Threshold Conversion for Field Emission Scanning Electron Micrograph of Glass-Alumina Composites in Determining the Activated Interfaces

Activated alumina interfaces in glass-alumina composites during isothermal sintering at 710°C by a novel colloidal processing was extracted by the threshold conversion of the micrograph obtained by a field emission scanning microscope. The relative ratio of the activated alumina interfaces in the final stage of sintering to that in the initial stage of sintering was calculated. The kinetics equations of both the evolution for the activated alumina interfaces during isothermal sintering and its effect on the linear shrinkage of the glass-alumina composites were established. The results show that the activated alumina interfaces in the final stage of sintering are 1.256 times more than that in the initial stage of sintering. The increased alumina interfaces decreases the total shrinkage rate of the glassalumina composites, in which a particular obstruction of the viscous flow of the glass matrix is suggested.


Introduction
Glass-alumina composites (G-A composites) are essential composites, for which two main categories exist, in one alumina or glass serve as matrix while the remaining phase is a dispersion; the other is the so-called sandwich structure in which bulk glass and bulk alumina are bonded together.For the first category, the effect of the alumina content, particle size variation on the bulk crystallization [1], mechanical properties [2] and interfacial fracture [3] is focused on.For the two-layer sandwich structure, the mechanical properties and the structure reliability [4] are focused on.For the three-layer sandwich structure, the so-called Laminated Low-temperature Cofired Ceramic (LTCC) is focused on, for which the effect of alumina on the sintering shrinkage for LTCC containing an inner-self-constraining layer [5] and the constrained sintering and densification kinetics [6] are extensively investigated.
Typically, in a G-A composites, the glass matrix exhibits a much higher sinterability compared to alumina [7,8].Sintering of glass has been widely investigated providing results on densification and flow during sintering [9].On the other hand, it has been confirmed that alumina does have a significant effect on the sintering kinetics [10][11][12], however, to our knowledge; it is still a question to determine its quantitative effect.Hence the determination of the quantitative details for alumina is a remaining problem.
To our knowledge, digital image processing has been proposed as an effective way for determining details in materials characterization [13,14].In this article, field emission scanning electron micrographs (FE-SEM) of fractured surfaces of G-A composites during isothermal sintering at 710°C are obtained.The activated alumina interfaces in the initial and final stage of sintering are extracted via the threshold conversion in digital image processing based on which the relative variation of the interfaces is calculated and was verified for availability with that obtained from an integrated liquid phase sintering model.Digital image processing can be an effective way of establishing a kinetics equation.

Experimental 2.1. Glass-alumina composites and characterization
47.5g glass powders (Na 2 O-CaO-SiO 2 system, prepared by our research group) with mean particle size of about 50µm and 2.5g alumina powders (Shanghai Chemicals Corporation, Shanghai, P. R. China) with a mean particle size of about 50µm were mixed homogeneously, and moistened by adding 8g distilled water.4wt% of the total weight of the mixed powders of PVA aqueous solution (10wt%) were added into the powders and mixed homogeneously for at least 1h.The suspensions were cast into a glass mould with an inner cavity dimension of 10cm×1cm×2cm, and then dried at ambient conditions for at least 24hs.The dried green body was then imbedded in the industrial alumina powders bed in the muffle to remove the PVA.A typical schedule for the removal of PVA and detailed discussions were given elsewhere [15,16].Sequentially, the body was treated at a heating rate of 5°C/min to 710°C, and held at 710°C for 2mins and 20mins, respectively.Then, the composites were fractured, and the microstructure of the fractured surfaces was observed by a Field Emission Scanning Electron Microscope (FE-SEM, JSM-6700, JEOL, Japan).No spraying of the Au film was conducted before observing with a purpose of protecting the structure details.

Image processing and analysis
Image processing was conducted in the Origin software (version 8.0) [17] and the basic steps are illustrated by: Firstly, histograms of the obtained micrographs (pseudo three-color image) of the fractured surface of G-A composites for 2mins and 20mins were analyzed for the gray scale levels distribution; Secondly, threshold conversion of the images was conducted based on the total gray scale levels distribution of the G-A composites and the alumina component, in which the lower and upper bounds of the threshold were determined; Thirdly, the local gray scale levels for the activated alumina grains were extracted by a discrete summation algorithm and normalized.Then the ratio of the activated alumina interfaces for 2mins to that for 20mins was calculated; Finally, the ratio of the activated alumina interfaces in the initial to that in the final stage of sintering was calculated, and the kinetics equation was established.

Structure evolution during isothermal sintering
The microstructures of the G-A composites for 2mins and 20mins are given in Fig. 1 (a) and (b), respectively.It can be seen that viscous flow of the glass matrix is the leading mechanism during sintering [7].The glass/alumina interfaces for 2mins and 20mins are given in Fig. 2 (a) and (b), respectively.Compared with samples sintered for 2mins, a more compacted bonding is exhibited for 20mins as obvious cavities at microns are residual along the interface for 2mins.On the other, good bonding can be confirmed by the rough fractured surface of the glass matrix due to the bonding between the glass and the alumina.

