Preparation of Zr(Mo,W)2O8 with a larger negative thermal expansion by controlling the thermal decomposition of Zr(Mo,W)2(OH,Cl)2∙2H2O

Solid solutions of Zr(Mo,W)2O7(OH,Cl)2∙2H2O with a preset ratio of components were prepared by a hydrothermal method. The chemical composition of the solutions was determined by energy dispersive X-ray spectroscopy (EDX). For all the samples of ZrMoxW2−xO7(OH,Cl)2∙2H2O (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0), TGA and in situ powder X-ray diffraction (PXRD) studies (300–1100 K) were conducted. For each case, the boundaries of the transformations were determined: Zr(Mo,W)2O7(OH,Cl)2∙2H2O → orthorhombic-ZrMoxW2−xO8 (425–525 K), orthorhombic-ZrMoxW2−xO8 → cubic-ZrMoxW2−xO8 (700–850 K), cubic-ZrMoxW2−xO8 → trigonal-ZrMoxW2−xO8 (800–1050 K for x > 1) and cubic-ZrMoxW2−xO8 → oxides (1000–1075 K for x ≤ 1). The cell parameters of the disordered cubic-ZrMoxW2−xO8 (space group Pa-3) were measured within 300–900 K, and the thermal expansion coefficients were calculated: −3.5∙10−6 – −4.5∙10−6 K−1. For the ordered ZrMo1.8W0.2O8 (space group P213), a negative thermal expansion (NTE) coefficient −9.6∙10−6 K−1 (300-400 K) was calculated. Orthorhombic-ZrW2O8 is formed upon the decomposition of ZrW2O7(OH,Cl)2∙2H2O within 500–800 K.

of an amorphous intermediate, which crystallizes as cubic β-ZrW 2 O 8 above 850 K. The strong exothermic effect at 1100 K is related to the decomposition of cubic β-ZrW 2 O 8 into oxides. The transformation of cubic α-ZrW 2 O 8 into cubic β-ZrW 2 O 8 is not registered by differential thermal analysis (DTA).
The DTA curve for ZrMo x W 2−x O 7 (OH,Cl) 2 •2H 2 O showed the expected endothermic peak, corresponding to the weight loss and formation of the orthorhombic phase of β-ZrMo 2 O 8 , while the two exothermic peaks at 700 and 800 K can be assigned to the crystallization of the cubic γ-ZrMo 2 O 8 and trigonal α−ZrMo 2 O 8 phases, respectively 10 .
We assumed that one of the cubic-ZrMo x W 2−x O 8 solutions may have a larger coefficient than that previously determined. We carefully investigated the conditions for obtaining cubic-ZrMo x W 2−x O 8 (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0) from precursors and measured their NTE coefficients.

Results and Discussion
Synthesis of the precursors and their characterization. We (Fig. 1) on a DRON-RM4 diffractometer (CuK α source, graphite monochromator at the diffracted beam, room temperature, 2θ range 5-60°). The experimental data were processed with the PowderCell program v.2.4 15 , and the data from the powder structural database powder diffraction file (PDF) were used as the reference 16 . The EDX spectral analysis was performed using a Hitachi TM3030 desktop scanning electron microscope and the Quantax70 microanalysis system.
The PXRD data showed that all the samples were single phase. We performed an EDX investigation for all the prepared samples and found that the preset stoichiometry was retained in the products of the reaction within the experimental uncertainty. Determining the content of molybdenum and tungsten in ZrMo x W 2−x O 7 (OH,-Cl) 2 •2H 2 O by the Zen-Retgers rule is extremely difficult because of the extreme similarity of the unit cell volumes (Table 1).  High-temperature experiments were carried with time-resolved diffractometry at channel 5b of the Siberian Synchrotron and Therahertz Radiation Centre 17,18 . The wavelength used was 1.516 A. The diffraction patterns were recorded by a one-coordinate detector (OD-3) developed in Budker Institute of Nuclear Physics of Siberian Branch Russian Academy of Sciences 19 . The exposure time for a frame was set to 1 minute. The samples were heated in air up to 1123 K at a rate of 10 K/min.

