*3.1. As-Received Sample*

HR-SEM showed that GQ sample contained fine powder with average grain size at the range of 250–350 nm. This yielded high-quality XRPD di ffractograms without preferred orientation

The crystal structures of Mg2TiO4 and MgTiO3 in sample GQ after 5 h annealing at 1200 ◦C and scanned at room temperature by XRD and analyzed by Rietveld software are given below, in comparison with previously published data. The Rietveld diagram is shown in Figure 1. The phase amounts in sample GQ found as 95.5 wt% MgTiO3 with 4.5 wt% MgTiO4.

**Figure 1.** (**a**) Rietveld diagram (FullProf) of sample GQ after 5 h annealing at 1200 ◦C and scanned in a Rigaku di ffractometer at room temperature (whole 2θ range). (**b**) Rietveld diagram (FullProf) of sample GQ after 5 h annealing at 1200 ◦C and scanned in Rigaku di ffractometer at room temperature (small 2θ range).

The lattice parameters of MgTiO3 in sample GQ at room temperature after annealing at 1200 ◦C for 5 h in comparison with ICDD data base are given in Table 1.


**Table 1.** RT lattice parameter of MgTiO3.

The lattice parameters of Mg2TiO4 in sample GQ at room temperature after annealing at 1200 ◦C for 5 h in comparison with ICDD data base are given in Table 2.

**Table 2.** Room temperature lattice parameters of Mg2TiO4.


The atomic positions of MgTiO3 in sample GQ at room temperature as refined after annealing at 1200 ◦C for 5 h in comparison with Reference [3] are given in Table 3 (\*Rwp 11.88, χ2 = 1.34).

**Table 3.** Ion positions in MgTiO3 as received. (\*) Hot stage before heat treatment; (\*\*) Rigaku conventional diffractometer.


The atomic position of Mg2TiO4 in sample GQ at room temperature after annealing at 1200 ◦C for 5 h in comparison with Reference [3] is given in Table 4.

**Table 4.** The atomic position of Mg2TiO4 (XRD data from Rigaku conventional diffractometer).


#### *3.2. High-Temperature XRD (HT-XRD)*

The lattice parameters versus temperature for the sample GQ containing geikielite and qandilite are listed in Table 5. The lattice parameters for the sample, which was scanned after 1 h in previous study [4], are given in Table 6.

**Table 5.** Lattice parameters of MgTiO3 and Mg2TiO4 as function of temperature in the present investigation (sample GQ). All parameters are given in Å.


\* uncertainty = 0.0003 Å. # uncertainty = 0.0008 Å.

**Table 6.** Lattice parameters of MgTiO3 as function of temperature in a previous investigation [4] of sol-gel product.


A uncertainty = 0.0002 Å. c uncertainty = 0.0005 Å.

Figure 2 shows that the lattice parameters versus temperature of the Mg2TiO4 perfectly integrated with literature data obtained by HT-ND [5].

**Figure 2.** Lattice parameter a of the reference Mg2TiO4 material versus temperature from HT-XRD of sample GQ in comparison to reported HT-ND data [5].

#### *3.3. Thermal Expansion Coe*ffi*cients for the Reference Material (Mg2TiO4)*

The lattice parameters versus T-25 (◦C) were fitted as a polynomial Aj(T) = Aj 0 + k1 (T − 25)+ k2 (T − 25)<sup>2</sup> as in Equation (5). Then, using Equation (6), αi j = ki/Aj 0 obtaining <sup>α</sup>A<sup>j</sup> = (Aj- Aj0)/[Aj 0 (T − 25)] = <sup>α</sup>1+ α2 (T − 25) as given in Equation (7), or γ = (Vj- Vj0)/[Vj 0 (T − 25)] = γ1+ γ2 (T − 25) as given in Equation (8). The thermal expansion coe fficients (TEC) for the Mg2TiO4 were calculated from the data of Table 1 and compared with published data [5] made by ND with the selection of similar temperature range. Equation (9) shows the TECs of Mg2TiO4 from this study HT-XRD (GQ sample) 25–890 ◦C

$$\begin{aligned} \alpha\_{\text{a}} &= 8.3 \times 10^{-6} + 2.9 \times 10^{-9} \text{ (T} - 25) \text{ [1/} \text{ $^{\circ}\text{C}]} \\ \gamma &= 2.5 \times 10^{-5} + 9.3 \times 10^{-9} \text{ (T} - 25) \text{ [1/} \text{$ ^{\circ}\text{C}]} \end{aligned} \tag{9}$$

