Grain Size Research Articles

Prediction of the hot flow behavior of AISI 321 stainless steel during dynamic recrystallization using sine hyperbolic constitutive equation and artificial neural network

The hot compression deformation behavior of AISI 321 austenitic stainless steel were studied under the strain rate and temperature ranges of 0.001–1 s−1 and 950–1200°C. The single peak hot flow curves indicated the occurrence of dynamic recrystallization in AISI 321 steel at applied deformation conditions. The microstructural observations showing the development of equaxed austenite grains further approved the results of flow curve analysis. The average size of austenite grains, when deformation is carried out at strain rate of 1 s−1, increases from 8 μm at 950°C to 61 μm at deformation temperature of 1200°C. After microstructure analysis, the flow behavior of AISI 321 steel was modeled using sine-hyperbolic constitutive equation and feed-forward back propagation artificial neural network. The mean absolute error related to the predicted flow stress values at different strains with the sine-hyperbolic constitutive equation is more than 2, and this value is less than unity for the neural network method. The obtained results efficiently indicate that the ANN model is more accurate in predicting the flow behavior of AISI 321 austenitic stainless steel when the dynamic recrystallization is the prevailing softening mechanism.

New Estimate on the Spatial Distribution of the Youngest Toba Tuff Ash

ABSTRACTHere, we introduce a new estimate on the areal extent and volume of globally dispersed Youngest Toba Tuff ash by considering the decay of grain size and primary ash thickness (PAT). The areal extent of ash dispersal is modelled by interpolating the farthest sites in four directions. For this modelling, it is assumed that (i) PAT at the farthest newly identified site is equal to the maximum size of grains retrieved and (ii) the ash particles blanket the earth up to the farthest sites in a non‐discrete manner. The volume of ash‐fall is calculated using two approaches: (i) the Voronoi tessellation and (ii) a GIS‐aided mathematical calculation. When the Voronoi tessellation estimated a maximum and minimum volume of ash as 2089 and 1276 km3, the GIS‐aided mathematical calculation yielded 1573 and 1312 km3 of dense‐rock equivalent, respectively. Thus, the GIS method provided a more narrower range than the Voronoi method.

Influence of full-cycle heat treatment on microstructure and mechanical properties of CLF-1 steel

Based on the manufacturing requirements of tritium breeding blankets for fusion reactors, it is valuable to study the microstructure evolution and mechanical properties of CLF-1 steel, a candidate structural material, during the full-cycle heat treatment from profile to component. The full-cycle heat treatment includes isothermal annealing and multiple quenching and tempering treatments. Results indicate that multiple quenching and tempering treatments refine the size of prior austenite grains and reduce dislocation density and the width of lath martensite. With the increase in the number of quenching and tempering treatments, the CLF-1 steels exhibit a slight decrease in tensile strength while the impact toughness noticeably improves. Research has found that the effect of isothermal annealing treatment includes an increase in the size of the prior austenite grains and precipitates, as well as a change in the matrix from martensite to ferrite. As a result, the tensile strength and impact energy decrease sharply, while the ductility improves after isothermal annealing treatment. Subsequent quenching and tempering treatment can recover the microstructure and mechanical properties.

Design and control the selection of martensitic variant to simultaneously improve strength and toughness of low-carbon martensitic steel

In this paper, the microstructure evolution and mechanical properties of low carbon steels during direct quenched and rolling followed by water-cooled processes were studied. Two experimental steels, which were directly quenched at 900 °C (Q900) and 1000 °C (Q1000), were compared with steels that were water-cooled after rolling at the same temperatures (R900 and R1000). Microstructural analyses using EBSD and TEM revealed that rolling reduced the size of prior austenite grains (PAGs), resulting in an average width of 3.6 μm, which influenced grain boundary distributions and variant selection. The best combination of strength, ductility and toughness was obtained in R900 steel, including tensile (with the yield strength of 1304 MPa, the total elongation of 22.95 %), Charpy impact (with the impact energy at 20 °C is 182 J), and fracture toughness evaluations (with the J1c is 326.28 KJ/m2), this demonstrates that R900 steel exhibited significantly enhanced strength and ductility compared to Q900 steel. Moreover, EBSD analysis of crack propagation paths highlighted the role of high-angle grain boundaries (HAGBs) in enhancing fracture toughness by deflecting cracks. These findings underscore the critical role of PAGs size in tailoring microstructures to achieve superior mechanical properties in low carbon martensitic steels, offering insights for advanced material design and application in demanding structural and industrial contexts.Keyworks.low-carbon martensitic steel; strength and toughness; martensitic transformation; ductile-to-brittle transition phenomenon; selection of martensitic variants.

