Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ELASTICITY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Dual Phase Synergy Enabled Large Elastic Strains of Nanoinclusions in a Dislocation Slip Matrix Composite

Freestanding nanomaterials (such as nanowires, nanoribbons and nanotubes) are known to exhibit ultra-large elastic strains and ultra-high strengths. However, harnessing their superior intrinsic mechanical properties in bulk composites has proven to be difficult. A recent breakthrough has overcome this difficulty by using a martensitic phase transforming matrix, in which ultra-large elastic strains approaching the theoretical limit is achieved in Nb nanowires embedded in the matrix. This discovery, whereas breaking a long-standing challenge, still limits our ability of harnessing the exceptional properties of nanomaterials and developing ultrahigh strength bulk materials to a narrow selection of phase transforming alloy matrices. In this study, we investigated the possibility to harness the intrinsic mechanical properties of nanoinclusions in conventional dislocation slip matrix based on a principle of synergy between the inclusion and the matrix. The small spacing between the densely populated hard and dislocation-impenetrable nanoinclusions departmentalize the plastic matrix into small domains to effectively impede dislocation motion within the matrix, inducing significant strengthening and large local elastic strains of the matrix, which in turn induced large elastic strains in the nanoinclusions. This dual phase synergy is verified in a Ti 3 Sn inclusions/B2-NiTi(Fe) plastic matrix model materials system. The maximum elastic strain of Ti 3 Sn inclusion obtained in the dislocation slip matrix is comparable to that achieved in a phase transforming matrix. As a result, this finding opens new opportunities for the development of high-strength nanocomposites.

42 ENGINEERING↗

One-Parameter Analytical Derivation in Modified Budyko Framework for Unsteady-State Streamflow Elasticity in Humid Catchments

The changes in climate and catchment properties have altered the hydrological processes significantly at different spatiotemporal scales around the world. In particular for finer time scales, changes in water storage, which has been commonly neglected for long-term temporal scales, may play an important role on hydrological processes. Nevertheless, few studies addressed this question in modifying the Budyko framework, with most of them remaining a steady-state assumption on catchment characteristics. Here, in this work, we derive new analytical formulas of unsteady-state streamflow elasticity in a modified Budyko framework, incorporating both storage change and one specific parameter for catchment properties. We study 78 humid catchments in the USA with simulation data of daily hydrological processes from a probability-distribution-based hydrological model (the modified HyMOD). As indicated by results, the annual storage change ratio is linearly correlated with the annual aridity index, and this relationship can be used to estimate elasticity coefficients with our formulas. The estimated elasticity coefficients perform well in simulating the annual streamflow with the power-law model. For different catchments, variability of the unsteady-state elasticity is higher than that of the steady-state elasticity. Unsteady-state streamflow coefficients show significant linear correlation with catchment properties, such as the average slope, average elevation, and catchment area. This study provides a new analytical approach to investigate the interannual stability of catchments with varying climate and catchment properties.

54 ENVIRONMENTAL SCIENCES↗

Simultaneous structure and elastic wave velocity measurement of SiO[subscript 2] glass at high pressures and high temperatures in a Paris-Edinburgh cell

An integration of multi-angle energy-dispersive x-ray diffraction and ultrasonic elastic wave velocity measurements in a Paris-Edinburgh cell enabled us to simultaneously investigate the structures and elastic wave velocities of amorphous materials at high pressure and high temperature conditions. We report the first simultaneous structure and elastic wave velocity measurement for SiO{sub 2} glass at pressures up to 6.8 GPa at around 500 C. The first sharp diffraction peak (FSDP) in the structure factor S(Q) evidently shifted to higher Q with increasing pressure, reflecting the shrinking of intermediate-range order, while the Si-O bond distance was almost unchanged up to 6.8 GPa. In correlation with the shift of FSDP position, compressional wave velocity (Vp) and Poisson's ratio increased markedly with increasing pressure. In contrast, shear wave velocity (Vs) changed only at pressures below 4 GPa, and then remained unchanged at {approx}4.0-6.8 GPa. These observations indicate a strong correlation between the intermediate range order variations and Vp or Poisson's ratio, but a complicated behavior for Vs. The result demonstrates a new capability of simultaneous measurement of structures and elastic wave velocities at high pressure and high temperature conditions to provide direct link between microscopic structure and macroscopic elastic properties of amorphous materials.

