Bimodal Grain Size Distribution Research Articles

Sediment-magnetic signature of land-use and drought as recorded in lake sediment from south-central Minnesota, USA

Sediment magnetic properties of a short core from Sharkey Lake, MN, record the effects of Euroamerican settlement and climate change over the last 150 yr. The onset of European-style farming led to increased erosion, reflected in high values of concentration-dependent parameters such as magnetic susceptibility (ĸ), Isothermal Remanent Magnetization (IRM), and Anhysteretic Remanent Magnetization (ARM). These high values are only partially due to increased supply of terrigenous material to the lake, and recent sediment contains an additional component of authigenic fine (single-domain) magnetite, most likely magnetosomes from magnetotactic bacteria. High organic productivity in the lake during the 1920s to 1940s drought increased this authigenic component resulting in highly magnetic fine-grained sediment. A comparison with older Holocene sediment from the same lake shows that, over time, most of the fine magnetic signal is lost after deposition, leading to decreases in magnetization and a bimodal grain size distribution of ultrafine, superparamagnetic grains and coarser multidomain particles, evident from measurements of ARM/IRM ratios, hysteresis measurements, and low-temperature analyses. The effects of dissolution and the superposition of climate and land-use signals complicate the use of recent sediments as modern analogs for sediment magnetic analyses.

Preservation and Grain-Size Trends of Holocene Wave-Dominated Facies Successions in Eastern Japan: Implications for High-Resolution Sequence Stratigraphic Analysis

Vertical grain-size trends provide significant information for the sequence stratigraphic analysis of siliciclastic wave-dominated facies successions. This paper discusses the relationships between the preservation timing and the grain-size trends of Holocene wave-dom- inated successions in two contrasting coastal plains: the Kujukuri and Sendai, using high-resolution AMS 14 C dating, depositional facies, and grain size. Modal grain size is proposed as a good criterion for eval- uating qualitative changes of depositional depth. The Kujukuri and Sendai successions are both fining-upward to coarsening-upward wave-dominated successions that have developed upon ravinement surfaces. The fining-upward part of the Kujukuri succession formed in regressive deposits during a highstand period, whereas that of the Sendai formed during transgression. A difference in the timing of the generation of upward fining is due to the varying preservation potential of transgressive shoreface deposits on the ravi- nement surface. In the Sendai area, the potential was much higher than in the Kujukuri area, because the Sendai ravinement surface had re- ceived greater sediment supply from the adjacent rivers during trans- gression. A differing rate of tectonic uplift between the areas was not critical to the preservation potential because of the short time scale. The successions show bimodal grain-size distributions in the basal parts and unimodal distributions elsewhere. The bimodality is consid- ered to be the result of mixing of a coarse transgressive lag with finer sediment derived from external sources. The finer mode forms a con- sistent trend with unimodal grain sizes in overlying deposits. The trend is of a simple upward coarsening in the Kujukuri and an upward fining to coarsening in the Sendai, showing distinctive correlation with chang- es of depositional depth. Thus, the vertical trend of the modal grain size (and not mean or median) is best for evaluating changes of de- positional depth in ancient wave-dominated facies successions.

Progressive Loss of Ferroelectricity Under Bipolar Pulsed Fields and Experimental Determination of Non-Switchable Polarization in Au/Ba0.5Sr0.5-TiO3/SrRuO3 Thin-Film Capacitors

175 nm-thick Ba0.5Sr0.5TiO3 (BST) thin film fabricated by pulsed laser deposition (PLD) technique is found to be a mixture of two distributions of material. We discuss whether these two components are nano-regions of paraelectric and ferroelectric phases, or a bimodal grain-size distribution, or an effect of oxygen vacancy gradient from the electrode interface. The fraction of switchable ferroelectric phase decreases under bipolar pulsed fields, but it recovers after removal of the external fields. The plot of capacitance in decreasing dc voltage (C(V ↓) versus that in increasing dc voltage C(V ↑) is a superposition of overlapping of two triangles, in contrast to one well-defined triangle for typical ferroelectric SrBi2Ta2O9thin films.

