Polymorphism in the family of Ln6−xMoO12−δ (Ln = La, Gd–Lu; x = 0, 0.5) oxygen ion- and proton-conducting materials

The formation of Ln6−xMoO12−δ (Ln = La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x = 0, 0.5) rare-earth molybdates from mechanically activated oxide mixtures has been studied in the range 900–1600 °C. The morphotropy and polymorphism (thermodynamic phase and kinetic (growth-related) transitions) of the Ln6−xMoO12−δ (Ln = La, Gd–Lu; x = 0, 0.5) molybdates have been analyzed in detail. As a result we have observed two new types of oxygen ion- and proton-conducting materials with bixbyite (Ia, no. 206) and rhombohedral (R, no. 148) structures in the family of Ln6−xMoO12−δ (Ln = La, Gd–Lu; x = 0, 0.5) molybdates. The heavy rare-earth molybdates Ln6−xMoO12−δ (Ln = Er, Tm, Yb; x = 0, 0.5) have been shown for the first time to undergo an order–disorder (rhombohedral–bixbyite) phase transition at 1500–1600 °C, and we have obtained compounds and solid solutions with the bixbyite structure (Ia). The stability range of the rhombohedral phase (R) increases with decreasing Ln ionic radius across the Ln6−xMoO12−δ (Ln = Er, Tm, Yb, Lu) series. We have detected a proton contribution to the conductivity of the rhombohedral La5.5MoO11.25 (2 × 10−4 S cm−1 at 600 °C in wet air) and high-temperature polymorph Yb6MoO12−δ bixbyite structure, (Ia) below 600 °C. At these temperatures, rhombohedral (R) Yb6MoO12 seems to be an oxygen ion conductor (Ea = 0.53–0.58 eV). The total conductivity of rhombohedral (R) Yb6MoO12 exceeds that of bixbyite Yb6MoO12−δ by more than one order of magnitude and is 3 × 10−5 S cm−1 at 500 °C. According to their high-temperature (T > 600 °C) activation energies, the lanthanum and ytterbium molybdates studied here are mixed electron–ion conductors.


Introduction
Ln 6 MoO 12 , Ln 6 WO 12 , and solid solutions based on these compounds have recently been the subject of intense research as promising environmentally friendly dyes, luminescent materials, effective catalysts, and oxygen ion and proton conductors. [1][2][3][4][5][6][7][8][9][10][11] Tungstates and molybdates in these series are known to undergo various structural transformations with decreasing Ln ionic radius. The compounds in the Ln 6 WO 12 series have the uorite structure (Fm 3m, no. 225) at Ln ¼ La-Pr, a pseudotetragonal structure at Ln ¼ Nd-Gd, and a rhombohedral structure (R 3, no. 148) at Ln ¼ Tb-Lu. The Ln 6 MoO 12 series has a morphotropic phase transition from the uorite structure at Ln ¼ La-Ho to a rhombohedral structure (R 3) at Ln ¼ Ho-Lu. It is also known that the molybdates exhibit a rich polymorphism, with polymorphic transformations between phases belonging to the uorite series. In particular, both the Fm 3m and R 3 polymorphs were obtained at high temperatures for the lanthanide molybdates with Ln ¼ La-Sm and Ho, whereas among the tungstates only for Y 6 WO 12 the formation of an R 3 phase (above 1200 C) and an Fm 3m uorite phase (at 1765 C) was reported. 12 It may be that the relatively poor polymorphism of the tungstates is due to the extremely high temperatures of thermodynamic order-disorder transitions in Ln 2 O 3 -WO 3 systems. However especially for Ln 6 WO 12 (Ln ¼ Y, La-Yb except Ce, Pm, Eu, Tb, Tm) the cubic high-temperature (T syn. > 1960 C) bixbyite polymorph (Ia 3, no. 206) was reported by Foex. 13 At the same time, a number of reports mention lowtemperature cubic Ln 6 MoO 12 and Ln 6 WO 12 phases, which exist, as a rule, in the range 700-1000 C and have rather broad diffraction lines. The formation of such low-temperature, poorly crystallized cubic phases was observed in the synthesis of compounds by various wet-chemical methods followed by annealing between 700 and 1000 C. For example, a low temperature uorite phase was observed in the synthesis of Y 6 WO 12 at 600 C using a polymerized complex method. 14 A uorite phase was detected in the range 800-1100 C for Lu 6 WO 12 and 800-1000 C for Lu 6 MoO 12 with the use of the citrate complexation method, followed by calcinations at these temperatures. 6 Recently, a low-temperature uorite-like bixbyite polymorph (Ia 3) has been obtained using the solution combustion reaction between 700 and 1000 C in Ln 6 MoO 12 (Ln ¼ Tm, Yb, Lu). 15 In a study of the formation of Ln 6 WO 12 (Ln ¼ Nd, Eu, Er) tungstates between 700 and 1480 C using a sol-gel complexation synthesis method, Escolastico et al. 16 obtained low-temperature uorites at temperatures from 700 to 1000 C.