Bayesian statistical analysis reveals spatial heterogeneity in Cyclone Thane deposits from Southeast India

Modern and geological records of storm sedimentary deposits preserved on siliciclastic coastlines are important archives to evaluate the past and current magnitude and impacts of.storms. Examination of modern storm deposits also offers the opportunity to evaluate the similarities and differences between storm and other coastal overwash processes and hazards.We examined the stratigraphy and sedimentary characteristics of the 31st December 2012 Cyclone Thane and underlying coastal units from 14 pits from six sites from the coastal zone of Tamil Nadu Province, southeast India. We analysed the grain size parameters, grain shape, and heavy mineral proportions of each deposit in high resolution and examined the sedimentary structures of each unit. For the first time, we use Bayesian factors to quantitatively evaluate the similarities and differences between the storm sedimentary deposits and other co-located coastal sedimentary deposits. At several sites, the storm deposits differ in several parameters from the underlying coastal deposits, but at some locations, distinguishing between different depositional units cannot be achieved. In comparing the storm deposits from the different sites, mean grain size results in the most coherent pattern with closely located sites having similar mean grain size, and more southerly sites being finer grained. The other measured parameters show a far less coherent pattern with adjacent sites often preserving larger differences than more distal sites attesting to very local hydrodynamic variations during sediment deposition. As with the sedimentary parameters, the sedimentary structures formed during sediment deposition preserved at each site are highly variable. To date, the presence of terminal foresets at the landward edge of washover fans remains the only diagnostic feature of storm deposition, but that this feature is not ubiquitous across all storm deposits. Our findings demonstrate the spatially heterogeneous nature of storm sediment deposition and the challenges of identifying storm deposits in coastal siliciclastic sequences. The use of Bayesian statistical approaches also offers a robust method for evaluating and discriminating between coastal sediment deposits that has many advantages over traditional frequentist approaches. This method can easily be applied to other sedimentary depositional environments.

Diffusive shock acceleration of dust grains at supernova remnants

Diffusive shock acceleration (DSA) is a prominent mechanism for energizing charged particles up to very large rigidities at astrophysical collisionless shocks. In addition to ions and electrons, it has been proposed that interstellar dust grains could also be accelerated through diffusive shock acceleration; for instance, at supernova remnants (SNRs). Considering interstellar dust grains of various sizes and compositions, we investigate the possibility of grain acceleration at young SNR shocks (throughout the free expansion and Sedov-Taylor phases) and the maximum energies reached by the accelerated grains. We investigate the potential implications for the abundance of refractory species relative to volatile elements in the cosmic-ray composition. We rely on semi-analytical descriptions of particle acceleration at strong shocks, and on self-similar solutions for the dynamics of SNR shock waves. For simplicity, type Ia thermonuclear SNRs expanding in a uniform interstellar medium are considered. We find that the acceleration of dust grains at relativistic speed is possible, up to a Lorentz factor of $ $ and a kinetic energy of $E_ k nuc 10^2$ GeV/nuc for the smaller grains of size $a $ cm. We find that the subsequent sputtering of grains can produce nuclei with a sufficient rigidity to be injected in the process of diffusive shock acceleration. Such a scenario can help naturally account for the overabundance of refractory elements in the Galactic cosmic-ray composition, provided that a fraction, $ $, of dust grains swept up by an SNR are energized through DSA.

Effect of deformation nanostructuring on ion-beam erosion of metals

The effect of deformation nanostructuring of copper, nickel, and titanium on ion-induced morphology and sputtering under 30 keV argon ions high-fluence irradiation along the normal to the surface has been studied. Sputtering of a layer commensurate with the size of metal grains leads to a uniform cone-shaped relief, the stationary erosion of which occurs with significant redepositing of atoms.