Depositional processes of the gravelly debris flow deposits, South Dolomite alluvial fan, Owens Valley, California

Coarse-grained debris flow was instigated in the South Dolomite alluvial fan of the Inyo Mountains piedmont, Owens Valley, California, by a concentration of flashy thunderstorm precipitation in 1984. The debris flow extends about 650 m from the fan apex to the Owens Lake, and forms levee deposits along the sides of the passing tract in the steep (6–26°) upper-fan (proximal) segment and lobe deposits at the flow terminus in the less steep (3–6°) lower-fan (distal) segment. Both the levee and lobe deposits consist of clast-supported, unstratified, poorly sorted, pebble-to-boulder-grade gravels. The length of the levees is much longer than that of lobe and the clasts exhibit flow-parallel [a(p)] long-axis orientation in the levees but flow-transverse [a(t)] orientation in the lobe, suggesting that the levees were formed by “pushing aside” mechanism, i.e., lateral (or oblique) accumulation of clasts from the surge heads. On the other hand, the lobe deposit was formed by sourceward incrementation of successive unsaturated debris flow surges. Detailed analyses of the grain-size distribution indicate distinct inverse grading of the clasts both in lobe and in levee deposits with respect to maximum clast size and graphic mean grain size. The inverse grading is mainly attributed to clast collision, with the upward displacement of large clasts due to dispersive pressure combined with kinematic sieving. It is notable however that the graphic mean size of the levee matrix shows normal grading, which can be explained by the combined effect of hindered settling and fluid turbulence. The bimodal grain-size distribution of the levee matrix suggests an incomplete mixing of coarser-grained surge head materials and finer-grained surge body and tail materials.

Geochemistry of aerosols of northwestern part of India adjoining the Thar desert

The northwestern part of India, which includes the Thar desert on its western side, is a hot and arid region with intense aeolian activity and transport of aerosols by the prevailing SW-W summer winds. Different size fractions of aerosols (free fall = FF, suspended particulate matter = SPM, PM 10 = <10 μm, and >10 μm) from air were sampled simultaneously at four locations along the dominant wind trajectory for ∼600 km. These aerosols and deposited surface sediments were characterized for their texture, mineralogy and geochemistry including REE and Sr isotopes. Within each size fraction, a bimodal distribution of grain size was observed. Quartz is the dominant mineral followed by K-feldspar, mica, calcite, chlorite and plagioclase. Garnet, amphibole, titanite and zircon are some of the identified heavy minerals. All samples, particularly those collected during summer, are compositionally homogeneous, including in their REE geochemistry, and are similar to average upper continental crust (UCC). However, in the winter aerosol samples, large deviations from the UCC composition are observed. This is attributed to meteorological parameters such as low wind velocity and temperature inversions in the winter season. During winter, secondary non-silicate and anthropogenic materials become important sources to Ca, Na, Mg, K, Ba and Ni budget; also reduction in the uptake and transport of heavy minerals lowered the concentration of Ti, Zr, Y, Cr, and REE in the aerosols. Geochemical coherence among aerosols, deposited surface sediments and the Thar sands, and the limited Sr isotopic data indicate that the Thar sediments and certain lithotectonic units of the Himalayan orogen are the proximal and distal crustal sources, respectively, for the aerosols in this region. Prevailing aridity and strong summer winds, and the presence of river alluvium in the Thar act together to transport silt rich dust, the removal of which could be a possible mechanism of ongoing desertification.

