Kinetics of Integrated Liquid Phase Sintering of Glass-Alumina Composite : Activated Pores Evolution

Activated pores in the glass-alumina composite during isothermal sintering at 710°C by colloidal processing were extracted by the threshold conversion of the micrograph obtained with a field emission scanning microscope. The relative ratio of the activated pores in the final stage of sintering to that in the initial stage of sintering was calculated. The kinetics equation of the evolution of the activated pores during isothermal sintering was established. The pores evolution confirms the viscous flow of the glass matrix, indicating the validity of the predominant liquid-phase sintering of the composite.


Introduction
Glass-alumina functionally gradient materials (G-A FGMs) are essential FGMs as the stress can be redistributed which can effectively inhibit the formation of Hertzian cone cracks owing to the gradual variation of the Young's modulus [1,2].The resistance to slidingcontact may be optimized as well [3].In 2006, Cannillo and co-workers proposed a method of percolating molten CaO-ZrO 2 -SiO 2 glass into a polycrystalline sintered alumina substrate to prepare G-A FGMs and the effect of sintering temperature and time on the penetration depth was studied [4][5][6].In addition, the crack propagation of the prepared G-A FGMs was simulated by coupling the finite element method with the Griffith theory, of which the numerical results indicated that pores deeply influenced the evolution damage [7].Recently, G-A FGMs using Na 2 O-CaO-SiO 2 glass and polycrystalline alumina as ingredient materials based on a novel freeform fabrication technology, was prepared by our research group [8,9].In the previous articles, sintering properties [10], integrated liquid-phase sintering mechanism [11], microstructure evolution [12], and pore independent crack propagation of the G-A FGMs [13] were discussed.
Typically, the local of the G-A FGMs can be regarded as glass-alumina composite (G-A composite).As for G-A composite, the sintering behavior has been confirmed to deviate from pure liquid phase sintering governed by viscous flow and to be determined by coactions of both glass and alumina [14], yet up to date, for which no quantitative method has been proposed.In a more recent article, we have checked the evolution of activated alumina interfaces during isothermal sintering [15].In this article, activated pores in the glass-alumina composite during isothermal sintering at 710°C by the colloidal processing are extracted by the threshold conversion of the micrograph obtained with a field emission scanning microscope, and the kinetics equation is established and discussed.

Preparation and characterization of the G-A Composite
In this article 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 mean particle size of about 50µm were mixed homogeneously, and moistened by adding 8g distilled water.The total weight of 4wt% of the mixed powders of PVA aqueous solution (10wt%) were added into the powders and mixed homogeneously for at least 1h.The suspensions were casted 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 detail discussions were given elsewhere [16].Sequentially, the body was treated at a heating rate of 5°C/min to 710°C at varied lengths of time and quickly cooled to room temperature in about 10 minutes.
The microstructure of the fractured surfaces was observed by the 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
The image processing was conducted in the software Origin (version 8.0) [17].In order to extract the pores, the local pixel counter-filling method was adopted during image processing.In a micrograph, the pores are characterized with lower gray scale levels in the inner part than that in the boundary area, based on which the inner part of a local individual pore is obtained and then the gray levels was changed to minimum.Applying this to all the pores in the fractured surface, then a binary micrograph was obtained using the threshold conversion method.It needs to be addressed that although the fractured surfaces are two dimensional, a relative ratio of the pores volume is finally used for the kinetics equation, aiding the valid estimation.
To calculate the relative volume of the activated volume, the local gray scale levels for the activated pores were calculated by a discrete summation algorithm and normalized.

Definition of the activated pores
In accordance with references [11,18], the effective activated volume of the pores 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

(
) ( )  ( ) , and ( ) , 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 pores, given by lowlevel lowlevel highlevel highlevel

Evolution of activated pores
The fractured surfaces of the G-A composite and the corresponding binary images at varied lengths of time at 710°C are given in Fig. 1.Calculating with a t o t a l 0 0 0 / N N N = , the relative pore volume at varied lengths of time is listed in Tab.I. From Fig. 1 and Tab.I, the total pore volume increases from 2mins to 4mins, then decreases till 14mins.For the microstructure at 2mins, no enough liquid-phase is formed by the large amount of vacancies, confirmed by the large amount of vacancies in the binary image.The pore volumes at 4mins, 10mins and 14mins are trained by the model given in eq. ( 5) [18], yielding the activated pore volume V + at the equilibrium state of 0.01, and the time constant τ of 5.02 min.The non-linear fitting results are given in Fig. 2.

Tab. I
According to reference [11,18], the sintering time dependent linear shrinkage controlled by pore evolution can be expressed by where K FP is a constant at fixed temperature, and if we define ( ) where ( )

Conclusion
Activated pores in the glass-alumina composite during isothermal sintering at 710°C by colloidal processing were extracted by the threshold conversion of the micrograph obtained with a field emission scanning microscope.The kinetics equations of the evolution of the activated pores during isothermal sintering were established.The pores evolution confirms the viscous flow of the glass matrix, indicating the validity of the predominant liquid-phase sintering of the composite.

Fig. 1 .
Fig. 1.Fractured surfaces and corresponding binary images at varied lengths of time at 710°C

Fig. 2
Fig. 2 Non-linear fit of the activated pore volume v as a function of time