Individual Grain Size Research Articles

Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost that is associated with their generation. We propose a novel approach to generate APDs with prescribed statistical properties, including fine control over the size of individual grains. To this end, we rely on fast optimal transport algorithms that stream well on Graphics Processing Units (GPU) and handle non-uniform, anisotropic distance functions. This allows us to find large APDs that best fit experimental data and generate synthetic high-resolution microstructures in (tens of) seconds. This unlocks their use for computational homogenisation, which is especially relevant to machine learning methods that require the generation of large collections of representative microstructures as training data. The paper is accompanied by a Python library, PyAPD, which is freely available at: www.github.com/mbuze/PyAPD.

Development and testing of the MicroMED sensor: From BreadBoard model to flight model

Suspended dust plays a critical role in regulating the Martian climate by influencing the atmospheric thermal gradient, altering the amount of infrared and visible energy absorbed and scattered by the atmosphere, and acting as condensation nuclei for CO2 ice-clouds particles. There are many well demonstrated, dust-related effects on martian climate which depend on dustsize, concentration, chemical and bulk composition. Currently, an accurate estimation of these parameters is lacking as they are derived from indirect measurement of the optical depth acquired from the surface and orbital data. These indirect measurements require a priori assumptions on the grain distribution curve and are hence subject to possible biases. To overcome these limitations, an optical particles counter called MicroMED has been developed under the National Institute of Astrophysics (INAF) leadership. MicroMED can measure the sizes of individual dust grains in a specific volume of air thus providing the grain size distribution and concentration. MicroMED has been selected to join the Dust Complex payload on board the ExoMars 2022. The Flight Model of the instrument has been developed and optimized starting from two prototype BreadBoard versions. Here we present the sub-systems that constitute MicroMED and their testing and characterization process, performed using the Breadboard models. We discuss the optimizations and improvements introduced on the basis of the prototype results and the overall performances of the final design.

MAGNETOTHERMAL PROPERTIES OF COPPER FERRITE

In this work, we carried out the directed synthesis of copper ferrite (CuFe2O4) by co-precipitation from solutions with an excess of alkali at a temperature of 373 К. The methods of scanning electron microscopy and X-ray phase analysis were used to study the crystal structure and surface morphology of copper ferrite. The ratio of the characteristic peaks of the diffractogram was carried out in accordance with the JCPDS database. It is shown that copper (II) ferrite crystallizes in the structure of the cubic spinel. Microphotographs of the synthesized copper ferrite samples at different magnifications are given. It is established that ferrite particles consist of conglomerates of crystals with different sizes of individual grains. Their small scatter in size is observed. The average particle size is in the range of 100-200 nm. Using a dynamic heat flux differential scanning calorimeter, the temperature dependence of the heat capacity of copper ferrite samples was obtained in the temperature range of 273–373 K. Using an original microcalorimetric setup in the temperature range of 288–346 K and with a change in the magnetic field induction from 0 to 1.0 T, thermodynamic characteristics were obtained - the magnetocaloric effect (MCE) and the change in entropy (ΔS) during the magnetization of copper (II) ferrite. It was found that with an increase in the magnitude of the magnetic field, the magnitude of the MCE increases and decreases with increasing temperature. It was found that the temperature dependences of the magnetocaloric effect and specific heat have an extreme character. In the region of room temperatures (308–315 K), a maximum of the magnetocaloric effect and a minimum of the specific heat are observed. This previously unknown anomalous behavior of the magneto-thermal properties of copper II ferrite was discovered for the first time.

The investigation of additive manufacturing and moldable materials to produce railway ballast grain analogs

The size and shape of individual grains, play an important role in the mechanical behavior of granular materials such as the strength and stability of railway ballast. The aim of this research is to study materials from which uniform, reproducible grains with irregular convex geometry can be created by molding and additive manufacturing technologies in order to create reproducible artificial assemblies that can be used in experiments. Packings with determined grain shape results more controlled investigations contrarily to using natural grains with random geometry. Specimens were made from railway ballast materials, materials used in the construction industry, additively manufactured and molded polymers, and certain low-strength materials. Uniaxial compression and bending tests were conducted on these specimens. The mechanical properties of typical railway ballast materials (basalt and andesite) were compared with the properties of artificially produced materials. The results show that for grain reproduction the molding technology is recommended with the use of polyester-crushed stone composite and ceramic powder. Furthermore, the additive manufacturing was recommended with PolyJet or Multi Jet Fusion technology as they have the feasibility to produce grains with similar material properties to the properties of basalt and andesite.

