alloy under high pressure using first-principles method based on density functional theory. By comparing the lattice dynamics and elasticity of the ferromagnetic and non-magnetic systems, it can be found that the spontaneous magnetization of the system induces the dynamic stability of the system at low pressure (less than 6 GPa). Furthermore, the magnetostriction induced by the spontaneous magnetization enhances the elastic modulus of the system. With the increase of pressure, in the pressure range of 130-290 GPa where the spin magnetic moment of the system decreases sharply, the elastic modulus exhibits an abnormal behavior, which leads to double peaks in Poisson's ratio v and Pugh's ratio B/G, correspondingly, double valleys appear in shear modulus G, Young's modulus E and Debye temperature ΘD, which are associated with dynamic instability in the 130-290 GPa. Finally, for the phonon spectrum at 260 GPa with a significant imaginary frequency, the metastable orthogonal Fmmm structure is obtained using the soft mode phase transition theory. After comparing the enthalpy differences with different structures, it is found that the ferromagnetic Fmmm structure is a metastable phase, which is dynamic stable at 0 GPa and 260 GPa.

Giant Viscoelasticity near Mott Criticality in PbCrO_{3} with Large Lattice Anomalies.

Coupling of charge and lattice degrees of freedom in materials can produce intriguing electronic phenomena, such as conventional superconductivity where the electrons are mediated by lattice for creating supercurrent. The Mott transition, which is a source for many fascinating emergent behaviors, is originally thought to be driven solely by correlated electrons with an Ising criticality. Recent studies on the known Mott systems have shown that the lattice degree of freedom is also at play, giving rise to either Landau or unconventional criticality. However, the underlying coupling mechanism of charge and lattice degrees of freedom around the Mott critical end point remains elusive, leading to difficulties in understanding the associated Mott physics. Here, we report a study of Mott transition in cubic PbCrO_{3} by measuring the lattice parameter, using high-pressure x-ray diffraction techniques. The Mott criticality in this material is revealed with large lattice anomalies, which is governed by giant viscoelasticity that presumably results from a combination of lattice elasticity and electron viscosity. Because of the viscoelastic effect, the lattice of this material behaves peculiarly near the critical end point, inconsistent with any existing university classes. We argue that the viscoelasticity may play as a hidden degree of freedom behind the Mott criticality.

Contribution of vanadium particles to thermal movement of correlated two-dimensional pancake Abrikosov vortices in Bi-2223 superconducting system

This article breaks new ground in understanding of variation in the magnetic strength performance, flux pinning and energy dissipation mechanism of polycrystalline bulk Bi1.8Sr2.0Ca2.2Cu3.0Oy (Bi-2223) superconducting materials added with the different vanadium concentration level (0.0≤x≤0.30) under the magnetic field strengths applied up to 5T for the first time. We provide the sophisticated and phenomenological discussions on the magnetoresistivity measurement results in three main sections along the paper. All the findings show that the increase of both the vanadium concentration in the crystal structure and external magnetic field strength damages significantly the magnetic strength performance, vortex dynamics, flux pinning ability and vortex lattice elasticity of bulk Bi-2223 superconducting ceramics. The vanadium addition promotes thermally the movement of correlated two-dimensional (2D) pancake Abrikosov vortices between the in-plane Cu–O2 layers in the valance band, vortex lattice elasticity, vortex dynamics, distance for interlayer Josephson couplings and flux pinning centers and the theoretical computations confirm the remarkable degradation in the formation of super-electrons in the Bi-2223 crystal system. Thus, the vanadium addition is anticipated to be one of the best selectable materials to examine the differentiation in the thermal movement of correlated 2D Pancake Abrikosov vortices in the bulk Bi-2223 superconducting system.

Antiviral compounds modulate elasticity, strength and material fatigue of a virus capsid framework

This study investigates whether the biochemical and antiviral effects of organic compounds that bind different sites in the mature human immunodeficiency virus capsid may be related to the modulation of different mechanical properties of the protein lattice from which the capsid is built. Mechanical force was used as a probe to quantify, in atomic force microscopy experiments at physiological pH and ionic strength, ligand-mediated changes in capsid lattice elasticity, breathing, strength against local dislocation by mechanical stress, and resistance to material fatigue. The results indicate that the effects of the tested compounds on assembly or biochemical stability can be linked, from a physics-based perspective, to their interference with the mechanical behavior of the viral capsid framework. The antivirals CAP-1 and CAI-55 increased the intrinsic elasticity and breathing of the capsid protein lattice and may entropically decrease the probability of the capsid protein to assemble into a functionally competent conformation. Antiviral PF74 increased the resistance of the capsid protein lattice to disruption by mechanical stress and material fatigue and may enthalpically strengthen the basal capsid lattice against breakage and disintegration. This study provides proof of concept that the interrogation of the mechanical properties of the nanostructured protein material that makes a virus capsid may provide fundamental insights into the biophysical action of capsid-binding antiviral agents. The implications for drug design by specifically targeting the biomechanics of viruses are discussed.