A distinction is made between thermodynamic phase transitions and kinetic (growth-related) order-disorder transitions. In the thermodynamic phase transitions, structural changes result from changes in thermodynamic conditions (pressure p and temperature T). The basic trends of structural changes caused by an increase in temperature or pressure were formulated by Goldschmidt: 17 the average coordination numbers (CNs) of atoms increase with increasing pressure and density and decrease with increasing temperature and decreasing density. High-temperature phases typically have higher symmetries than do low-temperature phases. In particular, many high-temperature phases have cubic structures, whereas low-temperature phases have lower symmetry. There are, however, exceptions. For example, the CN of one of the lanthanum atoms in La 2 S 3 increases from 7 to 8 as a result of the a-La 2 S 3 / g-La 2 S 3 phase transition at 1570 C. 18 There are also kinetic (growth-related) order-disorder transitions. These include the formation of a phase of a particular composition in the thermodynamic stability region of another phase with the same composition under the effect of kinetic factors such as crystal growth rate, particle attachment selectivity, etc. 19 This term was introduced by Chernov for describing the growth of a disordered crystal instead of an ordered, equilibrium crystal when slight differences in energy between sites become insignicant because of high growth rates. 20,21 Solid solutions with a particular structure can result from kinetic ordering and disordering transitions. 19 Kinetic disordering transitions may be due to poor statistical selection of different atoms at high crystal growth rates (atoms in the surface layer do not have enough time to occupy sites corresponding to an ordered state before the formation of the next layer). The result is a disordered solid solution (typically with the uorite structure according to X-ray diffraction (XRD) data). The formation of low-symmetry metastable phases (desymmetrization of crystals) in the case of ordered solid solutions is possible because the surface structure of a growing face differs signicantly from the bulk structure of the crystal.
The kinetic (growth-related) order-disorder transitions considered above are characteristic of inorganic crystalline solid solutions.
Recently, kinetic (growth-related) metastable uorite-pyrochlore (F*-P) transitions have also been classied with application to the pyrochlore family Ln 2 M 2 O 7 (Ln ¼ La-Lu; M ¼ Ti, Zr, Hf) oxygen-ion conductors. 22 The morphotropy and polymorphism (thermodynamic phase and kinetic (growth-related) transitions) of the Ln 2 M 2 O 7 (Ln ¼ La-Lu; M ¼ Ti, Zr, Hf) rareearth pyrochlores have been analyzed in detail. 22,23 The purpose of this work was to study the formation of rareearth molybdate Ln 6Àx MoO 12Àd (Ln ¼ La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x ¼ 0, 0.5) solid solutions in a wide temperature range, from 900 to 1650 C. To this end, precursors were synthesized using mechanical activation, a method that allows one to obtain homogeneous, highly dispersed oxide mixtures and occasionally leads to the formation of compounds at room temperature, i.e. ensures mechanochemical synthesis of mixed oxides. 24,25 Since a number of zirconium-doped rare-earth molybdates, Ln 5.4 Zr 0.6 MoO 12.3 (Ln ¼ Nd, Sm, Dy) and La 5.8 Zr 0.2 MoO 12.1 , were shown to possess oxygen ion and proton conductivity, 10,11 the total conductivity of some polymorphs of undoped Ln 6Àx -MoO 12Àd (Ln ¼ La, Yb; x ¼ 0, 0.5) was also measured in dry and wet air.

Experimental section
The Ln 6Àx MoO 12Àd (Ln ¼ La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x ¼ 0, 0.5) materials were prepared using the mechanical activation of starting oxides followed by high-temperature heat treatment of green compacts. All of the rare-earth oxides and molybdenum oxide used in our preparations were 99.9% pure.
Aer preheating the starting Ln 2 O 3 (Ln ¼ La, Gd, Dy, Ho, Er, Tm, Yb, Lu) oxides at 1000 C for 2 h, they were mixed with MoO 3 and co-milled in a SPEX 8000 ball mill for 1 h. MoO 3 was previously activated in a high energy Aronov ball mill for 4 min. The mechanically activated mixtures of the oxides were uniaxially pressed at 680-914 MPa and sintered at 900, 1100, and 1200 C for 4 h, and 1400, 1500 C and 1600 C for 3 h.
