ternary equilibrium diagram (Figure 2) Represent the three compositions in the SiO2-Al2O3-MgO system, the concentration of oxides was determining without loss on content and ignition of the MgO. The compositions of S1, S2and S3, were found in the region sapphirine which is small area in vicinity of 6 invariant points of cordierite [19]. The compositions S4 & S5 were located in cordierite region. The differences observation was related to raw materials which starting with and S4& S5 formulation with talc which gives the nearest composition of cordierite stoichiometric point, mainly to MgO and SiO2 concentration. One of the major problems of e cordierite is its small area of existence due to the vicinity of 6 invariant points
XRD measurements are performed at an angle of 10-80o with scanning speed of 5°/min using an LabX XRD-6000 X-ray Diffractometer from Shimadzu with CuKα radiation (1.5406AO) operated at 30 mA and 40 keV. The X- Ray data was plotted using the origin Pro software and the peaks were matched with JCPDS software to get the phases present. The corrected Debye-Scherrer formula was used calculated grain size (Dhkl) of the identified crystalline phase:

λ = wavelength of CuKα1 (1.54056 Å). However, the cordierite nanocrystalline size was determined as shown in Table 1.2 and it was in the range of 30–80 nm.
Table2: XRD spectral data for different samples
samples
|
2-Theta
|
d(nm)
|
I%
|
FWHM
|
G.S(nm)
|
S1
|
17.902
|
0.4957
|
6.3
|
0.159
|
65
|
52.319
|
0.1742
|
50.5
|
0.162
|
69
|
57.332
|
0.1607
|
98.5
|
0.195
|
54
|
S2
|
25.827
|
0.3448
|
85.6
|
0.218
|
42
|
36.922
|
0.2435
|
89.3
|
0.326
|
27
|
44.906
|
0.2018
|
62.9
|
0.299
|
30
|
S3
|
28.04
|
0.3175
|
86.6
|
0.17
|
59
|
32.74
|
0.2731
|
18.4
|
0.195
|
49
|
66.471
|
0.1404
|
86.4
|
0.153
|
81
|
S4
|
43.275
|
0.2089
|
17.4
|
0.177
|
58
|
47.633
|
0.1905
|
5.9
|
0.191
|
53
|
66.461
|
0.1406
|
67.6
|
0.161
|
75
|
S5
|
19.13
|
0.4635
|
5.5
|
0.167
|
60
|
35.272
|
0.2545
|
19.2
|
0.153
|
72
|
57.643
|
0.1598
|
100
|
0.163
|
70
|
The table 2 shows a summary of the results of the process for the X-ray diffraction examination, which include all parameters values ( were obtained for all the systems prepared by the chemical precipitation method that were clarified in the paragraph of the practical part.
The results in the table showed values at three peaks in the first system (S1)(1,1,1), which are at with grain size (G.S) 65nm,69nm and 54 nm respectively . This is shown in Figure 3, where this figure appeared at a temperature of 1250°C several systems added to the cordierite system, namely spinel, corundum and cristobalite , these systems result from an internal interaction of the three reactants (Mgo, Al2O3 ,SiO2) at temperatures below 1250°C, with regarding second system S2 (1,2,1) , it can be noted that system include cordierite with appearing sub system ( spinel, cristobalite, corundum) .
As the ratio of silica to alumina change because of the reaction of alumina and silica present in thechemical composition. The cordierite peaks cordierite began to show only at temperature of 1200 °C, and then intensified when the temperature reach 1250 °C. The cordierite phase was observed in the five compositions, at 1250 °C. Askin et al. [20] reported similar results.
The changes that have occurred to the system S3 (1,1,2) can be observed where S3 include high ratio in comparable with AL2O3 and Mgo , from figure 3, we notice the decline of the cordierite curve and the emergence of other systems (S3, S5) clearly as a result of side reactions between the materials.
The system S4 ( 2,1,2), the result show that spinel curves was dominant in addition to cordierite system and this is attributed to the reaction of AL2O3 and Mgo at temperature under 1250°C and formation of spinel .finally, the system S5 is a fixed system in which the cordierite system is achieved in a stable and clear way, in addition to other systems, and this means that at a temperature of 1250°C, cordierite can form at a ratio (2,2,5) and this is agreement with other author's results [17,18]
The densification temperature plays important role in the cristobalite and spinel phase transformation into cordierite phase. As the temperatures of sintering range 1200–1300 °C, cordierite phasewill be dominant phase, butcristobalite and spinel are undetectable.[21]
The peaks Mullite phase will start to disappear at 1200 °C, according to [22]When thetemperature reach 1250 °C the mullite phase may be react with (MgO) magnesium oxide in the talc to create cordierite phase. The average diameter of the particles less 100 nm, which is similar to previous studied reported that it is possible to obtained cordieritephase fromtalc and pure kaolin, [23]. For the system S5 which will the particles have diameter smaller than 100nm this may contributed to form cordierite phase, the kineticsreaction of solid state is effected by surface area. It was also found different sizes of the particle in the mixture of different components, it will be favor of wider distribution of the particles, lead to high area of the contact which is significant parameter in formation and diffusion new phase.
