The lattice dynamics in the polycrystalline shape-memory Heusler alloy Ni$_{50}$Mn$_{35}$In$_{15}$ has been studied by means of resonant ultrasound spectroscopy (RUS). RUS spectra were collected in a frequency range $100-1200$ kHz between 10 and 350 K. Ni$_{50}$Mn$_{35}$In$_{15}$ exhibits a ferromagnetic transition at 313 K in the austenite and a martensitic transition at 248 K accompanied by a change of the magnetic state. Furthermore it displays a antiferromagnetic to ferromagnetic transition within the martensitic phase. We determined the temperature dependence of the shear modulus and the acoustic attenuation of Ni$_{50}$Mn$_{35}$In$_{15}$ and compared it with magnetization data. Following the structural softening, which accompanies the martensitic transition as a pretransitional phenomenon, a strong stiffening of the lattice is observed at the martensitic magneto-structural transition. Only a weak magnetoelastic coupling is evidenced at the Curie temperatures both in austenite and martensite phase. The large acoustic damping in the martensitic phase compared with the austenitic phase reflects the motion of the twin walls, which freezes out in the low temperature region.
Strain engineering is a very effective method to continuously tune the electronic, topological, optical and thermoelectric properties of materials. In this work, strain-dependent phonon transport of recently-fabricated antimonene (Sb monolayer) under biaxial strain is investigated from a combination of first-principles calculations and the linearized phonon Boltzmann equation. It is found that the ZA dispersion of antimonene with strain less than -1\% gives imaginary frequencies, which suggests that compressive strain can induce structural instability. Experimentally, it is possible to enhance…
The single phase polycrystalline Ba1/4Sr3/4MnO3 layered perovskite manganite has been synthesized by combustion method having various crystallite sizes. The room temperature X-ray diffraction patterns reveal that Ba1/4Sr3/4MnO3 crystallizes into hexagonal crystal structure with space group P63/mmc as confirmed by Rietveld refinement. The scanning electron micrographs of Ba1/4Sr3/4MnO3 reveal uniform crystallite size of the samples. Effect of crystallite size on lattice strain and crystal structure has been studied using Rietveld refinement and Williamson-Hall plot, respectively. The structural…
Strain relief in lattice mismatched heteroepitaxy is mediated by formation and/or propagation of dislocations. Due to their technological significance, the process of strain relief in materials with face-centred cubic (fcc) lattices has been analyzed by several researchers1,2 following the work by Matthews and co-workers in the late 1960s to early 1970s3-6. In the Matthews model, it is assumed that the strain relieved by any misfit dislocation is equal to the edge component of the dislocation burgers vector in the interface plane. This assumption has been used in all subsequent analyses of str…
The lattice strain and domain switching behaviour was investigated as a function of cyclic field and grain orientation for a pseudorhombohedral composition of the high Curie point piezoelectric system xBiScO3 - (1-x)PbTiO3 (x = 0.40) by in-situ electric field diffraction technique with high energy synchrotron x-rays. Along the field direction, the system exhibts five time large strain along 100 as compared to the 111 direction. A one-to-one correspondence between the 200 lattice strain and the 111 domain switching suggests a strong correlation between the two phenomena.