Threshold conversion and the kinetics equation
For the threshold conversion of the images, the microstructures of alumina in the composites sintered for 2mins and 20mins are observed in Fig. 4 (a) and (b), respectively.The corresponding histograms are given in Fig. 5  It is obvious that both of the alumina in the composites show a histogram of double gray scale level distribution, and the median levels are 80 and 110.Based on this result, two principles for selecting Fig. 2 for threshold conversion are given: For the first principle, a fractured surface is chosen as the origin for digital image processing where the fracture tends to take place, which will aid extraction of the activated volume from a statistical viewpoint; For the second principle, the origin image for processing should contain glass, alumina, and the interface, which is essential for the analysis of the gray scale levels distribution.It needs to be addressed that effective pixels with higher gray scale levels are preserved and those with lower gray scale levels are all fixed to 0 in order to show the exact contribution of activated alumina interfaces.In accordance with [7,18], the effective activated volume of the activated alumina interfaces is defined as ln ( ) where the diffusion coefficient D is defined as and R is the gas constant, T is the sintering temperature, ΔG is the change in free energy, p is the pressure, γ is the geometric factor, a is a crystal lattice constant, and ν is the Debey frequency.At the onset of sintering, a system is characterized by a starting effective activated volume v 0 .From the viewpoint of processes occurring during sintering, it can be described as gravitation of the electronic system towards an equilibrium state [19].The equilibrium state of the system can be characterized by the equilibrium activated volume v + .The effective activated volume v of a system at any moment during the sintering process is a parameter that, with the increase of sintering time, gravitates towards the equilibrium activated volume.
From a physical viewpoint the effective activated volume of a system can be defined as v=(N 0 /N r )v + , where N 0 represents the concentration of all defects at any given moment and N r represents the equilibrium concentration of defects in the analyzed system.N 0 /N r can be rewritten as , where the superscripts lowlevel and highlevel demonstrate the lower and higher levels of the image processing results.A total ratio of the summation of the gray scale counts corresponding to lower levels lowlevel i n and that to the higher levels highlevel i n is calculated for estimating the evolution of the alumina interfaces, given by lowlevel lowlevel highlevel highlevel According to Fig. 7, N r /N 0 is determined as 1.25, indicating that the total alumina interfaces in the G-A composites sintered for 20mins are 1.25 times more than that for 2mins.

Kinetic equation for sintering shrinkage
According to [18], increment of the effective activated volume can be simply defined as In this case, the time constant τ is 113.9min, by introducing N r /N 0 of 1.25 into the above equation and taking into account of v=(N 0 /N r )v + , the v 0 /v + -1 is determined as -0.204, and eq.( 5) can be rewritten as 1 0.204 exp( ) 113.9 According to our previous established model for these G-A composites, the value of v 0 /v + -1 is from -0.29 to -0.11, which confirms the effectiveness of eq. ( 6).
According to [14], the sintering time dependent linear shrinkage can be expressed by 0 0 exp( ) ( ) 113.9 where K 0 is a constant, R is the gas constant, E is the process activation energy, T is the sintering temperature, n is a constant which depends on the process mechanism, and t is the sintering time.The parameter ϕ(t) represents a measure of the degree of sintering.If sintering is viewed as the consequence of increment of the activated alumina interfaces, then the degree of sintering can be defined as the ratio between the equilibrium activated volume and the effective activated volume, ϕ(t)=v + /v, then taking into account of eq. ( 7) we obtain 1 0 0 exp( ) 1 0.204 exp( ) 113.9 113.9 Eq. ( 8) is the alumina dependent kinetic equation for isothermal sintering at 710°C.It is obvious that the increased activated alumina interfaces have a negative effect on the increase of the linear shrinkage of the composites.The constant K 0 can be inferred as negative.From eq. ( 8), for the total shrinkage of G-A composites, alumina decreases the overall shrinkage governed by viscous flow of glass during sintering.

Conclusions
Threshold conversion for extracting the activated alumina interfaces in the glassalumina composites during isothermal sintering was conducted.Based on processing of FE-SEM micrographs of the G-A composites, the kinetic equation of the evolution of activated alumina interfaces corresponding with its effect on the linear shrinkage was established.Two basic conclusions are drawn as (1) the activated alumina interfaces in the final stage of sintering are 1.256 times higher than that in the initial stage of sintering; (2) the increased alumina interfaces decrease the shrinkage rate of the composites, during which a particular obstruction of the viscous flow of the glass matrix is confirmed.

Fig. 3 .
Fig. 3. Histograms of the gray scale levels for Fig. 2 (a) and (b) as the pseudo three-color images.

N
are the activated defects volume (in arb.units) at the given moment and the equilibrium state, and total 0 N , total r N are the total defects volume (in arb.units) at the given moment and the equilibrium state.Actually,