47 OTHER INSTRUMENTATION↗

Chirality dependent elastic properties of single-walled boron nitride nanotubes under uniaxial and torsional loading

The elastic behavior of single-walled boron nitride nanotubes is studied under axial and torsional loading. Molecular dynamics simulation is carried out with a tersoff potential for modeling the interatomic interactions. Different chiral configurations with similar diameter are considered to study the effect of chirality on the elastic and shear moduli. Furthermore, the effects of tube length on elastic modulus are also studied by considering different aspects ratios. It is observed that both elastic and shear moduli depend upon the chirality of a nanotube. For aspect ratios less than 15, the elastic modulus reduces monotonically with an increase in the chiral angle. For chiral nanotubes, the torsional response shows a dependence on the direction of loading. The difference between the shear moduli against and along the chiral twist directions is maximum for chiral angle of 15°, and zero for zigzag (0°) and armchair (30°) configurations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High pressure elastic properties of minerals from ab initio simulations: The case of pyrope, grossular and andradite silicate garnets

A computational strategy is devised for the accurate ab initio simulation of elastic properties of crystalline materials under pressure. The proposed scheme, based on the evaluation of the analytical stress tensor and on the automated computation of pressure-dependent elastic stiffness constants, is implemented in the CRYSTAL solid state quantum-chemical program. Elastic constants and related properties (bulk, shear and Young moduli, directional seismic wave velocities, elastic anisotropy index, Poisson's ratio, etc.) can be computed for crystals of any space group of symmetry. We apply such a technique to the study of high-pressure elastic properties of three silicate garnet end-members (namely, pyrope, grossular, and andradite) which are of great geophysical interest, being among the most important rock-forming minerals. The reliability of this theoretical approach is proved by comparing with available experimental measurements. The description of high-pressure properties provided by several equations of state is also critically discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Identification of crystalline elastic anisotropy in PZT ceramics from in-situ blocking stress measurements

High energy x-ray diffraction measurements of lattice strains were performed on a rhombohedral Lead Zirconate Titanate ceramic (PZT 55-45) under combinations of applied electric field and compressive stress. These measurements allow the construction of blocking stress curves for different sets of crystallographic orientations which reflect the single crystal elastic anisotropy. A micro-mechanical interpretation of the results is then proposed. Assuming cubic symmetry for the crystalline elastic stiffness tensor and isotropy for the macroscopic elastic properties, the elastic properties of the single crystal are extracted from the measured data. An anisotropy ratio close to 0.3 is found (compared to 1 for isotropic materials). The high level of anisotropy found in this work suggests that crystalline elastic anisotropy should not be neglected in the modelling of ferroelectric materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Elasticity and hardness of nano-polycrystalline boron nitrides: The apparent Hall-Petch effect

Nano-polycrystalline boron nitride (BN) is expected to replace diamond as a superhard and superstiff material. Although its hardening was reported, its elasticity remains unclear and the as-measured hardness could be significantly different from the true value due to the elastic recovery. In this study, we measured the longitudinal-wave elastic constant of nano-polycrystalline BNs using picosecond ultrasound spectroscopy and confirmed the elastic softening for small-grain BNs. We also measured Vickers and Knoop hardness for the same specimens and clarified the relationship between hardness and stiffness. The Vickers hardness significantly increased as the grain size decreased, while the Knoop hardness remained nearly unchanged. We attribute the apparent increase in Vickers hardness to the elastic recovery and propose a model to support this insight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Revisit of the relationship between the elastic properties and sound velocities at high pressures

The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find that the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.

36 MATERIALS SCIENCE↗

A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.

36 MATERIALS SCIENCE↗

Effects of configurational disorder on the elastic properties of icosahedral boron-rich alloys based on B{sub 6}O, B{sub 13}C{sub 2}, and B{sub 4}C, and their mixing thermodynamics

