We present thermodynamic relationships between the free energy of the phase-field crystal (PFC) model and thermodynamic state variables for bulk phases under hydrostatic pressure. This relationship is derived based on the thermodynamic formalism for crystalline solids of Larché and Cahn [Larché and Cahn, Acta Metallurgica, Vol. 21, 1051 (1973)]. We apply the relationship to examine the thermodynamic processes associated with varying the input parameters of the PFC model: temperature, lattice spacing, and the average value of the PFC order parameter, $\bar{n}$. The equilibrium conditions between bulk crystalline solid and liquid phases are imposed on the thermodynamic relationships for the PFC model to obtain a procedure for determining solid-liquid phase coexistence. The resulting procedure is found to be in agreement with the method commonly used in the PFC community, justifying the use of the common-tangent construction to determine solid-liquid phase coexistence in the PFC model. Finally, we apply the procedure to an eighth-order-fit (EOF) PFC model that has been parameterized to body-centered-cubic ($bcc$) Fe [Jaatinen et al., Physical Review E 80, 031602 (2009)] to demonstrate the procedure as well as to develop physical intuition about the PFC input parameters. We demonstrate that the EOF-PFC model parameterization does not predict stable $bcc$ structures with positive vacancy densities. This result suggests an alternative parameterization of the PFC model, which requires the primary peak position of the two-body direct correlation function to shift as a function of $\bar{n}$.
Thermodynamics of crystalline materials is analyzed using strain volumes, an incremental tensorial state variable which is the volume per unit mass multiplied by the incremental strain.
We investigate crystalline thermodynamic stable lithium silicides phases (LixSiy) with density functional theory (DFT) and a force-field method based on modified embedded atoms (MEAM) and compare our results with experimental data. This work presents a fast and accurate framework to calculate thermodynamic properties of crystal structures with large unit cells with MEAM based on molecular dynamics (MD). Mechanical properties like the bulk modulus and the elastic constants are evaluated in addition to thermodynamic properties including the phonon density of states, the vibrational free energy a…
Computational Investigation of Reactivity Parameters, UV-Vis and IR Spectra, NLO Properties, and Temperature-Dependent Thermodynamic Characteristics of Schiff-Based Interdigitated 5O.m (m=14,16) Liquid Crystalline Compounds: A DFT Analysis
The stability of organic solar cells is strongly affected by the morphology of the photoactive layers, whose separated crystalline and/or amorphous phases are kinetically quenched far from their thermodynamic equilibrium during the production process. The evolution of these structures during the lifetime of the cell remains poorly understood. In this paper, a phase-field simulation framework is proposed, handling liquid-liquid demixing and polycrystalline growth at the same time in order to investigate the evolution of crystalline immiscible binary systems. We find that initially, the nuclei t…
Three-dimensional topological insulators and topological crystalline insulators represent new quantum states of matter, which are predicted to have insulating bulk states and spin-momentum-locked gapless surface states. Experimentally, it has proven difficult to achieve the high bulk resistivity that would allow surface states to dominate the transport properties over a substantial temperature range. Here we report a series of indium-doped Pb$_{1-x}$Sn$_x$Te compounds that manifest huge bulk resistivities together with strong evidence of topological surface states, based on thickness-dependent…
Despite two decades of studies, the formation of metallic glasses, very promising systems for industrial applications, still remains mostly unexplained. This lack of knowledge hinders the search for new systems, still performed with combinatorial trial and error. In the past, it was speculated that some sort of "confusion" during crystallization could play a key role during their formation. In this article, we propose a heuristic descriptor quantifying such confusion. It is based on the "thermodynamic density of competing crystalline states", parameterized from high-throughput ab-initio calcul…
We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to redistribution of vacancy sinks and sources in the material during the creep process. We derive a general ex…
Metropolis Monte Carlo simulations of the eutectic NaK alloy are performed using the Second Moment Approximation (SMA) model potential across a wide range of temperatures at constant pressure. The alloy structure and thermodynamics are analyzed along with the atomic level structures using a variety of structure identification methods. Both enthalpy and density are followed along an annealing process that reveals a clear melting point around 250 K. At lower temperatures, two thermodynamic branches are identified as crystalline and amorphous solids.
Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however, becomes inadequate in discerning various topological crystalline phases [7-17], leading to great challenges in the experimental classification of the large family of topological crystalline materials [4-6]. Theories predict that disclinations, ubiquitous crystallographic defects, provide an effective probe of crystalline topology beyond edges [18-21], which…
We have computed second and third nonlinear optical susceptibilities of two crystalline bulk tellurium oxide polymorphs: $α$-TeO$_{2}$ (the most stable crystalline bulk phase) and $γ$-TeO$_{2}$ (the crystalline phase that ressembles the more to the glass phase. Third order nonlinear susceptibilities of the crystalline phases are two orders of magnitude larger than $α$-SiO$_{2}$ cristoballite, thus extending the experimental observations on glasses to the case of crystalline compounds. While the electronic lone pairs of Te contribute to those large values, a full explanation of the anisotropy o…
This review deals with the kinetic and thermodynamic fragility of bulk metallic glass forming liquids. The experimental methods to determine the kinetic fragility, relaxation behavior and thermodynamic functions of undercooled metallic liquids are introduced. Existing data are assessed and discussed using the Vogel-Fulcher-Tammann equation and in the frameworks of the Adam-Gibbs as well as the Cohen-Turnbull free volume approach. In contrast to pure metals and most non glass forming alloys, bulk glass formers are moderately strong liquids. In general the fragility parameter $D^{*} $ increases …
For topological insulators and topological crystalline insulators (TCIs), their exotic surface states are promising for fundamental condensed matter physics research as well as future electronics such as low-dissipation electronics and spintronics. However, the high bulk carrier density that often dominates the transport property is the major materials challenge, critically hindering our ability to study and manipulate the surface states. In this manuscript, we demonstrate an alloying strategy, SnSexTe1-x, to effectively reduce the bulk carrier density. As long as SnSexTe1-x remains in the cub…
We report temperature and thermal-cycling dependence of surface and bulk structures of double-layered perovskite Sr3Ru2O7 single crystals. The surface and bulk structures were investigated using low-energy electron diffraction (LEED) and single-crystal X-ray diffraction (XRD) techniques, respectively. Single-crystal XRD data is in good agreement with previous reports for the bulk structure with RuO6 octahedral rotation, which increases with decreasing temperature (~ 6.7(6)degrees at 300 K and ~ 8.1(2) degrees at 90 K). LEED results reveal that the octahedra at the surface are much more distort…
This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a sharpening instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The …
In order to improve the performance of existing technologies based on single crystal diamond grown by chemical vapour deposition (CVD), and to open up new technologies in fields such as quantum computing or solid state and semiconductor disc lasers, control over surface and bulk crystalline quality is of great importance. Inductively coupled plasma (ICP) etching using an Ar/Cl gas mixture is demonstrated to remove sub-surface damage of mechanically processed surfaces, whilst maintaining macroscopic planarity and low roughness on a microscopic scale. Dislocations in high quality single crystal …
A simple route to prepare Gd$_{0.7}$Sr$_{0.3}$MnO$_3$ nanoparticles by ultrasonication of their bulk powder materials is presented in this article. For comparison, Gd$_{0.7}$Sr$_{0.3}$MnO$_3$ nanoparticles are also prepared by ball milling. The prepared samples are characterized by X-ray diffraction (XRD),field emission scanning electron microscope (FESEM), energy dispersive X-ray (EDX), X-ray photoelectron spectroscope (XPS), and Superconducting Quantum Interference Device (SQUID) magnetometer. XRD Rietveld analysis is carried out extensively for the determination of crystallographic paramete…
We calculate the electronic and optical excitations of polythiophene using the GW approximation for the electronic self-energy, and include excitonic effects by solving the electron-hole Bethe-Salpeter equation. Two different situations are studied: excitations on isolated chains and excitations on chains in crystalline polythiophene. The dielectric tensor for the crystalline situation is obtained by modeling the polymer chains as polarizable line objects, with a long-wavelength polarizability tensor obtained from the ab-initio polarizability function of the isolated chain. With this model die…
