Distribution Of Grain Diameters Research Articles

The electrical conductivity of polycrystalline metallic films

We calculate the electrical conductivity of polycrystalline metallic films by means of a semi-numerical procedure that provides solutions of the Boltzmann transport equation, that are essentially exact, by summing over classical trajectories according to Chambers' method. Following Mayadas and Shatzkes (MS), grain boundaries are modeled as an array of parallel plane barriers situated perpendicularly to the direction of the current. Alternatively, according to Szczyrbowski and Schmalzbauer (SS), the model consists in a triple array of these barriers in mutual perpendicular directions. The effects of surface roughness are described by means of Fuchs' specularity parameters. Following SS, the scattering properties of grain boundaries are taken into account by means of another specularity parameter and a probability of coherent passage. The difference between the sum of these and one is the probability of diffuse scattering. When this formalism is compared with the approximate formula of Mayadas and Shatzkes (Phys. Rev. B 1, 103 (1986)) it is shown that the latter greatly overestimates the film resistivity over most values of the reflectivity of the grain boundaries. The dependence of the conductivity of thin films on the probability of coherent passage and grain diameters is examined. In accordance with MS we find that the effects of disorder in the distribution of grain diameters is quite small. Moreover, we find that it is not safe to neglect the effects of the scattering by the additional interfaces created by stacked grains. However, when compared with recent resitivity-thickness data, it is shown that all three formalisms can provide accurate fits to experiment. In addition, it is shown that, depending on the respective reflectivities and distance from a surface, some of these interfaces may increase or diminish considerably the conductivity of the sample. As an illustration of this effect, we show a tentative fit of resistivity data of gold films measured by Chen et al. (Appl. Phys. 60, 659 (2005)). Finally, we present a new version of Matthiessen's rule that describe, with high accuracy, the way in which the contributions from surface scattering and grain boundary combine to form the total resistivity of the sample.

Characterizing the sediment bed in terms of resistance to motion: Toward an improved model of saltation thresholds for aeolian transport

Abstract Models of aeolian transport thresholds generate a wide range of predictions, and error in threshold modeling leads to uncertainty in predicting aeolian events. This paper proposes a new characterization of the representative grain size for use in prediction of transport thresholds. This characterization is based on the distribution of resistance to motion in the sediment bed. The traditional grain size distribution uses a mean diameter to represent the sediment bed. However, the distribution of inertial forces resisting motion is not linearly proportional to the distribution of grain diameters, so that an arithmetic mean does not adequately represent the distribution of the resisting forces. A simple relation of shear stress to weight force is used to represent the threshold condition. Based on comparison with threshold observations drawn from the literature, the model provides reliable predictions of threshold stress and shear velocity for dry quartz grains over a wide range of grain sizes. Given that the dataset was drawn from studies employing a variety of experimental conditions and techniques, and that these studies spanned a range of nearly eight decades, the model is considered to provide a robust approximation of threshold conditions.

Technology and Electrophysical Properties of Multiferroic PZT–PFT Ceramics

Abstract We present the results of obtaining and investigating ceramic samples of solid solution (1-x)(PbZr0.53Ti0.47O3)- x(PbFe0.5Ta0.5O3) [i.e. (1-x)PZT-xPFT] with x =0.25, 0.35 and 0.45 obtained using conventional ceramic technology. These materials belong to class of materials known as multiferroics. Solid solutions PZT-PFT are the lowest-loss room-temperature multiferroics known, and as a result there are very interesting for magnetoelectric devices. Paper presents the results of termogravimetric investigations, EDS, XRD and main dielectric measurements. It has been stated that with increasing content of PFT decreases the mean diameter of grains and more wide distribution of grain diameters is observed. For x =0.25 sharp phase transition from ferroelectric phase to paraelectric one is observed and high values of dielectric permittivity. Composition PZT-PFT with x =0.45 has the lowest values of dielectric permittivity, and the transition is more diffused. The increase of x leads also to the shift of the temperature of maximum of dielectric permittivity towards lower temperatures. Samples with x =0.25 and x =0.35 exhibit very low values of dielectric losses up to about 100°C. Dielectric losses for samples with x =0.45 are higher. For obtained PZT-PFT samples we have investigated P-E hysteresis loops at room temperature for frequency 1 Hz. For composition x =0.25 it after application the field about 2.5 kV/mm polarization is equal approximately 28 μC/cm2, while for x =0.35, and x =0.45 after application the field about 2.0 kV/mm the polarizations are equal about 25 μC/cm2 and 20 μC/cm2 respectively. Very low values of losses and high values of polarization lead to the conclusion that interesting material PZT-PFT for applications should be composition with x =0.25.