Bimodal Microstructures in Nanocrystalline Al and Al-Mg Alloy Powders Prepared by Cryogenic Ball Milling

AbstractThe microstructures of nanocrystalline Al and Al-7.6 at% Mg alloy powders processed by cryogenic ball milling (i.e., cryomilling) and subsequent thermal annealing were characterized using transmission electron microscopy. The as-milled samples primarily consisted of equiaxed grains with average sizes of ∼ 26 nm. The annealing treatments at elevated temperatures resulted in bimodal grain-size distributions, with sub-micrometer-sized grains embedded in a matrix of nanocrystalline (&lt;50 nm) grains. The bimodal microstructures were formed during the processes of recovery and recrystallization.

Bimodal grain-size distribution of Chinese loess, and its palaeoclimatic implications

Grain-size analysis indicates that Chinese loess generally shows a bimodal distribution with a coarse and a fine component. The coarse component, comprising the main part of the loess, has pronounced kurtosis and is well sorted, which is interpreted to be the product of dust storms generated by low-altitude northwesterly winds. Its grain-size reflects the strength of the low-altitude circulation in the dust seasons of the year, and its percentage provides an indicator of the source area aridity and the frequency of dust storms. Conversely, the fine component has a wide grain-size range and is poorly sorted. Sedimentary illustrations based on the grain-size distribution characteristics of bulk samples and of detrital quartz suggest that the fine component probably represents the background dust load of the atmosphere and is mainly transported by high-altitude westerly airstreams. Its grain-size provides an estimate of the westerly air stream intensity. The coarse and fine components of a loess sample can be mathematically separated by fitting a designated mathematical distribution function to the measured grain-size data, and this procedure constitutes an approach for reconstructing the palaeowind system of Northern China.

Magnetic Imaging of Nanocomposite Magnets

Understanding the structure and magnetic behavior is crucial for optimization of nanocomposite magnets with high magnetic energy products. Many contributing factors such as phase composition, grain size distribution and specific domain configurations reflect a fine balance of magnetic energies at nanometer scale. For instance, magnetocrystalline anisotropy of grains and their orientations, degree of exchange coupling of magnetically soft and hard phases and specific energy of domain walls in a material. Modern microscopy, including Lorentz microscopy, is powerful tool for visualization and microstructure studies of nanocomposite magnets. However, direct interpretation of magnetically sensitive Fresnel/Foucault images for nanomagnets is usually problematic, if not impossible, because of the complex image contrast due to small grain size and sophisticated domain structure. Recently we developed an imaging technique based on Lorentz phase microscopy [l-4], which allows bypassing many of these problems and get quantitative information through magnetic flux mapping at nanometer scale resolution with a magnetically calibrated TEM [5]. This is our first report on application of this technique to nanocomposite magnets. In the present study we examine a nanocomposite magnet of nominal composition Nd{sub 2}Fe{sub 14+{delta}}B{sub 1.45} (14+{delta}=23.3, i.e. ''hard'' Nd{sub 2}Fe{sub 14}B-phase and 47.8 wt% of ''soft'' {alpha}-Fe phase ({delta}=9.3)), produced by Magnequenchmore » International, Inc. Conventional TEM/HREM study (Fig. 1-2) suggests that material has a bimodal grain-size distribution with maximum at d{sub max}=25 nm for Nd{sub 2}Fe{sub 14}B phase and d{sub max} = 15 nm for {alpha}-Fe phase (Fig.1c, Fig.2) in agreement with synchrotron X-ray studies (d{sub max}=23.5 nm for Nd{sub 2}Fe{sub 14}B [6]). Lattice parameters for Nd{sub 2}Fe{sub 14}B phase are a=8.80 and c=12.2 {angstrom}, as derived from SAED ring patterns (Fig.1a), again in good agreement with X-ray data. The fraction of large particles (of size 250 nm) is less then 57% of total amount of particles (Fig.1c, arrowed). Our new imaging technique allows visualization of domain structure in nanomagnets (Fig.3) in color code. Both projected magnetization and magnetic flux maps (Fig.3) reconstructed using Lorentz phase microscopy suggest a complex domain structure with an average domain size about 100x(100{approx}200) nm{sup 2} in a non-magnetized state. Large particles of darker contrast (of size {ge}50 nm, presumably {alpha}-Fe precipitates) or clusters of such particles act as effective concentrators for magnetic flux in nanocomposite matrix. The measured relative local-flux concentration by factor of 1.28 agrees well with theoretical ratio B{sub sat}({alpha}-Fe)/B{sub sat}(Nd{sub 2}Fe{sub 14}B)=1.31, strongly suggesting clustering of {alpha}-Fe particles that may have a detrimental effect on nanomagnet coercivity. Other smaller {alpha}-Fe particles (< 25 nm) do not disturb flux distribution, hence, they are magnetically coupled to Nd-Fe-B matrix grains as it was postulated by spring-exchange mechanism for nanocomposite magnets.« less