The geometric density of the as-prepared ceramics ranged from 64 to 96.38% of the theoretical one (Table 1). All samples were characterized structurally. X-ray diffraction (XRD) patterns of the polycrystalline samples were collected at room temperature on a DRON-3M automatic diffractometer (Cu Ka radiation, l ¼ 1.5418Å, Bragg-reection geometry, 35 kV, 28 mA) in the 2q range 13 to 65 (scan step 0.1 ). Table 1 summarizes the color, density, and crystallographic characteristics of the samples.
Energy dispersive X-ray spectroscopy (EDX) was realized by using a JEOL JSM-6390LA scanning electron microscope (SEM). An excitation energy of 20 keV was chosen as the accelerating voltage. The L-shells of Mo, La, Gd, Dy, Ho, Er, and Tm, and the M-shells of Yb and Lu were used for EDX analysis. 5-14 spectra were collected for each sample for Ln/Mo ratio determination. EDX measurements, as well as recording of the SEM images, were carried out in high vacuum mode (pressure p z 4 Â 10 À6 mbar). To prevent shis in the images and heating of the sample caused by charging effects, the sample was coated with a 4 nm gold layer (Quorum Q150R ES) before the analysis. Microanalysis data of the Ln and Mo-containing samples are presented in Table 2.
The electrical conductivity of Ln 6Àx MoO 12Àd (Ln ¼ La, Yb; x ¼ 0, 0.5) was characterized by two-probe AC impedance spectroscopy. Both faces of the disk-shaped polycrystalline samples sintered as described above (2-3 mm thick with a diameter of 9-10 mm) were covered with Pt ink (ChemPur C3605) and red at 1000 C for 30 min.
The temperature dependence of the total (electronic and ionic) conductivity of La 5.5 MoO 11.25 in dry and wet air was extracted from impedance spectra obtained using a Solartron 1260 frequency response analyzer. The spectra were recorded in the frequency range of 0.1 Hz to 1 MHz on cooling from 900 C to 150 C; the root mean square ac voltage amplitude was set to 150 mV. Depending on the atmosphere and temperature it took from 2 to 5 h for the samples to reach the equilibrium conductivity values. The relative humidity of the air fed into the sample stage was controlled by passing it over freshly dehydrated silica gel (designated "dry") or through a water saturator maintained at 20 C (designated "wet"), which ensured a constant water content of about 2%.
Electrical conductivity measurements of the two polymorphs, Yb 6 MoO 12 bixbyite (Ia 3) and Yb 6 MoO 12 rhombohedral (R 3), were performed using a P-5X potentiostat/galvanostat combined with a frequency response analyzer module (Elins Ltd, Russia) over the frequency range of 500 kHz to 0.1 Hz at a signal amplitude of 150 mV in the temperature range of 100-900 C. A dry atmosphere was created by passing air through KOH and a wet atmosphere through a water saturator held at 20 C. The air ow rate is 130 ml min À1 .

Results and discussion
Room-temperature synthesis of heavy rare-earth molybdate Yb 6 MoO 12 and intermediate rare-earth molybdate Ho 6 MoO 12 from oxides Fig. 1a shows XRD patterns illustrating the mechanochemical synthesis of Yb 6 MoO 12 from its constituent oxides. Scan 1 in Fig. 1a represents the XRD pattern of unmilled Yb 2 O 3 , which has the bixbyite structure (Ia 3) (ICDD PDF 18-1463). Its lattice  (8) parameter was determined to be a ¼ 10.402(2)Å. Scans 2 and 3 in Fig. 1a represent XRD patterns of MoO 3 before and aer grinding for 4 min in an Aronov vibrating ball mill. It is seen that the layered oxide MoO 3 readily amorphizes during grinding, and its lines become markedly broader. Also shown in Fig. 1a (scan 4) is the XRD pattern of a mixture of 3Yb 2 O 3 + MoO 3 (aer 4 min of grinding (Aronov mill)). Since the mixture contains a considerable amount of ytterbium oxide, the relative amount of MoO 3 is not very large. Aer 40 min of subsequent grinding in a SPEX 8000 mill, we observed complete dissolution of the molybdenum oxide in Yb 2 O 3 with the bixbyite structure (Ia 3). The resultant solid solution also had the bixbyite structure (Ia 3), and its lattice parameter was a ¼ 10.423(2)Å, i.e. it considerably exceeded that of the parent Yb 2 O 3 . Thus, it is reasonable to believe that an Yb 2 O 3 -based solid solution (Yb 6 MoO 12 ) forms even during grinding, so this process can be thought of as the room-temperature mechanochemical synthesis of Yb 6 MoO 12 with the bixbyite structure (Ia 3). Note also that subsequent annealing at 1600 C for 3 h had no signicant effect on its lattice parameter a ¼ 10.421(5)Å (Table 1). A similar situation was observed for Tm 6 MoO 12 with parameter a ¼ 10.465(2)Å, which exceeded that of the parent
Given this, we synthesized not only Ln 6 MoO 12 but also Ln 5.5 MoO 11.25 (Ln ¼ La, Gd, Dy, Ho, Er, Yb) in order to prevent the nal material from being multiphasic.
