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At least 541 records · Page 30

The classical-to-quantum crossover in the strain-induced ferroelectric transition in SrTiO3 membranes

Mechanical strain presents an effective control over symmetry-breaking phase transitions. In quantum paralelectric SrTiO3, strain can induce ferroelectric order via modification of the local Ti potential energy landscape. However, brittle bulk materials can only withstand limited strain range (~0.1%). Taking advantage of nanoscopically-thin freestanding membranes, we demonstrate an in- situ strain-induced reversible ferroelectric transition in freestanding SrTiO3 membranes. We measure the ferroelectric order by detecting the local anisotropy of the Ti 3d orbital signature using x-ray linear dichroism at the Ti-K pre-edge, while the strain is determined by x-ray diffraction. With reduced thickness, the SrTiO3 membranes remain elastic with >1% tensile strain cycles. A robust displacive ferroelectricity appears beyond a temperature-dependent critical strain. Interestingly, we discover a crossover from a classical ferroelectric transition to a quantum regime at low temperatures, which enhances strain-induced ferroelectricity. Our results offer new opportunities to strain engineer functional properties in low dimensional quantum materials and provide new insights into the role of ferroelectric fluctuations in quantum paraelectric SrTiO3.

36 MATERIALS SCIENCE↗

Tensile strains give rise to strong size effects for thermal conductivities of silicene, germanene and stanene

Based on first principles calculations and self-consistent solution of linearized Boltzmann-Peierls equation for phonon transport approach within a three-phonon scattering framework, we characterize lattice thermal conductivities k of freestanding silicene, germanene and stanene under different isotropic tensile strains and temperatures. In this work, we find a strong size dependence of k for silicene with tensile strain, i.e., divergent k with increasing system size, in contrast, the intrinsic room temperature k for unstrained silicene converges with system size to 19.34 W/m –1 K –1 by 178 nm. The room temperature k of strained silicene becomes as large as that of bulk silicon by 84 m, indicating the possibility of using strain in silicene to manipulate k for thermal management. The relative contribution to the intrinsic k from out-of-plane acoustic modes is largest for unstrained silicene, –39% at room temperature. The single mode relaxation time approximation, which works reasonably well for bulk silicon, fails to appropriately describe phonon thermal transport in silicene, germanene and stanene within the temperature range considered. For large samples of silicene, k increases with tensile strain, peaks at –7% strain and then decreases with further strain. In germanene and stanene increasing strain hardens and stabilizes long wavelength out-of-plane acoustic phonons, and leads to similar k behaviors to those of silicene. As a result, these findings further our understanding of phonon dynamics in group-IV buckled monolayers and may guide transfer and fabrication techniques of these freestanding samples and engineering k by size and strain for applications of thermal management and thermoelectricity.

36 MATERIALS SCIENCE↗

Partial strain relaxation effects on polarization anisotropy of semipolar (112{sup ¯}2) InGaN/GaN quantum well structures

Partial strain relaxation effects on polarization anisotropy of semipolar (112{sup ¯}2) InGaN/GaN quantum well (QW) structures were investigated using the multiband effective-mass theory. In the case of strain relaxation of ϵ{sub x′x′} along x′-axis, the polarization ratio gradually decreases with increasing strain relaxation. Also, with the strain relaxation by the same amount, the variation of the polarization ratio along x′-axis is shown to be much larger than that along y′-axis. However, the polarization switching is not observed even at a high In composition of 0.4 due to a small strain component (ϵ{sub x′x′}{sup 0}) with no strain relaxation. On the other hand, in the case of strain relaxation of ϵ{sub y′y′} along y′-axis, the polarization switching is observed, and the optical anisotropy is found to change from positive to negative with increasing strain relaxation. Also, the absolute value of the polarization ratio gradually decreases with increasing carrier density. However, the polarization switching due to the carrier density is not observed. Thus, the polarization switching observed at high carrier density may be attributed to inhomogeneous strain distribution in the InGaN layer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Strain tunable ferroelectric and dielectric properties of BaZrO{sub 3}