High-temperature shrinkage compensation of cesium-based geopolymer: Synergistic effects of kyanite decomposition, ceramization and phase transformation

Cesium-based geopolymers and their ceramization product, pollucite, exhibit excellent heat resistance and considerable potential as engineering materials for high-temperature environments. However, the substantial shrinkage of cesium-based geopolymer during the ceramization process hinders its wide application. In this study, cesium-based geopolymer composites were prepared and evaluated on their shrinkage compensation, with the addition of reinforcing phases of kyanite or corundum. Compared with the sample with the addition of corundum, the linear shrinkage of the sample with the addition of kyanite after heat treatment at 1400 °C was reduced from 15.30 % to 6.28 %, showing a decrease by 54.89 % in linear shrinkage. There was no reaction between kyanite and geopolymer at room temperature, and the ceramization process of the cesium-based geopolymer was not altered either. The decomposition of kyanite at 1200–1400 °C during heat treatment produced mullite and silica, which expanded the volume by 18 %. This compensated for the shrinkage that occurred during the subsequent processes of ceramization and sintering of geopolymer. Mullite and silica further reacted with CsAlSiO4-ANA (having the same cubic ANA type zeolite framework as pollucite) to form corundum and pollucite (CsAlSi2O6) at 1300–1400 °C, during which the average size of pollucite grains increased from 1.82 μm to 4.34 μm, with an increase of 238.46 %. The reaction in this stage prevented the volatilization of cesium in the high temperature, and the increase of pollucite particle size reduced the shrinkage and porosity. This study cast the light on the design and preparation of low-shrinkage, ceramizable, geopolymer composites by synergistic effects of kyanite decomposition, ceramization and high-temperature phase transformation.

Exploring the Influence of TCO Thickness and Ag Addition on Performance of CIGS Thin Film Solar Cells for Bifacial and Tandem Configurations

Cu (In, Ga) Se2 (CIGS) thin-film solar cells have attracted a lot of interest in the field of renewable energy sources because of their beneficial features, which include low production costs, excellent efficiency, and suitability for tandem, semitransparent (or bifacial), and flexible cell applications. The advancement of transparent-conducting oxide (TCO) back contacts for CIGS solar cells shows potential for several applications but their low power conversion efficiency is still an issue. The spontaneous formation of GaOx at the interface between the TCO and CIGS layers has impeded the efficient extraction of photocarriers and promoted the generation of charge recombination events near this interface. To enhance their performance, this work focuses on improving the connection of CIGS onto In2O3:Sn (ITO) substrates for application in bifacial semi-transparent CIGS solar cells. Initially, layers of ITO (Ar/O2 flux ratio = 20:0) ranging in thickness from 80 to 320 nm were deposited on glass substrates. The results demonstrated that the optical bandgap Eg of the ITO layer varied as a function of its thickness, which was explained by the Burstein-Moss (B-M) shift phenomena. Compared to the 80 nm-thick ITO layer, the band gap of the 320 nm-thick ITO layer increased by 0.029 eV. The open-circuit voltage (Voc) of the corresponding ITO/CIGS solar cells experienced a rise of 0.023 V, attributed to the reduction in the Schottky barrier at the ITO/CIGS interface. The 200 nm ITO thickness was found to be the ideal thickness. It shows better performance than other ITO thicknesses, with lower series resistance and shunt conductance. Moreover, the study implemented an advanced supply of silver-promoted low-temperature (T453oC). This procedure resulted in enhanced quality of crystallinity within the absorber. Furthermore, our results indicate that the addition of Ag can enlarge the size of grains of CIGS. It also identifies Ag as an effective strategy for boosting the efficiency of CIGS solar cells. To compare the performance of Mo and TCO-based devices, CIGS solar cells were fabricated on both Mo and TCO back contacts. ITO back contacts were employed in CIGS devices, and their performance was comparable to that of traditional CIGS solar cells fabricated with a Mo back metal electrode. Without any post-deposition treatment or anti-reflective coatings, the resultant devices obtained a power conversion efficiency of 16.86% with Mo back contact and 15.97% with ITO back contact under simulated AM 1.5 illumination. These outcomes demonstrate the success of our strategy and have important origination for fabricating more efficient solar cells and a cleaner, more environmentally friendly energy future. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Ministry of Science and ICT (No. 2023R1A2C1007386) and by the DGIST R&D programs of the Ministry of Science and ICT (24-ET-01).

Surface Nanocrystallization and Improvement of the Mechanical and Tribological Properties of AISI 304 Steel Using Multi-Pass Nanostructuring Burnishing.