DTA and high-temperature PXRD of ZrMo
The behaviours of the ZrMo x W 2−x O 7 (OH,Cl) 2 •2H 2 O samples upon thermal decomposition are similar (Fig. 2a), but some features depend on the value of "x". The decomposition of ZrMo x W 2−x O 7 (OH,Cl) 2 •2H 2 O begins at 450 K for x = 2 and increases linearly up to 500 K for x = 0. The first stage is accompanied by an endothermic effect and a weight loss (Fig. 3). The data from the high-temperature PXRD confirmed the following reaction: We calculated the molar ratio of the chloride ion to the hydroxide ion (In all the samples, the ratio was approximately 1:3.) based on the loss of the mass, which was measured by DTA, as described in article 9 .  The crystallite sizes did not increase with the temperature in our experiments. Allen 20 used a long heat treatment (8 hours at 573 K) to prepare good crystalline samples of orthorhombic-ZrMo x W 2−x O 8 .
The second transformation did not have a weight loss and was accompanied by an exothermal effect. The temperatures of the transformation (650-800 K) had a complex dependence on the parameter "x" (Fig. 2a). We observed the appearance of the peaks of a nicely crystalline cubic-phase ZrMo x W 2−x O 8 in the powder pattern. The width of the synthetic "window" for single-phase, cubic ZrMo x W 2−x O 8 was not large: 70-200 K (x = 0-1.4) and 30-50 K (x = 1.4-2.0). Preparation of pure cubic, single-phase samples required accurate work. The precursor had to be heated to the minimal possible temperature (blue line on Fig. 2b) and held for 10-60 minutes (60 minutes for x = 0 and 10 minutes for x = 2).
Further heating led to the formation of trigonal ZrMo x W 2−x O 8 at 500-700 K (x = 1.2-2.0) or decomposition of the material into constituent oxides at 1050 K (x = 0-1.0) (Fig. 2b). In study 14 , it was found that the resulting products with x ≤ 0.5 would decompose to WO 3 /MoO 3 and ZrO 2 upon a temperature increase, while for x > 0.5, the cubic phase would transform into the trigonal phase. Shi Yongfang 11 noted that the appearance of the trigonal phase occurs at relatively low temperatures, i.e., 861 K (x = 0.73) and 889 K (x = 0.53). This fact was confirmed in our work. Trace amounts of the trigonal phase were often present in all the PXRD patterns, while the cubic compound was the main phase. However, we did not observe the exothermal effect for the cubic-to-trigonal transformation for x = 0.2-0.8, 1.6, and 1.8 in the DTA experiments.
Trigonal ZrMo x W 2−x O 8 (x = 1.2-1.8) had a good thermal stability, and we found no evidence of its decomposition for x = 1.4, 1.6 and 1.8 under the conditions in our experiment. Trigonal ZrMo x W 2−x O 8 (x = 1.2) decomposed at 1150 K. However, trigonal ZrMo 2 O 8 decayed into oxides with an exo-effect at 925 K.
We should note that all the transformations of orthorhombic-cubic-trigonal-oxides are exothermic. This can be explained if all those phases (with the exception of the oxides) are metastable in our experimental temperature ranges. The transformations were accompanied by a decrease in the volume of the formula unit (V/Z), e.g., for x = 1.2 (Fig. 4): Our data directly indicated the formation of a poorly crystalline orthorhombic phase (Pmn2 1 ) of zirconium tungstate (ZrW 2 O 8 ) in the temperature range 550-825 K (Fig. 2).

NTE coefficient of cubic-ZrMo
The thermal expansion of cubic-ZrMo x W 2−x O 8 was investigated using variable temperature PXRD. Diffraction data were measured using a Bruker D8 Advance diffractometer (CuKα radiation) with a parallel-beam geometry with Göbel Mirrors. In situ experiments were carried out using an Anton Paar XRK900 reaction chamber. The patterns were measured in the 2θ range from 10 to 70° with a step of 0.05° and a collection time of 3 s per point. The heating rate was 12 K/min. The acquisition of the X-ray patterns was started when the given temperature was reached. Sample cooling was immediately performed. The profile analysis and structural refinement by the LeBail method were performed using the TOPAS v.4.3 program 21 , and the data from the powder structural database PDF were used as the standards 16 . The lengths of the coherent scattering domain were calculated using LVol-IB values (i.e., volume weighted mean column height based on the integral breadth).
When measuring the NTE coefficient, it is important to realize which form of cubic ZrMo x W 2−x O 8 is being measured, i.e., ordered or disordered. For ZrW 2 O 8, this transition is called α → β. In article 13 , the thermal effects for the transition (ordered → disordered) were measured, and a formula describing the temperature of the α → β transitions for cubic-ZrMo x W 2−x O 8 was proposed: T (K) = 432-168.45•x. We used it in our work to estimate whether the NTE coefficient belongs to the corresponding ordered or disordered form (Table 2). Of course, the dependence is not linear for x > 1; this is clearly visible when comparing the calculated and experimental values for x = 1.8 and 2.0 ( Table 2).
We were able to obtain reliable data for the NTE coefficients for only the disordered phase, except for x = 1.8. The calculated coefficients have similar values (from −3.5•10 −6 K −1 to −4.5•10 −6 K −1 ) and almost did not differ from those of the "pure components". Our value of the NTE coefficient, 3.5•10 −6 K −1 , for x = 0.4 did not coincide with the value 8    Solid solutions of cubic ZrMo x W 2−x O 8 in the ordered form have a higher coefficient of thermal expansion (CTE) in comparison to that of other materials, but they exist in a very limited and relatively low-temperature range, which limits their possible applications.
The disordered form of cubic ZrMo x W 2−x O 8 solid solutions does not have an advantage over that of the "pure components" in the value of CTE. The use of solid solutions is justified in the case when it is necessary to have a uniform CTE material for a certain temperature range (e.g., 250-800 K for x = 1.0).