An optical lattice with sound.

Quantized sound waves-phonons-govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (for example, by binding electrons into superconducting Cooper pairs)1-3. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff4. Optical-lattice realizations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose-Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallization that supports phonons via short-range, photon-mediated atom-atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions5 to exotic 'fractonic' topological defects6 in the quantum regime.

Elasticity solutions for nano-plane structures under body forces using lattice elasticity, continualised nonlocal model and Eringen nonlocal model

Elasticity solutions for nano-plane structures under body forces using lattice elasticity, continualised nonlocal model and Eringen nonlocal model

Lattice elasticity, waves and temperature from an interaction potential

Kinetic theory is taught to first-year students of physics as a plausible account of thermal equilibrium on the microscopic scale. However, it does not adequately clarify important properties like elasticity, lattice waves, phonons, optical oscillations, bandgap and so on, that are postulated through atomic vibrations. In this article, we apply simple computational tools in four computational experiments to study the effects of the vibrations of 373 atoms of a face-centered cubic crystal such as copper. We also discuss the perturbation modelling approach, the Sutton–Chen potential, and discrete integration. The experiments have different aims e.g. determining the steady-state atom arrangement starting from an arbitrarily specified cluster, the elasticity, the ensuing wave motion, lattice resonance, acoustic properties, and temperature rise. The calculated results agree well with their literature values.

Transferable Molecular Model of Woven Covalent Organic Framework Materials

Two woven covalent organic framework materials (COF-505 and COF-506) have been synthesized since 2016, and the latter demonstrated the ability to take up dyes and other small molecules. This opens the door to applications such as separations, sensing, and catalysis. However, accelerating the design of future woven materials by changing the chemistry of the "threads" will require a computational model for these materials. Since no such atomic-scale model exists, we have developed a protocol for optimizing a force field for woven materials which can be used as the input to molecular dynamics simulations. Their high density and elasticity made these COFs challenging to model at a semiempirical level. Our modeling approach required simultaneous optimization of lattice parameters and elasticity using density functional theory-derived energy barriers and available experimental results. We used this force field, parameterized to fit COF-505, without change, to predict the structure of COF-506. This model allowed us to predict an anisotropy in 505's elasticity and preferred directions for diffusion which cannot be seen experimentally. The pore size distribution for 506 is dominated by small pores (80% <10 Å dia.), though 5% of the pores are up to 20 Å in diameter. We confirmed the experimental result that gases (barring helium) do not diffuse appreciably in COF-505. We validated our (unaltered) force field model to accurately predict experimental uptake data for tetrahydrofuran and methyl orange dye in COF-506. We proposed an atomic-scale mechanism by which COF-505 becomes metallated and demetallated. In addition, in advance of experimental studies, we determined the ability of 505 to incorporate other metals, such as Zn and Fe, which might be considered artificial photosynthesis agents. These predictions validate that Cu was a particularly appropriate choice of metal center for the synthesis, showcasing the ability of this model to play a role in designing woven materials a priori.

Pressure variations of the 5f magnetism in UH3

Pressure variations of the Curie temperature of the 5f ferromagnet β-UH3 were studied using the Mo-alloyed hydride (UH3)0.82Mo0.18, which is stable in air and has very similar TC and magnetization per U atom. By means of ac magnetic susceptibility a linear decrease of TC was observed for pressures up to 3.2 GPa. The coefficient dTC/dp = −2.05 K/GPa gives dlnTC/dp = 1/T*dTC/dp ≈ −0.011 GPa−1. This value is smaller than expected for a 5f-band ferromagnet with relatively short U-U distances and suggests that UH3 may be more localized than expected. Among AnX compounds, similar dependence was found e.g. for US. Revisiting existing data on lattice elasticity for β-UH3, bulk modulus B ≈ 100 GPa can be assumed, leading to dlnTC/dlnV = 1.1. Experimental data are confronted with results of GGA + U electronic structure calculations. Plausible values of direct Coulomb U and Hund’s exchange J are deduced. The lattice compression was found to reduce predominantly the orbital moments.