We report on a direct measurement of cation and anion sub-lattice strain in an InAs/GaSb type-II strained layer superlattice (T2SLs) using atomic resolution Z-contrast imaging and advanced image processing. Atomic column positions in InAs and GaSb are determined by separating the cation and anion peak intensities. Analysis of the InAs/GaSb T2SLs reveals the compressive strain in the nominal GaSb layer and tensile strain at interfaces between constituent layers, which indicate In incorporation into the nominal GaSb layer and the formation of GaAs like interfaces, respectively. The results are c…
Micro-Laue diffraction and simultaneous rainbow-filtered micro-diffraction were used to measure accurately the full strain tensor and the lattice orientation distribution at the sub-micron scale in highly strained, suspended Ge micro-devices. A numerical approach to obtain the full strain tensor from the deviatoric strain measurement alone is also demonstrated and used for faster full strain mapping. We performed the measurements in a series of micro-devices under either uniaxial or biaxial stress and found an excellent agreement with numerical simulations. This shows the superior potential of…
This study presents a detailed examination of the lattice distortions introduced by glancing incidence Focussed Ion Beam (FIB) milling. Using non-destructive multi-reflection Bragg coherent X-ray diffraction we probe damage formation in an initially pristine gold micro-crystal following several stages of FIB milling. These experiments allow access to the full lattice strain tensor in the micro-crystal with ~25 nm 3D spatial resolution, enabling a nano-scale analysis of residual lattice strains and defects formed. Our results show that 30 keV glancing incidence milling produces fewer large defe…
High pressure structural distortions of the hexagonal close packed (hcp) element zinc have been a subject of controversy. Earlier experimental results and theory showed a large anomaly in lattice strain with compression in zinc at about 10 GPa which was explained theoretically by a change in Fermi surface topology. Later hydrostatic experiments showed no such anomaly, resulting in a discrepancy between theory and experiment. We have computed the compression and lattice strain of hcp zinc over a wide range of compressions using the linearized augmented plane wave (LAPW) method paying special at…
Lattice deformations of InAs self-assembled quantum dots, which were grown on (001) GaAs substrates and embedded in GaNAs strain compensating layers (SCLs), were examined with an ion-channeling method in Rutherford backscattering spectrometry. The channeling experiments demonstrated that the increase of the nitrogen concentrations in the GaNAs SCLs caused the indium lattice displacements along the [001] growth direction while those parallel to the (001) crystal plane were kept unchanged
In-situ electrochemical impedance spectroscopy was used to study the effect of lattice volume and strain on the proton conductivity of the yttrium-doped barium cerate proton conductor by applying the hydrostatic pressure up to 1.25 GPa. An increase from 0.62 eV to 0.73 eV in the activation energy of the bulk conductivity was found with increasing pressure during a unit cell volume change of 0.7%, confirming a previously suggested correlation between lattice volume and proton diffusivity in the crystal lattice. One strategy worth trying in the future development of the ceramic proton conductors…
A theory for conduction electron scattering by inhomogeneous crystal lattice strains is developed, based on the differential geometric treatment of deformations in solids. The resulting fully covariant Schrödinger equation shows that the electrons can be described as moving in a non-Euclidean background space in the continuum limit of the deformed lattice. Unlike previous work, the formalism is applicable to cases involving purely elastic strains as well as discrete and continuous distributions of dislocations --- in the latter two cases it clearly demarcates the effects of the dislocation str…
Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy.
Bravais lattices are the most fundamental building blocks of crystallography. They are classified into groups according to their translational, rotational, and inversion symmetries. In computational analysis of Bravais lattices, fulfilment of symmetry conditions is usually determined by analysis of the metric tensor, using either a numerical tolerance to produce a binary (i.e. yes or no) classification, or a distance function which quantifies the deviation from an ideal lattice type. The metric tensor, though, is not scale-invariant, which complicates the choice of threshold and the interpreta…
Strain engineering enables the direct modification of the atomic bonding and is currently an active area of research aimed at improving the electrocatalytic activity. However, directly measuring the lattice strain of individual catalyst nanoparticles is challenging, especially at the scale of a single unit cell. Here, we quantitatively map the strain present in rhodium@platinum (core@shell) nanocube electrocatalysts using conventional aberration-corrected scanning transmission electron microscopy (STEM) and the recently developed technique of 4D-STEM nanobeam electron diffraction. We demonstra…
The full lattice strain tensor and lattice rotations induced by a dislocation in pure tungsten were mapped using high-resolution transmission Kikuchi diffraction (HR-TKD) in a SEM. The HR-TKD measurement agrees very well with a forward calculation using an elastically isotropic model of the dislocation and its Burgers vector. Our results demonstrate that the spatial and angular resolution of HR-TKD in SEM is sufficiently high to resolve the details of lattice distortions near individual dislocations. This capability opens a number of new interesting opportunities, for example determining the B…
The phenomenon of ferromagnetic resonance (FMR) provides fundamental information on the physics of magnetic materials and lies at the heart of a variety of signal processing microwave devices. Here we demonstrate theoretically that substrate-induced lattice strains may change the FMR frequency of an epitaxial ferromagnetic film dramatically, leading to ultralow and ultrahigh resonance frequencies at room temperature. Remarkably, the FMR frequency varies with the epitaxial strain nonmonotonically, reaching minimum at a critical strain corresponding to the strain-induced spin reorientation trans…
We studied lattice expansion coefficient due to As using density functional theory with particular attention to separating the impact of electrons and ions. Based on As deactivation mechanism under equilibrium conditions, the effect of stress on As activation is predicted. We find that biaxial stress results in minimal impact on As activation, which is consistent with experimental observations by Sugii et al. [J. Appl. Phys. 96, 261 (2004)] and Bennett et al.[J. Vac. Sci. Tech. B 26, 391 (2008)].