The crucial role of epitaxial (in-plane) strain on the structural, electronic, energetic, ferroelectric, and dielectric properties of BaZrO{sub 3} (BZO) is investigated using density-functional theory calculations. We demonstrate that the BZO crystal subjected to a critical compressive (or tensile) strain exhibits non-trivial spontaneous polarization that is higher than that of well-known ferroelectrics BaTiO{sub 3}, while the BZO crystal is essentially paraelectric in the absence of strain. The electronic structure and Born-effective-charge analyses elucidate that the strain-induced paraelectric-to-ferroelectric transition is driven by the orbital hybridization of d-p electrons between zirconium and oxygen. Through the strain-induced paraelectric-to-ferroelectric phase transition, the dielectric response of BZO is significantly enhanced by the in-plane strain. The tensile strain increases the in-plane dielectric constant by a factor of seven with respect to that without the strain, while the compression tends to enhance the out-of-plane dielectric response. Therefore, strain engineering makes BZO an important electromechanical material due to the diversity in ferroelectric and dielectric properties.

36 MATERIALS SCIENCE↗

Controllable spin-charge transport in strained graphene nanoribbon devices

We theoretically investigate the spin-charge transport in two-terminal device of graphene nanoribbons in the presence of a uniform uniaxial strain, spin-orbit coupling, exchange field, and smooth staggered potential. We show that the direction of applied strain can efficiently tune strain-strength induced oscillation of band-gap of armchair graphene nanoribbon (AGNR). It is also found that electronic conductance in both AGNR and zigzag graphene nanoribbon (ZGNR) oscillates with Rashba spin-orbit coupling akin to the Datta-Das field effect transistor. Two distinct strain response regimes of electronic conductance as function of spin-orbit couplings magnitude are found. In the regime of small strain, conductance of ZGNR presents stronger strain dependence along the longitudinal direction of strain. Whereas for high values of strain shows larger effect for the transversal direction. Furthermore, the local density of states shows that depending on the smoothness of the staggered potential, the edge states of AGNR can either emerge or be suppressed. These emerging states can be determined experimentally by either spatially scanning tunneling microscope or by scanning tunneling spectroscopy. Our findings open up new paradigms of manipulation and control of strained graphene based nanostructure for application on novel topological quantum devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Electric-field-induced strain contributions in morphotropic phase boundary composition of (Bi{sub 1/2}Na{sub 1/2})TiO{sub 3}-BaTiO{sub 3} during poling

The microscopic contributions to the electric-field-induced macroscopic strain in a morphotropic 0.93(Bi{sub 1/2}Na{sub 1/2}TiO{sub 3})−0.07(BaTiO{sub 3}) with a mixed rhombohedral and tetragonal structure have been quantified using full pattern Rietveld refinement of in situ high-energy x-ray diffraction data. The analysis methodology allows a quantification of all strain mechanisms for each phase in a morphotropic composition and is applicable to use in a wide variety of piezoelectric compositions. It is shown that during the poling of this material 24%, 44%, and 32% of the total macroscopic strain is generated from lattice strain, domain switching, and phase transformation strains, respectively. The results also suggest that the tetragonal phase contributes the most to extrinsic domain switching strain, whereas the lattice strain primarily stems from the rhombohedral phase. The analysis also suggests that almost 32% of the total strain is lost or is a one-time effect due to the irreversible nature of the electric-field-induced phase transformation in the current composition. This information is relevant to on-going compositional development strategies to harness the electric-field-induced phase transformation strain of (Bi{sub 1/2}Na{sub 1/2})TiO{sub 3}-based lead-free piezoelectric materials for actuator applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mapping Strain-rate Dependent Dislocation-Defect Interactions by Atomistic Simulations

