Coarsening Rate Constant Research Articles

Systematic and quantitative testing simulations and theories on phase coarsening by experiments

Microgravity experiments on phase coarsening in solid-liquid mixtures provided an ideal tool to closely and accurately explore the kinetics of phase coarsening because the sedimentation and convective melt flow are eliminated in the International Space Station. In this study, we employed phase-field simulations to systematically investigate the microstructure evolution during phase coarsening at various volume fractions. Simulated microstructure evolution during phase coarsening are compared quantitatively with the microstructure evolution archived from microgravity experiments. Furthermore, kinetics of phase coarsening in Pb-Sn solid-liquid mixtures at various volume fractions is studied theoretically and numerically, which is compared with microgravity experiments. In particular, particle size distribution, relative coarsening rate constants, and scaled maximum particle radii, are predicted from theories, and deduced from microgravity experiments, then calculated from phase-field simulations. This systematic and quantitative study of phase coarsening confirms the consistency to the results from phase-field simulation, microgravity experiments and theories at lower volume fractions, and stimulates more careful microgravity experiments at higher volume fractions (≥0.7).

Effects of Nb on Creep Properties and Hot Corrosion Resistance of New Alumina-Forming Austenitic Steels at 700 °C

Effects of Nb on the creep resistance and hot corrosion behavior of the Fe-25Cr-35Ni-2.5Al-xNb (x = 0, 0.6, 1.2) Alumina-Forming Austenitic stainless steels (AFA steels) at 700 °C were investigated. The addition of Nb promoted the precipitation of both nanoscale NbC and γ′-Ni3(Al, Nb) phases, which exhibited very low coarsening rate constants. The nanoscale NbC and γ′-Ni3(Al, Nb) phases effectively impeded the migration of dislocations and led to an improvement in creep performance of the Nb-addition AFA steel. The corrosion of AFA steels in Na2SO4-25%K2SO4 at 700 °C was primarily driven by an “oxidation-sulfidation” mechanism. The addition of Nb, serving as a third element, facilitated the formation of protective Cr2O3 and Al2O3 films, which improved the hot corrosion resistance performance. However, the formation Nb2O5 was found to compromise the compactness of the oxide film, which adversely affected the corrosion resistance.

Effect of Co content on precipitation behavior of γ′ phase strengthened CoNi-based alloys

The CoNi-based alloys with nano-precipitates exhibit significant advantages in high-temperature applications due to their excellent thermal stability. This study investigates the influence of Co content (0 at%, 22.5 at%, 45.0 at%) on the morphological evolution, coarsening kinetics of γ' phases, and γ/γ' lattice misfit. The results reveal that the γ/γ' lattice misfit increases with increasing Co content. The addition of Co not only increases the number density of γ' phases but also effectively suppresses the coarsening of precipitates. Moreover, the coarsening rate constant of the γ' phase decreases with increasing Co content, with the alloy containing 45.0 at% Co exhibiting the lowest coarsening rate at 1.04 × 10−28 m3/s. Additionally, the increase in Co content enhances the hardness of the alloy, primarily due to the increased volume fraction of the γ' phase. This study contributes to understanding the mechanism of Co content variation on the characteristics and thermal stability of precipitates, providing support for the design of CoNi-based alloys.

Coarsening transitional kinetics of γ′ precipitates in a nickel-based single crystal superalloy during thermal exposure

The microstructural stability and coarsening kinetics of γ′ precipitates in a nickel-based single crystal superalloy (Ni-SX) were thoroughly investigated under various thermal exposure treatments. The evolutions of characteristic parameters including γ′ size, morphology, area fraction, and γ channel width were documented. Coarsening rate constants and particle size distributions (PSDs) were calculated and recorded based on measured precipitate sizes at temperatures ranging from 800 ℃ to 1100 ℃ and durations ranging from 100 h to 1010 h. The experimentally derived rate constants were compared with the calculated theoretical values from two mainstream models: matrix-controlled diffusion (LSW model) and interface-controlled diffusion (TIDC model). Notably, transitional coarsening kinetics of γ′ precipitates from the LSW model to the TIDC model was observed at high temperatures over time. Through a comprehensive consideration of key coarsening kinetics parameters such as elemental diffusivity, trans-interface diffusion coefficient, coarsening rate constant, γ/γ′ interfacial area, and solute mass transfer, the transformation of the coarsening kinetics from matrix-controlled diffusion to interface-controlled diffusion was quantitatively discussed. The emergence of the TIDC model as the dominant mechanism was attributed to relatively smaller solute mass transfer through the interface. Moreover, the degradation of γ/γ′ interfacial energy and interfacial area, coupled with the increase in solute diffusion coefficient in the matrix, facilitated the trans-interface diffusion to act as a limiting factor throughout the coarsening process.