Owing to their high producibility and resistance to corrosion, austenitic chromium-nickel steels are widely used in the chemical, petroleum, and food industries. However, their significant disadvantage lies in their poor structural performance, which cannot be improved by heat treatment. This significantly limits the usability of these steels in parts of machines that operate under friction loads. Hardening can be achieved by decreasing the size of grains and applying deformation-induced martensitic transformation. Nanostructuring burnishing (NSB) may be one of the technologies suited for producing parts of tribological assemblies with enhanced operating characteristics. Nanostructuring burnishing using a sliding indenter is being developed as a method of industrial surface nanocrystallization through severe plastic deformation used in the mechanical machining of various types of parts. This article investigates the possibility of enhancing the mechanical and tribological properties of nanocrystallized surfaces of austenitic steels, which are formed through nanostructuring burnishing using a tool with a natural diamond spherical indenter and a change in sliding speed from 40 to 280 m/min with one, three, and five passes. Increasing the tool sliding speed makes surface nanostructuring machining of big parts highly effective. This paper aims to establish the influence exerted by the sliding speed and number of indenter passes on the formation of a nanocrystalline structure, as well as on the modification of microhardness and residual stresses, texture, and tribological properties of the surface layer in the nanostructuring burnishing of AISI 304 steel. Transmission microscopy and microdurometry, 3D-profilometry, and tribological tests of surfaces nanocrystallized with the "ball-on-disk" scheme with dry and lubricated friction established the optimal values of speed and number of passes for a spherical indenter in nanostructuring burnishing.

Growth of amorphous ice grains by sintering in a protoplanetary disk

An icy grain in a protoplanetary nebula mainly consists of amorphous H2O ice and can grow through the migration of H2O molecules (sintering). The growth rate through sintering strongly depends on the diffusion constant of H2O molecules. I estimated the size of amorphous ice grains as a function of the sintering duration based on the diffusion constant of amorphous ice determined by the molecular dynamics simulation. It has been found that the growth proceeds in a wide disk region (∼20AU), and grain can grow to ∼10−3cm around the snowline. The growth of the icy grains can affect the evolution of the icy dust aggregates in a protoplanetary disk.

How short-term temperature stresses affect leaf micromorphology and ultrastructure of mesophyll cells in winter rye Secale cereale L.

The effect of short-term high (+ 40 °C, 2 h) (HT) and positive low-temperature (+ 4 C, 2 h) (LT) stresses on leaf micromorphology and ultrastructure of mesophyll cells in winter rye was investigated. After HT, leaf blade relief became reticulate, while under control conditions and after low-temperature stress, leaf blade relief was folded. The ultrastructure of the leaf mesophyll cells of control plants was nominal: in the chloroplasts of regular lenticular shape, a well-developed thylakoid system immersed in a fine-grained stroma was clearly visible. Short-term HT caused the destruction of thylakoid membranes. A wave-like packing of granal thylakoids, a significant expansion of the lumenal spaces, and a disruption of the structural connection between the granal and stroma thylakoids were noted. There was an accumulation of lipid drops in the cytoplasm. LT stress caused intensive formation of plastoglobules, a decrease in the number and size of starch grains in the chloroplasts. Destruction of thylakoid membranes was not seen. After HT stress, the mitochondria noticeably "swelled", and the membranes of the cristae became less contrasting. After LT stress, significant changes occurred in the morphology of organelles: some of the mitochondria kept a round shape, but some acquired a lenticular or "dumbbell" shape. It was found that, depending on the type of temperature exposure, various adaptive programs are implemented in plant cells, which are accompanied by a complex of ultrastructural changes, thanks to which plants are able to successfully tolerate short-term exposure to stressful temperatures during active vegetation.

Exploring the influences of resource limitation and plant aging on pollen development in Azorella nivalis Phil. (Apiaceae), a long-lived high-Andean cushion plant.

Angiosperm pollen, the male gametophyte, plays a crucial role in facilitating fertilization by protecting and transporting male sperm cells to the female pistil. Despite their seemingly simple structure, pollen grains undergo intricate development to produce viable sperm cells capable of fertilizing the egg cell. Factors such as resource limitation and plant aging can disrupt normal pollen development and affect pollen performance. We investigated the influence of plant resources and aging on pollen developmental failure in Azorella nivalis Phil., an exceptionally long-lived high-Andean species that grows in a stressful alpine environment. Leveraging the modular nature of plants, we aimed to identify intra-individual sources of variation in pollen developmental failure. By using pollen viability and variation in viable pollen grain size as indicators of pollen developmental performance, we assessed whether proxies of plant resource availability and aging influenced these pollen traits at the inter-individual, inter-flower and intra-flower levels. Our findings revealed decreased pollen viability in putative resource-depleted flowers and in shoots that experienced higher levels of meristematic divisions from the zygote (i.e., greater cell depth). Additionally, we observed increased variability in the size of viable pollen grains in resource-depleted anthers. Our study suggests that resource availability and shoot aging are critical determinants shaping pollen development in long-lived plants at the intra-individual level. These findings contribute to our understanding of how differences in male fitness can arise in plants, with implications for their evolutionary trajectory.