Determining the influence of ultra-dispersed aluminum nitride impurities on the structure and physical-mechanical properties of tool ceramics

This paper considers features related to manufacturing the chromium oxide-based tool material. The process involved ultra-dispersed powders made of aluminum nitride. It has been established that the destruction of chromium oxide at high sintering temperatures is prevented through the reaction sintering of chromium oxide (Cr2O3) and aluminum nitride (AlN). It was established that the structure of the composite depends both on the temperature and the duration of hot pressing. Thermodynamic calculations of the interaction between Cr2O3 and AlN showed that this interaction begins at a temperature of 1,300 °C. In contrast to hot pressing in the air, no СrN and Сr2N compounds were formed in a vacuum. With increasing temperature, the content of Al2O3 in solid solution becomes maximum at a temperature of 1,700 °C in the case of hot pressing in the air while in vacuum the content of Al2O3 remains unchanged within the entire temperature range of 1,300–1,700 °C. When increasing the time of hot pressing to 30 minutes, the size of individual grains reaches 10 μm. It has been shown that in the sintering process involving Cr2O3 and AlN, the plasma-chemical synthesis produces the solid solution (Cr, Al)2O3 at the interphase boundary, which improves the mechanical properties of the material. The influence exerted on the quality of the machined surface of tempered hard steel when machining by the devised tool material based on chromium oxide with an optimal admixture of 15 wt % of ultra-dispersed aluminum nitride powder was investigated. It was determined that the quality of the machined hard steel surface improved compared to standard imported tool plates. It was established that the resulting tool material, in addition to relatively high strength and crack resistance, also demonstrates high thermal conductivity, which favorably affects the quality of the machined steel surface, given that lubricants and coolants are not used during the cutting process.

Petrogenesis of Kaapvaal lamproites (aka orangeites) constrained by the composition of olivine and similarities with kimberlites and other diamondiferous lamproites

Kaapvaal lamproites, also known as orangeites, are H2O-rich, diamondiferous, highly micaceous, ultrapotassic rocks. Olivines in kimberlites have been shown to be extremely useful in tracking melt evolution, highlighting the importance of the chemical effects of SCLM assimilation on asthenosphere-derived melts. Kaapvaal lamproites are derived from melting metasomatised SCLM and may be expected to form an endmember to the asthenosphere melt-SCLM trend defined by kimberlites. In this contribution, we use olivine composition in Kaapvaal lamproites to further understand melt evolution in the SCLM and assess the similarity between Kaapvaal lamproite, other diamondiferous lamproites, and kimberlite petrogenesis in cratonic regions.We present olivine composition for representative on- and off-craton Kaapvaal lamproites from Finsch and Melton Wold, respectively. Olivines from these Kaapvaal lamproites are characterized by distinct core and rim zones, regardless of the size of individual grains. Polycrystalline grains are abundant at Finsch but relatively rare at Melton Wold. The olivine cores from both occurrences are predominantly Mg-rich (Fo>89) whereas Fe-rich cores (Fo<89) are rare. Mg-rich cores are interpreted to be derived from the disaggregation of mantle peridotites, including sheared peridotites, whereas Fe-rich cores are derived from olivines of the Cr-poor megacryst suite. The average Fo and NiO concentrations of the Melton Wold cores are lower than Finsch cores, likely related to less refractory off-craton mantle. The olivine rims at Finsch and Melton Wold are characterized by reverse zoning with ranges of Fo89-92 and Fo90-91, respectively. The rims are interpreted to represent crystallisation related to a complex interplay between increasing oxidation, assimilation of orthopyroxene, and increasing alkali content of the melt during evolution.The average core and rim compositions of Finsch and Melton Wold, in conjunction with data from diamondiferous lamproites of other cratonic regions, define a broad positive correlation. Kaapvaal lamproites have Mg-rich core and rim compositions, similar to that of Lac de Gras kimberlites, and interpreted to reflect sampling and equilibration of low volume Kaapvaal lamproite melt with refractory mantle. In contrast to Lac de Gras kimberlites, Kaapvaal lamproites have high abundances of groundmass phlogopite that reflect metasomatic material in the SCLM source, likely present as veins within refractory peridotite. This suggests that increasing proportions of melt-metasomatised SCLM interactions are not always linked with increasing Fe content of melts.We show that the petrogenesis of Kaapvaal lamproites is similar to that of kimberlites and lamproites from other cratonic regions, however, the high abundance of phlogopite and Fo-rich olivine rims suggest a distinct metasomatic lithology in the source and that olivine composition; i.e., a proxy for melt composition, may be strongly controlled by melt volume during melt-SCLM interactions.

