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The microstructure of the as-cast specimens mainly consisted of matrix-α (Al) and grain boundary (GB)-eutectic phase (α-Al + Mg(Zn,Cu,Al)2).
Results and Discussion Microstructure of the as-cast specimens Secondary electron images of as-cast microstructures reveal a non-dendritic grain structure and a white contrast of grain boundary (GB) phases as shown in Fig. 1.
The EDS result shown in Fig. 1(d) indicates that the elongated black area at the grain boundary in Fig. 1(b) is Mg2Si phase.
The number of these particles increased with increasing solution treatment time from 1 h to 8 h at 480 ⁰C as shown in Fig. 4(e) and Fig. 4(f).
Conclusions From the above study and experimental results it can be concluded that as-cast samples consist of two main phases: a non-dendritic grain structure of α-Al phase and grain boundary eutectic phase (α-Al+ Mg(Zn,Cu,Al)2).

The experiment results showed that the grain size of diamond wheel has great influence on the subsurface damage depth of the ground wafer.
The first group is marked as in the Fig.4 and other groups were numbered in a clockwise direction.
As the grain size increases, the subsurface damage depth increases.
From the Fig.8 and Fig.9, it can also be seen that the subsurface damage depth of ground wafer without spark-out process is larger than that with spark-out process and the subsurface damage depth of wafer ground by large grain size wheel is larger than that ground by small grain size wheel.
The subsurface damage depth increases as the grain size of grinding wheel increases and the subsurface damage depth of ground wafer without spark-out process is larger than that with spark-out process. 2.

The calculated grain size is below 30 nm according to Scherrer formula.
The powder appears to be plate-shaped and the morphology of the grain is irregular particle.
The mixed salt solution was respectively poured into four corundum crucibles, which were numbered A1, A2, A3 and A4.
It is clear that with the increase of temperature, the grain tends to grow up, but in general the grain is fine.
The grain size is uniform.

These additives create a grain refining effect, introducing microinhomogeneities of smaller scales and activated insoluble impurities, which are potential centers of crystallization [18, 19].
For the production of casting molds, the quartz sand with an average grain size of 0.2 mm has been used.
In comparison with other TST time modes, the melt holding time of 4…5 min (Fig. 1, c) and 8…10 min (Fig. 1, d) at superheating has the greatest grain refining effect observed by decreasing of average grain size of α-Al.
Additives of fine-grained charge materials act as melted microcoolers that increases the cooling rate of the melt.
Besides that, the addition of solid charge creates inoculating effect, introducing a large number of potential crystallization centers in the form of activated insoluble impurities and microinhomogeneities of smaller scales.

At this temperature, grain size is more uniform, and structure is the most dense.
But a large number of studies shown that the density of pure KNN lead-free piezoelectric materials only 90% of theoretical density, this kind of ceramic’s grain structure is coarse and loose, porous, performance is not ideal, due to phase stable temperature of solid solution is limited to 1140℃, easily volatilize of alkali metal elements through sintering process, making the stoichiometric ratio deviation from chemical measurement[6].
With the increase of sintering temperature, grain size gradually increased, so grains at 1080℃ is bigger than 1060℃.
Tanδ is related to grain size, gaps and defects.
At this temperature, grain size is more uniform, and structure is the most dense.

As long as the volume fraction of the grains in the system is far from the maximum packing density of the grain structure, the material can usually be assumed as a paste-like material.
In the presence of a larger number of particles, the behavior is dominated by the grains in the mixtures.
In the calculation procedure of the thickness of the excess paste, it is assumed that the shape of the grain particles is spherical.
In fact, as the grains inside the mixture are not exactly spherical the interlock between grains happens at the longer distance as predicted by spherical particles (Fig. 4).
Excess paste layer Sphere Grain (a) (b) Fig. 4: The contact zone between two elements: a) interaction through the excess paste layers; b) direct contact between the grains, in which the excess paste layer thickness is not effective anymore.

Dispersoids are well observed for all the alloys, although their size and number vary with homogenizing temperature.
It is revealed from Fig. 3 that both the relative frequency of very fine (� 0.2µm) dispersoids and the total number of dispersoids are higher in the alloy homogenized at 723K.
In the alloy homogenized at 773K, the total number of dispersoids reduces and relatively fine (0.4-0.6µm) dispersoids are predominantly observed.
For the core alloys homogenized at/cold rolled to 723K/30-45%, 773K/20-45%, 823K/20-37% and 873K/20-30%, a fully recrystallized structure with a coarse grain (above 200µm in mean grain size) is developed after brazing treatment (Figs. 6a and b).
The increased grain boundary area in the core could promote filler penetration into the core along the grain boundaries, and hence increases sagging distance (decreases sagging resistance). 1µµµµm1µµµµm1µµµµm Fig. 7 TEM image of brazing treated core alloy homogenized at 723K and CR to 20%.

It was observed for the same grain size, that the Vickers hardness, HV, changed with the kind of alloying elements as follows; VH(Al-Fe) > VH(Al-Ti) > VH(Al).
A Gaussian smearing [11] of 0.1 eV is applied to the occupation numbers.
The Hall-Petch relation [13, 14] between the yield strength and grain size for polycrystalline alloys, 2/1 0 − += kdyσσ (2) provides for the separate consideration of the yield strength of a single crystal σ0 and the grain boundary strengthening through the product of the microstructural stress intensity k and the grain diameter d.
Included are the theoretical results using misfit strain and the analytical results using the measured grain size and yield stress [1].
The analytical results obtained from Eq. (3) using the measured grain size and yield stress are also shown in this figure.

The average grain size for Ni and TiN is approximately 52.85 and 39.13 nm, respectively.
Ninety-four data were used to established AR model, and the other six data as a test data Sample Number TiN content/% Fig. 1 Data series of TiN nano-particles content Forecasted results of AR model.AR model was determined according to the optimal order and the corresponding estimated parameters which calculated above.
According to the XRD data, the average grain size for Ni and TiN calculated using Scherrer equation is approximately 52.85 and 39.13 nm, respectively.
TiN content/% Sample Number Fig. 2.The sample approximation curve of nano TiN particles content in composite coating Sample Number TiN content/% Fig. 3.The comparison between predicted value of and actual value of the TiN content (a) TiN powder, (b) Ni coating, and (c) Ni–TiN coating Fig. 4 .XRD patterns of the TiN powder and coatings Summary The method of Time Series Analysis can forecast the TiN content in Ni–TiN composite coatings.
XRD result demonstrates that the average grain size for Ni and TiN calculated is approximately 52.85 and 39.13 nm, respectively.

A number of PLS researches on ZrB2–SiC ceramics have been carried out recent years, showing that proper sintering aids are needed to reach full density in PLS process.
For denser samples, the fracture form is transformed to mainly intergranular fracture, indicating that the bonding strength of grain boundaries is relatively weaker than the ZrB2 grains.
The reduction of closed porosity is attributed to grain-boundary diffusion and grain-boundary migration, which are enhanced under the presence of an electrical field [9].
The other advantage brought by FAST process is that no obvious grain growth was observed for the highly dense sample sintered at 1950 °C which is high enough to promote grain growth because the grain-boundary migration is a thermally activated process.
Thus, the grain growth is effectively prohibited.