Site-specific effects of fertilizer on hay and grain yields of oats: evidence from large-scale field experiments.

Oat (Avena sativa L.) is a valuable crop due to its strong adaptability to marginal environments, making it an important component of agricultural systems in regions where other cereals may not thrive. The application of chemical fertilizer can influence oat hay and grain yield significantly. However, large-scale meta-analytical studies of the size and variability of oat hay and grain yields in response to fertilizer addition are still lacking. Based on 83 studies worldwide, this meta-analysis quantifies the impact of the addition of fertilizer on oat hay and grain yields under varying environmental conditions (e.g., soil nutrient levels, texture, and climate). The results confirmed that the fertilizer application increased oat hay yield by 48.9% and grain yield by 36.2%. This study demonstrated that balanced fertilization with nitrogen, phosphorus, and potassium generally enhances oat hay and grain yield despite large temporal and spatial variations. Boosted regression tree (BRT) models suggest that changes in hay and grain yield were primarily dominated by soil pH and nitrogen fertilizer. The response ratio (the natural logarithm of the mean values of hay yield or grain yield with and without fertilization, respectively) of hay yield declined linearly with soil pH. Elevation was the second most important factor affecting the change in response ratio of hay yield and the third most important factor affecting the change in response ratio of grain yield but climatic conditions were not the dominant factors affecting changes in oat hay or grain yield. Overall, these results will benefit producers considering site-specific fertilization management of oat. They could increase yields and save investment in fertilizer, and help to facilitate the genetic breeding of oat varieties with high nutrient use efficiency. © 2024 The Author(s). Journal of the Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Effect of rare earth doping on structural, morphological, optical, and magnetic properties of the Y1-x(Gd, Dy)xBaCuFeO5 (x = 0.2, 0.4, 0.6, and 0.8) ceramics

The effect of the rare earth (RE) ion substitution on the structural, morphological, optical and magnetic properties of the Y1-xRExBaCuFeO5 (RE = Gd, Dy; x = 0.2, 0.4, 0.6, and 0.8) multiferroic compounds grown by the solid-state reaction is evaluated using X-ray diffraction (XRD), scanning electron microscopy (SEM), dispersive X-ray spectroscopy (EDX), reflectance spectroscopy techniques diffuse (UV–vis–NIR) and vibrating sample magnetometry (VSM). The results indicate that the RE substitution led to growth of single-phase materials, with a tetragonal structure and P4mm symmetry. The morphological analysis shows the formation of polycrystalline materials composed of grains of various shapes and sizes. Furthermore, the compositional analysis reveals that the materials do not present elements other than those used in the synthesis. The band gap (Eg) is tuned from 0.88 to 0.90 eV upon RE substitution. The magnetization curves obtained in the Zero-Field-Cooled/Field-Cooled (ZFC-FC) modes between 50 and 390 K, reveal a paramagnetic behavior, which could be attributed to the dominance exerted by the magnetic moments of the Gd/Dy ions.

Highly Productive Laser Annealing Manufacturing Method Using Continuous Blue WBC (Wavelength Beam Combining) Technique.

Blue laser annealing can be used to obtain a high-mobility thin-film transistor (TFT) through a laser annealing (i.e., LTPS: low-temperature Poly-Si) process. However, the laser annealing process's low productivity (as well as high cost) is an issue because the high output power of blue lasers still needs to be addressed. Therefore, productivity can be improved if blue laser energy is efficiently supplied during the laser annealing process using a continuous wave laser instead of a conventional pulsed excimer laser. We developed a blue laser light source (440 ± 10 nm) using the wavelength beam combining (WBC) method, which can achieve a laser power density of 73.7 kW/cm2. In this semiconductor laser, when the power was increased s by 2.9 times, the laser scanning speed was increased by 5.0 times, achieving twice the productivity of conventional lasers. After laser annealing, the size of the crystal grains varied between 2 and 15 μm, resulting in a crystallization rate of 100% by Raman scattering rsult and low resistivity of 0.04 Ωcm. This increase in production capacity is not an arithmetic increase with increased power but a geometric production progression.