Non-destructive determination of phase, size, and strain of individual grains in polycrystalline photovoltaic materials

The non-destructive structural characterization of individual grains in thin-films photovoltaics based on polycrystalline materials is a powerful tool for revealing important details of the microstructure of solar cell absorbers. Here, we use three-dimensional X-ray diffraction (3DXRD) to obtain statistics on the phase, size, orientation and strain tensors of the grains, as well as their twin relations in Cu2ZnSnS4 (CZTS) absorbers. Moreover, this powerful approach allows the non-ambiguous determination of phases with distinct optical and electrical properties but similar lattice parameters, such as CZTS and ZnS. Our analysis over cumulative statistics of nearly 600 grains in polycrystalline CZTS reveals that a fraction of 2.5% corresponds to the ZnS secondary phase. Statistics of the strain distribution in the polycrystalline CZTS layer indicate an average tensile stress in the plane of the film of ~70 MPa and a compressive stress along the normal to the film of ~145 MPa. We found that 41% of the total number of grains in CZTS absorbers are Σ3 twins. We calculate the frequency of the six types of Σ3 boundaries, revealing that the 180° rotation along the axis<221>is the most frequent. Accessing the microstructure opens the possibility to study its influence on the properties of the film, such as bandgap variations due to strain or the role of twin boundaries in the charge transport mechanisms.

Active Carbon-Based Nanomaterials in Food Packaging

Carbon-based nanomaterials (CBN) are currently used in many biomedical applications. The research includes optimization of single grain size and conglomerates of pure detonated nanodiamond (DND), modified nanodiamond particles and graphene oxide (GO) in order to compare their bactericidal activity against food pathogens. Measurement of grain size and zeta potential was performed using the Dynamic Light Scattering (DLS) method. Surface morphology was evaluated using a Scanning Electron Microscope (SEM) and confocal microscope. X-ray diffraction (XRD) was performed in order to confirm the crystallographic structure of detonation nanodiamond particles. Bacteriostatic tests were performed by evaluating the inhibition zone of pathogens in the presence of carbon based nanomaterials. Raman spectroscopy showed differences between the content of the diamond and graphite phases in diamond nanoparticles. Fluorescence microscopy and adenosine-5′-triphosphate (ATP) determination methods were used to assess the bactericidal of bioactive polymers obtained by modification of food wrapping film using various carbon-based nanomaterials. The results indicate differences in the sizes of individual grains and conglomerates of carbon nanomaterials within the same carbon allotropes depending on surface modification. The bactericidal properties depend on the allotropic form of carbon and the type of surface modification. Depending on the grain size of carbon-based materials, surface modification, the content of the diamond and graphite phases, surface of carbon-based nanomaterials film formation shows more or less intense bactericidal properties and differentiated adhesion of bacterial biofilms to food films modified with carbon nanostructures.

Three-Dimensional Characterization of Morphology and Crystallography of a Gold Nanoisland Film

The morphological and crystallographic characteristics of noble metal nanoisland films play an important role in determining their properties, performance, and reliability. In this work we have applied a rapid three-dimensional orientation mapping technique in the transmission electron microscope (3D-OMiTEM) in the characterization of a gold nanoisland film. A volume of 200×1024×1024 nm3 has been analyzed, generating a 3D orientation map composed of more than 500 nanoislands and 7000 grains constituting the islands. The 3D shapes and sizes of individual islands and grains have been analyzed, revealing their true 3D morphological features and the correlation between the number of grains within individual islands and the size of the islands. The crystallographic orientations of the grains and the misorientations across the grain boundaries have been quantified, revealing a weak texture but a preferential presence of Σ3 and Σ9 grain boundaries in the gold nanoisland film.