Effect of Ti/Nb/Ta addition on the γ/γ' coherent microstructure in low-density and high-strength Co-Al-W-Mo-based superalloys

Coherent precipitation of cuboidal γ'-Co3(Al,W) nanoparticles in face-centered-cubic (FCC)-γ matrix is of great significance for improving high-temperature mechanical properties of Co-based superalloys. The present work developed a series of low-density Co-based superalloys in light of the cluster composition formula of [Al1-(Co,Ni)12]((Al0.5(Ti/Nb/Ta)0.5W0.5)(Mo0.5Cr0.5Co0.5)), where the addition of Ti, Nb, and Ta is mixed with an equimolar ratio. It is found that these designed alloys with different combinations of Ti/Nb/Ta, Ti/Nb, and Ti/Ta possess the coherent microstructure of cuboidal γ' nanoprecipitates in the FCC-γ matrix. The microstructural evolution of coherent γ/γ' during aging at 1173 K shows that these superalloys exhibit higher thermal stability at high temperatures. Even after aging for 1000 h, there do not exist any other precipitated phases on grain boundaries, except the coarse γ' precipitates. Also, the coarsening rate constants of cuboidal γ' nanoprecipitates in these alloys are very low (K = 5.76–6.03 nm3/s), which is mainly ascribed to a moderate lattice misfit (ε = 0.28 %-0.45 %) between γ and γ'. The stable γ/γ' microstructure renders the alloys with prominent mechanical properties, as evidenced by the high yield strength of σYS = 438–445 MPa at 1143 K. A large amount of stacking faults appear after compressive deformation and Lomer-Contrell dislocation locks are also formed due to the reaction of partial dislocations of stacking faults. Moreover, the microhardness (285–320 HV) in each alloy keeps almost constant with the aging time. Besides, these superalloys have a relatively lower density (8.67–8.89 g/cm3), among which the alloy containing Ti0.25Ta0.25 also exhibits a much higher γ' solvus temperature (1361 ± 2 K) than those of the existing Co-Al-W-based superalloys.

Precipitation and growth of Laves phase and NbC during aging and its effect on tensile properties of a novel 15Cr–22Ni–1Nb austenitic heat-resistant steel

The microstructure evolution and the mechanical properties of 15Cr–22Ni–1Nb austenitic heat-resistant steel were investigated during the aging up to 24 h at 780 °C, 820 °C and 860 °C. A large amount of Laves phase and nano-sized NbC were precipitated during the aging. The NbC particles exhibit excellent coarsening resistance, and the coarsening rate constant of nano-sized NbC particles is four orders of magnitude smaller than that of Laves phase during the aging at different temperatures. The room temperature tensile strength of the heat-resistant steel after aging at 820 °C for 4 h is highest among different aging treatments. The volume fraction of Laves phase increase with the increase in aging temperature and holding time, resulting in a decrease in the ductility of the heat-resistant steel. Ostwald ripening was observed during the aging for 8 h at different aging temperatures. Consequently, the high temperature ultimate tensile strength of heat-resistant steel after the aging for 8 h is lower than that for 4 h and 24 h. The precipitation strengthening contributed by Laves phase and nano-sized NbC was estimated. The yield strength contributed by submicron Laves phase particles is smaller than that provided by nano-sized NbC particles.