When analyzing the La 5.5 MoO 11.25 formation process, it is worth noting the formation of a metastable, low-temperature uorite phase at 900 C, which then transforms into a rhombohedral (R 3) phase at 1200 C (Fig. 2, scans 1 and 2). The formation of a metastable, low-temperature uorite phase was also observed in lutetium molybdate (Lu 6 MoO 12 ) synthesis 6 and was reported for Y 6 WO 12 and Ln 6 WO 12 (Ln ¼ Nd, Eu, Er, Lu) tungstates 14,16 prepared using wet-chemical methods and low temperature annealing at $700-1000 C.
Increasing the heat treatment temperature of La 5.5 MoO 11.25 from 1200 to 1600 and 1650 C led to the formation of a new phase that was also rhombohedral to a rst approximation and had an increased unit-cell volume (increased unit-cell parameter) (Fig. 2, scans 2-4). This phase was formed at 1600 C and prevailed in multiphase La 6 MoO 12 (Fig. 2, scan 5). Comparison of XRD data of the zirconium-substituted molybdate La 5.8 Zr 0.2 MoO 12.1 , 10 the La 5.5 MoO 11.25 synthesized in this study, and a molybdenum-rich La 28Ày (W 1Àx Mo x ) 4+y O 54+d tungstate 28 indicates that these solid solutions are identical in structure. Based on SAED results, Amsif et al. 28 proposed a rhombohedral cell with cells parameters ($28 Â 28 Â 9.8Å), and with an unusually large volume of 6600Å 3 . Thus, further research is needed, with the use of neutron and synchrotron Xray diffraction, to accurately determine the complex structure of La 5.5 MoO 11.25 .
Gd 6Àx MoO 12Àd (x ¼ 0, 0.5) formation from mechanically activated precursors Fig. 3a and b show XRD patterns illustrating the phase formation process in Gd 6 MoO 12 and Gd 5.5 MoO 11.25 , respectively, at 900, 1200, 1500, and 1600 C. For Gd 6 MoO 12 XRD of the sample aer heat treatment at 1100 C is presented also (Fig. 3a, scan  2). Heat treatment at 900 C leads to the formation of a tetragonal phase (with all of its diffraction lines markedly broadened) ( Fig. 3a and b, scans 1). A similar tetragonal phase was observed for Eu 6 WO 12 in the temperature interval 1200-1480 C. 16 At 1200 C, a tetragonal phase prevails ( Fig. 3a and b, scans 3 and 2 respectively). At high temperatures, 1500-1600 C, the Gd 5.5 -MoO 11.25Àd sample consists of a pure uorite (Fm 3m) phase (Fig. 3b, scans 3 and 4), whereas the Gd 6 MoO 12Àd sample contains impurity phases (Fig. 3a, scans 4 and 5). Aer annealing in the range 1500-1600 C, the latter sample has a non-uniform coloration, with black inclusions. It seems likely that it is difficult to obtain impurity-free uorite Gd 6 MoO 12Àd by  annealing at 1600 C because of the partial reduction of the material.
Ln 6Àx MoO 12Àd (Ln ¼ Dy, Ho, Er, Tm, Yb, Lu; x ¼ 0, 0.5) formation from mechanically activated precursors Fig. 4a and b show XRD patterns illustrating the phase formation process in Dy 6 MoO 12 and Dy 5.5 MoO 11.25 . Annealing at 900 C leads to the formation of metastable bixbyite (Ia 3), tetragonal, and rhombohedral (tracks) phases ( Fig. 4a and b,  scans 1). Annealing at 1200 C also yields a mixture of a bixbyite, a tetragonal, and a rhombohedral phase (tracks) (Fig. 4a and b, scans 2 and 3, respectively). High-temperature annealing, at 1500 C of Dy 6 MoO 12Àd (Fig. 4a, scan 3) and at 1600 C of Dy 5.5 MoO 11.25Àd (Fig. 4b, scan 5), leads to the formation of a pure uorite (Fm 3m) phase. Aer annealing at 1600 C, the Dy 6 MoO 12Àd sample contains impurities (Fig. 4a, scan 4), in contrast to Dy 5.5 MoO 11.25Àd (Fig. 4b, scan 5). The Dy-containing samples with the uorite structure have a non-uniform coloration (with black inclusions). The samples with the bixbyite structure have a more uniform coloration. Fig. 5a and b present XRD patterns illustrating the phase formation process in Ho 6 MoO 12 and Ho 5.5 MoO 11.25 . Here, lowtemperature ($900-1100 C) annealing also leads to the formation of a mixture of a metastable bixbyite phase (Ia 3), a tetragonal, and a rhombohedral phase (tracks) (Fig. 5a and b,  scan 1; Fig. 1b, scan 8). Aer heat treatment at 1600 C, Ho 6 -MoO 12Àd has the bixbyite structure (Ia 3) and Ho 5.5 MoO 11.25Àd has the uorite structure (Fm 3m). The Ho-containing samples with the uorite structure also have a non-uniform coloration, which seems to be evidence of partial reduction.
