**4. Discussion**

Figure 2 shows that the lattice parameters versus temperature of the reference material, Mg2TiO4, are in excellent agreemen<sup>t</sup> with the published HT-ND data [5]. Figure 4 shows a comparison between calculated lattice parameters versus temperature derived from Equations (9) and (10) showing complete overlapping of the lattice parameters of the reference material (Mg2TiO4) (Equation (9)) and published HT-ND study of Mg2TiO4 [5].

**Figure 4.** Calculated lattice parameters of Mg2TiO4 versus temperature, derived from Equations (9) and (10).

A comparison of Tables 5 and 6 shows that in MgTiO3 there was no significant change in the atomic positions along the experimental temperature range (25–890 ◦C).

There was excellent agreemen<sup>t</sup> with present and previous HT-XRD data of a sol-gel MgTiO3 product after 1 h firing [4] (Figure 3). The agreemen<sup>t</sup> with former HT-XRD on sol-gel products should be appreciated because, in contrast to usual TEC investigations, which are done on a single sample, it was done with different sample at each temperature. In order to eliminate the experimental scattering, the calculated lattice parameters versus temperature were plotted. Figure 5 shows that there was fair agreemen<sup>t</sup> between the lattice parameters versus temperature, between RT and 1300 ◦C, of all the sol-gel products of MgTiO3 studied in HT-XRD data (present work and Reference [4]) in comparison with published results of minor MgTiO3 phase in reference [7,8].

However, the lattice parameters of the sol-gel products were slightly lower. As presented in the literature [1,2], there is an asymmetric solubility gap in the geikielite with dissolving some amount of Ti at elevated temperatures. The lattice parameters of sample GQ (MgTiO3 with a small amount of Mg2TiO4) fit those of stoichiometric MgTiO3 as reported in Reference [4]. This supports the phase diagram [1,2] that there is no Mg solubility. Since sample Kar2 [7,8] was a mixture of small amounts of MgTiO3 and TiO2 with MgTi2O5 as a major compound, it is reasonable to attribute the slight decrease of the lattice parameter of MgTiO3 as stated in Reference [8] to some excess of Ti. In order to verify this hypothesis, we conducted an additional HT-XRD study of a second sol-gel product with a mixture of MgTiO3 and MgTi2O5. The xerogel with 1 < Mg:Ti < 2 was annealed 5 h at 1200 ◦C forming 78 wt% geikielite and 22 wt% karrooite. We designated this sample as "GK".

Figure 5 shows that at elevated temperatures, the lattice parameters of the MgTiO3 as obtained from HT-XRD were slightly higher than those in sample GQ and in reference [4]. Moreover, they fit very well with those of sample Kar2 [7,8]. This confirms our assumption that the gap between the lattice parameters originated from excess of Ti in the Kar2 geikielite sample from references [7,8].

**Figure 5.** (**a**) Calculated lattice parameter a of MgTiO3 versus temperature, derived from Equations (13) and (14) and experimental lattice parameter a of geikielite from sample GK. (**b**) Calculated lattice parameter c of MgTiO3 versus temperature, derived from Equations (13) and (14) and experimental lattice parameter c of geikielite from sample GK. (**c**) Calculated lattice volume of MgTiO3 versus temperature, derived from Equations (13) and (14) and experimental lattice volume of geikielite from sample GK.

The difference between the lattice volumes for sample *GQ*+ Reference [4] and sample *GK*+kar2 versus temperature is given in Figure 6, which shows that the gap between the lattice parameters increased with temperature until 1000 ◦C and then slightly decreased.

**Figure 6.** Difference between lattice volume of geikielite in GK sample in this work + references [7,8] and the GQ sample in this work+ reference [5] as function of temperature (using calculated data).

In this work, stoichiometric geikielite from eight samples made by sol-gel technique yielded new HT-XRD data. Therefore, as a result of the present work, it was found that there is no single set of TECs for the geikielite. It agrees with the phase diagram determined by Shindo [1] with an asymmetric solubility range in the geikielite. Both the sol-gel sample (GK) measured by HT-XRD and solid-state reaction (Kar2) measured by HT-ND were mixtures of geikielite and karrooite with maximum excess

of Ti in the geikielite. Furthermore, both GK and Kar2 samples had similar lattice parameters, higher than the new data of the stoichiometric geikielite. Neither sample preparation nor diffraction method modified the TECs in geikielite. The fact that the sample GQ data integrated in seven stoichiometric samples [4] agrees with the phase diagram determined by Shindo [1] with absence of Mg solubility.
