X-ray Diffraction Line Profile Research Articles

Lattice variation as a function of concentration and grain size in MgO–NiO solid solution system

The study aimed to understand how changes in crystal's size affect the lattice parameters and crystal structure of Mg1-xNixO solid solution for six X values ranging from x = 0 to x = 1. Mg1-xNixO was synthesized via two different wet-chemical techniques: the sol-gel and the microwave hydrothermal method, both followed by calcination at different temperatures of 673, 873, 1073, 1273 and 1473 K. As annealing caused grain growth, the varied temperature range allowed to examine a wide range of grain sizes. The lattice parameters and x values were determined from XRD (X-ray diffraction) peak positions and intensities respectively. The grain size was evaluated by XRD line profile analysis and supported by SEM (scanning electron microscope) observations. At the temperatures of 673 and 873 K grain size was in the nanometric range and from 1073 K and above grain size was in the micrometric range. A non-monotonic lattice variation versus grain size was found for each concentration. When grain size decreased there was a slight contraction, however for grain size in the nanometric range there was a severe lattice expansion. Both lattice parameter changes were explained by two effects acting together: contraction due to surface stress and expansion due to weakening of the ionic bonding at nanocrystalline particles. In this current research study, the lattice parameter was mapped in two dimensions: concentration and grain size. The findings of this study provided valuable insights into the lattice variation in the MgO–NiO solid solution system.

X-ray Diffraction Line Profile Analysis of Natural Calcite Minerals found in Southern Philippines by Williamson-Hall Method

This study employs the Williamson–Hall (W–H) models to examine the microstrains and crystallite sizes of CaCO3 occurring as calcite in limestone samples found in General Santos City and Sarangani Province, Southern Philippines. Using both the Uniform Deformation Model (UDM) and Uniform Stress Deformation (USDM) models, computations for average sizes were established to be identical, implying minimal strain influence. The consistency of resulting measurements extends to the microstrain, revealing uniform results for all samples. Correlation between crystallite sizes and microstrains in the calcite crystals was observed, where high-purity calcites exhibited larger crystallite sizes and microstrains. The crystallite sizes decrease with microstrains for calcites with higher Mg concentration, a finding that can be attributed to lattice distortion and the formation of defects. The release of stress forms these defects, thereby resulting in a reduction of microstrains. Moreover, the distinctly variable responses to strain exhibited by the samples could be influenced by either their anisotropic properties or other additional components. The W–H models, used jointly with UDM and USDM consistently predicted crystallite sizes, and thus offer valuable insights into the uniform stress responses of calcites. These promising results notwithstanding, USDM is shown to be especially relevant for anisotropic samples owing to the display deviations of crystallite sizes, a key feature of anisotropic natural calcites. The microscopic analysis is expected to provide additional understanding regarding the state of the limestone samples.

On some Features of the Grain and Subgrain Size in a Cu-Cr-Zr Alloy After ECAP Processing and Aging

A Cu-1Cr-0.1Zr alloy has been subjected to ECAP processing via route Bc and aging at 250-800°C. Electron BackScatter diffraction (EBSD), Transmission Electron Microscopy (TEM) and X-Ray Diffraction Line Profile Analysis (XRDLPA) techniques have been used to unveil some peculiarities of the grain and subgrain structure with a special emphasis on the comparison of the grain size estimated by the three techniques. For the alloy ECAP processed and aged up to 16 passes, the grain size (from EBSD, 0.2 < d < 5 μm), subgrain size (from TEM, d ~ 0.75 μm) and “apparent” average crystallite size (from XRDLPA, d < 0.25 μm) are manifestly different. The results were compared to the published data and analyzed based on the fundamental aspects of these techniques.