Probing the mechanisms of defect-defect interactions at strain rates lower than 106 s-1 is an unresolved challenge to date to molecular dynamics (MD) techniques. Here we propose a novel atomistic approach based on transition state theory and the concept of a strain-dependent effective activation barrier that is capable of simulating the kinetics of dislocation-defect interactions at virtually any strain rate, exemplified within 10-7 to 107 s-1. We apply this approach to the problem of an edge dislocation colliding with a cluster of self-interstitial atoms (SIA) under shear deformation. Using an activation-relaxation algorithm (1), we uncover a unique strain-rate dependent trigger mechanism that allows the SIA cluster to be absorbed during the process leading to dislocation climb. Guided by this finding, we determine the activation barrier of the trigger mechanism as a function of shear strain, and use that in a coarse-graining rate equation formulation for constructing a mechanism map in the phase space of strain-rate and temperature. Our predictions of a crossover from a defect recovery at the low strain rate regime to defect absorption behavior in the high strain-rate regime are validated against our own independent, direct MD simulations at 105 to 107 s-1. Implications of the present approach for probing molecular-level mechanisms in strain-rate regimes previously considered inaccessible to atomistic simulations are discussed.

activation mecanism↗

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB 2 C 2

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal f -electron intermetallic DyB 2 C 2 —whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal—as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stroboscopic x-ray diffraction microscopy of dynamic strain in diamond thin-film bulk acoustic resonators for quantum control of nitrogen-vacancy centers

Bulk-mode acoustic waves in a crystalline material exert lattice strain through the thickness of the sample, which couples to the spin Hamiltonian of defect-based qubits such as the nitrogen-vacancy (N-V) center defect in diamond. This mechanism has previously been harnessed for unconventional quantum spin control, spin decoherence protection, and quantum sensing. Bulk-mode acoustic wave devices are also important in the microelectronics industry as microwave filters. A key challenge in both applications is a lack of appropriate operando microscopy tools for quantifying and visualizing gigahertz-frequency dynamic strain. Here, in this work, we directly image acoustic strain within N-V center-coupled diamond thin-film bulk acoustic wave resonators using stroboscopic scanning hard x-ray diffraction microscopy at the Advanced Photon Source. The far-field scattering patterns of the nanofocused x-ray diffraction encode strain information entirely through the illuminated thickness of the resonator. These patterns have a real-space spatial variation that is consistent with the bulk strain’s expected modal distribution and a momentum-space angular variation from which the strain amplitude can be quantitatively deduced. We also perform optical measurements of strain-driven Rabi precession of of the N-V center spin ensemble, providing an additional quantitative measurement of the strain amplitude. As a result, we directly measure one of the six N-V spin-stress coupling parameters, 𝑏 =2.73⁢(2) MHz/GPa, by correlating these measurements at the same spatial position and applied microwave power. Our results demonstrate a unique technique for directly imaging ac lattice strain in micromechanical structures and provide a direct measurement of a fundamental constant for the N-V center defect spin Hamiltonian.

acoustic techniques↗

Construction of Lattice Strain in Bimetallic Nanostructures and Its Effectiveness in Electrochemical Applications

Bimetallic nanocrystals (NCs), associated with various surface functions such as ligand effect, ensemble effect, and strain effect, exhibit superior electrocatalytic properties. The stress-induced surface strain effect can alter binding strength between the surface active sites and reactants as well as their intermediates, and the electrochemical performance of bimetallic NCs can be significantly facilitated by the lattice-strain modification via their morphologies, sizes, shell-thickness, surface defectiveness as well as compositions. Here in this review, an overview of fundamental principles, characterization techniques, and quantitative determination of the surface lattice strain is provided. Various strategies and synthesis efforts on creating lattice-strain-engineered bimetallic NCs, including the de-alloying process, atomic layer-by-layer deposition, thermal treatment evolution, one-pot synthesis, and other efforts are also discussed. It is further outlined how the lattice strain effect promotes electrochemical catalysis through the selected case studies. The reactions on oxygen reduction reaction, small molecular oxidation, water splitting reaction, and electrochemical carbon dioxide reduction reactions are focused. In particular, studies of lattice strain arisen from core–shell nanostructure and defectiveness are highlighted. Lastly, the potential challenges are summarized and the prospects of lattice-strain-based engineering on bimetallic nanocatalysts with suggestion and guidance of the future electrocatalyst design are envisioned.