Ozone dose-response relationships for tropical crops reveal potential threat to legume and wheat production, but not to millets

The tropical-grown crops common bean (Phaseolus vulgaris), mung bean (Vigna radiate), cowpea (Vigna unguiculata), pearl millet (Pennisetum glaucum), finger millet (Eleusine coracana), amaranth (Amaranthus hypochonriacus), sorghum (Sorghum bicolour) and wheat (Triticum aestivum) were exposed to different concentrations of the air pollutant ozone in experimental Solardome facilities. The plants were exposed to ozone treatments for between one and four months, depending on the species. There was a large decrease in yield of protein-rich beans and cowpeas with increasing ozone exposure, partly attributable to a reduction in individual bean/pea weight. Size of individual grains was also reduced with increasing ozone for African varieties of wheat. In contrast, the yield of amaranth, pearl millet and finger millet (all C4 species) was not sensitive to increasing ozone concentrations and there was some evidence of an increase in weight of individual seedheads with increasing ozone for finger millet. Sorghum did not reach yield, but was not sensitive to ozone based on changes in biomass. Dose-response relationships for these crop species demonstrate that tropospheric ozone pollution could reduce yield of important crops, particularly legumes, in tropical regions such as sub-Saharan Africa.

Wheat individual grain-size variance originates from crop development and from specific genetic determinism.

Wheat grain yield is usually decomposed in the yield components: number of spikes / m2, number of grains / spike, number of grains / m2 and thousand kernel weight (TKW). These are correlated one with another due to yield component compensation. Under optimal conditions, the number of grains per m2 has been identified as the main determinant of yield. However, with increasing occurrences of post-flowering abiotic stress associated with climate change, TKW may become severely limiting and hence a target for breeding. TKW is usually studied at the plot scale as it represents the average mass of a grain. However, this view disregards the large intra-genotypic variance of individual grain mass and its effect on TKW. The aim of this study is to investigate the determinism of the variance of individual grain size. We measured yield components and individual grain size variances of two large genetic wheat panels grown in two environments. We also carried out a genome-wide association study using a dense SNPs array. We show that the variance of individual grain size partly originates from the pre-flowering components of grain yield; in particular it is driven by canopy structure via its negative correlation with the number of spikes per m2. But the variance of final grain size also has a specific genetic basis. The genome-wide analysis revealed the existence of QTL with strong effects on the variance of individual grain size, independently from the other yield components. Finally, our results reveal some interesting drivers for manipulating individual grain size variance either through canopy structure or through specific chromosomal regions.

Variation in Crystallographic Orientation and Twinning Activation with Size of Individual Grains in Rolled Magnesium Alloy

This study demonstrates that the size of an individual grain in a rolled AZ31 alloy is significantly related to the crystallographic orientation of the grain and the area fraction of the {10–12} twinned region formed in the grain after compression along the rolling direction. With an increase in the size of an individual grain from 11 μm to 80 μm, the angle between the c-axis of the grain and the normal direction of rolling plane decreases from 38° to 5.5° and the Schmid factor for {10–12} twinning of the grain increases from 0.29 to 0.5. As a result, the area fraction of the twinned region formed in the grain increases from 30% to 100% owing to the combined effect of an increase in the Schmid factor value and a decrease in the stress required for activation of twinning by the increased grain size. The grain size (GS), Schmid factor for {10–12} twinning (SFtwin), and twin fraction (TF) have the relation TF/SFtwin = 109.8 + 1.45GS.

MICROANALYSIS OF ELECTROSPARK COATINGS BASED ON ELECTROEROSION POWDERS

The development of modern engineering requires improvement of quality, reliability and durability of parts, assemblies and mechanisms. One of the efficient ways to solve these problems is to applyf functional coatings obtained by the method of electric-spark alloying (ESA). Main electrode materials are mostly sintered hard alloys, which cost due to expensive tungsten in them is relatively high. To solve this problem, a VK8 (90%) hard alloy powder (as a main part) and 10% of high speed steel powder, Gr. R6M5 are proposed to be used as an electrode material. One of the promising methods to produce powders from almost any conductive material, including hard alloy and high speed steel wastes, is the method of electroerosion dispersion (EED), characterized by relatively low energy costs and an environmentally friendly process. The aim of this work is to perform a microanalysis of a steel 30KHGSA section substrate and electrospark coating obtained by electrospark alloying by UR-121 using electrodes of a mixture of electroerosion powders VK8 (90%)+R6M5 (10%), obtained by electroerosion dispersion of hard alloy and high speed steel wastes in illuminating kerosene. To obtain a micro and nano powder of hard alloy and high speed steel wastes a unit for electric erosion dispersing of conductive materials was used. Microanalysis was performed by means of an inverted optical microscope OLYMPUS GX51. The microanalysis allowed us to determine the shape and size of individual grains and their relative positions to identify the presence of inclusions and microdefects and to judge on the properties of the substrate (30KHGSA) and the coating (VK8+R6M5).