On the analysis of grain size in bulk nanocrystalline materials via x-ray diffraction

The Warren-Averbach (WA) analysis and other simplified methods that are commonly used to determine the grain size of nanocrystalline materials are discussed in terms of accuracy and applicabilities. The nanocrystalline materials used in the present study are prepared by cryomilling of A1 powders and subsequent consolidation (hot isostatic pressing and extrusion). Transmission electron microscopy observations of the as-extruded nanocrystalline A1 reveal a bimodal distribution of grain sizes centered around 50 to 100 nm and 250 to 300 nm. It is shown that the grain size determined by the WA analysis agrees with the lower bound grain size (e.g., 50 to 100 nm) observed experimentally. In the case of the integral method, it is useful to use a parabolic (Cauchy-Gaussian (CG)) relationship to approximate instrumental broadening and separate the intrinsic broadening. Compared to the Cauchy-Cauchy (CC) and Gaussian-Gaussian (GG) approximations, this is shown to give the best results. In addition, the reliability of the Scherrer equation is also discussed.

Microstructural evolution during recovery and recrystallization of a nanocrystalline Al-Mg alloy prepared by cryogenic ball milling

The microstructural evolution during thermal annealing of a cryogenically ball milled Al-7.6 at% Mg alloy with a grain size of ~25 nm was examined using differential scanning calorimetry, x-ray diffraction, and transmission electron microscopy. Recovery occurs during annealing from 100 to 230 °C resulting in strain relaxation and grain coarsening, and recrystallization proceeds at higher temperatures up to about 370 °C with further grain growth. The stored enthalpy release during recovery was estimated to be ~450 J/mol, which is considerably higher than that in materials processed by other known cold-working methods. Only a fraction of the measured enthalpy was found to arise from the enthalpy releases due to grain coarsening and the reduction of high dislocation density. Both recovery and recrystallization give rise to non-uniform, bimodal grain-size distributions, which may result from heterogeneous nanostructures in the as-milled state. The detailed microscopic observations strongly support that grain coalescence is a feasible mechanism for grain coarsening during the recovery. In addition, the activation energy for recovery was calculated to be ~120 kJ/mol, indicating the process is diffusion-controlled (Mg in Al), whereas the activation energy for recrystallization was considerably higher, ~190 kJ/mol.

