Small Grains Research Articles

Thermal cycling performance of GYbZ/YSZ thermal barrier coatings with different microstructures based on finite element simulation

Three (Gd0.9Yb0.1)2Zr2O7/YSZ double ceramic layer (DCL) thermal barrier coatings (TBCs) with different microstructures were manufactured by electron-beam physical vapor deposition (EB-PVD). The thermal cycling behavior of the three TBCs was evaluated comparatively at 1150 ℃. The results showed that TBCs with small columnar grains exhibited the best thermal cycling performance among all the tested TBCs. The effect of microstructure on thermal cycling behavior, including crack evolution and failure mode was discussed. A finite element model tailored to the microstructural characteristics of the DCL coatings was established. Several in-plane stress concentration points appeared in the taller GYbZ column due to discontinuities in strain tolerance resulting from sudden structural or compositional changes. Analysis of the strain energy release rate variation for each concentration point suggested that the predicted delamination position and process aligned with experimental results.

Maize (Zea Mays L.) Response to Deficit Irrigation Levels at Different Growth Stages on its Yield and Water Use Efficiency at Koka, Central Rift Valley of Ethiopia

Water scarcity is among the major limitations for crop production. Improving water use efficiency of irrigated crops through water management options is crucial in water scarce areas. Field experiment was carried out at Wondo Genet Agricultural Research Center Koka Research site, to investigate the effect of water stress at different growth stage on yield and water use efficiency of maize. one optimum irrigation and eight growth stage based deficit levels(100% ETC at all growth stages, 75% ETC at all growth stages, 50% ETC at all growth stages, 75% ETC at development growth stage, 50% ETC at development growth stage, 75% ETC at mid growth stage, 50% ETC at mid growth stage, 75% ETC at late growth stage and 50% ETC at late growth stage) were imposed on maize (Zea mays L.) variety Melkassa II as a treatment and laid out in randomized complete block design (RCBD) with three replications. Results indicated that the different levels of growth stage based deficit levels had significant (p<0.01) effect on crop yield, harvest index and water use efficiency. Grain yield reduced with increased stress, whereas water use efficiency was increased with stress level increased. The highest grain yield of 6.4 t/ha and WUE of 1.01 kg/m3 were obtained at 100% ETC and 50% ETC at all growth stages, respectively. Also, 75% ETC at development stage and late stage treatments showed no significant variation with 100% ETC in grain yield. Water use efficiency observed at 75% ETC all growth stages treatment was statistically similar with that of 50% ETC at all growth stages treatment. Grain yield obtained from 50% ETC at mid growth stage was similar with 50% ETC at all growth stages, and water use efficiency was the least and this shows that maize was sensitive to moisture stress at mid growth stage than development and late growth stages. Therefore, maize could be irrigated at 75% ETC at all growth stages and by stressing development or late growth stages up to 50% ETC to increase water use efficiency with a small grain yield reduction for stressed scenario and for non stressed scenario with 100% ETC at all growth stages.

Blacklight sintering of BaZrO3-based proton conductors

Acceptor-doped BaZrO3, a ceramic proton conductor, is well researched for use in solid oxide fuel cells due to its proton conductivity and chemical stability. A major drawback of the material is the difficulty of sintering as it requires high sintering temperatures and long heating times (> 1600 °C, 24 h). An emerging sintering technology to mitigate this challenge is blacklight sintering, which uses a high-powered blue or UV light source to heat ceramics extremely fast leading to short sintering times and reduced energy demand. In this work, BaZr0.8Y0.2O3-δ (BZY20) and BaZr0.8Y0.1Sc0.1O3-δ (BZY10Sc10) were blacklight-sintered with a high-power blue laser in under four minutes. Even though the resulting samples have a gradient from large to small grains and structurally disordered grain boundaries, the proton conductivity is comparable to conventionally sintered samples. Hence, blacklight sintering is a promising technology with the potential to sinter BaZrO3 much faster, while saving energy.