36 MATERIALS SCIENCE↗

High strain rate nanoindentation testing: Recent advancements, challenges and opportunities

Recent advancements in electronics have renewed the interest in high strain rate nanoindentation testing, resulting in the development of new high strain rate nanoindentation test equipment and test methodologies. Here, in this work, the current state-of-the-art in high strain rate nanoindentation testing is critically reviewed, with focus on three key aspects - the testing equipment's dynamic mechanical and electronic response, test methodology, and post-processing of raw data to obtain hardness and strain rate. The challenges in instrument hardware design and post-test data analysis are discussed, along with optimal strain rate window for accurate high strain rate measurements. Specific focus will be on instrumented high strain rate testing using self-similar indenters at strain rates in excess of 100 s -1 , wherein load and depth of penetration into the sample are both measured or applied.

36 MATERIALS SCIENCE↗

Distributed strain sensing using Bi-metallic coated fiber optic sensors embedded in stainless steel

Silica fiber optic sensors are resistant to corrosive environments and high temperatures, making them attractive candidates for harsh conditions found in nuclear and aerospace industries. Moreover, fibers can be deployed remotely for continuous measuring of spatially distributed temperatures and strains. Here, this study investigated embedding a Ni/Cu bi-metallic coated fiber in a stainless-steel 316 (SS316) matrix using laser powder bed fusion towards functionalizing metal components for site-specific health monitoring. The embedded fiber was continuously interrogated during controlled heating to 1000°C. The measured fiber strains were similar to the expected differential thermal strains between the fiber and the SS316 matrix, until divergent behavior was observed at temperatures >500°C. No debonding at the matrix–coating–fiber interfaces was observed during microscopy, but significant interactions between the coatings and matrix resulted in diffusion-driven chemistry variations and Kirkendall void formation. Applying the strain-lag theory revealed plastic behavior in the Ni coating at temperatures >500°C, limiting the strain transfer to the fiber at higher temperatures. It was estimated that the elastic modulus in the Ni coating had decreased from ~200 GPa at room temperature to below 40 GPa, starting at 600°C. The low elastic modulus above 600°C is within the margin of what the tangent modulus would be in the case of bilinear isotropic hardening. Regardless of the divergent strain transfer at higher temperatures, the fiber was exposed to the equivalent of 1.9 % engineering strain at 1000°C, but measured only a 0.7 % engineering strain due to the poor strain transfer. Although compensating for the plastic behavior of Ni proved challenging, the bonding of a brittle silica fiber to a metal matrix surviving to 1000°C invites potential iterations on coating material for future application. For example, the embedded fiber is sufficient for acoustic energy transfer, realizing high temperature distributed acoustic sensing.

36 MATERIALS SCIENCE↗

A streamlined approach to characterize microalgae strains for biomass productivity under dynamic climate simulation conditions

Screening microalgae strains under static light and temperature flask conditions cannot directly quantify the biomass productivities of algae growing in the dynamically fluctuating light and temperature conditions of outdoor ponds. In this effort, we describe a testing pipeline that screens for productivity under climate simulated conditions. A validated, miniaturized Laboratory Environmental Algae Pond Simulator (mini-LEAPS) photobioreactor was used to determine optimal medium salinities and biomass productivities of cold-tolerant microalgae collected from Arctic, subarctic, Antarctic, and subalpine habitats. Strains characterized in this effort include: Chlorella antarctica UTEX1959, Chlorella sp. UTEXSNO69, Chloromonas rosae UTEXSNO11, Phaeodactylum tricornutum UTEX646, and Stichococcus minutus CCALA727. Observed productivities of the characterized strains ranged from 1.74 ± 0.25 to 8.18 ± 0.81 g m –2 day –1 (as ash-free dry weight). For each strain, a temperature tolerance profile was generated to identify the most appropriate season (s) for cultivation. The two most promising strains, Chlorella sp. UTEX SNO69 and P. tricornutum UTEX646, were tested alongside the DISCOVR winter benchmark strain Monoraphidium minutum 26B-AM in outdoor open ponds at the PNNL Algae Testbed (PAT) in Arizona. Further, under cold-season outdoor pond conditions, Chlorella sp. UTEXSNO69 achieved average areal biomass productivities of 8.21 ± 0.50 g m –2 day –1 , not significantly different from that of the benchmark strain (8.52 ± 0.43 g m –2 day –1 , p > 0.05). Under spring outdoor pond conditions, P. tricornutum UTEX646 achieved average areal biomass productivities 10.34 ± 0.27 g m –2 day –1 , not significantly different from that of the benchmark (10.07 ± 0.50 g m –2 day –1 ) under the tested conditions (p > 0.05). The streamlined pipeline was thus demonstrated to successfully characterize productive microalgae strains for outdoor deployment by weeding out algae strains that were not productive under the tested dynamic light and temperature conditions.