An equation to represent grain-size distribution: Reply

The authors wish to thank the discusser for putting together his case for the possibility of using a log-normal type representation to characterize particle size distributions. Log-normal type plots have found a degree of acceptability in the area of hydrology; however, similar attempts to use log-normal distributions have not been met with the same enthusiasm in the soil mechanics discipline. Geotechnical engineers do not view particle size distribution as statistical or probability-based information related to the number of particles associated with each particle size range. In the original paper, the authors point out that “Gardner (1956) proposed a two-parameter, log-normal distribution to provide representation of grain-size distribution data.” The idea of using log-normal distributions to characterize grainsize distribution curves has been around for a long time. It does not appear to have gained significant acceptability in geotechnical engineering nor engendered further research interest. It was against this background that the present research study was formulated. It was decided to further investigate the use of an empirical, mathematically based equation where the fitting parameters had some physical meaning. The equations were focused on the generally accepted “percent passing” versus the logarithm of the particle size plots. There has been a recent proliferation of studies related to the estimation of the soil-water characteristic curve from a grain-size distribution curve in the soil science and related disciplines. This also encouraged further attempts to mathematically characterize the grain-size distribution curve. The use of a continuous mathematical equation that can be differentiated and integrated has appeal because it can be used for further analysis in soil mechanics. There appears to be a fundamental difficulty in viewing a grain-size distribution curve as a purely statistical phenomenon since the grain-size distribution is commonly plotted as a “percent passing” by mass (as opposed to a cumulative distribution based on the number of particles) versus the logarithm of the particle size. The “percent passing” by mass does not lend itself to a statistical evaluation in the same way as if the number of particles was being assessed (Ang and Tang 1975). The largest particles have the dominance with respect to mass but in general, have the least influence on soil behavior. For example, only 30% clay size particles render the behavior of the soil like that of a clay soil. Hazen (1930) suggested that the D10 size of particles best represented the particle size for the assessment of the coefficient of permeability of a soil. In other words, conventional statistical measures based strictly on frequency do not provide the geotechnical engineer with the most meaningful parameters required when attempting to foresee the mechanical and hydraulic behavior of a soil. As a result, D50 does not have special meaning over other “percent passing” values in soil mechanics. Part of the natural bias towards the coarse end of the particle size spectrum (i.e., because of the mass basis for presentation of the data) is overcome in soil mechanics by plotting particle size on a logarithm scale. The differentiation of the percent passing grain size curve gives a log-normal type distribution, but this is not often used by geotechnical engineers. The particle size scale is equally spaced on a logarithm scale, and while this presents some difficulties in interpretation, it still appears to be a meaningful way to visualize the particle sizes in the distribution. The discusser states that he feels “that this paper represents a continued divergence from available approaches.” The authors maintain that it might represent a divergence from approaches quite common to hydrology; however, the approach proposed is consistent with the historical and present interpretive procedures used in soil mechanics. The authors used a four-parameter equation in the case of a unimodal grain-size distribution curve and a sevenparameter equation in the case of a bimodal grain-size distribution curve. This may appear to be a large number of parameters, but the parameters come out of a regression analysis and allow a consistently accurate representation of the entire grain-size curve. When used in conjunction with a

Incipient granular mass flows at the base of sediment-laden floods, and the roles of flow competence and flow capacity in the deposition of stratified bouldery sands

Extraordinary floods commonly produce thick deposits as a result of the entrainment and transport, often at high concentrations, of large volumes of clastic detritus. This paper describes the sedimentology of a stratified bouldery sand deposit generated by a 20-km 3-breakout flood from intracaldera Lake Taupo following the 1.8-ka Taupo eruption. The proximal deposit is characterised by a strongly bimodal grain-size distribution, with downstream-fining boulders enclosed in a poorly sorted and weakly bedded coarse sand to gravel matrix. This combination of characteristics is inferred to reflect simultaneous deposition of small and large particles by two distinct mechanisms: (i) accretion of the sandy matrix from an incipient basal granular mass flow as the flood lost capacity, and (ii) progressive emplacement of the boulders as the flood lost the competence to roll them along the channel floor. The first mechanism is a product of a nonlinear particle concentration gradient in the sediment-laden flow, which caused it to segregate into a basal incipient granular mass flow that formed the transient depositional system indicated by the lithofacies. The second mechanism is a function of the superjacent, turbulent, turbid flow that acted as the primary transporting system. This pairing of transport and depositional systems is likely to characterise many sediment-laden aqueous flows with clay mineral concentrations too low to develop non-Newtonian rheologies, such as jökulhlaups and lahars that entrain unweathered pyroclastic material. Qualitative and quantitative differences in the way bedload is transported in the presence of this basal granular mass flow, as compared to simple water, make impossible accurate estimates of flow competence based on Shields entrainment functions for beds of both uniform and mixed grain size distribution.