Temperature dependence of kinetics pathway of γ′ precipitation in Co-Al-W superalloys: A phase-field study

The expeditious development of novel Co-based superalloys depends on achieving a compressive understanding of the kinetics path way of γ′ precipitates. This paper investigates the temperature dependence of evolution processing and mechanism of γ′ phase in a model Co-9.5Al-9W (at%) alloy using phase-field method. The simulated microstructures during aging at 700, 800 and 900 ℃ show that spherical γ′ quickly changes to cuboidal aged at 900 ℃ while transforms into irregular interconnected morphology at low temperature, which is consistent well with experimental observations. By characterizing the long-range parameters, this irregular γ′ is attributed to the coalescence of adjacent precipitates with the same domain, primarily driven by the decrease of interfacial energy. The temporal evolution of average size of the γ′ precipitates suggests classical Lifshitz-Slyozov-Wagner coarsening at the three temperatures, and the coarsening rate constants K are determined. The temperature dependence of K is clarified by analyzing the thermodynamic driving force and chemical mobility. Additionally, the effects of particle inter-distance, shape and size on γ′ evolution are discussed from the perspective of diffusion potential.

Precipitation and coarsening kinetics of H-phase in NiTiHf high temperature shape memory alloy

Precipitate hardening is the most easiest and effective way to enhance strain recovery properties in NiTiHf high-temperature shape memory alloys. This paper discusses the precipitation, coarsening and age hardening of H-phase precipitates in Ni50Ti30Hf20 alloy during isothermal aging at temperatures between 450 °C and 650 °C for time to 75 h. The H-phase mean size and volume fraction were determined using transmission electron microscopy. Precipitation kinetics was analyzed using the Johnson-Mehl-Avrami-Kolmogorov equation and an Arrhenius type law. From these analyses, a Time-Temperature-Transformation diagram was constructed. The evolution of H-phase size suggests classical matrix diffusion limited Lifshitz-Slyozov-Wagner coarsening for all considered temperatures. The coarsening rate constants of H-phase precipitation have been determined using a modified coarsening rate equation for non-dilute solutions. Critical size of H-phase precipitates for breaking down the precipitate/matrix interface coherency was estimated through a combination of age hardening and precipitate size evolution data. Moreover, time-temperature-hardness diagram was constructed from the precipitation and coarsening kinetics and age hardening of H-phase precipitates in Ni50Ti30Hf20 alloy.

Effect of long-term aging on microstructural stability and tensile deformation of a Fe–Ni-based superalloy

The microstructural evolution, tensile behavior and deformation mechanism of a Fe–Ni-based superalloy for advanced ultra-supercritical coal-fired power plant during long-term isothermal exposure at 700–800 °C for 500–3000 h were investigated. The coarsening rate constant of γ′ phase in the alloy exposured at 700 °C, 750 °C and 800 °C were about 47.543 nm3/h, 277.963 nm3/h and 2201.937 nm3/h, respectively. The activation energy for γ′ growing is around 250.24 kJ/mol. The results showed Al, Ti and Ni elements primarily gathered into γ′ precipitates, while Cr and Fe mainly partitioned into γ matrix in Fe–Ni base alloy. After long-term aging, there was no precipitation of harmful phases such as the η and σ phases, but the decomposition of MC + γ → M23C6 + γ′ was observed. The microcracks were prone to initiate and propagate around pores formed by MC decomposition and lamellar M23C6 carbide, which might result in the premature fracture failure of the alloy. The yield strength first remained stable with a slight increase in the γ′ phase diameter and then decreased after further thermal exposure. The variation of tensile strength with precipitate size could be rationalized by the transformation between shearing model and Orowan looping mechanism of γ′ precipitates with increasing the γ′ precipitate size.

Phase-field simulation of diffusion-controlled coarsening kinetics of γ’ phase in Ni–Al alloy

Abstract Morphology evolution and coarsening kinetics of γ’ (Ni3Al) precipitates in Ni–Al alloy were investigated quantitatively using the interface diffusion-controlled, the bulk diffusion-controlled, and the interface diffusion-controlled elastic strain models. By calculating the γ’ phase number density, volume fraction, and particle radius, the effects of diffusion and elastic strain on the γ’ phase growth and coarsening were clarified. The coarsening rate constants are smaller in the bulk diffusion-controlled and the interface diffusion-controlled elastic strain models than those of the interface diffusion-controlled model, which is due to the long-range diffusion of Al atoms and the retardant effect of coherent strain between the γ’ and γ phases, respectively. The linear fitting on the cubic exponent shows the comparable associate coefficient that gives no superiority to the different models in Ni–Al alloy.