Microstructure and Performance of the Hot-Pressed Silicon Nitride Ceramics with Lu<sub>2</sub>O<sub>3</sub> Additives

The influence of Lu2O3 on phase transformation and seeds morphology was investigated. The result showed that the β-Si3N4 seeds with up to 95% β phase content could be obtained with 2wt% Lu2O3 as the additive content under 1750°C for two hours. The microstructure and mechanical properties of hot-pressed Si3N4 ceramics, using 9wt.% of Lu2O3• additives were investigated by the means of MTS measurements and Vickers indentation crack size measurements, as well as XRD and SEM. It was known that the high fracture toughness of Si3N4 ceramics was attributed to the rodlike morphology of β-Si3N4 grains. And the reinforcement effect and mechanism of β-Si3N4 seed were studied. It was found that the grain size and its distribution influence the property and microstructure of Si3N4 ceramics, namely, the relative narrow distribution of grain diameter in some extent and relative wide range of bimodal distribution of grain aspect ratio could improve the property of Si3N4 ceramics. The improvement in the fracture toughness with the amount of additive was mainly attributed to elongated grain growth during the sintering process.The high temperature properties of self-reinforced Si3N4 with different additives were studied. By this method, self-reinforced Si3N4 ceramics with an increment of 10~20 percent of fracture toughness was successfully fabricated.

Nano-structured GeySi1-y:H Films Deposited by Low Frequency Plasma for Photovoltaic Application

ABSTRACTIn this work we present the study of fabrication, Ge incorporation, structure and electronic properties of nano-structured GeySi1-y:H films with y>0.5 prepared by low frequency (LF) PECVD. GeySi1-y:H films were deposited by LF PECVD at a frequency f= 110 kHz from SiH4+GeH4+H2 gas mixture. SiH4 and GeH4 flows were varied to fabricate the films in wide range of 0<y<l. Hydrogen dilution was varied in the range of RH =20 to 80. Structure of the films was studied by AFM and SEM with consequent image processing to extract statistical parameters such as grain distribution and mean values. Composition of the films was characterized by SIMS and EDX. Electronic properties were characterized by temperature dependence of conductivity, spectral dependence of optical absorption. Sub-gap absorption was characterized by Urbach energy, EU; and defect absorption, αD. We observed grain like nano-structure with Gauss distribution of grain diameters by both AFM and SEM measurements. The most interesting films had mean grain diameter<D> = 24.0±0.7 nm, dispersion D=11.0±0.2 nm and fill factor FF=0.313, Ge content y=0.96-0.97(by SIMS and EDS). These films showed also the lowest values of Urbach energy EU = 0.030 eV and low defect absorption αD = 5×102 cm −1 (at photon energy hv = 1.04 eV) indicating on low density of localized states in mobility gap. Doped films have been also fabricated and studied. Finally we shall discuss application of the above films in photovoltaic devices.

Media noise reduction in Co-based longitudinal media with new Co co-precipitated NiP/Al substrate

To decrease the grain size and grain size distribution in longitudinal media, a small amount of oxygen exposure onto either normal NiP or Co co-precipitated Co-NiP/Al-alloy substrates has been used. The substrate surfaces of both media were dry-etched by RF-plasma prior to oxygen exposure. The exposure of 3.5 L of oxygen onto the normal NiP substrate surface reduces the grain diameter from 10.0 nm to 8.8 nm while maintaining the standard distribution of grain diameter of about 1.4 nm. As a result, the media signal to noise ratio increases by 0.6 dB. By adding 400 ppm of Co into NiP plated substrate and combined with 1.5 L of oxygen exposure, the grain diameter and the standard distribution of grain diameter decrease from 9.2 nm to 8.3 nm. As a result, the media signal to noise ratio increases by 1.0 dB.