The performance of organic solar cells strongly depends on the bulk heterojunction (BHJ) morphology of the photoactive layer. This BHJ forms during the drying of the wet-deposited solution, because of physical processes such as crystallization and/or liquid liquid phase separation (LLPS). However, the process-structure relationship remains insufficiently understood. In this work, a recently developed, coupled phase field fluid mechanics framework is used to simulate the BHJ formation upon drying. For the first time, this allows to investigate the interplay between all the relevant physical pro…
Metallic glasses have attracted considerable interest in recent years due to their unique combination of superb properties and processability. Predicting bulk metallic glass formers from known parameters remains a challenge and the search for new systems is still performed by trial and error. It has been speculated that some sort of "confusion" during crystallization of the crystalline phases competing with glass formation could play a key role. Here, we propose a heuristic descriptor quantifying confusion and demonstrate its validity by detailed experiments on two well-known glass forming all…
We investigate the atomistic mechanism of homogeneous nucleation during solidification in molybdenum employing transition path sampling. The mechanism is characterized by the formation of a pre-structured region of high bond-orientational order in the supercooled liquid followed by the nucleation of the crystalline bulk phase within the center of the growing solid cluster. This precursor plays a crucial role in the process, as it provides a diffusive interface between the liquid and crystalline core, which lowers the interfacial free energy and facilitates the nucleation of the bulk phase. Fur…
Atomically-abrupt interfaces in transition metal oxide (TMO) heterostructures could host a variety of exotic condensed matter phases that may not be found in the bulk materials at equilibrium. A critical step in the development of such atomically-sharp interfaces is the deposition of atomically-smooth TMO thin films. Optimized deposition conditions exist for the growth of perovskite oxides. However, the deposition of rutile oxides, such as VO$_2$, with atomic-layer precision has been challenging. In this work, we used pulsed laser deposition (PLD) to grow atomically-smooth VO$_2$ thin films on…
PbZrxTi1-xO3 (PZT) is one of the technologically most important ferroelectric materials. Bulk single-domain single crystals of PZT have never been synthesized for a significant compositional range across the solid-solution phase diagram. This leaves the fundamental properties of PZT under debate. Synthesis of defect-free single crystalline films enables us to unambiguously determine the intrinsic quantities that describe ferroelectric materials, such as spontaneous polarization and dielectric constant. Defect-free single crystalline, strained PbZr0.2Ti0.8O3 thin films were grown by pulsed-lase…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at interfaces, and the kinematics of such defects is discussed in some detail. A Gibbsian variational argument is used to derive the necessary bulk and interfacial conditions for multi-phase equilibrium (crystal-crystal and crystal-melt) where the allowed lattice variations involve the creation and transport of defects in the bulk and at the phase interface. An i…
We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that the leading singularities of correlation functions can be analyzed within an effective renormalizable model in which the kinetic energy of in-plane phonons and subleading geometrical nonlinearities in the expansion of the strain tensor are neglected. For membranes at zero temperature, governed by zero-point motion, the RG equations of the effective model provide a systematic derivation of logarith…
Point defects play a crucial role in crystalline materials as they do not only impact the thermodynamic properties but are also central to kinetic processes. While they are necessary in thermodynamic equilibrium spontaneous defect formation in the bulk is normally considered highly improbable except for temperatures close to the melting point. Here, we demonstrate by means of atomistic simulations that processes involving concerted atomic motion that give rise to defect formation are in fact frequent in body-centered cubic metals even down to about 50% of the melting temperature. It is shown t…
The neural-network interatomic potential for crystalline and liquid Si has been developed using the forward stepwise regression technique to reduce the number of bases with keeping the accuracy of the potential. This approach of making the neural-network potential enables us to construct the accurate interatomic potentials with less and important bases selected systematically and less heuristically. The evaluation of bulk crystalline properties, and dynamic properties of liquid Si show good agreements between the neural-network potential and ab-initio results.
