Thermal Expansion of MgTiO3 Made by Sol-Gel Technique at Temperature Range 25–890 °C

MgTiO3 is a material commonly used in the industry as capacitors and resistors. The high-temperature structure of MgTiO3 has been reported only for materials synthesized by the solid-state method. This study deals with MgTiO3 formed at low temperatures by the sol-gel synthesis technique. Co-precipitated xerogel precursors of nanocrystalline magnesium titanates, with Mg:Ti ratio near 1:1, were subjected to thermal treatment at 1200 °C for 5 h in air. A sample with fine powders of MgTiO3 (geikielite) as a major phase with Mg2TiO4 (qandilite) as a minor phase was obtained. The powder was scanned on a hot-stage X-ray powder diffractometer at temperatures between 25 and 890 °C. The lattice parameters and the atomic positions of the two phases were determined as a function of temperature. The thermal expansion coefficients of the geikielite were derived and compared with previously published data using the solid-state synthesis technique, providing insights on trends in materials properties at elevated temperature as a function of synthesis. It was found that the deviation of the present results in comparison to previously reported data do not originate from the method of synthesis but rather from the fact that there is an asymmetric solubility gap in geikielite. The lattice parameters of this study present the property of stoichiometric MgTiO3 and are compared to previously reported non-stoichiometric MgTiO3 with excess of Ti. The values of lattice parameters of the non-stoichiometric versus temperature of geikielite found the same for both solid-state reaction and sol-gel products.


Synthesis
The magnesium titanates were prepared by the sol-gel method using metalorganic precursors: diethyl ethoxymagnesiomalonate, prepared by metallation of diethyl malonate (1), and titanium(IV) tetra-tert-butoxide (Aldrich), dissolved in anhydrous 2-propanol. The hydrolysis step was carried out at nearly room temperature, using a stream of hot air (about 100 • C) containing water vapor (superheated steam), during about 3 hours, to ensure total hydrolysis. The precipitated solid was filtered, washed with 2-propanol and left to dry in air for several days, until a constant weight was obtained. After analysis of the Mg and Ti content, this solid served as starting material for thermal treatment.
The powders were initially fired at 600 • C for 3 h. After the initial treatment, the sample with Mg:Ti 1.  (1). However, the expected Mg:Ti ratio was confirmed by inductively coupled plasma (ICP). The amount of impurities was below 10 ppm. Additional treatments were made at 1200 • C for 5 h in order to obtain well-crystallized powders. After the 1200 • C treatment, the sample was found with 95% geikielite and 5% qandilite. It was designated as "GQ" (major phase geikielite and minor phase qandilite) and will be referred to as such throughout the manuscript. The qandilite within GQ served as the internal standard.

RT XRD Measurements
The samples for HT-XRD studies were characterized by a Rigaku powder X-Ray Diffractometer. Data were collected in the conventional Bragg-Brentano configuration (theta/2theta) by means of Cu K α radiation at 40 kV and 30 mA. The K β was filtered out by graphite monochromator attached to the detector. Phase characterization from XRD data was made by using public domain FullProf/WinPlotter software [9]).

HT XRD Measurements
X-ray diffraction was performed on a Bruker D8 Advance in Bragg-Brentano geometry using an X-ray source with a Cu anode having a K α1 emission wavelength of 1.5406 angstroms. Samples were placed in an Anton Paar XRK-900 high-temperature reaction chamber using a Macor sample stage. The influence of the thermal expansion of the stage was measured by calibrating the stage height as a function of temperature using an alignment slit. The temperature of the sample was controlled using and Anton Paar TCU 750 controller by mounting a K-type thermocouple in the sample holder adjacent to the sample. A linear PSD detector (LYNXEYE XE-T) was used with an opening of 2.94 degrees. The diffraction pattern was recorded from two-theta of 10 degrees until 120 degrees using a coupled theta/two-theta scan type. Data points were acquired in increments of 0.02 degrees with an acquisition time of 0.25 s. Lattice parameters were fitted using TOPAS software with a TCHZ function. The refined parameters included the lattice parameters, sample displacement and zero error. The line position and effect of instrumental broadening and asymmetry were calibrated by SRM 660c LaB 6 .
The diffractograms were also analyzed by the program Powder-Cell [10]. In this step, the phases were easily identified, and the unit cells were verified for the thermal expansion. Grain shape and size was assessed by HR-SEM.

Thermal Expansion Methodology
It is essential to know the dimensions of ceramic materials as function of temperatures in order to calculate the dimensions of objects working at elevated temperatures and to evaluate thermal stresses during temperature changes. For practical reasons it is suggested to define the relative dimension change of a material by Equation (1): where L(T) is the size of one dimension at temperature T, L 0 is the size of the same dimension at ambient temperature, T is the working temperature and T 0 is the ambient temperature (usually the ambient temperature is 25 • C).
In the case of linear thermal expansion, Equation (1) becomes where α is the linear thermal expansion coefficient. For a general case it is possible to define or where ∆L = L(T) − L 0 and ∆T = T − T 0 Neglecting the contribution of enhanced vacancy formation at higher temperatures to the size of a sample of matter, the thermal expansion of a periodical crystalline matter can be modeled by measuring its lattice parameters as function of temperature. By using HT diffraction, each lattice parameter, A j , can be obtained directly from the measurement as In this case, the non-linear thermal coefficients will be given as From Equation (3) it is then possible to define an overall thermal expansion coefficient along a crystal axis A j as Similarly, for unit cell volume V we define the volumetric thermal expansion as It should be noted that this methodology is valid only where there is no phase transformation or significant crystal structure change in the range of measurements.