59 BASIC BIOLOGICAL SCIENCES↗

High phenotypic and genotypic plasticity among strains of the mushroom-forming fungus Schizophyllum commune

Schizophyllum commune is a mushroom-forming fungus notable for its distinctive fruiting bodies with split gills. It is used as a model organism to study mushroom development, lignocellulose degradation and mating type loci. It is a hypervariable species with considerable genetic and phenotypic diversity between the strains. In this study, we systematically phenotyped 16 dikaryotic strains for aspects of mushroom development and 18 monokaryotic strains for lignocellulose degradation. There was considerable heterogeneity among the strains regarding these phenotypes. The majority of the strains developed mushrooms with varying morphologies, although some strains only grew vegetatively under the tested conditions. Growth on various carbon sources showed strain-specific profiles. The genomes of seven monokaryotic strains were sequenced and analyzed together with six previously published genome sequences. Moreover, the related species Schizophyllum fasciatum was sequenced. Although there was considerable genetic variation between the genome assemblies, the genes related to mushroom formation and lignocellulose degradation were well conserved. These sequenced genomes, in combination with the high phenotypic diversity, will provide a solid basis for functional genomics analyses of the strains of S. commune.

59 BASIC BIOLOGICAL SCIENCES↗

Strain localization and elastic-plastic coupling during deformation of porous sandstone

In this paper, results of axisymmetric compression tests on weak, porous Castlegate Sandstone (Cretaceous, Utah, USA), covering a range of dilational and compactional behaviors, are examined for localization behavior. Assuming isotropy, bulk and shear moduli evolve as increasing functions of mean stress and Mises equivalent shear stress respectively, and as decreasing functions of work-conjugate plastic strains. Acoustic emissions events located during testing show onset of localization and permit calculation of observed shear and low-angle compaction localization zones, or bands, as localization commences. Total strain measured experimentally partitions into: A) elastic strain with constant moduli, B) elastic strain due to stress dependence of moduli, C) elastic strain due to moduli degradation with increasing plastic strain, and D) plastic strain. The third term is the elastic-plastic coupling strain, and though often ignored, contributes significantly to pre-failure total strain for brittle and transitional tests. Constitutive parameters and localization predictions derived from experiments are compared to theoretical predictions. In the brittle regime, predictions of band angles (angle between band normal and maximum compression) demonstrate good agreement with observed shear band angles. Compaction localization was observed in the transitional regime in between shear localization and spatially pervasive compaction, over a small range of mean stresses. Finally, in contrast with predictions, detailed acoustic emissions analyses in this regime show low angle, compaction-dominated but shear-enhanced, localization.