The elastic properties of alloys between boron suboxide (B{sub 6}O) and boron carbide (B{sub 13}C{sub 2}), denoted by (B{sub 6}O){sub 1−x}(B{sub 13}C{sub 2}){sub x}, as well as boron carbide with variable carbon content, ranging from B{sub 13}C{sub 2} to B{sub 4}C are calculated from first-principles. Furthermore, the mixing thermodynamics of (B{sub 6}O){sub 1−x}(B{sub 13}C{sub 2}){sub x} is studied. A superatom-special quasirandom structure approach is used for modeling different atomic configurations, in which effects of configurational disorder between the carbide and suboxide structural units, as well as between boron and carbon atoms within the units, are taken into account. Elastic properties calculations demonstrate that configurational disorder in B{sub 13}C{sub 2}, where a part of the C atoms in the CBC chains substitute for B atoms in the B{sub 12} icosahedra, drastically increase the Young’s and shear modulus, as compared to an atomically ordered state, B{sub 12}(CBC). These calculated elastic moduli of the disordered state are in excellent agreement with experiments. Configurational disorder between boron and carbon can also explain the experimentally observed almost constant elastic moduli of boron carbide as the carbon content is changed from B{sub 4}C to B{sub 13}C{sub 2}. The elastic moduli of the (B{sub 6}O){sub 1−x}(B{sub 13}C{sub 2}){sub x} system are also practically unchanged with composition if boron-carbon disorder is taken into account. By investigating the mixing thermodynamics of the alloys, in which the Gibbs free energy is determined within the mean-field approximation for the configurational entropy, we outline the pseudo-binary phase diagram of (B{sub 6}O){sub 1−x}(B{sub 13}C{sub 2}){sub x}. The phase diagram reveals the existence of a miscibility gap at all temperatures up to the melting point. Also, the coexistence of B{sub 6}O-rich as well as ordered or disordered B{sub 13}C{sub 2}-rich domains in the material prepared through equilibrium routes is predicted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of elastic precursor decay in pre-heated aluminum films under ultra-fast laser generated shocks

Here, this article presents results from laser-driven shock compression experiments performed on pre-heated pure aluminum films at temperatures ranging from 23 to 400 °C. The samples were vapor deposited on the surface of a 500 μm thick sapphire substrate and mounted onto a custom holder with an integrated ring-heater to enable variable initial temperature conditions. A chirped pulse amplified laser was used to generate a pulse for both shocking the films and for probing the free surface velocity using Ultrafast Dynamic Ellipsometry. The particle velocity traces measured at the free surface clearly show elastic and plastic wave separation, which was used to estimate the decay of the elastic precursor amplitude over propagation distances ranging from 0.278 to 4.595 μm. Elastic precursors (which also correspond to dynamic material strength under uniaxial strain) of increasing amplitudes were observed with increasing initial sample temperatures for all propagation distances, which is consistent with expectations for aluminum in a deformation regime where phonon drag limits the mobility of dislocations. The experimental results show peak elastic amplitudes corresponding to axial stresses of over 7.5 GPa; estimates for plastic strain-rates in the samples are of the order 10 9 /s. The measured elastic amplitudes at the micron length scales are compared with those at the millimeter length-scales using a two-parameter model and used to correlate the rate sensitivity of the dynamic strength at strain-rates ranging from 10 3 to 10 9 /s and elevated temperature conditions. The overall trend, as inferred from the experimental data, indicates that the temperature-strengthening effect decreases with increasing plastic strain-rates.

36 MATERIALS SCIENCE↗

Determination of single-crystal elastic moduli of Li RE F 4 ( RE =Y, Gd, and Tb) by resonant ultrasound spectroscopy

The tetragonal fluoro-scheelite Li RE F 4 compounds (RE = rare earth) have been shown to exhibit a variety of useful optical and magnetic properties. While LiYF 4 has been widely studied, many of the fundamental thermodynamic properties of other members of this family remain unknown. Here, we report the complete elastic tensors (C ij ) of single-crystalline LiYF 4 , LiTbF 4 , and LiGdF 4 using resonant ultrasound spectroscopy and density functional theory (DFT). Here we compare the results for LiYF 4 with prior experimental results using time-of-flight ultrasound methods. This is the first report, however, of the experimental elastic tensors of LiTbF 4 and LiGdF 4 . The present results point to a softening of the elastic moduli of the Li RE F 4 system when Y is replaced by the larger ionic radius of Tb or Gd. Furthermore, we find that just 0.3% doping with Nd on the Y site also leads to a slight softening of the moduli. The variation of the elastic moduli as a function of temperature up to 216°C was also measured. A nearly linear softening of all seven independent elastic moduli was observed with increasing temperature. Phonon dispersions and phonon density of states obtained by DFT support the experimental finding of a significantly higher sound velocity due to lighter Y atoms in LiYF 4 , as compared to heavier LiTbF 4 and LiGdF 4 .