A highly sensitive and selective ZnO-based ammonia sensor: Fe- doping effect

Abstract This study investigates the gas sensing capabilities of ZnO and Fe-doped ZnO films prepared via a cost-effective spin coating method. The films were characterized optically, structurally, and morphologically. X-ray diffraction revealed good crystal quality with a polycrystalline nature, and wurzite structure, though crystal quality and crystallite size decreased with Fe doping. Optical measurements indicated an increased optical band gap from 3.205 ± 0.002 to 3.220 ± 0.002 eV after Fe doping. Scanning electron microscope images confirmed spherical grainy structures with reduced grain sizes after Fe doping. Gas sensing measurements at room temperature (RT) at an exposure of vapors of various toxic chemicals (acetone, ethanol, propanol, methanol, and ammonia), demonstrated a highly selective nature of ZnO and Fe-ZnO towards the ammonia. The Fe-doping into ZnO improved the ammonia sensing capability of ZnO film. The Fe-ZnO film exhibited a gas response of 388.8 ± 5.5 at 400 ppm ammonia exposure, which was nearly 10 times larger than that of ZnO film with a response/recovery time of 22/51 s, good stability, and good repeatability. The Fe-ZnO film’s higher response is attributed to its smaller grain sizes and surplus of charge carriers after Fe doping which promote the adsorption of extra oxygen ions onto the film’s surface and the subsequent interaction between the adsorbed oxygen ions ammonia molecules. It could detect up to the lower limit of 1 ppm ammonia with a response of 24.2 ± 0.9, which is better than the previous reports. These results reveal the Fe-ZnO film as a viable material for developing a cost-effective and efficient ammonia sensor at room temperature.

Experimental simulation of the ancient production of gold granules

Granulation is an ancient and sophisticated decorative technique. The production of granules is a crucial part of this process but has rarely been studied. The present study employed three techniques—pouring method, heating method, and crucible method—to produce gold granules. The success ratio of granule formation, granule surface morphology, microstructure, and formation were analyzed to identify the techniques used in archaeological objects. The cooling medium significantly influenced small granule formation, microstructure, and grain size. Both heating and crucible methods could control the granule formation, but these methods produced distinct microstructures. Based on these experimental granules, the probable production methods of ancient gold balls were identified. The present study provided microscopic information for determining ancient gold granule production techniques.

Effect of Horizontal Continuous Casting Parameters on Cyclic Macrosegregation, Microstructure, and Properties of High-Strength Cu–Mg Alloy Cast Rod

AbstractThe objective of this paper is to present the effect of horizontal continuous casting parameters on macrosegregation and its effect on microstructures, textures, mechanical properties, and electrical resistivity of Cu–Mg alloy rod. By increasing the pulling distance and intermittent extraction time, chemical macrosegregation was observed along the longitudinal section of the cast rod, which reached a distance of 40 mm. Three areas were identified along the length of the material, especially at high pulling distance: with decreasing, quasi-stable, and increasing Mg concentration area. As the pulling distance increased, the difference in the observed extreme values of Mg concentration increased. Two distinct zones of different grain size were also observed. The first zone was formed of large columnar grains with a preferred direction of solidification $$\langle 100\rangle$$ ⟨ 100 ⟩ inclined to the axis of the wire, followed by a second zone formed of small grains of random texture. Consequently, difference in resistivity occurred from one zone to another and the resistivity increased from 37.5 to 41 nΩm. Likewise, the hardness varied between the values of 90 up and 110 Hv. The most homogenous chemical composition was obtained with up to 6 mm of pulling distance and up to 3 seconds of intermittent extraction time.

Room-Temperature Ripening Enabled by Hygroscopic Salts for Hole-conductor-Free Printable Perovskite Solar Cells with Efficiency Over 20 .

Solution-processed perovskite films generally possess small grain sizes and high density of grain boundaries, which intensify non-radiative recombination of carriers and limit the power conversion efficiency (PCE) of solar cells. In this study, we report the room-temperature ripening enabled by the synergy of hygroscopic salts and moisture in air for efficient hole-conductor-free printable mesoscopic perovskite solar cells (p-MPSCs). Treating perovskite films with proper hygroscopic salts in damp air induces obvious secondary recrystallization, which coarsens the grains size from hundreds of nanometers to several micrometers. It's proposed that the hygroscopic salt at grain boundaries could absorb moisture and form a complex which could not only serve as mass transfer channel but also assist in the dissolution of perovskite grains. This activates mass transfer between small grains and large grains since they possess different solubilities, and thus ripens the perovskite film. Consequently, p-MPSCs treated with the hygroscopic salt of NH4SCN show an improved power conversion efficiency of 20.13 % from 17.94 %, and maintain >98 % of the initial efficiency under maximum power point tracking at 55±5 °C for 350 hours.