Effect of Sn Addition on the Microstructure and Age-Hardening Response of a Zn-4Cu Alloy

The aim of this research is to assess the influence of Sn inclusion on the microstructure evolution and age-hardening response of a Zn-4Cu alloy. This is the first study to correlate the age-hardening response to the microstructure of Zn-4Cu alloy reinforced with different Sn contents. A series of Zn-4Cu-Sn alloys were successfully fabricated with different Sn concentrations in the range of 0.0–4.0 wt.% using permanent mold casting. The microstructure of Zn-4Cu-Sn alloys was investigated by means of a scanning electron microscope (SEM) attached with an energy dispersive spectroscope (EDS) and X-ray diffraction (XRD) line profile analysis. At room temperature, the Vickers microhardness measurements were used to assess the age-hardening response of alloys. The results show that the microhardness of the Zn-4Cu (ZC) binary alloy increases a little bit from 76 to 80 HV as the aging time increases from 2 to 128 h, respectively. For aging times up to 16 h, the microhardness of all Sn-containing alloys decreases but then increases again. The lowest hardness belongs to the ZC-1.5Sn alloy, and the Sn-Zn-3.0Sn alloy has the highest; the other alloys fall somewhere in between. At high aging times (64 and 128 h), the microhardness of all Sn-containing samples increased continuously with an increasing Sn content from 0.0 to 3.0 wt.%. When the Sn-containing alloys (3.5 and 4.0 wt.% Sn) were aged for 64 and 128 h, the hardness declined by 7.94% and 8.90% compared to their peak aging hardness values, respectively. By considering the structural changes that occur in the Zn-4Cu-Sn alloys, the reasons for the observed variations in microhardness data with increasing Sn content and aging time were elucidated. X-ray diffraction (XRD) data was analyzed to determine the zinc matrix’s lattice parameters, c/a ratio, and unit cell volume variations.

Micro-structural analysis of oxygen irradiated V-4Cr-4Ti by X-ray and electron back scattered diffraction

The effect of O6+ion irradiation on the microstructure of pre-deformed V-4Cr-4Ti alloy has been reported in this study. Changes in the microstructure has been assessed using detail X-ray diffraction line profile analysis in terms of the coherent domain size, rms micro-strain, dislocation density, their nature and their arrangement etc., revealing the importance of pre-deformation in controlling the material response to irradiation. The results are supported by Electron back scattered diffraction and Transmission electron microscopy. Energy Dispersive X-ray analysis has been used to map the micro-chemical changes caused in the sample due to the ion irradiation. Vicker's micro-hardness values were determined to understand the effect of irradiation on the mechanical property of the alloy. The results are explained in terms of the occurrence of vacancy-solute complexes, the formation of which isestablished using Density Functional Theory calculations..

X-Ray Diffraction line profile analysis of defects and precipitates in high displacement damage neutron-irradiated austenitic stainless steels

Irradiation-induced defects and the precipitates in the wrapper material of the Indian Fast Breeder Test Reactor (FBTR), SS 316 are analyzed using the synchrotron source-based Angle Dispersive X-Ray Diffraction (ADXRD) technique with X-rays of energy 17.185 keV (wavelength ∼0.72146 Å). The differences and similarities in the high displacement damage samples as a function of dpa (displacement per atom) and dpa rate in the range of 2.9 × 10−7- 9 × 10−7dpa/s are studied. Ferrite and M23C6 are commonly observed in the present set of high displacement damage 40–74 dpa SS 316 samples irradiated at temperatures in the range of 400–483 °C. Also, the dislocation density has increased as a function of the irradiation dose. The X-ray diffraction peak profile parameters quantified such as peak shift and asymmetry show that the irradiation-induced defects are sensitive to the dpa rate-irradiation temperature combinations. The increase in yield strength as a function of displacement damage is also correlated to the dislocation density.

Effect of Si on the evolution of plasticity mechanisms, grain refinement and hardness during high-pressure torsion of a non-equiatomic CoCrMnNi multi-principal element alloy