36 MATERIALS SCIENCE↗

Temperature-dependent elastic constants of thorium dioxide probed using time-domain Brillouin scattering

Herein we report the adiabatic elastic constants of single-crystal thorium dioxide over a temperature range of 77–350 K. Time-domain Brillouin scattering, an all-optical, non-contact picosecond ultrasonic technique, is used to generate and detect coherent acoustic phonons that propagate in the bulk perpendicular to the surface of the crystal. These coherent acoustic lattice vibrations have been monitored in two hydrothermally grown single-crystal thorium dioxide samples along the (100) and (311) crystallographic directions. The three independent elastic constants of the cubic crystal (C 11 , C 12 , and C 44 ) are determined from the measured bulk acoustic velocities. The longitudinal wave along the (100) orientation provided a direct measurement of C 11 . Measurement of C 44 and C 12 was achieved by enhancing the intensity of quasi-shear mode in a (311) oriented crystal by adjusting the polarization angle relative to the crystal axes. We find the magnitude of softening of the three elastic constants to be ~2.5% over the measured temperature range. Good agreement is found between the measured elastic constants with previously reported values at room temperature, and between the measured temperature-dependent bulk modulus with calculated values. We find that semi-empirical models capturing lattice anharmonicity adequately reproduce the observed trend. We also determine the acoustic Grüneisen anharmonicity parameter from the experimentally derived temperature-dependent bulk modulus and previously reported temperature-dependent values of volumetric thermal expansion coefficient and heat capacity. This work presents measurements of the temperature-dependent elasticity in single-crystal thorium dioxide at cryogenic temperature and provides a basis for testing ab initio theoretical models and evaluating the impact of anharmonicity on thermophysical properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Elastically mediated interactions between grain boundaries and precipitates in two-phase coherent solids

In this work, we investigate analytically and numerically the interaction between grain boundaries and second phase precipitates in two-phase coherent solids in the presence of misfit strain. Our numerical study uses amplitude equations that describe the interaction of composition and stress [R. Spatschek and A. Karma, Phys. Rev. B 81, 214201 (2010)] and free-energies corresponding to two-dimensional hexagonal and three-dimensional BCC crystal structures that exhibit isotropic and anisotropic elastic properties, respectively. We consider two experimentally motivated geometries where (i) a lamellar precipitate nucleates along a planar grain boundary that is centered inside the precipitate, and (ii) a circular precipitate nucleates inside a grain at a finite distance to an initially planar grain boundary. For the first geometry, we find that the grain boundary becomes morphologically unstable due to the combination of long-range elastic interaction between the grain boundary and compositional domain boundaries, and shear-coupled grain boundary motion. We characterize this instability analytically by extending the linear stability analysis carried out recently [P.-A. Geslin, Y.-C. Xu, and A. Karma, Phys. Rev. Lett. 114, 105501 (2015)] to the more general case of elastic anisotropy. The analysis predicts that elastic anisotropy hinders but does not suppress the instability. Simulations also reveal that, in a well-developed nonlinear regime, this instability can lead to the break-up of low-angle grain boundaries when the misfit strain exceeds a threshold that depends on the grain boundary misorientation. For the second geometry, simulations show that the elastic interaction between an initially planar grain boundary and an adjacent circular precipitate causes the precipitate to migrate to and anchor at the grain boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Elastic, mechanical, and thermodynamic properties of Bi-Sb binaries: Effect of spin-orbit coupling

Using first-principles calculations, we systematically study the elastic stiffness constants, mechanical properties, elastic wave velocities, Debye temperature, melting temperature, and specific heat of several thermodynamically stable crystal structures of BixSb 1-x (0 < x < 1) binaries, which are of great interest due to their numerous inherent rich properties, such as thermoelectricity, thermomagnetic cooling, strong spin-orbit coupling (SOC) effects, and topological features in the electronic band structure. We analyze the bulk modulus (B), Young's modulus (E), shear modulus (G), B/G ratio, and Poisson's ratio ($\nu$) as a function of the Bi concentration in BixSb 1-x . The effect of SOC on the above-mentioned properties is further investigated. In general, we observe that the SOC effects cause elastic softening in most of the studied structures. Three monoclinic structures of Bi-Sb binaries are found to exhibit significantly large auxetic behavior due to the hingelike geometric structure of bonds. The Debye temperature and the magnitude of the elastic wave velocities monotonically increase with increasing Sb concentration. However, anomalies were observed at very low Sb concentration. We also discuss the specific-heat capacity versus temperature data for all studied binaries. Our theoretical results are in excellent agreement with the existing experimental and theoretical data. The comprehensive understanding of the material properties such as hardness, mechanical strength, melting temperature, propagation of the elastic waves, auxeticity, and heat capacity is vital for practical applications of the studied binaries.