Effect of Twin‐Plane Reentrant Edge on the Coarsening Behavior of Barium Titanate Grains

When BaTiO3 ceramics were sintered at relatively low temperatures (≤1250°C), the grains with reentrant edges caused by a (111) double twin grew exclusively. As a result, a microstructure with a bimodal grain‐size distribution composed of platelike large grains and fine matrix grains was obtained. In contrast, at the usual sintering temperature between 1250° and 1350°C, grains containing a (111) double twin did not exhibit any growth advantage. In this case, a coarse and uniform microstructure was obtained. When this coarse‐grained specimen was further heat‐treated at 1365°C, the grains possessing a double twin were observed to grow exclusively again. The results were explained in terms of a coarsening process controlled by two‐dimensional nucleation.

Microstructure development of Al 2O 3–13wt.%TiO 2 plasma sprayed coatings derived from nanocrystalline powders

The development of constituent phases and microstructure in plasma sprayed Al 2O 3–13wt.%TiO 2 coatings and reconstituted nanocrystalline feed powder was investigated as a function of processing conditions. The microstructure of the coatings was found to consist of two distinct regions; one of the regions was completely melted and quenched as splats, and the other was incompletely melted with a particulate microstructure retained from the starting agglomerates. The melted region predominantly consisted of nanometer-sized γ-Al 2O 3 with dissolved Ti 4+, whereas the partially melted region was primarily submicrometer-sized α-Al 2O 3 with small amounts of γ-Al 2O 3 with dissolved Ti 4+. The ratio of the splat microstructure to the particulate microstructure and thus the ratio of the γ-Al 2O 3 to α-Al 2O 3 can be controlled by a plasma spray parameter, defined as the critical plasma spray parameter (CPSP). This bimodal distribution of microstructure and grain size is expected to have favorable impact on mechanical properties of nanostructured coatings, as has been observed before.

Effects of Yttrium Doping α‐Alumina: I, Microstructure and Microchemistry

The influence of yttrium doping on the microstructure and microchemistry of hot‐pressed α‐alumina was investigated using a combination of electron microscopy techniques. The implications of microstructure and microchemistry on the improved creep behavior of the doped material are discussed. The samples doped only with yttrium had a bimodal grain‐size distribution that was strongly correlated to the frequency and distribution of Y3Al5O12 (YAG) precipitates in the microstructure. Yttrium segregated to most of the grain boundaries, with a normal excess concentration of Gamma= 3.3 ± 0.9 atoms/nm2 at random boundaries. Two types of twin boundaries (Sigma3 and Sigma7) accommodated no yttrium. None of the boundaries or triple‐point junctions contained a glassy grain‐boundary phase. Strong interaction of the grain boundaries and dislocations with YAG precipitates indicated a pinning mechanism by the precipitates. Yttrium doping did not appear to favor formation of special boundaries in α‐alumina.

Effects of oxidation and abnormal grain growth on the magnetic properties of thin Fe–SiO2 granular films

In the Fe–SiO2 granular system the effects of oxidation and abnormal grain growth on the magnetic behavior are significant. As film thickness is reduced a larger fraction of Fe grains intersect the free surface and are prone to oxidation even in good vacuum conditions. Films coated with protective SiO2 layers were found to be unaffected by oxidation. The presence of a surface during annealing also affects the microstructural evolution. Transmission electron microscopy observations revealed a bimodal distribution of Fe grain sizes in uncoated films due to grain merger assisted by surface diffusion. This bimodal distribution of Fe grain sizes is associated with a coercivity (Hc) vs vol. % Fe curve containing two peaks. By contrast, SiO2 coated films exhibited a uniform microstructure without unusually large grains and a smoother Hc vs vol. % Fe curve with a well defined maximum. Room temperature coercivities of ∼1000 Oe can be routinely achieved in Fe–SiO2 granular films as thin as 10 nm. X-ray photoelectron spectroscopy studies showed evidence for the chemical interaction between Fe and SiO2 in SiO2/Fe/SiO2 trilayer model film samples.