The present study unraveled the defining role of small silicon (Si) addition (5 atomic %) in dramatically altering the plasticity mechanisms, grain refinement and hardening response of a non-equiatomic CoCrMnNi multi-principal element alloy (MPEA) during high-pressure torsion (HPT) processing. Both the Si-free and the Si-added MPEAs had a face-centered cubic (FCC) structure and were subjected to a quasi-constrained HPT processing at 6 GPa pressure to different number of turns (0.5 and 5). Microstructure evolution was studied at the center and edge of the HPT-processed discs using X-ray diffraction line profile analysis (XLPA) and transmission electron microscopy (TEM). Si addition altered the predominant plasticity mechanism from micro-band formation to extensive occurrence of nano-twinning at the early stage of HPT processing. At later stages of HPT processing, both alloys exhibited deformation twinning but its propensity was considerably higher for the Si-added MPEA, as revealed by ∼50% higher twin fault probability. Additionally, the Si-added MPEA showed ∼30% higher dislocation density at any given stage of HPT processing compared to the Si-free MPEA. A significantly accelerated nano-structuring coupled with a finer saturation grain size was observed in the Si-added MPEA (34 nm for Si-free versus 23 nm for Si-added). These effects can be explained by the influence of Si addition on lowering the stacking fault energy (SFE) (from ∼40 mJ/m2 in Si-free to ∼20 mJ/m2 in Si-added MPEA) and increasing the solute pinning effect of Si on lattice defects. The plasticity mechanisms at nano-scale were also influenced by the presence of Si as confirmed by the formation of nano-twins and stacking faults inside the nano-grains for the Si-added and Si-free MPEAs, respectively. The differences in plasticity mechanisms and microstructure evolution resulted in enhanced hardness in the early stages of HPT processing for the Si-added MPEA, but the difference in hardness between the two alloys tended to be reduced at higher strains.

Effect of Oxygen Ion Irradiation on Nb-1Zr-0.1C Alloy Characterized Using X-Ray Diffraction Line Profile Analysis

One of the proposed materials for structural application in compact high-temperature reactors (CHTRs) is Nb-1Zr-0.1C alloy. Using the Variable Energy Cyclotron at the Variable Energy Cyclotron Centre, Kolkata, Nb-1Zr-0.1C alloy was irradiated with a 160-MeV oxygen (O6+) ion up to three different doses. Emulation of neutron irradiation by ion irradiation could be achieved as the weighted recoil spectra of the oxygen ion are found to be similar to the neutron recoil spectra of CHTRs within recoil energy ranging from 100 eV to 100 keV. The irradiated materials along with one as-received sample were characterized using different X-ray diffraction line profile analyses (XRDLPAs) to systematically evaluate microstructural parameters. A decrease in the domain size with an increase in microstrain and dislocation density is observed at first dose and then found to saturate with further irradiation. An increase in the Wilkens arrangement parameter indicates the formation of less correlated dislocations (clusters) after irradiation. Transmission electron microscopy analysis of as-received and highest-dose samples shows the formation of densely populated defect clusters after irradiation. Nanohardness increased after irradiation due to pinning of the dislocation movement by point defects and defect clusters/loops, as well as carbides in the matrix. The results extracted from the XRDLPAs are compared with our earlier studies of light ion–irradiated (H+) Nb-1Zr-0.1C alloy and oxygen-irradiated pure Nb to understand the effect of the type of ion and the alloying elements, respectively, on the evolution of the microstructure. It may be concluded that changes in dose and dose rate affect the movement of point defects toward sinks. Hence, possible correlated dislocation formation is observed in light ion–irradiated Nb alloy, but correlation is found to decrease with dose for heavy ion–irradiated Nb alloy. On the other hand, the presence of finely dispersed carbides restricts the formation of dislocation loops by making complexes with the defects in heavy ion (O6+)–irradiated Nb-1Zr-0.1C alloy, which is in contrast to pure Nb irradiated using the heavy ion (O6+) in a similar environment.

X-ray diffraction line profile analysis for the detection of the propensity to sensitize

