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Consequently, the matrix of transition probabilities of the ith fraction particles developed by Han and He [2] can be changed as (1) The derivation presented below is for the grains of fraction i, denoted by a subscript i.
The average particle number transferred from static state 1 to bedload (state 2) in unit area per unit time period is (2) (3) where Li=average length of single-step; Ui=average velocity of sediment particle; ti=time of exchange between bed load and bed material. ρs=sediment density; g=gravity acceleration; K2=particle number in saltation state(bedload) in unit water column. n0i is the average number of static sediment particles and can be determined according to the following equation (4) where m0=density coefficient for bed materials. approximately equal to 0.4[2].For equilibrium

The oxidation and corrosion properties of Si3N4 ceramics are dependent upon a number of processing and materials variables.
The grain boundary and triple point phases that are formed from the remains of the sintering additives after densification play a critical role on many high temperature properties including oxidation and corrosion [1,2].
Using this experimental setup measurements on the oxidation and corrosion resistance of a number of hot pressed Si3N4 based ceramics were investigated.
In particular composition number 4 of Si3N4+Y2O3 achieves a sintered density of only 88 % of its theoretical.

It is assumed that the velocity gradient can be decomposed into nonplastic and plastic parts. . (1) The plastic part of the velocity gradient is defined as the sum of all slip systems, , (2) where indicates a specific slip system and is the number of slip systems.
The number of crystal grains is set to 512, which can be considered as a sufficient number for an analysis of polycrystalline magnesium [5].

The crystal structure and/or defect structure are then expected to be controlled by alloying with a substitutional element, especially when the number of valence electrons of alloying element is different from that of the component atoms.
Since the chemical composition of a chimney-ladder phase MnX2n-m is related to the numbers of the M and X subcells in the unit cell, the X/M atomic ratio of the chimney-ladder compound is directly related to the ratio cX/cM by the following equation: 1 M X2 2 M X −       −= − == c c n mn y .
Fig. 3 shows a TEM bright field (BF) image and the SAED patterns obtained from marked regions inside a single grain in a (Ru0.4Mn0.6)Si1.75 alloy.
Assuming that the number of the valence electrons of the Mn is 7, then the VEC values are larger than 14 for the Ru1-xMnxSiy chimney-ladder phases observed in this study, which implies the n-type semiconducting behavior of the Ru1-xMnxSiy chimney-ladder phases.

This is because the soil density is larger, the distance between the particles is smaller, the continuity of grain intergranular non-freezing moisture is better beneficial to salinity migration under freezing.
Acknowledgements This work was supported by grants of the State Key Program of National Natural Science Foundation of China(grant number: 41430642, 41330636), Natural Science Foundations of China (grant numbers: 41402243, 41372267, 41302247) and Doctoral Program Foundation of Higher Education of China (grant number: 20120061110054).

The material was characterized by insufficient purity, low density and large grain size due to the long sintering process.
A decade later, the BIOLOX® of 2nd generation was proposed: produced from an improved raw material, it was characterized by finer grains resulting in a better performance.
This material was manufactured combining the sintering with a hot isostatic pressing, which allowed to reduce grain size and to improve both mechanical strength and wear resistance.
Indeed, ceramics are highly biocompatible and show the lowest wear rate, and thus are suitable to young and active patients, whose number is extremely increasing in the last decade.
Also numerical tools are under remarkable development, since they can reduce the need/number of experimental tests which are time consuming and expensive.

In contrast, the formation of coarse precipitates at grain boundaries was reported for an elevated tool temperature of 350 °C.
With decreasing hardness level to 153 HV in the transition zone at location (ii), a higher number of coarse particles can be seen.
For location (iv), the microstructure show a very high amount of coarse lath-shaped precipitates and a significantly decreased number of fine precipitates.
The coarse particles dominate the microstructure while the total number of precipitates decreases.
Raabe, Segregation assisted grain boundary precipitation in a model Al-Zn-Mg-Cu alloy, Acta Materialia. 156 (2018) 318–329. doi:10.1016/j.actamat.2018.07.003

Feynman, nanotechnology has been a hot topic. [1] At the nanoscale, Feynman's notions have been demonstrated in physics, chemistry, and biology in a number of fundamental ways.
A number of recent construction projects [5] illustrate how nanotechnology is being used.
An AFM study of the development of CSH in tricalcium silicate grains revealed that the creation of CSH occurs as an aggregation of identical elementary clusters.
AFM experiments revealed electrostatic forces between cement grains or surfaces, contradicting the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [10].
Between 3% and 30% relative humidity, AFM studies of cement paste surfaces revealed a change in surface structure from coarse to fine grains.

Introduction A large number of ceramic materials have been proposed as solid oxide ion conductors for application in devices such as solid oxide fuel cells (SOFC) and oxygen sensors.
The aim of the present contribution is to extend this analysis to the role played by the average A and/or B cations size in the electrical properties of a large number of highly disordered pyrochlores.
One can observe the characteristic semicircles found in this kind of plots for polycrystalline ionic conductors: one due to the bulk response, at the highest frequencies, and a second one at the lowest frequencies which is related to the grain boundary response.
These fits are shown in figure 2 as solid lines, which show excellent agreement with data points except at the lowest frequencies in M '(ω), where the influence of a grain boundary contribution is present in the data (see figure 1 and previous paragraph) but not considered in the fits.
We have used the ionic radii given by Shannon [19], and for this analysis we have considered a common coordination number of 8 for both positions 16c and 16d, instead of 8 and 6 respectively as in ideal or ordered pyrochlores, which is reasonable since all of them are present in a highly disordered anion sublattice.

The thin film deposition process exerts a number of effects such as crystallographic orientation, morphology, topography, densification of the films..
X-ray diffraction studies were undertaken in an attempt to determine the phases present, and perhaps an estimate of grain size from line broadening.