Low-temperature-resistivity plateau observed in $\rm SmB_6$ single crystal,which is due to surface, not bulk, conduction has been confirmed from electrical transport measurements. Recently, the correlation between bulk thermodynamic measurements and the low-temperature-resistance plateau in $\rm SmB_6$ have been investigated and a change in Sm valence at the surface has been obtained from x-ray absorption spectroscopy and x-ray magnetic circular dichroism. Here we show that the statement of the report are not supported by the results from x-ray absorption spectroscopy and x-ray magnetic circul…
Magnetism in palladium has been the subject of much work and speculation. Bulk crystalline palladium is paramagnetic with a high magnetic susceptibility. Palladium under pressure and palladium nanoclusters have generated interest to scrutinize its magnetic properties. Here we report another possibility: Palladium may become an itinerant ferromagnet in the amorphous bulk phase at atmospheric pressure. Atomic palladium is a d$^{10}$ element, whereas bulk crystalline Pd is a d$^{10-x}$(sp)$^{x}$ material; this, together with the possible presence of 'unsaturated bonds' in amorphous materials, may…
We report a phonon density of states measurement of $α$-ZnCl$_{2}$ using the coherent inelastic neutron scattering technique and a lattice dynamical calculation in four crystalline phases of ZnCl$_{2}$ using a transferable interatomic potential. The model calculations agree reasonably well with the available experimental data on the structures, specific heat, Raman frequencies and their pressure variation in various crystalline phases. The calculated results have been able to provide a fair description of the vibrational as well as the thermodynamic properties of ZnCl$_{2}$ in all its four pha…
Co-intercalation is a potential approach to influence the voltage and mobility with which cations insert in electrodes for energy storage devices. Combining a robust thermodynamic model with first-principles calculations, we present a detailed investigation revealing the important role of H$_2$O during ion intercalation in nano-materials. We examine the scenario of Mg$^{2+}$ and H$_2$O co-intercalation in nano-crystalline Xerogel-V$_2$O$_5$, a potential cathode material to achieve energy density greater than Li-ion batteries. Water co-intercalation in cathode materials could broadly impact an …
We investigated elastic loss in GaAs/AlGaAs multilayers to help determine the suitability of these coatings for future gravitational wave detectors. We measured large ($\approx 70$-mm diameter) substrate-transferred crystalline coating samples with an improved substrate polish and bonding method. The elastic loss, when decomposed into bulk and shear contributions, was shown to arise entirely from the bulk loss, $ϕ_{\mathrm{Bulk}} = (5.33 \pm 0.03)\times 10^{-4}$, with $ϕ_{\mathrm{Shear}} = (0.0 \pm 5.2) \times 10^{-7}$. These results predict the coating loss of an 8-mm diameter coating in a 35…
We report the effects of cobalt doping on the magnetic properties of two-dimensional van der Waals ferromagnet Fe3GeTe2. Single crystals of (Fe{1-x}Cox)3GeTe2 with x=0-0.78 were successfully synthesized and characterized with x-ray diffraction, energy dispersive x-ray spectroscopy and magnetization measurements. Both the Curie-Weiss temperature and ferromagnetic (FM) ordered moment of Fe3GeTe2 are gradually suppressed upon Co doping. A kink in zero-field-cooling low field M(T) curve which is previously explained as an antiferromagnetic transition is observed for samples with x=0-0.58. Our deta…
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of ''traditional'' techniques for melting-point calculations, as well as with literature values.