Prior studies have revealed that the sensitization kinetics of 5xxx-series Al-Mg alloys are responsive to the dislocation content, with lower dislocation densities leading to higher rates of sensitization. In this work, X-ray line profile analysis (LPA) was employed to non-destructively assess the dislocation density in 5083 and 5456 alloys samples in various tempers and thermomechanical processing states. Using a conventional laboratory powder diffractometer with a Cu-Kα sealed tube source, it is shown that the approach has the ability to discriminate between samples of disparate tempers (H131, H116, and solutionized and water quenched). Destructive electron backscattered diffraction (EBSD) measurements on select samples confirm the variations, from the perspective of geometrically necessary dislocation density. Experiments were also performed using softer X-rays generated using a Cr Kα sealed tube source, which would render the approach more portable, due to lower shielding requirements. Unfortunately, Cr radiation was not successful due to the limited number of accessible diffraction peaks. Using the dislocations densities measured using LPA together with an established constitutive model permits accurate prediction of the mechanical strength of the alloys of the above disparate tempers. However, the technique does not appear capable of discriminating between samples within a given temper (e.g., H116). Use of a more highly monochromatic X-ray source could render the technique useful for a comprehensive structural health monitoring system for 5xxx alloys prone to sensitization.

X-ray diffraction line profile analysis of defects in neutron-irradiated austenitic stainless steels at low displacement damage levels

Neutron irradiation-induced microstructural changes in variants of austenitic stainless steels were characterized using the Angle Dispersive X-Ray Diffraction (ADXRD) technique with a synchrotron X-ray source of energy 14.968 keV (wavelength ∼0.82833 Å). SS 304 L(N), SS 316 L(N), and SS 316 materials were neutron-irradiated to low displacement damage levels (1–6.75 dpa) in the Fast Breeder Test Reactor at Kalpakkam at temperatures in the range ∼380 °C-400 °C. The effect of the irradiation-induced defects on X-ray diffraction peak profile parameters such as peak broadening, peak shift, and asymmetry were quantified and related to dislocation density. Peak broadening is found to increase as a function of dpa in most of the cases. Considering the highest dpa sample, lattice contraction has been shown by SS 304 L(N) and SS 316 whereas lattice expansion is exhibited by SS 316 L(N). Asymmetry in peak broadening is found to decrease in case of the highest dpa sample. Ferrite volume percent is seen to have increased as a function of dpa in SS 304 L(N) and SS 316 L(N) but not observed in SS 316. SS 304 L(N) has shown a greater propensity towards the austenite to ferrite transformation and 5 dpa sample has about 18 vol% of α-ferrite. However, in case of 5 dpa SS 316 L(N), ferrite content has increased to ∼4 vol% . The increase in yield strength was also related to the dislocation density amongst all three grades of stainless steel. SS 304 L(N) showed saturation in dislocation density and yield strength around 2 dpa whereas SS 316 L(N) showed linear behaviour up to the highest dpa.

Formation and Microstructural Evolution of Ferritic ODS Steel Powders during Mechanical Alloying.

Ferritic ODS steel elemental powder compositions with various Zr content (0.3-1.0 wt.%), ground in a Pulverisette 6 planetary ball mill, were extensively studied by X-ray diffraction line profile analysis, microscopic observations, microhardness testing and particle size measurements. A characteristic three-stage process of flattening the soft powders, formation of convoluted lamellae and, finally, formation of nanocrystalline grains was observed. In order to quantify the microstructural properties, expressed mainly in terms of crystallite size and dislocation density, a methodology for detailed and accurate microstructure analysis of nanosized and severely deformed materials was proposed by the Whole Powder Pattern Modelling (WPPM) approach. In the case of the proposed ODS alloy composition, the overlapping of Fe and Cr Bragg reflections makes the microstructure analysis certainly more complicated. The results showed that the microstructure of powders evolved towards the nanocrystalline state consisting of fine (diameter of ~15 nm) and narrowly dispersed domains, with extensive dislocation density exceeding 1016 m-2.

Investigation of Quantitative Evaluation of Rolling Contact Fatigue Cracks in Rail Steel by X-Ray Diffraction Line Profile Analysis

Investigation of Quantitative Evaluation of Rolling Contact Fatigue Cracks in Rail Steel by X-Ray Diffraction Line Profile Analysis

Dislocations and crystallite size distribution of cadmium oxide thin films synthesized by spray pyrolysis technique