Rapid preparation of Cu(111) foil with large single-crystal grains through a graphene induction and contactless annealing method

There is a growing interest in preparing large-size Cu(111) foil for achieving high performance in various applications. In this work, a simple two-step method using graphene induction and contactless annealing was designed to rapidly prepare Cu(111) foil with large single-crystal grains. The graphene film grown on the Cu surface in the first step by chemical vapor deposition serves as a template for the orientation transition of the Cu foil in a subsequent high-temperature annealing. The (111) orientation transformation of the entire Cu foil was achieved within 20 min with single-crystal grains in size of above 30 cm2, and the corresponding speed is ten times higher than that prepared in traditional annealing process. This work provides a facile and rapid fabrication approach for preparing Cu(111) foil with large grains.

Evaluation of high-entropy (Cr, Mn, Fe, Co, Ni)-oxide nanofibers and nanoparticles as passive fillers for solid composite electrolytes

Solid-state electrolytes (SSEs) could represent the key to solve safety issues of lithium-ion batteries (LIBs). Among them, those obtained by homogenously dispersing inorganic nanofillers into a polymer matrix combine advantages of all SSE typologies. In this work, high-entropy (Cr,Mn,Fe,Co,Ni) oxide (HEO) with different morphology (nanoparticles or nanofibers) are evaluated as passive fillers for the preparation of composite polyethylene oxide (PEO)-based SSEs. By varying their preparation conditions (calcination at 400 or 800°C for 0.5 or 2 h, followed by rapid cooling) different size and crystallization degree of the oxide grains are obtained. The results of the electrochemical testing of the PEO/HEO composites evidence the crucial role of the filler microstructure and morphology. The best results in terms of electrolyte resistance (22.5 Ω), electrochemical stability window (4.7 V), Li+ transference number (0.37) and ionic conductivity (3.0⋅10−4 S cm−1 at 65°C) are obtained by using well crystallized HEO nanofibers with highly defective surface. The suitability of the most promising composite for practical applications is validated by successfully using it in full cell with commercial high-voltage cathode materials.

Microstructural evolution and mechanical properties of the in situ La2O3 particle-reinforced titanium alloy prepared by dual-wire-arc directed energy deposition

TA15 titanium alloy components produced via wire-arc direct energy deposition (WA-DED) face challenges related to grain coarsening, suboptimal mechanical properties, and pronounced anisotropy. To address these issues, the current study employed a dual-wire-arc directed energy deposition (DWA-DED) approach to fabricating the alloys by introducing LaF3 quantitatively into the deposition metal using a metal cored wire. The incorporation of LaF3 was predicated on the in situ reaction: 6[O] + 6[H] + 2 LaF3 = La2O3 + 6HF. This reaction effectively removed [H] and [O] from the molten pool, diminishing the presence of the brittle intermetallic compounds and concurrently enhancing toughness. The addition of LaF3 resulted in a notable 56.8% increase in elongation and a 33.1% boost in impact toughness. Moreover, the DWA-DED quantitatively introduced [La], facilitating the precipitation of La2O3 particles. This precipitation reduced the size of primary columnar grains (PCGs) and promoted heterogeneous nucleation of α-laths. As a result, the elongation of the PCGs’ boundaries diversified the α phase transformation, resulting in the reduced multiple of uniform density (MUD) along the building direction. As a result, the isotropy ratio between vertical and horizontal directions also increased, underscoring the efficacy of LaF3 in mitigating anisotropic behaviour in WA-DEDed titanium alloys.

Fluid flow in three-dimensional porous systems shows power law scaling with Minkowski functionals

Integral geometry uses four geometric invariants—the Minkowski functionals—to characterize certain subsets of three-dimensional (3D) space. The question was, how is the fluid flow in a 3D porous system related to these invariants? In this work, we systematically study the dependency of permeability on the geometrical characteristics of two categories of 3D porous systems generated: (i) stochastic and (ii) deterministic. For the stochastic systems, we investigated both normal and lognormal size distribution of grains. For the deterministic porous systems, we checked for a cubic arrangement and a hexagonal arrangement of grains of equal size. Our studies reveal that for any three-dimensional porous system, ordered or disordered, permeability k follows a unique scaling relation with the Minkowski functionals: (a) volume of the pore space, (b) integral mean curvature, (c) Euler characteristic, and (d) critical cross-sectional area of the pore space. The cubic and the hexagonal symmetrical systems formed the upper and lower bounds of the scaling relations, respectively. The disordered systems lay between these bounds. Moreover, we propose a combinatoric F that weaves together the four Minkowski functionals and follows a power-law scaling with permeability. The scaling exponent is independent of particle size and distribution and has a universal value of 0.428 for 3D porous systems built of spherical grains.