In the case of Er 6 MoO 12 (Fig. 6a), at 900 C we observe the formation of a metastable bixbyite (Ia 3) phase mixed with a rhombohedral phase (tracks) (Fig. 6a, scan 1). Above 1200 C,  we also obtain a mixture of a bixbyite and a rhombohedral phase (tracks) (Fig. 6a, scan 2). Heat treatment at 1400 C yields well-crystallized rhombohedral Er 6 MoO 12 (Fig. 6a, scan 3), which transforms almost completely into a bixbyite phase at 1500 C (Fig. 6a, scan 4). At 1600 C, we obtain a well-crystallized high-temperature bixbyite (Ia 3) phase Er 6 MoO 12Àd (Fig. 6a, scan 5). Fig. 6b compares the XRD patterns of Er 6 MoO 12Àd and Er 5.5 MoO 11.25Àd aer annealing at 1600 C. The former material has the bixbyite structure (Ia 3) and the latter has the uorite (Fm 3m) structure. To examine the inuence of annealing time on the phase formation process at a low temperature (1200 C), the mechanically activated mixture of the oxides 3Er 2 O 3 + MoO 3 was sintered at 1200 C for 4 and 40 h, respectively (Fig. 6c). We observed the formation of an Er 6 MoO 12Àd bixbyite cubic phase (metastable) (Fig. 6c, scan 1) in the thermodynamic stability region of the rhombohedral (R 3) Er 6 MoO 12 phase with the same composition under the effect of kinetic factors. 19 The transformation into the stable rhombohedral (R 3) Er 6 MoO 12 phase can be induced by a longer heating duration (Fig. 6c, scan  2). This is a kinetic (growth-related) transition from metastable bixbyite to the stable rhombohedral (R 3) Er 6 MoO 12 at 1200 C. A similar process (from metastable uorite to the stable rhombohedral (R 3)) was recently reported as an irreversible, rst order diffusional ordering process for the Ln 6 WO 12 (Ln ¼ Y, Ho, Er, Yb). 29 Yb 6 MoO 12 and Yb 5.5 MoO 11.25 have identical phase formation sequences ( Fig. 7a and b). A metastable bixbyite phase (Ia 3) is formed at 900 C ( Fig. 7a and b, scans 1). The stability range of the rhombohedral (R 3) phase, 1200 to 1500 C, is broader in comparison with that of Er 6 MoO 12 (Fig. 7a, scans 2-4; Fig. 7b, scans [3][4][5]. Aer annealing at 1600 C, both Yb 6 MoO 12Àd and Yb 5.5 MoO 11.25Àd have the high-temperature bixbyite structure (Ia 3) (Fig. 7a and b, scans 5 and 6, respectively). Thus, Ho, Er, and Yb molybdates are characterized by the formation of a metastable bixbyite phase below 1000 C, and at high temperatures we observe order-disorder (rhombohedralbixbyite) phase transitions for Ln 6 MoO 12 (Ln ¼ Er, Yb). Tm 6 MoO 12 was also found to undergo an order-disorder (rhombohedral-bixbyite) phase transition, like Ln 6 MoO 12 (Ln ¼ Er, Yb) (Fig. 8, scans 1 and 2). At the same time, Lu 6 MoO 12 seems to undergo an order-disorder transition at higher temperatures, like La 5.5 MoO 11.25 , as evidenced by the fact that, in the range 1400-1600 C, Lu 6 MoO 12 retains the rhombohedral structure (Fig. 8, scans 3 and 4). A metastable uorite phase (Fm 3m) was obtained previously for Lu 6 MoO 12 in the range 800-1000 C using a wet-chemical method. 6 It seems likely that above 1600 C this compound exists as a high-temperature uorite phase, rather than as a bixbyite phase.