The measurement of the Avogadro constant by counting Si atoms is based on the assumption that Si balls of about 94 mm diameter have a perfect crystal structure up to the outermost atom layers. This not the case because of the surface relaxation and reconstruction, the possible presence of an amorphous layer, and the oxidation process due to the interaction with the ambient. This paper gives the results of density functional calculations of the strain components orthogonal to crystal surface in a number of configurations likely found in real samples.
BAs is III-V semiconductor with ultra-high thermal conductivity, but many of its electronic properties are unknown. This work applies predictive atomistic calculations to investigate the properties of BAs heterostructures, such as strain effects on band alignments and carrier mobility, considering BAs as both a thin film and a substrate for lattice-matched materials. The results show that strain decreases the band gap independent of sign or direction. In addition, biaxial tensile strain increases the in-plane electron and hole mobilities by more than 60% compared to the unstrained values due t…
The stoichiometric Ni$_{50}$Mn$_{25}$In$_{25}$ Heusler alloy transforms from a stable ferromagnetic austenitic ground state to an incommensurate modulated martensitic ground state with a progressive replacement of In with Mn without any pre-transition phases. The absence of pre-transition phases like strain glass in Ni$_{50}$Mn$_{25+x}$In$_{25-x}$ alloys is explained to be the ability of the ferromagnetic cubic structure to accommodate the lattice strain caused by atomic size differences of In and Mn atoms. Beyond the critical value of $x$ = 8.75, the alloys undergo martensitic transformation …
We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) confirm, that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use high-resolution X-ray diffraction (HRXRD) to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain …
Ion-irradiated FeCr alloys are useful for understanding and predicting neutron-damage in the structural steels of future nuclear reactors. Previous studies have largely focused on the structure of irradiation-induced defects, probed by transmission electron microscopy (TEM), as well as changes in mechanical properties. Across these studies, a wide range of irradiation conditions has been employed on samples with different processing histories, which complicates the analysis of the relationship between defect structures and material properties. Furthermore, key properties, such as irradiation-i…
We report on the effect of epitaxial strain on magnetic and optical properties of perovskite LaCrO3 (LCO) single crystal thin films. Epitaxial LCO thin films are grown by pulsed laser deposition on proper choice of substrates to impose different strain states. A combined experimental and theoretical approach is used to demonstrate the direct correlation between lattice-strain and functional properties. The magnetization results show that the lattice anisotropy plays a critical role in controlling the magnetic behavior of LCO films. The strain induced tetragonality in the film lattice strongly …
Two-dimensional (2D) magnetoelectric multiferroics are promising multifunctional materials for miniaturized logic and memory devices. Herein, we explore the effectiveness of strain-engineering for tuning the properties of a recently predicted 2D antiferromagnetic-ferroelectric, VOCl2 monolayer. Interestingly, we find that magnetic-ordering and electric polarization can be tuned independently using uniaxial tensile strain along different in-plane lattice vectors. A 4% tensile strain along lattice vector b induces a transition from an antiferromagnetic (AFM) ground state with an out-of-plane mag…
Two-dimensional group IV transition-metal dichalcogenides have encouraging thermoelectric applications since their electronic and lattice properties can be manipulated with strain. In this paper, we report the thermoelectric parameters such as electrical conductivity, Seebeck coefficients, electrical relaxation times, and the mode dependent contributions to the lattice thermal conductivity of ZrX$_2$ (X = S, Se, Te) from first principles methods. Our calculations indicate that due to tensile strain, the powerfactor increases while simultaneously decreasing the lattice thermal conductivity thus…