Hetero-Nucleation Induced [111]-Oriented Mixed Halide Perovskite for Stable Pure Red Light-Emitting Diodes.

Mixed halide 3D perovskites are promising for bright, efficient, and wide-color gamut light-emitting diodes (LEDs) due to their excellent carrier transport, high luminescence, and easily tunable bandgaps. However, serious halide ion migration inside mixed halide 3D perovskite results in poor operational and spectral stability of the as-fabricated LEDs. Here, a hetero-nucleation crystallization strategy is reported to grow [111]-orientationpreferred mixed halide 3D perovskite CsPbI3-xBrx thin films for stable pure red LEDs. This hetero-nucleation crystallization is enabled by the addition of phosphoric acid (H3PO4) complexation, which promotes the growth of small perovskite grains into large grains with uniform [111]-orientation. The obtained [111]-orientation preferred film exhibits excellent stability under light or electric field stimulus as revealed by model analysis and experimental results compared to that of [001]-orientation preferred film. Thus, based on the [111]-orientationpreferred film, the fabricated LED exhibits an external quantum efficiency of 22.8%, a maximum brightness of 12000cdm-2, and a half-life time of 4080min under 1.5mA cm-2. More importantly, the electroluminescence spectrum of the device remains stable during the continuous operation of 4080min, showcasing the significant spectral stability improvement enabled by the hetero-nucleation induced [111]-orientation strategy.

Temperature gradient mechanism in the heterogeneous nucleation of inoculated alloy: A quantitative phase-field study

The grain size of solidification microstructure has a significant influence on the mechanical properties of castings. Generally, smaller grain size makes the strength of castings higher. Therefore, inoculation is an effective strategy to reduce grain size and improve casting performance. In this work, the phase-field method combined with the free growth model is employed to simulate the solidification of inoculated aluminum alloy with temperature gradient. The simulations indicate that a higher temperature gradient slows the progression of already nucleated grains into impingement growth and enhances the undercooling of the melt ahead of the solid-liquid interface. Hence, more inoculants have chance to get the corresponding nucleation undercooling, promoting grain nucleated sequentially along the gradient direction. These results are consistent with previous real-time observed experiments. This work may provide guidance on improvement of the theoretical models for predicting grain size of inoculated alloys and the optimization of casting process to obtain refined grains in inoculated ingots.

Effect of Heat Treatment on Corrosion Behavior of S275 Mild Steel Using Accelerated DC Voltage, LPR, and EIS

AbstractThis study used an external DC voltage of 1.5 V to accelerate corrosion in heat-treated S275 mild steel samples at different time intervals. LPR and EIS were used to study the corrosion behavior of original and quenched steel samples. There was only a negligible difference in the corrosion rate (CR) for the original and the quenched samples up to 30 min of voltage application in a 3.5% NaCl electrolyte media. When the exposure time increased to 60 min, the original sample showed seven times higher CR than the quenched samples. The pits on the surface of the original samples acted as cathodes, enhancing the reaction rate on the surface and increasing its CR dramatically. This led to bimodal corrosion, where the first part is led by concentration and diffusion; while, the second part is led by localized corrosion. The smaller pits on the original surface samples served as cathodic reaction centers, exacerbating corrosion. The corrosion rate of the original samples ranged from 0.8 to 7.8 mmpy; whereas, the corrosion rate of the quenched samples remained consistently around 0.8 mmpy. This trend can be observed in long-term corrosion in different metals. The uniformly oriented martensitic microstructure and the quenched samples’ small grain size prevented the enhanced ion penetration due to applied voltage. This study analyses the long-term stability of structural steel samples in marine environments by accelerating the corrosion rate by an applied external DC voltage.