Cadmium oxide (CdO) thin films have been successfully deposited on amorphous glass substrates by spray pyrolysis technique at a temperature, 573 °K using aqueous solution of cadmium nitrate 4-Hydrate powder with a concentration of 0.1 M. The X-ray diffraction (XRD) studies have revealed that the films exhibit cubic crystal structure. The modified Williamson–Hall and Warren–Averbach methods are used successfully for analyzing the XRD line profile for determining the crystallite size, dislocation densities and crystallite size distribution in CdO thin films. The crystallite size (D) and integral breadths (d) (D = 44.139 nm and d = 32.237 nm) are obtained by the modified Williamson Hall, while the area-weighted average grain sizes and volume-weighted obtained of modified Warren–Averbach method are xvol=46,06nm andxarea=29,7nm, respectively. The size parameter (Lo), dislocation density (ρ), effective outer cut-off radii (Re) and dislocation arrangement parameter (μ) gotten of Warren–Averbach are 35.53 nm, 2.0 × 1015 m−2, 7 nm and 0.31 nm, respectively. The particle size distribution (x) derived of XRD and estimated of size parameter is the size distribution function f(x) of log-normal.

Characterization of ion-induced microstructural changes in oxygen irradiated Ti–6Al–4V

The change in microstructure and mechanical properties ofTi–6Al–4V alloy due to 160 MeV O6+ ion irradiation has been reported here. Detailed X-ray diffraction line profile analyses have been used to evaluate the microstructural parameters and characterize the nature of defects and their arrangements. The results indicate saturation of size of the coherent region, the dislocation density and its arrangement with dose, which points to an optimized final microstructure of irradiated material. This was also supported by the Vicker’s microhardness measurements. Electron back scattered diffraction study was used to assess the changes in microstructure in terms of the evolution of misorientation boundaries within the grains due to irradiation-induced defects. All the results support the radiation resistance nature of Ti–6Al–4V alloy. Finally, comparison has been made with earlier proton irradiation results, and the difference has been related to the nature of the displacement cascade produced by light and heavy ions.

Investigations on Dry Sliding Wear Behavior of a Wire Arc Additively Manufactured Nickel-based Superalloy

ABSTRACT Wire Arc Additive Manufacturing (WAAM) is a low-cost method of fabricating large components from advanced materials such as nickel-based superalloys. Nickel-based superalloys have varied industrial applications and suit the WAAM method due to their excellent weldability when used in conjunction with metal inert gas welding equipment used in the current study. All WAAM specimens were subjected to a standard dry sliding wear test to examine wear behavior. During the wear study, load, sliding velocity, and sliding distance were all considered for both wrought and WAAM alloy. The lowest wear was observed at a lower load and higher sliding velocity, whereas the highest wear was observed at a higher load and lower sliding velocity. Wear mechanisms and wear debris corresponding to lowest and highest wear conditions were also being investigated. The transition from lowest to highest wear rate in both alloys was attributed to the transition from abrasive to adhesive and delamination wear mechanisms. Microstructure analysis revealed that the nickel-based WAAMed alloy had an equiaxed dendritic structure, whereas the nickel-based wrought alloy had a cellulose structure. Both specimens had a stable austenite structure in the Ni-Fe-Cr phase, as determined by X-ray diffraction analysis. The X-ray diffraction line profile analysis technique by the Williamson-Hall relationship revealed that WAAM alloys have higher micro-strain, higher dislocation density, and smaller crystallite size when compared to wrought alloys. The experimental results showed a 23% increase in hardness and a considerable improvement in wear resistance in the WAAMed alloy compared to the wrought alloy.

Micro-strains, local stresses, and coherently diffracting domain size in shock compressed Al(100) single crystals

