it is generally believed that nano - grained ceramics have their unique mechanical characteristics that are not commonly found in their coarse - grained counterparts .
strength is an important aspect of material for mechanical and particular applications under loading and static pressure . in some case , it is desirable to optimize strength to improve performance .
transparent mgal2o4 ceramic has received considerable attention and has been widely studied [ 3 - 6 ] because of its high melting point , good mechanical strength , high resistance against chemical attack , and extraordinary optical properties [ 7 - 11 ] .
presently , extensive work has been performed in studying the fabrication , micro - morphology   and transparent mechanism   of transparent mgal2o4 nano - ceramic . however , there is limited research on investigating one of the fundamental parameters of transparent mgal2o4 nano - ceramic the yield strength at high pressure and temperature .
the aim of this work is to study the yield strength of transparent mgal2o4 nano - ceramic at pressure up to 5 gpa and temperature up to 900c through the analysis of the shape of x - ray diffraction lines .
we carried out x - ray diffraction experiments on transparent mgal2o4 nano - ceramic using x - ray ( cuk ) diffractometer ( model dx-2500 ) .
the nano - mgal2o4 powder , with a median particle size of 30 nm , was prepared by a low - cost melted - salt technique .
two separated layers of nano - mgal2o4 and nacl cylinder were loaded inside a cubic pyrophyllite cell , which is a pressure - transmitting medium , and assembled to the press - standing piece with other modules including a carbon heater .
the temperature was measured by a nichrome - nisi thermocouple , which was passed through the press - standing piece in advance of calibrating the sintering temperature .
the samples were compressed from 1 to 5 gpa at room temperature and then heated from 300 to 900c under 4 gpa .
the samples peaks broaden asymmetrically , with a much more severe broadening on the large angular dispersive ( 2 ) side of the peak , as shown in the bottom two curves of fig .
1 . the results reveal that the applied pressure only affects the bridge parts of the grains .
meanwhile , the generated stress is not enough to cause any yielding at this stage . as pressure increases gradually , differential strain and small grain size are two major causes of peaks broadening .
during heating at constant pressure ( 4 gpa ) , the overall peaks remained almost unchanged up to 400c .
the peaks are significantly sharp and become more symmetric at temperatures above 400c , which is a clear proof of stress relaxation accompanied by stress redistribution over the entire sample ( fig .
it is interesting to note that the peaks shift to lower 2. this shift is apparently due to the effect of heating .
the profile of the observed diffraction peaks is a convolution of integrated effect of instrument response , grain size , and differential strain (  ) because of stress heterogeneity , lattice deformation , and dislocation density at high pressure and temperature .
we express that the observed full width at half maximum ( fwhm ) can be denoted as dobs .
according to the classic williamson - hall method and its subsequent variations , the differential strain (  ) of samples is defined as ( 221 ) , ( 013 ) and ( 222 ) diffraction lines of mgal2o4 at selected pressure and temperature conditions : a 1 gpa , room temperature , b 2 gpa , room temperature , c 3 gpa , 600c and d 4 gpa , 600c here , dins is the peak width at a stress - free state and d(p , t ) is the d spacing of a given lattice plane . in our calculations ,
we subtract the instrument resolution , but we can not disjoin the various contributions to the peak width changes .
therefore , we determined the strain by the ratio of the peak width to the peak position according to d spacing   such defined strain  can be derived from the slope of d versus d(p , t ) plot ( fig .