Bulk photovoltaic (BPV) effect, a second order nonlinear process that generates static current under light irradiation, requires centrosymmetric broken systems as its application platform. In order to realize measurable BPV photocurrent in spatially centrosymmetric materials, various schemes such as chemical doping, structural deformation, or electric bias have been developed. In the current work, we suggest that magnetic proximity effect via van der Waals interfacial interaction, a contact-free strategy, also breaks the centrosymmetry and generate large BPV photocurrents. Using the Bi2Te3 qui…
Parameters determining the performance of the crystalline oxides zirconia (ZrO_2) and hafnia (HfO_2) as gate insulators in nanometric Si electronics are estimated via ab initio calculations of the energetics, dielectric properties, and band alignment of bulk and thin-film oxides on Si (001). With their large dielectric constants, stable and low-formation-energy interfaces, large valence offsets, and reasonable (though not optimal) conduction offsets (electron injection barriers), zirconia and hafnia appear to have a considerable potential as gate oxides for Si electronics.
Quantum Computing of Phonon Spectra and Thermal Properties of Crystalline Solids
Central University of Punjab（旁遮普中央大学）；Siksha ’O’ Anusandhan University（锡卡奥安桑丹大学）；Bikash’s Quantum (OPC) Private Limited（比卡斯量子（单一成员私人有限公司））；Indian Institute of Science Education and Research (IISER) Kolkata（印度科学教育研究学院加尔各答分校）
The increasing availability of a variety of two-dimensional materials has generated enormous growth in the field of nanoengineering and nanomechanics. Recent developments in thin film synthesis have enabled the fabrication of freestanding functional oxide membranes that can be readily incorporated in nanomechanical devices. While many oxides are extremely brittle in bulk, recent studies have shown that, in thin membrane form, they can be much more robust to fracture as compared to their bulk counterparts. Here, we investigate the ultimate tensile strength of SrTiO$_3$ membranes by probing free…
We show that a deep-learning neural network potential (DP) based on density functional theory (DFT) calculations can well describe Cu-Zr materials, an example of a binary alloy system that can coexist in several ordered intermetallics and as an amorphous phase. The complex phase diagram for Cu-Zr makes it a challenging system for traditional atomistic force-fields that fail to describe well the different properties and phases. Instead, we show that a DP approach using a large database with ~300k configurations can render results generally on par with DFT. The training set includes configuratio…
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of crystal defects is challenged because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the defect-free, homogeneous bulk and derive the grain bo…
We introduce a combined Restrained MD/Parallel Tempering approach to study the difference in free energy as a function of a set of collective variables between two states in presence of unknown slow degrees of freedom. We applied this method to study the relative stability of the amorphous vs crystalline nanoparticles of size ranging between 0.8 and 1.8 nm as a function of the temperature. We found that, at variance with bulk systems, at low T small nanoparticles are amorphous and undergo an amorphous-to-crystalline phase transition at higher T. On the contrary, large nanoparticles recover the…
Pb$_{0.77}$Sn$_{0.23}$Se is a novel alloy of two promising thermoelectric materials PbSe and SnSe that exhibits a temperature dependent band inversion below 300 K. Recent work has shown that this band inversion also coincides with a trivial to nontrivial topological phase transition. To understand how the properties critical to thermoelectric efficiency are affected by the band inversion, we measured the broadband optical response of Pb$_{0.77}$Sn$_{0.23}$Se as a function of temperature. We find clear optical evidence of the band inversion at $160\pm15$ K, and use the extended Drude model to a…
The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gij) for ground state and saddle point configurations. We analyze finite size-effects in the calculation of Gij, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain and discuss the differenc…
Neutron scattering experiments have been performed to elucidate magnetic properties of the quasicrystal approximant Au$_{70}$Si$_{17}$Tb$_{13}$, consisting of icosahedral spin clusters in a body-centered-cubic lattice. Bulk magnetic measurements performed on the single crystalline sample unambiguously confirm long-range ordering at $T_{\rm C} = 11.6 \pm 1$ K. In contrast to the simple ferromagnetic response in the bulk measurements, single crystal neutron diffraction confirms a formation of intriguing non-collinear and non-coplanar magnetic order. The magnetic moment direction was found to be …
It is suggested that at the melting temperature the thermal phonon vibration is in self-resonance with the lattice vibration of the surface atomic/molecular layer. This self resonance occurs at a well defined temperature and triggers the detachment of the atomic/molecular sheet or platelets from the surface of the crystal. Thermodynamic data of five substances is used to test this hypothesis. The calculated average phonon vibrational wavelengths are equal with or harmonics of the d-spacing of the atomic/molecular sheets. The proposed model is able to explain all of the features of melting.