Microstructural Design of Silicon Nitride with Improved Fracture Toughness: I, Effects of Grain Shape and Size

The use of self‐reinforcement by larger elongated grains in silicon nitride ceramics requires judicious control of the microstructure to achieve high steady‐state toughness and high fracture strength. With a distinct bimodal distribution of grain diameters, such as that achieved by the addition of 2% rodlike seeds, the fracture resistance rapidly rises with crack extension to steady‐state values of up to 10 MPam1/2 and is accompanied by fracture strengths in excess of 1 GPa. When the generation of elongated reinforcing grains is not regulated, a broad grain diameter distribution is typically generated. While some toughening is achieved, both the plateau (steady‐state) toughness and the R‐curve response suffer, and the fracture strength undergoes a substantial reduction. Unreinforced equiaxed silicon nitride exhibits the least R‐curve response with a steady‐state toughness of only 3.5 MPam1/2 coupled with a reduced fracture strength.

A Study of the Relation between Distribution of Grain Diameters and Metallurgical Properties in Recrystallized Steel Sheet

A Study of the Relation between Distribution of Grain Diameters and Metallurgical Properties in Recrystallized Steel Sheet

Effect of Microstructure of Fracture Stress and Fracture Toughness of Silicon Nitride.

Microstructure and mechanical properties of HP, HP/GP and HP/HIP-Si3N4 were studied using scanning electron microscopy, bending tests and the indentation fracture method. The distribution of grain diameter was analyzed to clarify the relationship between microstructure and mechanical properties (bending strength and fracture toughness value). It is shown that bending strength increased with decreasing the grain diameter. The results also showed that a Hall-Petch relationship was recognized for grain diameter and fracture stress. The fracture toughness value shows a linear relationship with σF√(βda), and is closely related to aspect ratio of Si3N4 grain. From these grain morphological analysis results, it is concluded that the microstructure composed of Si3N4 grains having both small grain diameter and large aspect ratio is effective to improve both fracture strength and fracture toughness.

Room temperature recrystallization of nanocrystalline thin copper foils

AbstractThin copper foils (100 micrometers thick) are produced by electrolysis on anodized titanium substrates. A sharp distribution of grain diameter is observed around 200 nanometers. The X-ray diffraction pattern shows a slight preferential orientation of the crystals with the (111) planes parallel to the substrate. This X-ray diffraction pattern evolves at room temperature. After 60 days, a preferential orientation of the (200) planes parallel to the substrate is observed. This effect is associated with the recrystallisation of the foil with growth of large copper grains (diameter higher than 5 micrometers) as observed by high resolution transmission electron microscopy.The structural evolution of the copper foils is studied by electron microscopy, X-ray and electron diffractions at different temperatures.The mechanical properties of the foils are also studied as a function of time after electrodeposition.

Kinetics of Diffusional Phase Transformation during Heating and Cooling Processes and Its Application to Simulation of Welding Process.

Adequate kinetic equations are required to express phase transformations which include reverse processes of heating as well as cooling during welding, heat treatment and so on. Governing equations which depend on temperature, elastic strain and distribution of grain diameter of a material are proposed in order to enable the representation of the diffusional transformation during the continuous process between heating and cooling. Diagrams of time-temperature-transformation (T-T-T) and time-temperature-austenitization (T-T-A) are calculated for eutectoid steel. Based on the kinetic theory proposed in this paper, a method of the welding process is presented using a viscoplastic constitutive equation, which may cover the region of molten and solidified states. Numerical results show the practical modes of temperature, structure change and induced stress/strain in the process.

Microstructural Development During Gas‐Pressure Sintering of α‐Silicon Nitride

Gas‐pressure sintering of α‐Si3N4 was carried out at 1850 ° to 2000°C in 980‐kPa N2. The diameters and aspect ratios of hexagonal grains in the sintered materials were measured on polished and etched surfaces. The materials have a bimodal distribution of grain diameters. The average aspect ratio in the materials from α‐Si3N4 powder was similar to that in the materials from β‐Si3N4 powder. The aspect ratio of large and elongated grains was larger than that of the average for all grains. The development of elongated grains was related to the formation of large nuclei during the α‐to‐β phase transformation. The fracture toughness of gaspressure‐sintered materials was not related to the α content in the starting powder or the aspect ratio of the grains, but to the diameter of the large grains. Crack bridging was the main toughening mechanism in gas‐pressure‐sintered Si3N4 ceramics.