In situ x-ray diffraction (XRD) measurements and their analysis in Al single crystals shock compressed along the [100]-direction were utilized to examine shock wave induced microstructural heterogeneities. High-resolution XRD line profiles for the 200, 400, and 600 Al peaks were measured in uniaxial strain compression states to either 5.6 or 11.7 GPa and partial stress release to 3.5 or 6.6 GPa, respectively. Broadening of the XRD line profiles was analyzed to determine the magnitude of the longitudinal micro-strain distribution (0.195% and 0.28% full width at half maximum for 3.5 and 6.6 GPa stresses, respectively) and the size of coherently diffracting domains (CDDs) (0.125 and 0.07 μm for 3.5 and 6.6 GPa stresses, respectively). From the longitudinal micro-strain distributions, the distribution of local stress differences (or stress deviators) was obtained in the shocked state. The full width at half maximum of this distribution, a measure of the local stress inhomogeneities, is greater than half of the macroscopic stress difference for both 3.5 and 6.6 GPa peak stresses, suggesting considerable variation in local stress deviators. The CDD sizes determined here are comparable to characteristic length scales for defect-free regions determined from defect density measurements in post-shock recovery experiments. The present work represents an important step in understanding material microstructure and inhomogeneities in the shock-compressed state.

Microstructural and mechanical characterisation of WC–Co alloys elaborated by liquid phase sintering and hot isostatic pressing: study of WC crystallites size evolution

ABSTRACT This work aims at the characterisation and study of WC tungsten carbide crystallites size evolution as well as of the microstructure of WC–Co alloys produced by liquid phase sintering and by hot isostatic pressing (HIP). The goal of this study is to demonstrate a possible improvement in mechanical and surface properties by using hot isostatic pressing (HIP) compared to liquid phase sintering. Two types of cemented carbides containing 11 and 20 wt-% of cobalt have been produced by two different techniques. The alloys microstructures were characterised by scanning electron microscopy (SEM). The size evolution and dimensions of WC crystallites were derived from Wagner-Halder and Williamson-Hall methods following the exploitation of X-ray diffraction line profiles. Vickers micro-hardness tests were also performed in this study. It is found that there is a clear improvement in micro-hardness for materials densified by hot isostatic pressing (HIP).

Revealing the decomposition mechanisms of dislocations and metastable α' phase and their effects on mechanical properties in a Ti-6Al-4V alloy

The metastable α' phase and dislocation characteristics (e.g., density and constituents) are of vital importance for the mechanical responses of (α+β) titanium alloys. In this work, to reveal the in-depth decomposition mechanisms of dislocations and metastable α' and their influences on mechanical properties in a Ti-6Al-4V (α+β) alloy, the thermal stability of different microstructures tailored by various cooling approaches were investigated utilizing scanning electron microscope, electron backscattered diffraction, transmission electron microscope and X-ray diffraction line profile analysis. The results showed that the initial characteristics of α' and α laths and dislocation density were influenced by the cooling methods remarkably. The thermal stability of Ti-6Al-4V alloy increased with decreasing cooling rate. The improvement in thermal stability can be ascribed by the decrement in dislocations, partitioning of the alloying elements and grain orientations variation of the α' lath and α phase. It is also found that the plastic strain accommodation of β→α' transformation was dominated by <a> dislocations. During stabilization annealing treatments, the <a>, <c> and <c+a> dislocations simultaneously decomposed. The decomposition of dislocations and metastable α' phase during various stabilization annealing and the particular twins and stacking faults microstructures formed during quenching have a great influence on the properties of the studied Ti-6Al-4V alloy.

Post irradiated microstructure and mechanical properties of pure V

Proton irradiation has been carried out on pure vanadium samples and the changes in the microstructure and mechanical properties have been evaluated as a function of dose. The microstructural parameters such as domain size and microstrain have been assessed along different crystallographic planes using the X-ray diffraction line profile analysis methods such as simplified breadth and the modified Rietveld technique. No significant change in the dislocation density is observed as a function of dose from the XRD results. However, the results of positron annihilation spectroscopy in terms of positron lifetime and S-parameter clearly indicated the formation of small defect clusters with irradiation. Transmission electron microscopy investigation confirmed the presence of small dislocation loops in the irradiated samples. Molecular dynamics simulations carried out to model the formation of irradiation-induced defects clusters with irradiation dose support the experimental observation of small defect clusters and increasing cluster size with dose. The yield strength and tensile strength showed systematic increase with irradiation dose corroborating with the results of microhardness measurement. The fractography of the tensile samples clearly showed the characteristics of brittle fracture in the irradiated samples.

Correlative image learning of chemo-mechanics in phase-transforming solids.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on LiXFePO4, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.