Evaluation of fat grains in gothaj sausage using image analysis

Fat is an irreplacable ingredient in the production of sausages and it determines the appearance of the resulting cut to a significant extent. When shopping, consumers choose a traditional product mostly according to its appearance, based onwhat they are used to. Chemical analysis is capable to determine the total fat content in the product, but it cannot accurately describe the shape and size of fat grains which the consumer observes when looking at the product. The size of fat grains considered acceptable by consumers can be determined using sensory analysis or image analysis. In recent years, image analysis has become widely used when examining meat and meat products. Compared to the human eye, image analysis using a computer system is highly effective, since a correctly adjusted computer program is able to evaluate results with lower error rate. The most commonly monitored parameter in meat products is the aforementioned fat. The fat is located in the cut surface of the product in the form of dispersed particles which can be fairly reliably identified based on color differences in the individual parts of the product matrix. The size of the fat grains depends on the input raw material used as well as on the production technology. The present article describes the application of image analysis when evaluating fat grains in the appearance of cut of the Gothaj sausage whose sensory requirements are set by Czech legislation, namely by Decree No. 326/2001 Coll., as amended. The paper evaluates the size of fat mosaic grains in Gothaj sausages from different manufacturers. Fat grains were divided into ten size classes according to various size limits; specifically, 0.25, 0.5, 0.75, 1.0, 1.5, 2.0, 2.5, 5.0, 8.0 and over 8 mm. The upper limit of up to 8 mm in diameter was chosen based on the limit for the size of individual fat grains set by the legislation. This upper limit was not exceeded by any of the products. On the other side the mosaic had the hightest representation of 0.25 mm fat grains.

The Shape and Structure of Titanium Dioxide Nanoparticles

Paper deals with problems of nanoparticles and nanomaterials applied in technical practice. In this time, we are looking for and examining ways of their best properties utilization. When being applied on the base material (metal, plastic, glass, incl. paper, cloth, etc.) In the form of very thin layer, then the base material can obtain very different properties, mostly advantageous, including improvement of their mechanical properties. To obtain these properties, it is necessary to apply nanomaterials in the form of very thin layer and for this purpose we need extremely fine granular nanoparticles that can be produced by means of fine milling technology. Resulting size, structure and shape of individual particles grains have the deciding influence on the successful application of these nanomaterials layers.

Polycrystalline diamond aggregates from the Mir kimberlite pipe, Yakutia: Evidence for mantle metasomatism

Polycrystalline diamond aggregates (boart, framesites, diamondites) have been widely studied but their origin is poorly understood. We report the results of a study in situ of two polished fragments of fine-grained (40–400μm size of individual diamond grains) dense polycrystalline diamond aggregates from the Mir pipe containing visible multiple interstitial garnet inclusions. They were analyzed for major and trace elements of inclusions and one of them — for δ13C and N abundance and isotopic composition of host diamonds. These aggregates are classified as variety IX by Orlov (1977). No cavities were observed in these samples. Sixty two irregular garnet grains and one clinopyroxene inclusion were detected and analyzed in sample Mr 832. Garnets are homogeneous within single grains but variable in Mg# [100Mg/(Mg+Fe)] from 60 up to 87 and CaO contents (3.3–5.3wt.%) among grains with a trend to negative correlation. Low Cr (550–640ppm) confirms eclogitic (E-type) paragenesis. High Na2O contents (5.2wt.%) of a single pyroxene inclusion are additional evidence of eclogitic nature of this sample. Wide variations in trace elements (ppm) are characteristic for garnet grains: Sr (2.7–25.6), Y (9.7–14.1), Zr (15.6–38.7) and positive Eu anomaly is present. The δ13C of diamonds within studied sample is variable (−6.4÷−9.8 ‰) as well as N abundance (75–1150ppm) and δ15N −27, −38, −58 ‰. The second peridotitic (U/P-type) sample Mr 838 contains eight inclusions of Mg-rich Cr-pyropes (Mg# ~85, Cr2O3 3.2–3.4wt.%) and magnesite inclusion with 4.35wt.% FeO and 1.73wt.% CaO. Trace element content in pyropes is relatively uniform (ppm): Sr (0.4–1.6), Y (13.2–13.4) and Zr (13.0). We conclude that heterogeneous distribution of the trace elements among garnet grains in Mr 832 and magnesite presence in Mr 838 are indicative of the effects of mantle metasomatism and rapid crystallization shortly before the eruption of the kimberlite.

