However, peak positions cannot move because of the collective recrystallization of ceramics ("...grains will grow up during the sintering...").

The higher the sintering temperature, the larger are the grains. This is for all materials that. Explanation is quite simple: entropy of fine-grained structure is smaller than the entropy of coarse-grained microstructure. In other words, coarse-grained structures are thermodynamically favorable structures as fine-grained. The increase in temperature allows the transformation of the structure towards thermodynamically favorable variant.

Some useful references:

 http://link.springer.com/article/10.1007%2FBF02385646#page-1

 www.setaram.com/wp-content/uploads/2015/01/L0080.pdf

www.math.psu.edu/cao/Papers_PDF/Randall-3-98.pdf

http://www.google.ro/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0CE8QFjAHahUKEwjK15ui04fIAhWK0hoKHQ5tAVw&url=http%3A%2F%2Fdigitalcommons.uconn.edu%2Fcgi%2Fviewcontent.cgi%3Farticle%3D6504%26context%3Ddissertations&usg=AFQjCNEjenHm8U1C73HiAGlwiPR4keA_EQ

In case of Silica (SiO2), the amount of crystobalite formed is directly related to the temperature of sintering. Injection molded silica mix (with wax as binder) converts slowly from amorphous form to the crystalline form, as sintering temperature is increased. Based on the application, the amount of crystallanity is controlled. For example in the case of investment casting, complete conversion of crystobalite is avoided as crystobalite is brittle and when completely transformed, breaks into powders. Since, ceramic cores have to withstand the temperature and metallostatic pressures of liquid metal, the crystobalite content is controlled for sufficient strength during pouring and sufficient brittleness to become powder as the stresses increase on its surface due to contracting metal. 

Very very thanks to all but I want to know more about the effect of sintering temperature on peak positions, lattice strain and lattice parameters or volume of unit cell.

Unit cell volume vs. sintering temperature? 

As I know there is no exact formula which connect volume and temperature . There are only experimental  data for well known materials  and approximate theoretical dependences. So count on their strength. 

Sintering of ceramics in presence of microwave or mm wave can produce fine micro-structure at lower temperature.  It will help achieving desirable properties in PZT.

grain growth is higher at higher temperature. with reference to peak and lattice strain this could be due to the impurities reaction that could happen at higher temperature. check what impurities are there in the powder.  

Dear Friend get a copy of the article from DMRL-Library, may be of some use

best wishes

Dr P K Maitra

Chapter

Recent Advances in Science and Technology of Materials

pp 193-201

Mechanical Properties and Microstructure of Glass Ceramics and Phase Separated Glasses

J. Zarzycki

Dear Dr. Kumar:

I copy again your question to approach each part, as follow:

“How does the sintering temperature affect the micro-structure of the ceramics?”

See, seems that there is some kind of equivocal or misconception at about the question.

The microstructure of a ceramic is the term used to describe the structure of ceramic in the micrometers scale. The microstructure elements are grains, grain-boundaries and pores. Despite of preponderance of grains, the major concepts applied to characterize grain can be extended to characterize pores and grains-boundaries, is est, size, size distribution and mutual orientation. The same ideas persist if the ceramic is polyphasic.

The microstructure is function of a set of factors determined in green body yet. It is possible to cite some of them as particle size, distribution of particle size, agglomerate fraction, aggregate fraction and apparent density of green body.

As whole, the effects of sintering temperature are connected with thermal activation of mechanisms the mass-transport that can be classified in two groups, as non-densifying and densifying. Well, in a gross manner but short, the actuation of densifying mechanism promote of shortening of distance between center of particles that leads to increasing of densification via shrinkage of compact ceramic. After rearrangement, with slight increasing of density (shrinkage), the ceramic submitted to sintering non-densifying, preponderate non-densifying mechanisms.

All ceramics, in fact compound, exhibit further sintering temperature. The fast way to access this temperature is running a dilatometry. Sintering temperature below of proper temperature does not allow high densification level, at around 98 % of theoretical density. Sintering temperature beyond of the proper sintering temperature gives grain growth only. But, each case should be approached with careful. Also, there are characteristics of compound. PZT powder can exhibit a loss of PbO to the atmosphere by volatilization. Further control of this phenomenon is necessary.

“If we sintered a ceramics at different sintering temperatures then how does it affect the micro-structural properties i. e. peak positions, lattice strain and lattice parameters or volume of unit cell.”

See, here is the source of possible kind of equivocal or misconception at about the question. From my viewpoint, after i.e. (ist est) the terms listed as follow: peak (diffraction lines) positions, lattice strain and lattice parameters or volume of unit cell are elements of structure nor microstructure.

“For the PZT ceramics we observed that volume of unit cell is increasing with sintering temperature. What is the reason?”

There are broad set of factors but temperature of sintering of undoped compounds should be at around 1200 oC. Long time of sintering and/or higher temperature gives volatilization of PbO that affect both microstructural and structural factors.

Kind regards

Marcos Nobre

Before studying any sintering effects you need to provide the stability of your chemical composition. If you observe increasing of a unit cell, it means that some changes are going in your composition. Thus, the conditions of sintering were chosen incorrectly...

Peaks positions can move with internal stress in your sample, but most of the time your unit cell's volume will decrease instead of increasing.

Peak positions can move only because of changes in a lattice parameter. Mainly it is going with changes in the chemical composition of a sample. Internal stresses only change the intensity of peaks (or parameters of Gauss curve for a peak), so usually we compare the ratio of intensity for neighbour peaks to evaluate the degree of residual stresses in a sample.

You most probably incorporate impurity atoms into your structure and that will change the unit cell size.

I agree with all the previous answers to your question. My oppinion is that, may be, you have some change in the composition of your ceramic, either with some evaporation or sublimation of one of the constituants (typically Pb), or some diffusion towards the sintering support of the ceramic (that is classical!). Take care also on the evolution of the unit cell (as a consequence of the evolution of the composition) at the surface of the ceramic that may be different to the one at the core of the ceramic.

However, peak positions cannot move because of the collective recrystallization of ceramics ("...grains will grow up during the sintering...").

Sintering temperature affects the grain size and density of the ceramics. Sometimes high sintering temperature leads to impurity phase. If impurity phase arise peaks will appear in XRD. In pure phase no change will appear in peak positions. But intensity of the peaks will vary on the basis of sintering temperature.