15 GEOTHERMAL ENERGY↗

Comparative study of two Saccharomyces cerevisiae strains with kinetic models at genome-scale

The parameterization of kinetic models requires measurement of fluxes and/or metabolite levels for a base strain and a few genetic perturbations thereof. Unlike stoichiometric models that are mostly invariant to the specific strain, it remains unclear whether kinetic models constructed for different strains of the same species have similar or significantly different kinetic parameters. This important question underpins the applicability range and prediction limits of kinetic reconstructions. To this end, herein we parameterize two separate large-scale kinetic models using K-FIT with genome-wide coverage corresponding to two distinct strains of Saccharomyces cerevisiae: CEN.PK 113-7D strain (model k-sacce306-CENPK), and growth-deficient BY4741 (isogenic to S288c; model k-sacce306-BY4741). The metabolic network for each model contains 306 reactions, 230 metabolites, and 119 substrate-level regulatory interactions. The two models (for CEN.PK and BY4741) recapitulate, within one standard deviation, 77% and 75% of the fitted dataset fluxes, respectively, determined by 13 C metabolic flux analysis for wild-type and eight single-gene knockout mutants of each strain. Strain-specific kinetic parameterization results indicate that key enzymes in the TCA cycle, glycolysis, and arginine and proline metabolism drive the metabolic differences between these two strains of S. cerevisiae. Our results suggest that although kinetic models cannot be readily used across strains as stoichiometric models, they can capture species-specific information through the kinetic parameterization process.

59 BASIC BIOLOGICAL SCIENCES↗

A Type–Curve Approach for Evaluating Aquifer Properties by Interpreting Shallow Strain Measured During Well Tests

Strains occur at shallow depths in response to pressure changes during well tests in an underlying aquifer, and recent developments in instrumentation have made it feasible to measure essentially the full strain tensor. Simulations using poroelastic analyses indicate that shallow normal strains are approximately proportional to the logarithm of time when a well is injecting into or pumping from a deep aquifer or reservoir. The drawdown is also a linear function of log time, as shown by the classic Cooper-Jacob type-curve analysis. The time when the semilog straight line intercepts the zero-strain axis is similar to the time determined from the Cooper-Jacob pressure analysis, and it can be used to estimate hydraulic diffusivity, suggesting that horizontal strain data can be used directly to estimate aquifer properties. This approach was validated using measurements from shallow (30-m deep) borehole strainmeters during an injection test at a 530-m-deep sandstone aquifer/reservoir in Oklahoma. The results show intercept times for the shallow normal strain data are essentially the same as for deep pressure data from an equivalent radial distance. The slopes of the semilog plots of the pressure and the strain increase at the same time, suggesting that they both respond to a lateral aquifer boundary. Significantly, though, strain was measured at shallow depths while the pressure data were measured at 530-m depth. This suggests that strain data from shallow depths could be an effective way to improve the characterization of an underlying aquifer.

54 ENVIRONMENTAL SCIENCES↗

Using the Shallow Strain Tensor to Characterize Deep Geologic Reservoirs

Abstract Storing and recovering water, carbon, and heat from geologic reservoirs is central to managing resources in a changing climate. We tested the hypothesis that the strain tensor caused by injecting or producing fluids can be measured at shallow depths and interpreted to advance understanding of underlying deep aquifers or reservoirs. Geodetic‐grade strainmeters were deployed at 30 m depth overlying the Bartlesville Formation, a 500‐m‐deep sandstone near Tulsa, OK. The strainmeters are 220 m east of injection well 9A completed in a permeable lens at the base of the Bartlesville Formation. Water was injected into well 9A at approximately 1.0 L/s during four tests that ranged in duration from a few hours to a few weeks. The horizontal strain increased (tension) and the circumferential strain was a few times larger than the radial strain. The vertical strain decreased (compression) during injection. Strain rates were approximately 100 nε/day during the first few hours, but the rates decreased and were approximately 10 nε/day during most of the tests. Four independent methods of poroelastic simulation and inversion predict reservoir properties and geometries that are similar to each other and consistent with independent information about the reservoir. All strain interpretations predict that a boundary to the permeable lens occurs beneath the vicinity of the strainmeters, which is consistent with core data from the site. The boundary of the permeable lens is located by matching the vertical, radial and circumferential strains, which demonstrates the value of measuring the strain tensor.

Murdoch, Lawrence C.↗