Low temperature atomic layer deposition of PbO2 for electrochemical applications

A low temperature atomic layer deposition (ALD) process for PbO2was developed using bis(1-dimethylamino-2-methyl-2-propanolate)lead(II), Pb(DMAMP)2, and O3as the reactants, with a high growth rate of 2.6 Å/cycle. PbO2readily reduces under low oxygen partial pressures at moderate temperatures making it challenging to deposit ALD PbO2from Pb2+precursors. However, thin films deposited with this process showed small crystalline grains of α-PbO2and β-PbO2, without signs of reduced PbOxphases. The ALD PbO2thin films show the high electrical conductivity characteristic of bulk PbO2. In situ measurements of ALD PbO2film conductivity during growth suggest a reaction mechanism by which sub-surface oxygen mobility contributes to the growth of resistive PbO or PbOxduring the Pb(DMAMP)2surface reaction step, which is only fully oxidized from Pb2+to Pb4+during the O3reaction step. These films were electrochemically reduced to PbSO4in H2SO4and then reoxidized to PbO2, demonstrating their suitability for use as an electrode material for fundamental battery research and other electrochemical applications.

What causes the ultraviolet extinction bump at the cosmic dawn?

Abstract The enigmatic ultraviolet (UV) extinction bump at 2175 Å, the strongest spectroscopic absorption feature superimposed on the interstellar extinction curve, has recently been detected at the cosmic dawn by the James Webb Space Telescope (JWST) in JADES-GS-z6-0, a distant galaxy at redshift z ≈ 6.71, corresponding to a cosmic age of just 800 million years after the Big Bang. Although small graphite grains have historically long been suggested as the carrier of the 2175 Å extinction bump and graphite grains are expected to have already been pervasive in the early Universe, in this work we demonstrate that small graphite grains are not responsible for the UV extinction bump seen at the cosmic dawn in JADES-GS-z6-0, as the extinction bump arising from small graphite grains is too broad and peaks at wavelengths that are too short to be consistent with what is seen in JADES-GS-z6-0.

Self-powered γ-In2Se3/p-Si heterojunction for photodetection: exploring humidity and light intensity dependent photoresponse

In this study, high-quality γ-In2Se3 thin films were successfully deposited on p-Si substrates via the RF sputtering technique. Structural characterization using XRD and Raman spectroscopy confirmed the formation of the hexagonal γ-phase of In2Se3 film. FESEM analysis revealed the presence of small, homogeneous, and well-defined grains in the prepared γ-In2Se3 film. EDS analysis confirmed the stoichiometric composition (∼ 2:3) of the In2Se3 films. XPS further validated the presence of In, Se, and Si elements in the deposited films. Band gap analysis using UV-visible spectroscopy yielded a value of 1.96 eV for the γ-In2Se3 film. Integration of γ-In2Se3 with p-type Si enhanced photoresponsivity of 47.9 mA/W, photosensitivity of 282, and photo detectivity of 8.45 × 1010 Jones. The self-powered γ-In2Se3/p-Si heterojunction-based photodetector exhibited rapid rise time attributed to the type II band alignment structure, facilitating efficient electron-hole pair separation and minimizing recombination. Furthermore, humidity and light intensity-dependent photodetector properties of γ-In2Se3/p-Si heterojunction photodetector were also investigated. An increase in photocurrent from 271 to 291 µA was observed with rising humidity levels, indicating the device’s sensitivity to humidity variations. Furthermore, light intensity dependence studies revealed a linear relationship between photocurrent and incident light intensity, demonstrating the device’s reliable response across various illumination levels.

Evolution of microstructure and tensile behavior in an interstitial strengthened high entropy alloy

The microstructural evolution and mechanical properties of Fe61.5Cr17.5Ni11.5Al8C1.5 high-entropy alloys (HEAs) were investigated to establish an optimal set of annealing conditions that would result in reasonable recrystallized fractions across the different temperatures and durations. The evolution of the microstructure was analyzed, tracking the transformation from the rolling texture to the recrystallization texture, as well as any phase transformations that occurred. The grain size distribution, overall microstructural features, and the effects of annealing temperature and time on the tensile properties of the HEAs were examined and discussed. The alloy was subjected to cold rolling and subsequent annealing treatments, revealing a single FCC phase after homogenization at 1260 °C. The cold-rolled samples retained the FCC structure at lower annealing temperatures (400 °C and 500 °C) but underwent a phase transformation to BCC at higher temperatures (600 °C to 900 °C). Microstructural characterization demonstrated that cold rolling introduced a high density of dislocations, while annealing facilitated recrystallization and grain growth. The tensile tests indicated that HEA samples exhibited a yield strength of 570 MPa and ductility of ∼36 % with large grain size after a long annealing at elevated temperature. In contrast, after being heat-treated at 1200 °C for 2 min, HEAs restrict FCC-to-BCC phase transformation and exhibit small grain size (3.2 µm) with M23C6-like carbide precipitation in the FCC matrix. Smaller grains provide additional boundaries, which restrict dislocations to bypass these boundaries. While carbide precipitates at grain boundaries and inside grains, it strengthens the material by pinning grain boundaries and restricting dislocation movement, resulting in a yield strength of 610 MPa and ductility of ∼41 %.