A comparison of theory and simulation with microgravity experiments on phase coarsening

A quantitative understanding of microstructure evolution during phase coarsening is crucial to the optimization of processing, final structure, and properties of materials at high homologous temperatures. For example, microgravity experiments on phase coarsening in Pb-Sn solid-liquid mixtures allowed the kinetics of phase coarsening to be followed more closely and more accurately by eliminating sedimentation and convective melt flow. In this study we developed phase-field simulations to study microstructure evolution during solid-liquid phase coarsening. Physical properties for Pb-Sn solid-liquid mixtures were calculated using CALPHAD. Simulated microstructure features during phase coarsening are compared quantitatively with the microstructure evolution and kinetics extracted and archived from microgravity experiments. In particular, experimental particle size distribution and coarsening rate constant are predicted from theory, and deduced from microgravity experiments, then calculated from phase-field simulations. The new results from phase field simulations agree with the results from archived microgravity experiments for a lower volume fraction alloy, and still acceptably for Pb-Sn alloys with higher volume fraction.

Impact of Suspended Solids on Coarsening of Ice.

Suspended solids, such as silica particles and cellulose fibers, were added to a sucrose aqueous solution, and ice crystals were coarsened at −10 °C. From the radius of the ice crystals, the coarsening rate constant was obtained using the Lifshitz–Wagner equation and the impact of the suspended solid on the coarsening of ice was evaluated. The results showed that the addition of the silica particle suppressed coarsening, but this behavior was not dependent on particle size. It was also shown that cellulose fibers suppressed coarsening more than silica particles. In order to clarify these causes, the present study investigated the correlation between Lw–Lmea and the coarsening rate constants obtained from different suspensions. Lw is the latent heat of fusion (calculated value) corresponding to the water content of the suspension, while Lmea is the latent heat of fusion (measured value) obtained by thermal analysis. A correlation was observed between Lw–Lmea and the logarithm of the coarsening rate constant. Lw–Lmea represents the volume of water that did not form ice crystals on the addition of the suspended solid (volume of unfrozen water at −10 °C), with a larger Lw–Lmea associated with greater inhibition of coarsening. The present findings suggest that suspended solids inhibit coarsening by promoting ice crystal melting.

Effects of 1 at.% Ta substitution for 1 at.% W on the coarsening kinetics and deformation behavior of γʹ-strengthened CoNi-base superalloys

The coarsening behavior of the γʹ precipitates and compression deformation mechanism of the γʹ-strengthened CoNi-base superalloys are investigated. By substituting 1 at.% Ta for 1 at.% W, the 4W2Ta alloy exhibits a higher γʹ solvus temperature of 1218 °C and a lower mass density of 8.93 g/cm3. During the aging process from 900 to 1000 °C, both of the 5W1Ta and 4W2Ta alloys show stable γ/γʹ two-phase microstructure. The coarsening behavior of the γʹ precipitates in the two alloys follows the classical Lifshitz-Slyozov-Wagner (LSW) model. The coarsening rate constant of the 4W2Ta alloy is approximately two times lower than that of the 5W1Ta alloy, which is attributed to its larger lattice mismatch due to the addition of Ta. Besides, compared with the 5W1Ta alloy, the 4W2Ta alloy has higher high-temperature strength and shows different deformation behavior. When the deformation temperature is lower than 800 °C, pairs of dislocations shear the γʹ precipitates and γ matrix. At 800 °C, stacking faults (SFs) appear in the γʹ precipitates and increase with the increasing temperature, whereas most of dislocations bypass the γʹ precipitates at 1000 °C.

Design, phase equilibria, and coarsening kinetics of a new [formula omitted] precipitation-hardened multi-principal element alloy

Multi-principal element alloys (MPEAs), with dispersed nanometric precipitates in a ductile matrix, are attracting a considerable amount of literature’s attention. Understanding the coarsening kinetics and potential properties of such alloys is crucial for future developments in the field. In the present study, we report a new precipitation-hardened multi-principal element alloy, Cr29.7Co29.7Ni35.4Al4.0Ti1.2 (at%), developed with the aid of the CALPHAD method. The alloy has a tough Cr-Co-Ni FCC matrix and nanometric L12 precipitates. After standard heat treatments, the alloy was aged at 850 °C for different aging times and the coarsening kinetics was investigated. The evolution of mechanical properties as a function of aging time was evaluated through microhardness tests. An increment of 106 HV 0.5 was observed compared to the sample in the solution-treated condition. This hardness increment was higher than that of conventional superalloys with a similar volume fraction of precipitates. Experimental data indicate that particle growth during coarsening is governed by diffusion controlling mechanism. The coarsening rate constant was lower than that of traditional wrought superalloys aged at the same temperature, indicating better thermal stability of the current MPEA. Furthermore, experimental particle size distributions show a good correlation with the curve predicted by the Lifshitz–Slyozov–Wagner (LSW) theory. Deviations and the applicability of this theory for MPEAs are discussed.