2 ) , which is an image of the complex contributions to the overall peak width changes .
figure 2 shows the significant slope changes associated with six selected pressure  temperature conditions . with increasing pressure from 1 to 5 gpa at room temperature ,
the derived differential strains increased dramatically , such as  = 0.0766  10 at p = 1 gpa and  = 0.4466  10 at p = 5 gpa , respectively .
the strains described here are derived from the peak broadening , which are different from the regular strains . as temperature ( above 400c )
is increased at constant pressure ( 4 gpa ) , there is a rapid reduction in the differential strain , which is probably caused by thermally induced strain relaxation because of a small increase in the internal cell pressure .
the slopes of straight lines provide differential strain information for the sample the grain size , especially when it goes down to nano - meter , contributes significantly to the diffraction line broadening .
hence , we investigated details about the dependence of the differential stress as a function of pressure , and temperature could be revealed by introducing the grain size in the same plot .
the strains have been derived for sample and for all high pressure / temperature observed .
we obtain the young s modulus values of 294 gpa for samples by nano - indentation experiment .
the calculated differential stresses and average grain size at various pressure and temperature conditions as blank - squares and solid - circles plots , respectively ( fig .
3 ) . as pressure increases , we observed two obvious yield points for samples , one at p = 3 gpa in the elastic deformation stage and the other at p = 4 gpa .
we think that the first yield represents  micro / local  due to the grain - to - grain contacts and thus local plastic deformation because of high stress concentration , and the second yield represents the onset of  macro / bulk  plastic deformation of the entire sample .
moreover , there is a slight addition of differential stress after the yielding when pressure changes from 4 to 5 gpa .
meanwhile , the diffraction peak widths do not vary as much after the entire sample yields .
our experiment results show that the dislocation density of the sample reaches certain saturation . the yield strength and average grain size as function of pressure ( left panel ) and temperature ( right panel ) .
the lines are meant to guide the eye only we studied temperature effects on the yield strength of sample at 4 gpa .
3 , right ) , there is a dramatically addition in the differential stress , which can be explained on the basis of our early discussion . above 400c ,
the stress drops drastically with heating to 700c due to thermally induced stress relaxation . on the other hand
, there is a slight negative slope in the differential stress with the temperature above 700c , which indicates that the sample gradually approaches a stress - free state .
the plot still shows grain size effects on the sample at this high pressure and temperature ( fig .
3 , blue - solid - circles ) . figure 3 , left reveals that there is no apparent grain growth at different high pressure .
the results show that both stress relaxation and grain growth occur simultaneously during the temperature increases . to further take this interpretation , palosz   and gleiter   developed a model for nano - crystals , which are generally viewed to consist of two structurally distinct components , a crystalline core and a surface layer
. the differential strain may also be due to the difference in elastic properties between these two components .
as grain size gradually grows with increasing temperature , the distinction between these two components is expected to diminish , which may also explain the more rapid decrease in the strength with increasing temperature .
in summary , yield strength is an important constitutive property of materials to define the onset of plastic deformation . and
we have shown the yield strength of transparent mgal2o4 nano - ceramic as a function of high pressure / temperature .
the excellent data reveal that the differential stress in nano - ceramic decreases as defects decrease during temperature increase , while grain growth further sharpens the diffraction peak .
more importantly , the low temperature ( 400c ) for the onset of stress relaxation has attracted attention regarding the performance of transparent mgal2o4 nano - ceramics as an engineering material .
this work was supported by nsfc of p. r. china under grant no 50272040 , fok ying tong education foundation under grant no 91046 , youth foundation of science and technology of sichuan province under grant no 03zq026 - 03 , nsfc of p. r. china under grant no 50742046 and nsfc of p. r. china under grant no 50872083 .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
 we report here experimental results of yield strength and stress relaxation measurements of transparent mgal2o4 nano - ceramics at high pressure and temperature . during compression at ambient temperature , 
 the differential strain deduced from peak broadening increased significantly with pressure up to 2 gpa , with no clear indication of strain saturation . however , by then , warming the sample above 400c under 4 gpa , stress relaxation was obviously observed , and all subsequent plastic deformation cycles are characterized again by peak broadening . 
 our results reveal a remarkable reduction in yield strength as the sintering temperature increases from 400 to 900c . 
 the low temperature for the onset of stress relaxation has attracted attention regarding the performance of transparent mgal2o4 nano - ceramics as an engineering material . 
Introduction
Experiment and Discussion
Conclusion
Acknowledgments
Open Access