A Significant Method for Estimation of the Grain Size of Polycrystalline Materials

A method has been proposed to estimate the grain size, which is defined as the grain size distribution in three dimensions, from the measured distribution of linear intercept length. The method is developed on the assumption that the grain size distribution is log normal in three dimensions. The three-dimensional grain size distribution is expressed as that of the “grain diameter” D defined as the equivalent volume diameter; the distribution of D is estimated from ln Dg and ln σg (where Dg is the geometric mean of D and σg is the geometric standard deviation for D). The estimation is based upon the theoretical distribution of linear intercept length calculated numerically from a tetrakaidecahedron grain structure model with log-normal distribution of grain diameter. The values of Dg and ln σg are determined by applying the ‘discrete’ least squares method to the measured linear intercept length distribution on the basis of the calculated results. The present method has made it possible to evaluate the fundamental parameters of Dg and ln σg defining three-dimensional distribution of grain size from measurements on the cross-sectional structure. Futher, the influence of grain size distribution on the estimation of mean grain sizes by the two representative methods, the intercept method and the planimetric method, has been discussed from the calculation in the above model and the analysis of the experimental results. As a result, it has been concluded that the grain size distribution has a significant effect on the estimation of the mean grain size.

Plane section and spatial characteristics of equiaxed β-brass grains

A study was undertaken to define better the concept of the statistical grain. A cube having edges of 52·1 mm was cut from a slowly cooled β-brass ingot which had equiaxed grains. The distributions of sizes and shapes of grain sections on the faces of the cube were determined. The grains were then separated in a solution of mercurous nitrate and nitric acid. Observations were made of the relationship between grain diameter and the number and shapes of faces. For the 941 separated whole grains, the frequency of distribution of grain diameters obeyed the log–normal law. A plane distribution curve was derived for the statistical grain which enables spatial distributions to be calculated from measurements made on a plane section.MST/825

New substrate causes a stir : Jerry Lyman. Electronics p. 94 (7 December 1978)

We calculate the electrical conductivity of polycrystalline metallic films by means of a semi-numerical procedure that provides solutions of the Boltzmann transport equation, that are essentially exact, by summing over classical trajectories according to Chambers' method. Following Mayadas and Shatzkes (MS), grain boundaries are modeled as an array of parallel plane barriers situated perpendicularly to the direction of the current. Alternatively, according to Szczyrbowski and Schmalzbauer (SS), the model consists in a triple array of these barriers in mutual perpendicular directions. The effects of surface roughness are described by means of Fuchs' specularity parameters. Following SS, the scattering properties of grain boundaries are taken into account by means of another specularity parameter and a probability of coherent passage. The difference between the sum of these and one is the probability of diffuse scattering. When this formalism is compared with the approximate formula of Mayadas and Shatzkes (Phys. Rev. B 1, 103 (1986)) it is shown that the latter greatly overestimates the film resistivity over most values of the reflectivity of the grain boundaries. The dependence of the conductivity of thin films on the probability of coherent passage and grain diameters is examined. In accordance with MS we find that the effects of disorder in the distribution of grain diameters is quite small. Moreover, we find that it is not safe to neglect the effects of the scattering by the additional interfaces created by stacked grains. However, when compared with recent resitivity-thickness data, it is shown that all three formalisms can provide accurate fits to experiment. In addition, it is shown that, depending on the respective reflectivities and distance from a surface, some of these interfaces may increase or diminish considerably the conductivity of the sample. As an illustration of this effect, we show a tentative fit of resistivity data of gold films measured by Chen et al. (Appl. Phys. 60, 659 (2005)). Finally, we present a new version of Matthiessen's rule that describe, with high accuracy, the way in which the contributions from surface scattering and grain boundary combine to form the total resistivity of the sample.

A Study of the Relation between Distribution of Grain Diameters and Flow Stress in Mild Steel

A Study of the Relation between Distribution of Grain Diameters and Flow Stress in Mild Steel

軟鋼の混粒と変形応力についての一考察

軟鋼の混粒と変形応力についての一考察

The distribution of grain diameters in polycrystalline magnesium oxide

Grain diameters in porous and nonporous magnesium oxide are shown to be distributed in the same way as in a metal. The spread of the distribution appears to be influenced by the purity of the ceramic, but not by the average grain size.