On the effect of Ti addition on microstructural evolution, precipitate coarsening kinetics and mechanical properties in a Co–30Ni–10Al–5Mo–2Nb alloy

In this work, the effect of varying Ti content on the γ/γ' microstructure, precipitate coarsening kinetics, and mechanical properties in a series of Co-30Ni-10Al-5Mo-2Nb-xTi alloys (where x = 0, 1, 2, 3, and 4 at. %) is presented. An addition of 2 at. % Ti and beyond changes the γ′ morphology from rod shape (alloys containing 0 and 1 at. % Ti) to cuboidal shape (alloys containing 2 to 4 at% Ti) when aged beyond 500 h at 900 °C. The composition profiles obtained by STEM-EDS analysis reveal a strong partitioning of Ni, Ti, Al, and Nb in the γ′ precipitate, whereas partitioning of Mo changes from (KMo>1) γ′ precipitates for Co-30Ni-10Al-5Mo-2Nb alloy to equal proportion in both the phases (KMo∼1) for alloys containing 1 at.% Ti or more. Among the alloys studied, Co-30Ni-10Al-5Mo-2Nb-4Ti alloy exhibits an excellent combination of low mass density (8.19 g/cc) and high γ′ solvus temperature (1117 °C). The addition of Ti to the base 2Nb0Ti alloy introduces a 0.2% proof stress anomaly with temperature with a peak in strength was observed at 770 °C. The experimentally determined temporal evolution of average γ′ precipitate size suggests an LSW model-based evaporation-condensation (EV) coarsening mechanism in alloys containing 1 and 2 at% Ti. In contrast, a combined EV and coalescence/coagulation coarsening mechanisms operates in alloys with 3 and 4 at% Ti at the aging temperature of 900 °C. Despite the increase in γ/γ′ stability, the coarsening rate constant, calculated using modified LSW based coarsening model, increases by six times with an increase in Ti content from 1 to 4 at.%.

Roles of the semisolid heating on the microstructure of a hypereutectic Al\u2013Fe\u2013Cu alloy

A hypereutectic Al–Fe–Cu alloy with a high-volume fraction ferro-aluminum second phase (AlFe phases for short) was reheated in the solid–liquid region and the microstructure evolution was investigated. During semisolid heating, the high-melting AlFe phases in the Al–Fe–Cu alloy were demonstrated to stunt the grain growth and to block the liquid coalescing and the solid moving. Consequently, the grain sizes in the alloy increased rapidly and then slowly with increasing holding time, and the grains increased gradually with increasing temperature. Smaller grain grew into the large grain but it did not continually grow into the larger grain with increasing temperature or holding time. The shape factor (SF) of the alloy increased gradually and then decreased quickly with increasing temperature or holding time. The major alloying elements in addition to magnesium in the hypereutectic Al–Fe–Cu alloy were finally enriched at the grain boundaries or around the AlFe phases. Besides dissolving in the grains or AlFe phases, copper also diffused between the grains or around AlFe phases, resulting in the formation of diverse Cu-enriched zones. Cu constituents in the inter-grains are outnumbered in the intra-grains. The coarsening kinetics of the alloy was controlled by grain boundary diffusion. The coarsening rate constants K in the initial stage of heating (5–20 min) were several times larger than that in the later stage of heating (20–60 min), indicating the blocking effect of AlFe phases on coarsened grain being obvious.