Thus, in this study, Ln 6 MoO 12 (Ln ¼ Er, Yb, Tm) and solid solutions based on these compounds were shown for the rst time to undergo high-temperature order-disorder (rhombohedral-bixbyite) phase transitions (T PT $ 1500 C), and we iden-tied metastable bixbyite phases forming below 1000 C.
Morphotropic and thermodynamic order-disorder (uoriterhombohedral phase-bixbyite) transitions Fig. 9 shows the unit-cell parameter a as a function of the Ln ionic radius of the Ln 5.5 MoO 11.25Àd (Ln ¼ Er-Gd) molybdates with the uorite structure aer annealing at 1600 C. The a cell parameter is seen to rise linearly with the Ln ionic radius. Also shown in Fig. 9 is the a cell parameter of the metastable uorite phase La 5.5 MoO 11.25Àd synthesized at 900 C. Fitting the dependence of a on the Ln ionic radius of the Ln 5.5 MoO 11.25Àd (Ln ¼ Er-Gd) molybdates at 1600 C by a straight line, we nd that the a of high-temperature La 5.5 MoO 11.25 markedly exceeds that of metastable uorite La 5.5 MoO 11.25 .
The data in Fig. 10 illustrate the morphotropic uoritebixbyite phase transition in the Ln 6 MoO 12Àd molybdates aer annealing at 1600 C for 3 h. Fig. 10 and Table 1 present the unit-cell parameter as a function of the Ln 3+ ionic radius of Ln 6 MoO 12Àd (Ln ¼ Yb, Tm, Er, Ho, Dy, Gd). The heavy rare-earth molybdates Ln 6 MoO 12Àd (Ln ¼ Ho, Er, Yb, Tm) crystallize in the bixbyite structure (Ia 3) and the intermediate rare-earth molybdates Ln 6 MoO 12Àd (Ln ¼ Dy, Gd) crystallize in the uorite structure (Fm 3m). The Ho 6Àx MoO 12Àd (x ¼ 0, 0.5) molybdates were shown to exist in two phases, with the uorite and bixbyite structures, and the heavy rare-earth molybdates Ln 6 MoO 12 (Ln ¼ Er, Tm, Yb) exist as rhombohedral and bixbyite phases. Fig. 11 plots the unit-cell parameters against the Ln 3+ ionic radius of rhombohedral Ln 6 MoO 12 (Ln ¼ Er, Tm, Yb, Lu) prepared at 1400 C (3 h). Both a and c increase with the Ln 3+ ionic radius. Note that the temperature stability range of the rhombohedral phase increases with decreasing Ln 3+ ionic radius. In particular, the rhombohedral phase of Er 6 MoO 12 exists only aer a short 3 h annealing at 1400 C, whereas that of Yb 6Àx MoO 12Àd (x ¼ 0, 0.5) exists aer annealing in the range 1200-1500 C (Table 1; Fig. 7a and b). However the true stability region of the Er 6 MoO 12 rhombohedral phase starts from 1200 C as shown by long temperature annealing (40 h) at 1200 C (Fig. 6c, scan 2). Rhombohedral (R 3) Tm 6 MoO 12 also exists below 1600 C (Table 1; Fig. 8). The rhombohedral phase of Lu 6 MoO 12 persists at 1600 C, and it seems to undergo disordering at a higher temperature.
In this study, using brief annealing (3 h) of mechanically activated oxide mixtures, we were able to obtain hightemperature bixbyite Ln 6 MoO 12Àd (Ln ¼ Ho, Er, Tm, Yb) in the range 1400 to 1600 C. The stability of the heaviest rareearth molybdates and tungstates, Ln 6 Mo(W)O 12 (Ln ¼ Tm, Yb, Lu), was studied qualitatively by Aitken et al. 27 and was shown to be even higher than that of Ln 2 O 3 (Ln ¼ Tm, Yb, Lu).
Microanalysis data of the Ln and Mo-containing samples synthesized in this work are presented in Table 2. These results suggest that no considerable molybdenum loss occurred in the samples during short high-temperature annealing in the range 1200-1600 C. These results agree with data of rhombohedral R 6 MoO 12 (R ¼ Tm-Lu, Y). 27 It is worth noting, however, that the accuracy of determining the Ln/Mo ratio by EDX spectroscopy decreases with increasing synthesis temperature and is lower for the heavy rare-earth molybdates in comparison with the light and intermediate rare-earth molybdates. Note also that the accuracy of determining the Ln/Mo ratio is not very high in the case of the mixed-phase samples synthesized at 1200 C ( Table  2, samples A and B). The data in Fig. 12 illustrate the Mo distribution over the Yb 6 MoO 12Àd (Table 2, no. 23) (Fig. 12a and  b) and Ho 6 MoO 12Àd (Table 2, no. 10) (Fig. 12c and d) samples synthesized at 1600 C. The Mo is seen to be evenly distributed throughout the samples. Similar data were obtained for all of the samples, independent of the synthesis temperature.