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 diffractograms without preferred orientation The crystal structures of Mg 2 TiO 4 and MgTiO 3 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% MgTiO 3 with 4.5 wt% MgTiO 4 .
Crystals 2020, 10, x FOR PEER REVIEW 4 of 13 In this case, the non-linear thermal coefficients will be given as From Equation (3) it is then possible to define an overall thermal expansion coefficient along a crystal axis A j as Similarly, for unit cell volume V we define the volumetric thermal expansion as It should be noted that this methodology is valid only where there is no phase transformation or significant crystal structure change in the range of measurements.

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 diffractograms 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.  The lattice parameters of MgTiO 3 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. The lattice parameters of Mg 2 TiO 4 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. The atomic positions of MgTiO 3 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, χ 2 = 1.34). The atomic position of Mg 2 TiO 4 in sample GQ at room temperature after annealing at 1200 • C for 5 h in comparison with Reference [3] is given in Table 4.

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 MgTiO 3 and Mg 2 TiO 4 as function of temperature in the present investigation (sample GQ). All parameters are given in Å.

Thermal Expansion Coefficients for the Reference Material (Mg 2 TiO 4 )
The lattice parameters versus T-25 ( • C) were fitted as a polynomial A j (T) = A j 0 + k 1 (T − 25)+ k 2 (T − 25) 2 as in Equation (5). Then, using Equation (6), α i j = k i /A j 0 obtaining α A j = (A j-A j 0) /[A j 0 (T − 25)] = α 1 + α 2 (T − 25) as given in Equation (7), or γ = (V j-V j 0) /[V j 0 (T − 25)] = γ 1 + γ 2 (T − 25) as given in Equation (8). The thermal expansion coefficients (TEC) for the Mg 2 TiO 4 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 Mg 2 TiO 4 from this study HT-XRD (GQ sample) 25-890 • C 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 coefficient is~0.3%. Equation (10) shows the TEC of Mg 2 TiO 4 from previously published data [5], studied by HT-ND for selected temperature range 25-890 • C.

Thermal Expansion Coefficients for MgTiO 3
There was excellent agreement between the high-temperature lattice parameter data of MgTiO 3 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 affect the TECs of the geikielite. HT-XRD data of the GQ sample together with published data [4,8] of MgTiO 3 are plotted in Figure 3. 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).  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 MgTiO 3 are given in Equation (11).
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). 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 MgTiO 3 are given in Equation (13).
Thermal expansion expressions for solid-state reaction products calculated from HT-ND studies between 23 and 1212 • C of MgTiO 3 made by solid-state reaction [7,8] are given in Equation (14).

Atomic Positions
Selected data of the refined atomic positions for geikielite as refined by the Rietveld method, are given in Table 7. After cooling to room temperature, the sample returned into the initial as-received RT crystallographic data of qandilite and geikielite. The lattice parameters were in (Å): MgTi 2 O 4 (qandilite) a = 8.4404 (6) and MgTiO 3 (geikielite): a = 5.054 (1); c = 13.905 (2). The atomic positions for the geikielite are given in Table 7 (column GQPOST). Figure 2 shows that the lattice parameters versus temperature of the reference material, Mg 2 TiO 4 , are in excellent agreement 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 (Mg 2 TiO 4 ) (Equation (9)) and published HT-ND study of Mg 2 TiO 4 [5]. Figure 2 shows that the lattice parameters versus temperature of the reference material, Mg2TiO4, are in excellent agreement 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].  There was excellent agreement with present and previous HT-XRD data of a sol-gel MgTiO3 product after 1 h firing [4] (Figure 3). The agreement 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 agreement 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].

Discussion
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]. There was excellent agreement with present and previous HT-XRD data of a sol-gel MgTiO 3 product after 1 h firing [4] (Figure 3). The agreement 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 agreement between the lattice parameters versus temperature, between RT and 1300 • C, of all the sol-gel products of MgTiO 3 studied in HT-XRD data (present work and Reference [4]) in comparison with published results of minor MgTiO 3 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 (MgTiO 3 with a small amount of Mg 2 TiO 4 ) 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 MgTiO 3 and TiO 2 with MgTi 2 O 5 as a major compound, it is reasonable to attribute the slight decrease of the lattice parameter of MgTiO 3 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 MgTiO 3 and MgTi 2 O 5 . 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 MgTiO 3 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]. 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.
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. 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).

Conclusions
Accurate thermal expansion coefficients were measured for sol-gel products of stoichiometric MgTiO3. The lattice parameters of MgTiO3 made by sol-gel synthesis measured in HT-XRD between 25 and 890 °C are well integrated with the previously reported HT-XRD study of sol-gel MgTiO3 product between 700 and 1300 °C. The lattice parameters of stoichiometric MgTiO3 sol-gel products are slightly lower than nonstoichiometric MgTiO3 with maximal excess of Ti. It is assumed the TECs of geikielite depend on deviations from stoichiometry. Neither sample preparation nor diffraction method modified the TECS in geikielite. . 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.

Conclusions
Accurate thermal expansion coefficients were measured for sol-gel products of stoichiometric MgTiO 3 . The lattice parameters of MgTiO 3 made by sol-gel synthesis measured in HT-XRD between 25 and 890 • C are well integrated with the previously reported HT-XRD study of sol-gel MgTiO 3 product between 700 and 1300 • C. The lattice parameters of stoichiometric MgTiO 3 sol-gel products are slightly lower than nonstoichiometric MgTiO 3 with maximal excess of Ti. It is assumed the TECs of geikielite depend on deviations from stoichiometry. Neither sample preparation nor diffraction method modified the TECS in geikielite.