Tungsten is the main candidate material for plasma-facing armour components in future fusion reactors. Bombardment with energetic fusion neutrons causes collision cascade damage and defect formation. Interaction of defects with helium, produced by transmutation and injected from the plasma, modifies defect retention and behaviour. Here we investigate the residual lattice strains caused by different doses of helium-ion-implantation into tungsten and tungsten-rhenium alloys. Energy and depth-resolved synchrotron X-ray micro-diffraction uniquely permits the measurement of lattice strain with sub-…
Ferroelectric BaTiO3 films with large polarization have been integrated with Si(001) by pulsed laser deposition. High quality c-oriented epitaxial films are obtained in a substrate temperature range of about 300 deg C wide. The deposition temperature critically affects the growth kinetics and thermodynamics balance, resulting on a high impact in the strain of the BaTiO3 polar axis, which can exceed 2% in films thicker than 100 nm. The ferroelectric polarization scales with the strain and therefore deposition temperature can be used as an efficient tool to tailor ferroelectric polarization. The…
The objective of this work is to describe the tunnel electron current in single barrier magnetic tunnel junctions within a new approach that goes beyond the single-band transport model. We propose a ballistic multi-channel electron transport model that can explain the influence of in-plane lattice strain on the tunnel magnetoresistance as well as the asymmetric voltage behavior. We consider as an example single crystal magnetic Fe(110) electrodes for Fe/Insulator/Fe and Fe/Insulator/La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ tunnel junctions, where the electronic band structures of Fe and La$_{0.67}$Sr$_…
We report the epitaxial growth of PdTe$_2$ ultrathin films on topological insulator Bi$_2$Se$_3$. A prominent Moiré pattern was observed in STM measurements. The Moiré periodicity increases as film thickness decreases, indicating a lattice expansion of epitaxial PdTe$_2$ thin films with lower thicknesses. In addition, our simulations based on Moiré Metrology reveal uniaxial lattice strains at the edge of PdTe$_2$ domains, and anisotropic strain distributions throughout the Moiré supercell with a net change in lattice strain up to ~2.9%. Our DFT calculations show that this strain effect leads t…
Recently, lattice dynamics of the highly strained europium monoxide, as a promising candidate for strong ferroelectric-ferromagnet material, applied in the next-generation storage devices, attracted huge attention in the solid-state electronics. Here, the authors investigate the effect of tensile strain on dielectric properties of pulsed laser deposited EuO thin films from 10 to 200 K. A nearly 3% out-of-plane lattice compression is observed as the film thickness was reduced to 8 nm, which could originate from the lattice mismatch between film and a LaAlO3 substrate. The temperature and freque…
Understanding the coupling between spin and phonons is critical for controlling the lattice thermal conductivity ($κ_l$) in magnetic materials, as we demonstrate here for CrX$_3$ (X = Br and I) monolayers. We show that these compounds exhibit large spin-phonon coupling (SPC), dominated by out-of-plane vibrations of Cr atoms, resulting in significantly different phonon dispersions in ferromagnetic (FM) and paramagnetic (PM) phases. Lattice thermal conductivity calculations provide additional evidence for strong SPC, where particularly large $κ_l$ is found for the FM phase. Most strikingly, PM a…
The key obstacle toward realizing integrated gallium nitride (GaN) electronics is its low hole mobility. Here, we explore the possibility of improving the hole mobility of GaN via epitaxial matching to II-IV nitride materials that have recently become available, namely ZnGeN$_2$ and MgSiN$_2$. We perform state-of-the-art calculations of the hole mobility of GaN using the ab initio Boltzmann transport equation. We show that effective uniaxial compressive strain of GaN along the $[1\bar{1}00]$ by lattice matching to ZnGeN$_2$ and MgSiN$_2$ results in the inversion of the heavy hole band and spli…
We have investigated the out-of-plane lattice relaxation related to the ferroelectric transitions in epitaxial BaTiO$_3$ (BTO) films using synchrotron X-ray diffraction. Under either compressive strain or tensile strain, there is evidence for two structural phase transitions as a function of temperature. The transition temperature $T_C$ is a strong function of strain, which can be as much as 100 K above the corresponding $T_C$ in bulk. Under compressive strain, the tetragonality of BTO unit cell implies that the polarization of the first ferroelectric phase is out-of-plane, while under tensile…