Analyzing the features of material nonlinearity evaluation in a rectangular aluminum beam using Rayleigh waves: theoretical and experimental study

This study proposes a new parameter to evaluate the material nonlinearity in a thick Aluminum (Al) beam having rectangular cross section using Rayleigh waves. This parameter yields a true value of material nonlinearity using the amplitudes of Rayleigh wave harmonics, in contrast to the relative value yielded by the conventional nonlinearity parameter β′. The Rayleigh wave harmonics are generated in a thick Al 1100 specimen through experiments to estimate its inherent material nonlinearity. This inherent nonlinearity is embedded in the material via lattice elasticity and reckoned using the higher order elastic coefficients. With this experimental investigation, it is found that the accurate evaluation of material nonlinearity is highly dependent on the tone burst cycles in the excitation signal. It is also found that there is a small amount of contribution to the material nonlinearity parameter from the imaginary part of the shear wave component. Furthermore, the relationship between material nonlinearity evaluated using the proposed parameter, excitation frequency, propagation distance, and tone burst cycles in the excitation signal have been unveiled. After knowing these relationships, the material nonlinearity evaluated using the proposed parameter is compared with that obtained from a physics-based nonlinearity parameter containing higher order elastic coefficients. The deviation between the results is minimal. Thus, with the use of amplitudes of harmonics of the Rayleigh wave generated through the experiments, the proposed parameter can evaluate the true material nonlinearity of thick Al beams with fair accuracy.

Degradation in fundamental characteristic features of Bi-2212 superconducting ceramic material with Sr/Ti partial substitution

The present work investigates the vital differentiations in some basic characteristic properties including the crystallinity quality, flux pinning mechanism, superconducting, dc electrical features, grain boundary coupling problems and strength of connection between the superconducting grains in the poly-crystallized Bi2.1Sr2.0−xTixCa1.1Cu2.0Oy cuprate ceramic materials with the partial aliovalent substitution of Sr2+ impurities for the Ti4+ foreign additives in the crystal system. All the materials are prepared by the standard solid-state reaction method, and the characterization of samples produced is thoroughly performed by the typical experimental measurements such as dc electrical resistivity over the temperature, critical current density and powder X-ray diffraction investigations. It is obvious that all characteristic properties tend to diminish constantly with the augmentation of the aliovalent Sr/Ti partial replacement level, and in case of x = 0.10 they reach the global minimum values. To illustrate, the low Bi-2212 superconducting phase diverges from the stabilization because of new induced permanent crystal structure (crystallinity) problems such as the voids, porosity, defects, texturing, cracks, grain boundary coupling problems, grain alignment distributions, stress raisers, omnipresent flaws and crack initiation sites in the crystal system. Besides, the presence of Ti impurities leads to the formation of new impurity phases related to very low superconducting and characteristic TiO2 phase, being favored by either the decrement of c lattice cell parameter or increment of a-axis length. The similar findings are observed in the temperature dependent electrical resistivity measurements. Namely, the electrical resistivities at the normal state are found to increase dramatically from about 74.75–180.47 mΩcm whereas the offset and onset critical temperature values are recorded to diminish from 82.11 K (for the pure sample) to 50.52 K (for the sample prepared with x = 0.10 substitution level) and 84.03–75.14 K, respectively, with the enhancement in the substitution level. Likewise, the Sr/Ti partial replacement affects negatively not only the thermal fluxon motions of correlated two-dimensional pancake vortices but also the ability and strength of vortex lattice period, elasticity, effective and active energy barriers for the flux pinning centers in the Bi-2212 superconducting crystal lattice. In this respect, the Sr/Ti partial substitution mechanism is ploughed to improve the fundamental characteristic features.

SciPhon: a data analysis software for nuclear resonant inelastic X-ray scattering with applications to Fe, Kr, Sn, Eu and Dy

The synchrotron radiation technique of nuclear resonant inelastic X-ray scattering (NRIXS), also known as nuclear resonance vibrational spectroscopy or nuclear inelastic scattering, provides a wealth of information on the vibrational properties of solids. It has found applications in studies of lattice dynamics and elasticity, superconductivity, heme biochemistry, seismology, isotope geochemistry and many other fields. It involves probing the vibrational modes of solids by using the nuclear resonance of Mössbauer isotopes such as 57Fe, 83Kr, 119Sn, 151Eu and 161Dy. After data reduction, it provides the partial phonon density of states of the Mössbauer isotope that is investigated, as well as many other derived quantities such as the mean force constant of the chemical bonds and the Debye velocity. The data reduction is, however, not straightforward and involves removal of the elastic peak, normalization and Fourier-Log transformation. Furthermore, some of the quantities derived are highly sensitive to details in the baseline correction. A software package and several novel procedures to streamline and hopefully improve the reduction of the NRIXS data generated at sector 3ID of the Advanced Photon Source have been developed. The graphical user interface software is named SciPhon and runs as a Mathematica package. It is easily portable to other platforms and can be easily adapted for reducing data generated at other beamlines. Several tests and comparisons are presented that demonstrate the usefulness of this software, whose results have already been used in several publications. Here, the SciPhon software is used to reduce Kr, Sn, Eu and Dy NRIXS data, and potential implications for interpreting natural isotopic variations in those systems are discussed.