Microstructural evolution of Mg-10Gd-3Y-1Zn-0.4Zr (wt%) alloy prepared by strain-induced melt activation process

The semisolid billets of Mg-10Gd-3Y-1Zn-0.4Zr (wt%) alloy were prepared by the strain-induced melt activation (SIMA) route, and the effects of isothermal heating parameters on the morphology and coarsening kinetics of primary solid grains were studied. It was found that the average grain size increased with the increase of isothermal time while the grain size showed different changing laws with the temperature at different isothermal times. The growth behavior of the primary solid grains was predominantly governed by the Ostwald ripening mechanism, although there is coalescence mechanism in some cases. As the isothermal temperature increased from 550 °C to 590 °C, the coarsening rate constant increased continuously and then declined when the temperature was further increased to 610 °C. Compared with other SIMA processed magnesium alloys, the present alloy showed a significantly lower grain coarsening rate constant due to the inhibiting effect of rare earth (RE) elements on coarsening. This research has provided an insight into the microstructural evolution of Mg-RE alloy under different heating conditions, and will provide valuable information for potential industrial applications.

On the effect of Fe in L12 strengthened Al–Co–Cr–Fe–Ni–Ti complex concentrated alloy

In this study, the effect of Fe in precipitation strengthened Al-Co-Cr-Fe-Ni-Ti complex concentrated alloys (CCAs) is investigated. The amount of Fe significantly affected the γ′ morphology, microstructural stability, lattice misfit, solvus temperature and mechanical behaviour. The decrease in the Fe content from 11.5 (Al7.8Co20.6Cr12.2Fe11.5Ni40.7Ti7.2) to 0 (Al7.8Co20.6Cr12.2Ni52.2Ti7.2) at% changed the precipitate morphology from spherical to cuboidal upon 50h ageing at 900°C. Also, the lattice misfit and solvus temperature of the alloy increased from 0.097 to 0.41% and 1109 to 1199°C, respectively, with the complete removal of Fe from the alloy system. Coarsening studies at 900°C (up to 550h) revealed that the γ′ coarsening was driven by evaporation and condensation (EC) mechanism in Al7.8Co20.6Cr12.2FexNi52.2-xTi7.2 (x=11.5, 5 and 0, in at%) alloys. The coarsening rate constants (Kr) were calculated for the three alloys; among them, the alloy without Fe showed the least value (2.83 × 10−27 m3 s−1). The obtained results on the effect of Fe in L12 strengthened CCAs offer a new platform for the development of advanced high-temperature alloys.

Effect of Reheating in the Solid–Liquid Region on Al-5Fe-4Cu-Based Alloys

Two Al-5Fe-4Cu-based alloys, AF1 alloy and AF15 alloy, with a high-volume fraction of second-phase iron-bearing intermetallics (AlFe phases for short) were reheated to a solid–liquid region, and the microstructural evolution of the alloys was investigated. During heating in the solid–liquid region, the high-melting-point solid AlFe phases were demonstrated to stunt grain growth, block liquid convection, restrict diffusion and coalescence, and reduce movement of solids. This mechanical barrier affected semisolid heating and prompted the formation of grains with increased high-angle grain boundaries (HAGBs), resulting in alloys with smaller grain sizes and lower coarsening rate constants. Consequently, the grains from the earlier stage (5–20 min) of isothermal heating were several times larger than those from the later stage (20–60 min), whereas average diameter of the grains increased with elevated heating temperatures and prolonged holding time. The coarsening of Al-5Fe-4Cu-based alloys is predominantly controlled by grain boundary diffusion. The AF15 alloy had a higher fraction of AlFe phases and more complex phase morphologies than the AF1 alloy. Furthermore, it had coarsening rate constants only one-fifth to one tenth those of the AF1 alloy.

The Effect of Equal Channel Angular Pressing on Coarsening Kinetics of AZ80–0.2Y–0.15Ca Alloy in Semisolid State

Semisolid samples of the AZ80–0.2Y–0.15Ca wt% (AZ80M) magnesium alloy are fabricated using equal channel angular pressing (ECAP) followed by semisolid isothermal heating treatment. The effect of the number of ECAP passes on the coarsening dynamics of the alloy at different semisolid temperatures is investigated. The results show that as the number of ECAP passes increases, the coarsening rate constant (K) shows a similar trend downward and then upward at different temperatures. And the K value of the sample after three passes of ECAP processing (3P) is the lowest, which is primarily attributed to the maximum proportion of high‐angle grain boundaries (HAGBs) and the most uniform grain size in the 3P sample. At high solid fractions, a high proportion of HAGBs hinders the coalescence of the adjacent solid grains. At low solid fractions, uniform and fine grains result in insufficient driving force for the Ostwald ripening process. These lead to the lowest K value in the 3P sample.