Effect of α‐Si3N4Particle Size on the Microstructural Evolution of Si3N4Ceramics

The effects of initial particle size on the microstructure of silicon nitride ceramics produced by pressureless sintering have been investigated. The microstructures of the silicon nitride ceramics varied considerably with the size of the initial powder. With decreasing powder size, abnormal grain growth was enhanced, which resulted in significant bimodal distribution of grain size. The observed results are discussed in relation to the two‐dimensional nucleation and growth theory for faceted crystals.

Evolution of surface structure, microstructure, and superconducting properties during YBa2Cu3O7a-axis thin film growth

The evolution of surface structure, grain microstructure, and superconducting transition temperature ofa-axis YBa2Cu3O7thin films has been studied as a function of film thickness. The grain size increases and develops a bimodal distribution of grain size during film growth, concurrent with an improvement inTc. The surface structure does not represent the grain size, but rather the development of the bimodal grain structure follows the formation of the surface structure. The results are discussed in terms of thin film growth modes.

Volume strain, strain type and flow path in a narrow shear zone

This study explores the state of finite strain and changes in the mean kinematic vorticity number, grain size, whole-rock chemistry and mineralogy across an upper amphibolite-facies shear zone in a metadiorite, northern Malawi, east-central Africa. P–T conditions during shear-zone formation and deformation were approximately 700–750 °C and 5–7 kbar and are slightly less than P–T conditions for the regional peak of metamorphism. The major rock-forming minerals, plagioclase, hornblende, biotite, and quartz, were deformed by crystal-plastic processes accompanied by, except for hornblende, dynamic recrystallization. The modal abundance of all four major rock-forming minerals shows no systematic change from the country rock into and across the shear zone, indicating that shear-zone development was not associated with retrograde mineral reactions. The grain size of the major rock-forming minerals decreases within the shear zone. Plagioclase and hornblende, which occur as porphyroblasts outside the shear zone, exhibit a bimodal grain-size distribution within the shear zone. Quartz has a unimodal grain-size distribution in the shear zone. Major and trace element chemistry does not change systematically across the shear zone, implying no volume change in the mylonite. Matrix strain data for plagioclase and hornblende by the Fry method and fabric strain as deduced from Rf/φ analysis of plagioclase and quartz grains demonstrate a slightly constrictional strain type (K≈1.5) across the shear zone. The quantitative finite-strain data for the different residual minerals as obtained by unlike methods show no systematic variation, but recrystallized plagioclase grains record higher strain than the residual grains. The mean kinematic vorticity number changes from approximately 0.3 outside to approximately 0.8 within the shear zone, indicating that the bulk deformation path deviated from progressive simple shear. The estimates for finite strain and the degree of noncoaxiality account for approximately 50% of thinning normal to the shear zone.

Characterization of Cast Metals with Probability Distribution Functions

AbstractCharacterization of microstructure using a probability distribution function (PDF) provides a means for extracting useful information about material properties. In the extension of classical PDF methods developed in our research, material characteristics are evolved by propagating an initial PDF through time, using growth laws derived from consideration of heat flow and species diffusion, constrained by the Gibbs-Thomson law. A model is described here that allows for nucleation, followed by growth of nominally spherical grains according to a stable or unstable growth law. Results are presented for the final average grain size as a function of cooling rate for various nucleation parameters. In particular we show that the model describes linear variation of final grain size with the inverse cube root of cooling rate. Within a subset of casting parameters, the stable-to-unstable manifests itself as a bimodal distribution of final grain size. Calculations with the model are described for the liquid to epsilon phase transition in a plutonium I weight percent gallium alloy.