Assessing exchange-correlation functionals for elasticity and thermodynamics of [formula omitted]-[formula omitted]: A density functional perturbation theory study

Elastic and thermodynamic properties of negative thermal expansion (NTE) α-ZrW2O8 have been calculated using PBEsol and PBE exchange-correlation functionals within the framework of density functional perturbation theory (DFPT). Measured elastic constants are reproduced within ∼2% with PBEsol and ∼6% with PBE. The thermal evolution of the Grüneisen parameter computed within the quasi-harmonic approximation exhibits negative values below the Debye temperature, consistent with observation. The standard molar heat capacity is predicted to be CP0=192.2 and 193.8 J mol-1K-1 with PBEsol and PBE, respectively. These results suggest superior accuracy of DFPT/PBEsol for studying the lattice dynamics, elasticity and thermodynamics of NTE materials.

Novel elastic, lattice dynamics and thermodynamic properties of metallic single-layer transition metal phosphides: 2H-M2P (Mo2P, W2P, Nb2P and Ta2P)

Recently, there has been a surge of interest in the research of two-dimensional (2D) phosphides due to their unique physical properties and wide applications. Transition metal phosphides 2H-M2Ps (Mo2P, W2P, Nb2P and Ta2P) show considerable catalytic activity and energy storage potential. However, the electronic structure and mechanical properties of 2D 2H-M2Ps are still unrevealed. Here, first-principles calculations are employed to investigate the lattice dynamics, elasticity and thermodynamic properties of 2H-M2Ps. Results show that M2Ps with lower stiffness exhibit remarkable lateral deformation under unidirectional loads. Due to the largest average Grüneisen parameter, single-layer Nb2P has the strongest anharmonic vibrations, resulting in the highest thermal expansion coefficient. The lattice thermal conductivities of Ta2P, W2P and Nb2P contradict classical theory, which would predict a smaller thermal conductivity due to the much heavier atom mass. Moreover, the calculations also demonstrate that the thermal conductivity of Ta2P is the highest as well as the lowest thermal expansion, owing to its weak anharmonic phonon scattering and the lowest average Grüneisen parameter. The insight provided by this study may be useful for future experimental and theoretical studies concerning 2D transition metal phosphide materials.

Formation of artificial flux pinning centers in Bi-2223 cuprate superconductor with Ni impurities and enhanced resistant to thermal fluxon motions of correlated 2D pancake vortices in new matrix

This comprehensive study attempts to find out the evaluation of magnetoresistivity performance and flux pinning centers in the Bi-2223 superconductor with nickel impurities and diffusion annealing temperature interval 650 °C–850 °C by means of magnetotransport measurements (0–5T). It is found that the cooper-pair probabilities as well as pinning of thermal fluxon motions of two-dimensional (2D) pancake vortices and interlayer Josephson coupling between the isolated grains considerably improve with the annealing temperature up to 700 °C as a result of enhancement in the effective flux pinning regions. However, from 700 °C onwards the potential energy barriers decrease significantly due to the increment of permanent structural problems in the crystal system. Namely, the presence of excess Ni impurities develops the recoupling linelike/discrete pancakelike nature. In this respect, the bulk sample exposed to the diffusion annealing temperature of 850 °C exhibits the worst magnetic performance characteristics. The flux lines in the material more easily jump to neighboring states due to the cooper pair-breaking mechanism, and thus the thermal fluxon motions of 2D pancake vortices lead to the energy dissipation. We also discuss the differentiation of vortex lattice elasticity for the materials with the aid of the theoretically calculated quantities such as the thermodynamic critical field (μ0Hc), irreversibility field (μ0Hirr), lower critical field (μ0Hc1), upper critical field (μ0Hc2), penetration depth (λ), coherence length (ξ) and Ginzburg Landau parameter (κ). According to the computational values, the optimum annealing temperature of 700 °C strengthens the pinning of 2D pancake vortices, vortex lattice period and elasticity as a result of the decrease in the inter-plane interaction energy. To sum up, 700 °C favors the applications of bulk Ni surface-layered Bi-2223 compounds in rather higher magnetic fields for a major innovation.