Upon application of a uniform strain, internal sub-lattice shifts within the unit cell of a non-centrosymmetric dielectric crystal result in the appearance of a net dipole moment: a phenomenon well known as piezoelectricity. A macroscopic strain gradient on the other hand can induce polarization in dielectrics of any crystal structure, even those which possess a centrosymmetric lattice. This phenomenon, called flexoelectricity, has both bulk and surface contributions: the strength of the bulk contribution can be characterized by means of a material property tensor called the bulk flexoelectric…
We perform systematic angle-resolved photoemission spectroscopic measurements on the lead tin telluride Pb1-xSnxTe pseudobinary alloy system. We show that the (001) crystalline surface, which is a crystalline surface symmetric about the (110) mirror planes of the Pb1-xSnxTe crystal, pos- sesses four metallic surface states within its surface Brillouin zone. Our systematic Fermi surface and band topology measurements show that the observed Dirac-like surface states lie on the symmetric momentum-space cuts. We further show that upon going to higher electron binding energies, the surface states' …
A new class of materials, Topological Crystalline Insulators (TCIs) have been shown to possess exotic surface state properties that are protected by mirror symmetry. These surface features can be enhanced if the surface-area-to-volume ratio of the material increases, or the signal arising from the bulk of the material can be suppressed. We report the experimental procedures to obtain high quality crystal boules of the TCI, SnTe, from which nanowires and microcrystals can be produced by the vapour-liquid-solid (VLS) technique. Detailed characterisation measurements of the bulk crystals as well …
Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys Pb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p Hamiltonian for topological surface states from electronic structure of the bulk, thereby providing a microscopic understanding of b…
Ab initio density functional theory (DFT) and DFT plus coherent potential approximation (DFT+CPA) are employed to reveal, respectively, the effect of in-plane strain and site-diagonal disorder on the electronic structure of cubic boron arsenide (BAs). It is demonstrated that tensile strain and static diagonal disorder both reduce the semiconducting one-particle band gap of BAs, and a V-shaped p-band electronic state emerges -- enabling advanced valleytronics based on strained and disordered semiconducting bulk crystals. At biaxial tensile strains close to 15% the valence band lineshape relevan…
Pb$_{1-x}$Sn$_x$Te has been shown to be an interesting tunable topological crystalline insulator system. We present a magneto-terahertz spectroscopic study of thin films of Pb$_{0.5}$Sn$_{0.5}$Te. The complex Faraday rotation angle and optical conductivity in the circular basis are extracted without any additional assumptions. Our quantitative measures of the THz response allow us to show that the sample studied contains two types of bulk carriers. One is $p$-type and originates in 3D Dirac bands. The other is $n$-type and appears to be from more conventional 3D bands. These two types of carri…
We observe that the yield strength of a variety of materials, including highly structured and densely packed metals, alloys and semi-crystalline polymers is reasonably approximated by the thermal energy density of the material. This suggests that it is related to the entropic cost of the irreversible work done during plastic deformation rather than the enthalpic cost that depends on the elastic modulus of the material. Here we propose that the entropic cost of material rearrangement in crystalline solids arises from the difference in the uncertainty in building block positions before and after…