36 MATERIALS SCIENCE↗

Elastic scattering in the 12 N + 197 Au system at 𝐸 lab = 70 MeV

Halo structure is an interesting exotic configuration developed in some light weakly bound nuclei, where a valence particle orbits a nuclear core. Signatures of halo structure can be observed in the angular distributions of the elastic scattering induced by these nuclei at energies around the Coulomb barrier. There are some well-studied reactions with neutron-rich halo nuclei, such as 6 He and 11 Li . However, the information is scarce on the proton-rich side. Recent works confirm the halo structure in the 8B nuclei but still lack more experimental studies for other proton-halo candidates, such as 12 N and 17 F. In this work, we report experimental data for the elastic scattering of 12 N on 197 Au target at 𝐸 lab = 70 MeV. The 12 N is a proton-rich nucleus with proton separation energy 𝑆 𝑝 = 600 keV, which is higher than the 8 B (𝑆 𝑝 = 137 keV) and almost the same as the 17 F (𝑆 𝑝 = 601 keV). Data were obtained at the Cyclotron Institute of Texas A&M University where the 12 N radioactive beam was produced by the momentum achromatic recoil spectrometer. The calculation of the optical model was used to fit the measured angular distribution for the elastic scattering and to obtain the reaction cross section 𝜎 𝑅 . We also performed continuum discretized coupled-channel calculations to compare with the experimental data. The angular distribution of the elastic cross sections exhibits a suppression of the Fresnel peak. From the fitting of the optical model, we obtain the total reaction cross section, 𝜎 𝑅 = 1269 ± 41 mb. The agreement between the CDCC calculation and the experimental elastic scattering data is limited and the breakdown does not exhaust the measured 𝜎 𝑅 . The resulting reduced reaction cross section 𝜎 Red for 12 N + 197 Au is large and comparable to the one obtained for the 8 B + 208 Pb system. This suggests a strong decoupling of the valence proton from the core because of the low binding energy and a dynamic polarization effect. Here, more research is required to estimate the contribution of core excitation.

Elastic scattering reactions↗

Effect of directed aging on nonlinear elasticity and memory formation in a material

Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to modify dramatically the elastic properties of our systems in the nonlinear regime. Using simulations, we study two models for the microscopic evolution of properties of such a material; the first considers changes in the material strength, while the second considers distortions in the microscopic geometry. Both models capture different aspects of the experiments including the encoding of memories of the aging history of the system and the dramatic effects on the material’s nonlinear elastic properties. Our results demonstrate how aging can be used to create complex elastic behavior in the nonlinear regime.

36 MATERIALS SCIENCE↗

TU-F-BRF-02: MR-US Prostate Registration Using Patient-Specific Tissue Elasticity Property Prior for MR-Targeted, TRUS-Guided HDR Brachytherapy

Purpose: High-dose-rate (HDR) brachytherapy has become a popular treatment modality for prostate cancer. Conventional transrectal ultrasound (TRUS)-guided prostate HDR brachytherapy could benefit significantly from MR-targeted, TRUS-guided procedure where the tumor locations, acquired from the multiparametric MRI, are incorporated into the treatment planning. In order to enable this integration, we have developed a MR-TRUS registration with a patient-specific biomechanical elasticity prior. Methods: The proposed method used a biomechanical elasticity prior to guide the prostate volumetric B-spline deformation in the MRI and TRUS registration. The patient-specific biomechanical elasticity prior was generated using ultrasound elastography, where two 3D TRUS prostate images were acquired under different probe-induced pressures during the HDR procedure, which takes 2-4 minutes. These two 3D TRUS images were used to calculate the local displacement (elasticity map) of two prostate volumes. The B-spline transformation was calculated by minimizing the Euclidean distance between the normalized attribute vectors of the prostate surface landmarks on the MR and TRUS. This technique was evaluated through two studies: a prostate-phantom study and a pilot study with 5 patients undergoing prostate HDR treatment. The accuracy of our approach was assessed through the locations of several landmarks in the post-registration and TRUS images; our registration results were compared with the surface-based method. Results: For the phantom study, the mean landmark displacement of the proposed method was 1.29±0.11 mm. For the 5 patients, the mean landmark displacement of the surface-based method was 3.25±0.51 mm; our method, 1.71±0.25 mm. Therefore, our proposed method of prostate registration outperformed the surfaced-based registration significantly. Conclusion: We have developed a novel MR-TRUS prostate registration approach based on patient-specific biomechanical elasticity prior. Successful integration of multi-parametric MR and TRUS prostate images provides a prostate-cancer map for treatment planning, enables accurate dose planning and delivery, and potentially enhances prostate HDR treatment outcome.

60 APPLIED LIFE SCIENCES↗