We have studied the effect of the misfit on the equilibrium shape of three-dimensional pyramidal islands grown on a foreign substrate in the case of incomplete wetting (Volmer-Weber mode of growth). We have found that tensile islands have smaller aspect ratios compared with compressed islands owing to its better adhesion to the substrate. The average strains of consecutive layers decrease faster with thickness in compressed than in tensile islands. The strains decrease rapidly with thickness, with the consequence that above a certain height, the upper layers of the pyramid become practically u…
The influence of lattice strain and Mg vacancies on the superconducting properties of MgB2 samples has been investigated. High quality samples with sharp superconducting transitions were synthesized. The variation in lattice strain and Mg vacancy concentrations were obtained by varying the synthesis conditions. It was found that high strain (~1%) and the presence of Mg vacancies (~ 5 %) resulted in lowering the Tc by only 2 K.
Various two-dimensional (2D) materials with graphene-like buckled structure emerge, and the $β$-phase AsP monolayer has been recently proposed to be thermodynamically stable from first-principles calculations. The studies of thermal transport are very useful for these 2D materials-based nano-electronics devices. Motivated by this, a comparative study of strain-dependent phonon transport of AsP monolayer is performed by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). It is found that the lattice thermal conductivity ($κ_L$) of AsP mon…
An increasing number of two-dimensional (2D) materials have already been achieved experimentally or predicted theoretically, which have potential applications in nano- and opto-electronics. Various applications for electronic devices are closely related to their thermal transport properties. In this work, the strain dependence of phonon transport in monolayer SiC with a perfect planar hexagonal honeycomb structure is investigated by solving the linearized phonon Boltzmann equation. It is found that room-temperature lattice thermal conductivity ($κ_L$) of monolayer SiC is two orders of magnitud…
Oxygen-defect control has long been considered an influential tuning knob for producing various property responses in complex oxide films. In addition to physical property changes, modification to the lattice structure, specifically lattice expansion, with increasing oxygen vacancy concentrations has been reported often and has become the convention for oxide materials. However, the current understanding of the lattice behavior in oxygen-deficient films becomes disputable when considering compounds containing different bonding environments or atomic layering. Moreover, tensile strain has recen…
We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron at high pressures using both first-principles linear response quasiharmonic calculations based on the full potential linear-muffin-tin-orbital (LMTO) method and the particle-in-cell (PIC) model for the vibrational partition function using a tight-binding total-energy method. The tight-binding model shows excellent agreement with the all-electron LMTO method. When hcp structure is stable, the calculated geometric mean frequency and Helmholtz free energy of hcp Fe from PIC and linear response lattice dynamics agree ver…
The electronic structure of interfaces between lattice-mismatched semiconductor is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain -- continuum elasticity (CE, treated as a finite difference problem) and atomistic elasticity (AE). While for small strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g. 7% for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C_2 sy…
The maximum recoverable strain of most crystalline solids is less than 1% because plastic deformation or fracture usually occurs at a small strain. In this work, we show that a SrNi$_2$P$_2$ micropillar exhibits pseudoelasticity with a large maximum recoverable strain of ~14% under uniaxial compression via unique reversible structural transformation, double lattice collapse-expansion that is repeatable under cyclic loading. Its high yield strength (~3.8$\pm$0.5 GPa) and large maximum recoverable strain bring out the ultrahigh modulus of resilience (~146$\pm$19MJ/m$^3$) a few orders of magnitud…