Natural variation in the promoter of qRBG1/OsBZR5 underlies enhanced rice yield

Seed size, a key determinant of rice yield, is regulated by brassinosteroid (BR); however, the BR pathway in rice has not been fully elucidated. Here, we report the cloning and characterization of the quantitative trait locus Rice Big Grain 1 (qRBG1) from single-segment substitution line Z499. Our data show that qRBG1Z is an unselected rare promoter variation that reduces qRBG1 expression to increase cell number and size, resulting in larger grains, whereas qRBG1 overexpression causes smaller grains in recipient Nipponbare. We demonstrate that qRBG1 encodes a non-canonical BES1 (Bri1-EMS-Suppressor1)/BZR1(Brassinazole-Resistant1) family member, OsBZR5, that regulates grain size upon phosphorylation by OsGSK2 (GSK3-like Kinase2) and binding to D2 (DWARF2) and OFP1 (Ovate-Family-Protein1) promoters. qRBG1 interacts with OsBZR1 to synergistically repress D2, and to antagonistically mediate OFP1 for grain size. Our results reveal a regulatory network controlling grain size via OsGSK2–qRBG1–OsBZR1–D2–OFP1 module, providing a target for improving rice yield.

The influence of the weighted average diameter of the ball on the particle size of the final product

Objective. Currently, cement is crushed in mills to a specific surface area of 2500-3000 and 3500-4500 cm2/g or more. Further grinding of clinker sharply worsens the properties of the resulting product. The relevance of the topic is due to the increased interest in reducing material and energy costs in the process of clinker grinding. The purpose of the work is to study the effect of different assortment of grinding media and weighted average ball diameter on the particle size of the final product, performing particle size analysis by particle diffraction. Method. To obtain reliable experimental data, a specially developed model of the grinding unit was used. Analysis of particle size by diffraction or spatial distribution (scattering spectrum) of scattered light was carried out using a laser analyzer. Result. A research methodology has been developed that meets the modern capabilities of experimental technology. Experimental studies have been conducted on clinker grinding in a laboratory mill. The combined effect of different assortments of grinding bodies and the average weighted diameter of the ball on the particle size of the final product has been determined. Conclusion. Studies of the curves of the final product obtained using different weighted average ball diameters have shown that large impact energy is not required to grind small grains; the diameter of the grinding bodies should decrease as the grain size of the material decreases. Therefore, the balls must have a minimum diameter, but sufficient to destroy the particles of the material.

The role of Teff crop in Ethiopian life: consumption and contribution to rural livelihoods

Teff (Eragrostis tef) is believed to be the smallest grain in the world. It is the most important crop in Ethiopia in terms of production and consumption. Smallholder farmers produce Teff, and it is the main source of income for farmers in comparison to other cereal crops. Teff is the daily staple food for over 50 million Ethiopians. There is a need for information on agricultural consumption, disaggregated at district level, to support evidence-based decision-making at local level. The objective of this paper is to understand the consumption of Teff among rural smallholder producers at district level and assess the position of Teff among cereals in the lives of Ethiopian rural farmers. The study employed a multistage sampling technique to select the top Teff producing regions, districts, and kebeles (small administrative units) and collected primary data through focus group discussions (FGDs), key informants, and questionnaire respondents. The survey collected qualitative and quantitative data from 357 households. FGD, key informant interview (KII) participants and survey respondents were drawn from the same areas where the survey was conducted. The quantitative and qualitative data were subjected to statistical and content analysis respectively. The study findings revealed that on average households consume 26.92% of their Teff production per year. Moreover, there is a shift in the consumption of Teff which might be due to improved standards of living among the farmers, a health-conscious community, and improved income from Teff sales. Although Teff is a staple grain in Ethiopia, there is a statistically significant variation in Teff consumption among districts.

Does long-term radiation exposure in Chornobyl impact the reproductive structures of Nuphar lutea (Linné) Smith?