Yield increase: GRFs provide the key

Three independent genetic studies reveal that the GRF–miR396 module regulates rice grain yield by controlling the number of spikelets or the size of individual grains. These findings provide promising targets for significantly increasing crop yield.

Grain-Size Based Additivity Models for Scaling Multi-rate Uranyl Surface Complexation in Subsurface Sediments

The additivity model assumed that field-scale reaction properties in a sediment including surface area, reactive site concentration, and reaction rate can be predicted from field-scale grain-size distribution by linearly adding reaction properties estimated in laboratory for individual grain-size fractions. This study evaluated the additivity model in scaling mass transfer-limited, multi-rate uranyl (U(VI)) surface complexation reactions in a contaminated sediment. Experimental data of rate-limited U(VI) desorption in a stirred flow-cell reactor were used to estimate the statistical properties of the rate constants for individual grain-size fractions, which were then used to predict rate-limited U(VI) desorption in the composite sediment. The result indicated that the additivity model with respect to the rate of U(VI) desorption provided a good prediction of U(VI) desorption in the composite sediment. However, the rate constants were not directly scalable using the additivity model. An approximate additivity model for directly scaling rate constants was subsequently proposed and evaluated. The result found that the approximate model provided a good prediction of the experimental results within statistical uncertainty. This study also found that a gravel-size fraction (2 to 8 mm), which is often ignored in modeling U(VI) sorption and desorption, is statistically significant to the U(VI) desorption in the sediment.

Snow stratigraphic heterogeneity within ground‐based passive microwave radiometer footprints: Implications for emission modeling

Two-dimensional measurements of snowpack properties (stratigraphic layering, density, grain size, and temperature) were used as inputs to the multilayer Helsinki University of Technology (HUT) microwave emission model at a centimeter-scale horizontal resolution, across a 4.5 m transect of ground-based passive microwave radiometer footprints near Churchill, Manitoba, Canada. Snowpack stratigraphy was complex (between six and eight layers) with only three layers extending continuously throughout the length of the transect. Distributions of one-dimensional simulations, accurately representing complex stratigraphic layering, were evaluated using measured brightness temperatures. Large biases (36 to 68 K) between simulated and measured brightness temperatures were minimized (−0.5 to 0.6 K), within measurement accuracy, through application of grain scaling factors (2.6 to 5.3) at different combinations of frequencies, polarizations, and model extinction coefficients. Grain scaling factors compensated for uncertainty relating optical specific surface area to HUT effective grain size inputs and quantified relative differences in scattering and absorption properties of various extinction coefficients. The HUT model required accurate representation of ice lenses, particularly at horizontal polarization, and large grain scaling factors highlighted the need to consider microstructure beyond the size of individual grains. As variability of extinction coefficients was strongly influenced by the proportion of large (hoar) grains in a vertical profile, it is important to consider simulations from distributions of one-dimensional profiles rather than single profiles, especially in sub-Arctic snowpacks where stratigraphic variability can be high. Model sensitivity experiments suggested that the level of error in field measurements and the new methodological framework used to apply them in a snow emission model were satisfactory. Layer amalgamation showed that a three-layer representation of snowpack stratigraphy reduced the bias of a one-layer representation by about 50%.

Measuring volume and density of a barley grain using ellipsoid approximation from a 2-D digital image

A digital imaging method was developed to determine the size, weight, volume and density of individual barley grains. Calibrations were developed using morphological measurements based on 2-D digital images, and were validated using a range of bulk barley samples. The validation of the grain diameter (minor) and grain weight algorithms gave high correlation coefficients ( r = 0.93 and 0.97, respectively, P < 0.01), with low standard errors (0.09 mm and 1.37 mg, respectively) when compared to physical measurements. Estimated grain volume and density from image data, using three different mathematical approaches were compared: Model 1, a general ellipsoid; Model 2, a combination of two cone frustums with an ellipse top and base; and Model 3, a set of elliptical cylinders representing pixels along the image length. Derived grain volume data using Model 2 when compared to gas displacement volume measurements gave significant correlations ( r = 0.97, P < 0.01) with the lowest standard error (0.97 mm 3), in contrast to volume data estimated using Model 1 and Model 3. Even though Model 2 gave accurate and precise results for grain volume, Model 1 (with the slope adjusted) gave the highest correlation ( r = 0.63, P < 0.01) with the lowest standard error (0.055 mg/mm 3) for estimating grain density from image data, compared to gas displacement density measurements.