Plastic flow behavior of low carbon steel has been studied at room temperature during tensile deformation by varying the initial strain rate of 3.3x10e-4 1/sec to the final strain rate ranging from 1.33x10e-3 1/sec to 2.0x10e-3 1/sec at a fixed engineering strain of 12%. Haasen plot revealed that the mobile dislocation density remained almost invariant at the juncture where there was a sudden increase in stress with the change in strain rate and the plastic flow was solely dependent on the velocity of mobile dislocations. In that critical regime, the variation of stress with time was fitted wi…
The authors study the elastic deformation field in lattice-mismatched core-shell nanowires with single and multiple shells. The authors consider infinite wires with a hexagonal cross section under the assumption of translational symmetry. The strain distributions are found by minimizing the elastic energy per unit cell using the finite element method. The authors find that the trace of the strain is discontinuous with a simple, almost piecewise variation between core and shell, whereas the individual components of the strain can exhibit complex variations.
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical (2nd-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products …
(Li,Al)-co-doped magnesium spinel (Li$_x$Mg$_{1-2x}$Al$_{2+x}$O$_4$) is a solid lithium-ion electrolyte with potential use in all-solid-state lithium-ion batteries. Interfaces with spinel electrodes, such as Li$_y$Mn$_2$O$_4$ and Li$_{4+3z}$Ti$_5$O$_{12}$, may be lattice-matched, with potentially low interfacial resistances. Small lattice parameter differences across a lattice-matched interface are unavoidable, causing residual epitaxial strain. This strain potentially modifies lithium diffusion near the interface, contributing to interfacial resistance. Here we report a density functional the…
Phosphorene has been attracted intense interest due to its unexpected high carrier mobility and distinguished anisotropic optoelectronic and electronic properties. In this work, we unraveled strain engineered phosphorene as a photocatalyst in the application of water splitting hydrogen production based on density functional theory calculations. Lattice dynamic calculations demonstrated the stability for such kind of artificial materials under different strains. The phosphorene lattice is unstable under compression strains and could be crashed. Whereas, phosphorene lattice shows very good stabi…
Adsorption of a molecule or group with an atom which is less electronegative than oxygen (O) and directly interacting with the surface is very relevant to development of PtM (M=3d-transition metal) catalysts with high activity. Here, we present theoretical analysis of the adsorption of NH3 molecule (N being less electronegative than O) on (111) surfaces of PtM(Fe,Co,Ni) alloys using the first principles density functional approach. We find that, while NH3-Pt interaction is stronger than that of NH3 with the elemental M-surfaces, it is weaker than the strength of interaction of NH3 with M-site …
We present a study of the lattice response to the compressive and tensile biaxial stress in La0.67Sr0.33MnO3 (LSMO) and SrRuO3 (SRO) thin films grown on a variety of single crystal substrates: SrTiO3, DyScO3, NdGaO3 and (La,Sr)(Al,Ta)O3. The results show, that in thin films under misfit strain, both SRO and LSMO lattices, which in bulk form have orthorhombic (SRO) and rhombohedral (LSMO) structures, assume unit cells that are monoclinic under compressive stress and tetragonal under tensile stress. The applied stress effectively modifies the BO6 octahedra rotations, which degree and direction c…
We consider the case of a chiral soliton lattice subjected to uniaxial elastic strain applied perpendicular to the chiral axis and derive through analytical modelling the phase diagram of magnetic states supported in the presence of an external magnetic field. The strain induced anisotropies give rise to three distinct non-trivial spin textures, depending on the nature of the strain, and we show how these states may be identified by their signatures in Lorentz transmission electron microscopy (TEM). Experimental TEM measurements of the Fresnel contrast in a strained sample of the prototypical …