The 1986 Chornobyl Nuclear Power Plant accident caused radioactive contamination of water bodies within the Pripyat River floodplain, resulting in the accumulation of radionuclides by macrophytes, which are fundamental species in water ecosystems. Yellow water lily Nuphar lutea (L.) Smith., a macrophyte playing a significant role in the formation of vegetation cover in aquatic ecosystems, is commonly considered as a bioindicator of water pollution. In this study, we investigate the potential of N. lutea as an indicator of radionuclide contamination in water bodies, particularly through changes in its reproductive structures, such as pollen viability, morphology of pollen grains, seeds, and fruits. Our findings reveal that pollen viability remains stable at total absorbed dose rates below 14.4 μGy/h, with only 1–4% of sterile grains. However, beyond this threshold the percentage of sterile grains increases nearly fivefold, pointing to high internal plant exposure to 90Sr. A similar trend was observed in the allometry and size of pollen grains, where small and flattened grains are formed in the reservoir with the highest external radiation dose rate (≥14.4 μGy/h). On the other hand, while morphometric parameters of fruits are influenced by radiation, their variation appears to be the result of a combination of physicochemical factors and the trophic status of a water body. Our research highlights the adverse impact of long-term radiation exposure on the male reproductive system of N. lutea and shows the potential of using the pollen grains sterility as an indicators of heavily radionuclide-contaminated water bodies. Additionally, we observed gradual changes in a pollen allometric length-to-width coefficient as the radiation dose level increases.

Relaxation behaviour, conductive grains and resistive boundaries of bismuth-based double perovskite Bi2-xLaₓFeGaO₆

The successful synthesis of the ceramic Bi2-xLaxFeGaO6 powder ceramic sample with varying La content (x = 0.01, 0.03, 0.07, 0.10) were synthesized via the solid-state method. Analysis using X-ray diffraction at room temperature was carried out to examine its structure, revealing a crystallite size of approximately 22.07–50.84 nm. This size indicates the potential applications in microwave technology due to its small grain size, which has the capability to enhance microwave absorption properties. The dielectric constant of the material shows an increase with the frequency applied, in accordance with the behaviour anticipated by the dielectric HN model and Debye model. This model proposes that the material's dielectric response can be manipulated by modifying the applied frequency, making it a valuable tool in the material design for specific purposes. The full width at half maximum (FWHM) curve of the electrical modulus displayed variability, suggesting the existence of a non-Debye relaxation mechanism in the material. This indicates that the material could possess distinct electrical properties that might be beneficial for certain applications. The outcomes demonstrated a negative temperature coefficient resistance (NTCR), indicating a decrease in the material's resistance with increasing temperature. Such behaviour can be advantageous in situations where temperature variations require monitoring or regulation. The Cole-Cole plot illustrated that the grains exhibit conductive behaviour at lower frequencies, a crucial insight for comprehending the material's electrical properties. In conclusion, these results indicate that the ceramic Bi2-xLaxFeGaO6 for x = 0.01, 0.03, 0.07, 0.1) showcases promising attributes for various applications, particularly in microwave technology and electrical conductivity.

Predictive mechanical property and fracture behavior in high-carbon steel containing high-density carbides via artificial RVE modeling

The mechanical properties and fracture behavior of high-carbon steel are closely related to the microstructural characteristics. This work developed the artificial representative volume element (RVE) model to explore the effects of microstructural characteristics on mechanical properties and fracture behavior of high-carbon steel containing high-density carbides under uniaxial tension. A series of RVEs with different ferrite grain sizes, particle volume fractions, and particle sizes were generated based on the RSA algorithms. The mechanism-based plasticity model and the three uncoupled damage models were implemented into the RVE modeling. The model parameters were calibrated by the corresponding simulation between in-situ μ DIC and microstructure-based RVE simulation. The predicted mechanical properties and fracture strain from the RVE simulation were in good agreement with the experimental results. Simulated results from a series of RVEs quantified the effects of ferrite grain sizes, particle volume fractions, and particle sizes on strength, elongation, and damage evolution of high-carbon steel containing high-density carbides: strength increases with increasing particle volume fraction while elongation decreases, as well as excessively large or small grain and particle size were not favored to improve elongation. These results were attributed to the damage and internal stress partition.