Given this, using mechanochemical synthesis, we were able to produce rather dense ceramics with uorite and related (rhombohedral (R 3) and bixbyite (Ia 3)) structures, and it is of obvious interest to study not only the structure but also the electrical properties of these polymorphs. Indeed, as shown     rare-earth molybdates with the rhombohedral and bixbyite structures.
Total conductivity of La 5.5 MoO 11.25 in dry and wet air The impedance spectra obtained for the rhombohedral La 5.5 MoO 11.25 (T syn. ¼ 1600 C) in dry and wet air are given in Fig. 13. In the low-temperature range the spectra showed two separate semicircles that were attributed to the sample bulk and electrode polarization. The values of the equivalent specic bulk and electrode capacitances extracted via non-linear least squares tting (C b $ 10 À12 F cm À1 and C el $ 10 À5 F cm À2 ) are consistent with the aforementioned interpretation. Fig. 14 presents the total conductivity of La 5.5 MoO 11.25 (T syn. ¼ 1600 C) in dry and wet air extracted from these data (Fig. 13). An increase of total conductivity in wet air as compared to the conductivity in dry air is indicative of hydration of this sample resulting in proton conductivity. The Arrhenius plot of the conductivity of La 5.5 MoO 11.25 shows an inection point at $600 C in a wet atmosphere. A shi from predominant proton conduction at low temperature to predominant electron conduction in the high temperature range takes place. As far as the conductivity of La 5.5 MoO 11.25 in dry air is concerned, we believe that a small amount of residual water might have caused a slight increase in conductivity at the lowest temperatures (below 200 C). The marginal change of slope at $600 C is probably related to the onset of oxygen ion conductivity as the concentration of protons is very low under dry air. The activation energies for conduction in this sample below and above 600 C are indicated in Table 3.
Even though the conductivity of La 5.5 MoO 11.25 (2 Â 10 À4 at 600 C) is lower than that of La 6Àx WO 12Àd , 7-9 the more complex structure of La 5.5 MoO 11.25 seems to ensure higher stability of this compound in a reducing atmosphere. 30 Particular features of its microstructure may also play a role. 31 Total conductivity of two Yb 6 MoO 12 polymorphs: bixbyite (Ia 3) and rhombohedral (R 3) in dry and wet air Fig. 15 shows the typical impedance spectra of bixbyite Yb 6 -MoO 12Àd (Ia 3) at low temperatures (480 and 525 C, Fig. 15a) and at higher temperatures (650 and 700 C, Fig. 15b). The spectra each consist of two arcs of circles and can be described using an equivalent circuit consisting of two series connected elements, each composed of a parallel connected resistance (R) and constant phase element (CPE). The impedance of the constant phase element can be represented as where A is a proportionality factor and the exponent P is related to the phase angle.
The real-axis intercept of the high-frequency arc is the bulk resistance of the material, R bulk . Note that the center of the highfrequency arc is slightly depressed relative to the real axis (the exponent P is near 0.9). This behavior may be caused by inductive interferences in the tubular furnace used in our measurements. The apparent capacitance (A) is $10 À11 F cm À1 , which corresponds to the geometric capacitance of the material. The other arc (at medium and low frequencies) represents the contribution of electrode polarization at the electrode/ electrolyte interface to the impedance response of the system. Note that R bulk decreases with increasing air humidity (Fig. 15a). This points to proton conductivity, whose contribution to the total conductivity of the material increases with decreasing temperature. Fig. 16 shows the typical impedance spectra of rhombohedral (R 3) Yb 6 MoO 12 at low (525 and 570 C) (Fig. 16a) and higher (650 and 700 C) (Fig. 16b) temperatures. In contrast to the spectrum of Yb 6 MoO 12Àd with the bixbyite structure (Ia 3), the impedance response of this system consists of one arc of a circle, which can be represented by an equivalent circuit composed of a parallel connected resistance (R) and constant phase element (CPE). The real-axis intercept is the bulk resistance of the material. Note that the center of the arc is also slightly depressed relative to the real axis (the exponent P is near 0.8). The apparent capacitance (A) of the material is also $10 À11 F cm À1 . Fig. 17 presents the temperature dependency of the total conductivity of Yb 6 MoO 12Àd (Ia 3) and Yb 6 MoO 12 (R 3) in dry and wet air. An increase of total conductivity in wet air as compared to the conductivity in dry air is indicative of hydration of Yb 6 -MoO 12Àd bixbyite at T < 600 C resulting in proton conductivity (Fig. 17, curves 1 and 2). Above 600 C, the electronic conductivity increases, which is accompanied by changes in activation energy (Table 3). Above 600 C, bixbyite Yb 6 MoO 12Àd has mixed conductivity. Rhombohedral (R 3) Yb 6 MoO 12 has no proton conductivity below 600 C and seems to be an oxygen ion conductor in dry air (E a ¼ 0.53-0.58 eV) ( Table 3). The activation energy for oxygen ion conduction typically falls in the range 0.6-1 eV. However, a number of oxygen ion conductors have lower  At T > 600 C the activation energy of rhombohedral (R 3) Yb 6 MoO 12 conductivity is E a ¼ 0.98 eV (Table 3) and we can suppose that ionic conductivity contribution prevails in rhombohedral (R 3) Yb 6 MoO 12 at these temperatures. As shown earlier, the proton conductivity of zirconiumdoped molybdates decreases markedly with decreasing Ln ionic radius. 10 The highest proton conductivity is offered by the La-and Nd-containing solid solutions. With decreasing ionic radius across the lanthanide series, the proton contribution to the total conductivity decreases, and Dy 5.4 Zr 0.6 MoO 12.3 has insignicant proton conductivity. 10 The Arrhenius plot of the conductivity of rhombohedral (R 3) Yb 6 MoO 12 has a characteristic break at 550 C (Fig. 17, curves 3 and 4). In previous studies of zirconium-doped rare-earth molybdates and tungstates, such breaks were interpreted as evidence of a change in the dominant carrier type. 7,10 In a dry atmosphere at low temperatures (below 550 C), charge transport is mainly due to oxygen ions, whereas at high temperatures electrons and holes prevail at low and high oxygen partial pressures, respectively. Rhombohedral (R 3) Yb 6 MoO 12 seems to have purely oxygen ion conductivity in wet air below 550 C (Table 3), whereas the conductivity of La 5.5 MoO 11.25 has a signicant proton contribution (Fig. 14). Above 600 C, both rhombohedral (R 3) and bixbyite Yb 6 -MoO 12Àd have growing electronic conductivity contribution, which increases with temperature ( Table 3).
The total conductivity of rhombohedral (R 3) Yb 6 MoO 12 is more than an order of magnitude higher than the conductivity of Yb 6 MoO 12Àd bixbyite, and is 3 Â 10 À5 S cm À1 at 500 C.

Conclusions
We have investigated the phase formation processes of Ln 6Àx -MoO 12Àd (Ln ¼ La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x ¼ 0, 0.5) rareearth molybdates in the range 900-1600 C. The materials have been synthesized via mechanical activation of oxide mixtures, which ensured the formation of molybdates even during milling. Our data on low-temperature phase formation and crystallization processes in the range 900-1100 C demonstrate the formation of a metastable uorite, bixbyite, and tetragonal or rhombohedral phase, depending on the Ln ionic radius.
High-temperature synthesis in the range 1400-1600 C allowed us to detect for the rst time thermodynamic orderdisorder (rhombohedral (R 3)-bixbyite (Ia 3)) phase transitions in the heavy rare-earth molybdates Ln 6Àx MoO 12Àd (Ln ¼ Er, Tm, Yb; x ¼ 0, 0.5). The stability range of the rhombohedral phase increases with decreasing Ln ionic radius.
The total conductivity of La 5.5 MoO 11.2 and two Yb 6 MoO 12 polymorphs, with rhombohedral (R 3) and bixbyite (Ia 3) structures, has been determined in dry and wet air using impedance spectroscopy. Below 600 C, the conductivity of La 5.5 MoO 11.25 and bixbyite Yb 6 MoO 12Àd (Ia 3) has a signicant proton contribution. Rhombohedral (R 3) Yb 6 MoO 12 has oxygen ion conductivity under these conditions (T < 550 C). At 600 C in wet air, the conductivity of undoped La 5.5 MoO 11.25 , which has a complex structure derived from the rhombohedral one, is 2 Â 10 À4 S cm À1 . The conductivity of rhombohedral (R 3) Yb 6 MoO 12 in air at 600 C is 1 Â 10 À4 S cm À1 and that of bixbyite Yb 6 -MoO 12Àd at 600 C is 1 Â 10 À5 S cm À1 . So we have obtained and investigated the rst members of oxygen ion-and/or protonconducting materials with the bixbyite (Ia 3) and rhombohedral (R 3) structure in the family of Ln 6Àx MoO 12Àd (Ln ¼ Ho, Er, Tm, Yb, Lu; x ¼ 0, 0.5) molybdates.