The diameter of the about all particles of composite S5 are a smaller than 2 μm, which may related to the cordierite formation, since kinetics of the solid state reaction is infected by surface area. The waste mixture also was found that containing particle with different sizes favored distribution of a wider particle size, will increasing the contact area, which is a important factor in the formation and diffusion of cordierite phase. The largest mean particle size of Composition S5 70 nm.
Figure 3 X-ray diffraction shows, the XRD patterns of the compositions after sintering at 1250 °C.The most detected phases were spinel, magnesia, cristobalite and corundum peaks as shown in Figure3. The result of reaction between silica, alumina and magnesia at 1250 °C, in the system (MgO·Al2O3·SiO2) resulted in dominant phase emergence of cordierite, which is the aim of this study.
Greater intensity peaks of composition S4 was observed from the Analysis of the peaks of cordierite for the system S3 and S4, this due to the smaller grain size, which making them more reactive. furthermore, at this temperature there was a small increase in cristobalite peaks
at 1200 °C,Cordierite started to formthe intense peaks showed increasingly at 1250 °C. for Composition S5 figure 3 which was similar to composition S4,
the mechanism can beexplaining this, always more probable of solid state has been considered reaction between binary compounds, and then among three compounds. For this reason, the formation of the cordierite (2MgO·5SiO22Al2O3) will start from the two compounds reaction, or a binary compound and an oxide reaction.
The presence of impurities in the raw materials which been used, can cause the formation of glassy phase, but considering the effectis not significant so that it will be not considered.
Scanning electron microscope examination
The structure was examined with Field-Emission scanning electron microscopy of MIRA3 TESCAN, the figure 4 represent the morphology of system S1 where the particles agglomerate slightly and most of them are spherical with a small number of reunion at lower sintering
The shapes and magnifications show the coherence and complete interaction between the materials and that the value of the diametersD1= 76.27 nm, D2= 42.63nm, D3=73.51 nm, and the figure 5 represent the percentages of the substances involved in the reaction, and it can be observed that there is a consistency and accuracy in the preparation process that was interpreted by EDXtest.
The figure 6 shows an electron microscope image of the S2 system. Through the image, it is shown that the average particle size is between 44-59 nanometers, and the shape of the precipitated particles is close to the cuboid. It is noted in the image that there is great homogeneity in the reactants and high fusion at degrees of 1250°C.The results of EDX in figure 7 show that there is a great convergence of the stoichiometric ratio of practical work with the results of EDX according to the system (1,2,1) (MgAl4SiO9) and this explains the accuracy of the results of using the preparation method. For system S1 and S2 the high content of alumina has not high impact on cord rite formation because the reaction with other constituent need slightly higher than this temperature.
regarding system S3 (MgAl2Si2O8), the figures 8 was clarified that the average particle size is between 31 to 123 nanometers. It is also shown that the particle size is semi-cubic and semi-rectangular. As for the EDX test, the results in figure 9 showed a degree of accuracy between the theoretical side and the results of the EDX test, and this proves the success of the appropriate preparation process.
Figure 10 shows the FESEM images of sample S4 (Mg2Al2Si2O9), the average grain size range is (34-58) nm with homogeneity of the structure,Clearly, it is not possible to distinguish between the materials, as we can observe the uniform distribution of the particles and figure 11 show EDAX result
The figure 12 shows the system S5 (Mg2Al4Si5O18), and we note the formation of cordierite in a homogeneous and clear manner, and the grain size ranges between 33 and 49 nanometers, as can be explained by the EDX test in figure 13, the highest peak intensity for oxygen element followed by silica, alumina and magnesia respectively and this is explaining the accuracy of chemical precipitation method for preparing cordierite system.
Microstructure analysis for the specimens systems S3, S4 and S5 as shown in Figures (8,10,12), after heat treatment with applied 42°C/min heating rate and 120 minutes holding time at 1250 oC as sintering temperature.
The microscopic structure of specimen S3, which was prepared by sintering at 1250°C, shows that the crystal structure was circular in shape similar to round petals, a shape which is almost similar to that observed by the source [24].
The researchers investigate the growth and nucleation of cordierite crystals processes from liquid phase and indicated there are three different shapes, presented the structure such as first solid nucleate crystals inclusions in liquid phase and radially growth as rose petals, second The crystals isolated growth from both compact crystal layers and outer surfaces third growth from the center of specimen. The configuration of the crystals of the S4 system which is sintered at 1250 °C hexagons and elongated petals presented the morphology, the appearance is similar to finding which is reported by [25].
Crystals structure of component S4 is showglassy phase with heterogeneous crystals and an elongated tube-like morphology, which is due to the composition hashigh amount of flux. Also needle structure are visible may be related to mullite phase as shown in figure 10. Hexagonal crystals structure showed in composition S5 which is similar to morphology observed by [26,27]. This component was formulated with precursor of MgO and talc, which is may be responsible of different morphology, like the nucleation and parallel surfaces growth of the hexagons structure.