Since the uncertainty of the lattice parameter is ~0.1% and the uncertainty in the temperature is ~0.2%, the maximum uncertainty of the terms in the reported equations for thermal expansion coe fficient is ~0.3%. Equation (10) shows the TEC of Mg2TiO4 from previously published data [5], studied by HT-ND for selected temperature range 25–890 ◦C.

$$\begin{aligned} \alpha\_{\mathfrak{a}} &= 9.2 \times 10^{-6} + 1.9 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}\\ \gamma &= 2.7 \times 10^{-5} + 6.2 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]} \end{aligned} \tag{10}$$

#### *3.4. Thermal Expansion Coe*ffi*cients for MgTiO3*

There was excellent agreemen<sup>t</sup> between the high-temperature lattice parameter data of MgTiO3 made in the present investigation by comparison to the results found in the higher temperature range for xerogels from the HT-XRD in situ study of seven samples [4], as shown in Table 6. It seems that the presence of qandilite did not a ffect the TECs of the geikielite. HT-XRD data of the GQ sample together with published data [4,8] of MgTiO3 are plotted in Figure 3.

**Figure 3.** (**a**) Lattice parameter a, (**b**) lattice parameter c and (**c**) cell volume versus temperature for MgTiO3 from present GQ and previous samples HT di ffraction. Data taken from this work and [4,7,8].

For the present HT-XRD study, with the data collected at a temperature range between 25 and 890 ◦C, the overall thermal expansion coefficients for the MgTiO3 are given in Equation (11).

$$
\alpha\_{\rm a} = 8.4 \times 10^{-6} + 2.0 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$

$$
\alpha\_{\rm c} = 1.1 \times 10^{-5} + 1.7 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]} \tag{11}
$$

$$
\gamma = 2.8 \times 10^{-5} + 6.5 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$

TECs obtained from previous sol-gel product at a temperature range between 700 and 1300 ◦C [4] (using Table 6) are given in Equation (12).

$$\alpha\_{\rm a} = 8.6 \times 10^{-6} + 1.8 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}$$

$$\alpha\_{\rm c} = 1.3 \times 10^{-5} + 9.510^{-10} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]} \tag{12}$$

$$\gamma = 2.1 \times 10^{-5} + 3.0 \,\mathrm{^\circ} \,\mathrm{[T - 25)} \,\mathrm{[1/°C]}$$

Thermal expansion expression for the sol-gel derived products are calculated by combining the present and previous HT-XRD data [4] (Tables 5 and 6) with the whole temperature range (25–1300 ◦C), and the overall thermal expansion coefficients for MgTiO3 are given in Equation (13).

$$
\alpha\_{\rm a} = 8.5 \times 10^{-6} + 1.9 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$

$$
\alpha\_{\rm c} = 1.1 \times 10^{-5} + 1.7 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]} \tag{13}
$$

$$
\mathrm{v} = 2.8 \times 10^{-5} + 6.0 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$

Thermal expansion expressions for solid-state reaction products calculated from HT-ND studies between 23 and 1212 ◦C of MgTiO3 made by solid-state reaction [7,8] are given in Equation (14).

$$
\alpha\_{\rm a} = 9.4 \times 10^{-6} + 1.8 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$

$$
\alpha\_{\rm c} = 1.2 \times 10^{-5} + 1.2 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]} \tag{14}
$$

$$
\gamma = 3.1 \times 10^{-5} + 4.0 \times 10^{-9} \,\mathrm{(T - 25)} \,\mathrm{[1/°C]}
$$
