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Introduction Alumina ceramic has been found a wide application in a number of abrasive wear environments, such as in balls, mills, cutting tools, dies, and so on [1].
As an additive, La2O3 decrease grain sizes and improve ceramics density [7].
The micrograph clearly shows that grain sizes of ceramic samples with Tb4O7 doped are smaller than S1, and grains become bigger with increasing of Tb4O7.
And terbium ions in liquid phases could inhibit ions migration, which prevent grain growth and make grain sizes small, to improve wear resistant of ceramic samples.
Grain size effect on abrasive wear mechanisms in alumina ceramics.

After tempering at 650°C, the average size and number of these rectangular precipitates don't change obviously (Fig. 2b).
Determination of effective grain size measured by EBSD.
Large number of boundaries falls into the range of below 10° in misorientation angles in all these samples.
The boundaries existing in this region should be related to the boundaries between packets transformed from different {111}γ planes and the prior austenite grain boundaries. 0 10 20 30 40 50 60 0 10 20 30 40 (a) Number fraction (%) Misorientation angle (deg) 0 10 20 30 40 50 60 0 10 20 30 40 (b) Number fraction (%) Misorientation angle (deg) 0 10 20 30 40 50 60 0 10 20 30 40 (c) Number fraction (%) Misorientation angle (deg) Fig. 3 Grain boundary misorientation distribution of ULCB steels in as-rolled (a) and tempering at 650°C (b) and 700°C (c) condition.
At the tempering of 700°C the average grain size increases to 2.7µm.

The constitutive relations of grain boundry.
Periodic assumption is used to ensure the grain geometry is continuum and material parameters of grain interiors are uniform in the grains of each boundary of the opposite edges pair.
In the present study, the intragranular material properties are allowed to vary from grain to grain but the individual grains are taken to be isotropic with different Young moduli, and parameters of cohesive interfacial model are the same for all grain boundaries in the sample.
From the cyclic stress-strain curves result we can find that cyclic strain hardening is more obvious with the increase of tension-compression cycle numbers.
Meanwhile the plastic dissipation energy is smaller with the with the increase of cycle numbers, in which intergranular cracks are initiation and extended.

The tensile properties are also improved with the refinement of grain structure.
The Al-Ti-C master alloy, as a good refiner for Al/Mg based alloy [1,2], has been extensively studied by a number of researchers.
The mean grain size was measured by linear intercept method.
Birol, Grain refining efficiency of Al-Ti-C alloys, J.
Mahmudi, Grain boundary strengthening in a fine grained aluminium alloy, Scripta Mater.

A large number of dimples are observed on the fracture surface, implying as ductile fracture.
It can also be seen that from the weld zone to the base metal, the number of LAGBs decreased gradually.
A large number of shear dimples were observed.
From the weld zone to the base metal, the number of low angle grain boundaries is gradually reduced.
In the 35J / mm sample, the number of low angle grain boundaries was about 0.29, and a large number of deformation twins can be formed during the deformation process, which has a great contribution to the strength of the weld.

Creep resistance of specimens made of coarse grain material was significantly higher than the resistance of fine grain material.
Images of macro and microstructure of IN-713C superalloy as well as their morphological parameters Heat Evaluation of the structure of superalloy Carbide content in surface area AA Morphological parameters of macrostructure 1 AA = 0.74 % N = 33 -number of grains, A = 0.76 mm2 - mean surface area of a grain 2 AA = 0.92 % N = 14 -number of grains A = 1.93 mm2 - mean surface area of a grain 3 AA = 0.95 % N = 25 -number of grains, A = 0.86 mm2 - mean surface area of a grain 4 AA = 0.86 % N = 10 - number of grains, A = 2.67 mm2 - mean surface area of a grain It comes out from the tests of macrostructure of the nickel superalloy that both with (blue modification filter for heat 2) and without (white filter for heat 4) volumetric modification in the casting experiment, coarse-grained structure was obtained.
Creep resistance vs. selected morphological parameters of structure IN-713C nickel superalloy samples Heat Creep resistance tz [h] Rate of steady-state creep Vu [s-1] Carbide content in surface area AA [%] Number of grains on specimen section N Ratio of carbide content in surface area and number of grains AA/N [%] 1 25.4 3.27*10-7 0.74 33 0.022 2 26.7 3.05*10-7 0.92 14 0.066 3 28.3 2.8*10-7 0.95 25 0.038 4 50.0 1.38*10-7 0.86 10 0.086 In the research of creep relatively lower creep resistance of sample from heat 2 was found (showing coarse-grained microstructure) as compared to sample from heat 4 with similar number of macrograins in the cross section.
This influence is good described by the implemented parameter AA/N, (ratio of carbide content in surface area and number of grains in specimen, Table 2).
With the increase of parameter AA/N both in the close-grained (heat 1 and 3) and coarse-grained (heat 2 and 4) group of the produced superalloys creep resistance tz was higher.

Impedance spectrum was analysed to obtain the behaviour of grain core and grain boundary responses by a fitting procedure using brick-layer model.
Further calculation of grain size by means of ImageJ software revealed that the grain size of the modified BCZY was around 88 nm.
Grain arc could not exist at such temperature due to the incapability of impedance spectroscopy to measure grain response according to Barison S. et al. [7].
Consequently, the total effect on the conductivity is smaller than that of microcrystalline materials, although the number of grain boundaries per unit length increases in smaller grain size condition and eventually provide higher conductivity value for nano-sized sample.
The Electrical Characterization of Grain Boundaries in Ultra-Fine Grained Y-TZP, Mater.

Significant feature in silicon carbide crystal structure is its polytypism, which exhibits a number of different one-dimensional ordering sequences without any stoichiometric variation.
According to Ramsdell [20], the notation of these polytype consists of one number describing the number of layers (A, B or C-layer) associated with the unit cell, and a letter indicating the crystal system (cubic (C), hexagonal (H) or rhombohedral (R)).
Another hypothesis assumes that boron modifies the properties of grain boundaries by lowering the grain boundary energy.
Fig. 6 (b) shows a lattice fringe imaging of a near (111) grain boundary having no amorphous or crystalline intergranular/grain boundary phase [76].
It should be noted that epitaxial crystalline grain-boundary films were often formed on the (0 0 0 1) grain-boundary surface of the matrix -SiC grains.

The grain size of porous HA was sub-micron and MgO which existed in the grain boundary of HA as a second phase particles that played the roles of inhibiting the HA grain growth.
The paper deals with the preparation and micro structure of the Mg containing porous HA with ultra-fine grain.
The specimen were heated in 1100-1200℃ for 1-3 hours for the preparation of Porous HA with ultra-fine grain containing Mg.
Characterization The porous hydroxyapatite ceramic were characterized by using a number of methods such as wide angle X-ray diffraction, transmission electron microscopy, scanning electron microscopy (SEM), SEM in combination with energy dispersive X-ray spectroscopy(SEM-EDX), X-ray photoelectron spectroscopy.
Grain size and morphology of nano HA[J].

A pattern of structural states was obtained among the models with fast decrease in growth rate of recrystallized grain and weak grain growth.
Such approach is efficient only in case of large number of experimental data in investigation of plastic deformation at different temperatures and strain rates.
Let us assume that: ( ) ( )θβββττ == ,G - is the grain growth intensity coefficient.
Depending on the value of K the possible case is reduction or grain growth (Fig. 3).
The kinetics of changing the grain created according to the following models: size depends on growth intensity [4] - is fast damping of grain growth rate; - is the weak growth of grains; - are calculated points [2] As a result of solving the Eq. 1 and Eq. 8 obtained that the function ( )γτ,nV shows oscillating behavior.