Polymorphism in the family of Ln_6−xMoO_12−δ (Ln = La, Gd–Lu; x = 0, 0.5) oxygen ion- and proton-conducting materials

Abstract

The formation of Ln_6−xMoO_12−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 Ln_6−xMoO_12−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 (Ia3̄, no. 206) and rhombohedral (R3̄, no. 148) structures in the family of Ln_6−xMoO_12−δ (Ln = La, Gd–Lu; x = 0, 0.5) molybdates. The heavy rare-earth molybdates Ln_6−xMoO_12−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 (Ia3̄). The stability range of the rhombohedral phase (R3̄) increases with decreasing Ln ionic radius across the Ln_6−xMoO_12−δ (Ln = Er, Tm, Yb, Lu) series. We have detected a proton contribution to the conductivity of the rhombohedral La_5.5MoO_11.25 (2 × 10⁻⁴ S cm⁻¹ at 600 °C in wet air) and high-temperature polymorph Yb₆MoO_12−δ bixbyite structure, (Ia3̄) below 600 °C. At these temperatures, rhombohedral (R3̄) Yb₆MoO₁₂ seems to be an oxygen ion conductor (E_a = 0.53–0.58 eV). The total conductivity of rhombohedral (R3̄) Yb₆MoO₁₂ exceeds that of bixbyite Yb₆MoO_12−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

Ln₆MoO₁₂, Ln₆WO₁₂, 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.^1–11 Tungstates and molybdates in these series are known to undergo various structural transformations with decreasing Ln ionic radius. The compounds in the Ln₆WO₁₂ series have the fluorite structure (Fm3̄m, no. 225) at Ln = La–Pr, a pseudotetragonal structure at Ln = Nd–Gd, and a rhombohedral structure (R3̄, no. 148) at Ln = Tb–Lu. The Ln₆MoO₁₂ series has a morphotropic phase transition from the fluorite structure at Ln = La–Ho to a rhombohedral structure (R3̄) at Ln = Ho–Lu. It is also known that the molybdates exhibit a rich polymorphism, with polymorphic transformations between phases belonging to the fluorite series. In particular, both the Fm3̄m and R3̄ polymorphs were obtained at high temperatures for the lanthanide molybdates with Ln = La–Sm and Ho, whereas among the tungstates only for Y₆WO₁₂ the formation of an R3̄ phase (above 1200 °C) and an Fm3̄m fluorite 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 Ln₂O₃–WO₃ systems. However especially for Ln₆WO₁₂ (Ln = Y, La–Yb except Ce, Pm, Eu, Tb, Tm) the cubic high-temperature (T_syn. > 1960 °C) bixbyite polymorph (Ia3̄, no. 206) was reported by Foex.¹³

At the same time, a number of reports mention low-temperature cubic Ln₆MoO₁₂ and Ln₆WO₁₂ 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 fluorite phase was observed in the synthesis of Y₆WO₁₂ at 600 °C using a polymerized complex method.¹⁴ A fluorite phase was detected in the range 800–1100 °C for Lu₆WO₁₂ and 800–1000 °C for Lu₆MoO₁₂ with the use of the citrate complexation method, followed by calcinations at these temperatures.⁶ Recently, a low-temperature fluorite-like bixbyite polymorph (Ia3̄) has been obtained using the solution combustion reaction between 700 and 1000 °C in Ln₆MoO₁₂ (Ln = Tm, Yb, Lu).¹⁵ In a study of the formation of Ln₆WO₁₂ (Ln = Nd, Eu, Er) tungstates between 700 and 1480 °C using a sol–gel complexation synthesis method, Escolastico et al.¹⁶ obtained low-temperature fluorites 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 La₂S₃ increases from 7 to 8 as a result of the α-La₂S₃ → γ-La₂S₃ 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 insignificant 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 fluorite 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 significantly 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 fluorite–pyrochlore (F*–P) transitions have also been classified with application to the pyrochlore family Ln₂M₂O₇ (Ln = La–Lu; M = Ti, Zr, Hf) oxygen-ion conductors.²² The morphotropy and polymorphism (thermodynamic phase and kinetic (growth-related) transitions) of the Ln₂M₂O₇ (Ln = La–Lu; M = Ti, Zr, Hf) rare-earth pyrochlores have been analyzed in detail.^22,23

The purpose of this work was to study the formation of rare-earth molybdate Ln_6−xMoO_12−δ (Ln = La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x = 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_5.4Zr_0.6MoO_12.3 (Ln = Nd, Sm, Dy) and La_5.8Zr_0.2MoO_12.1, were shown to possess oxygen ion and proton conductivity,^10,11 the total conductivity of some polymorphs of undoped Ln_6−xMoO_12−δ (Ln = La, Yb; x = 0, 0.5) was also measured in dry and wet air.

Experimental section

The Ln_6−xMoO_12−δ (Ln = La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x = 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.

After preheating the starting Ln₂O₃ (Ln = La, Gd, Dy, Ho, Er, Tm, Yb, Lu) oxides at 1000 °C for 2 h, they were mixed with MoO₃ and co-milled in a SPEX 8000 ball mill for 1 h. MoO₃ 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 Kα radiation, λ = 1.5418 Å, Bragg-reflection geometry, 35 kV, 28 mA) in the 2θ range 13° to 65° (scan step 0.1°). Table 1 summarizes the color, density, and crystallographic characteristics of the samples.

Table 1 Properties of the solid solutions

Sample no.	Composition	Synthesis temperature	Color	Relative density, %	Structure	Unit-cell parameters, Å
1	La5.5MoO11.25	900 °C-3 h	Grey	—	Fm3̄m (metastable)	a = 5.478(1)
2	La5.5MoO11.25	1600 °C-3 h	Dirty-yellow	91.1	Complex rhombohedral phase
3	Gd6MoO12−δ	1600 °C-3 h	Speckled yellow	90.05	Fm3̄m + traces of admixtures	a = 5.382(3)
4	Gd5.5MoO11.25−δ	1500 °C-3 h	Speckled yellow	95.68	Fm3̄m	a = 5.378(2)
5	Gd5.5MoO11.25−δ	1600 °C-3 h	Speckled yellow	96.25	Fm3̄m	a = 5.379(1)
6	Dy6MoO12−δ	1500 °C-3 h	Speckled orange	84.32	Fm3̄m + traces of admixtures	a = 5.312(2)
7	Dy5.5MoO11.25−δ	1500 °C-3 h	Speckled orange	92.86	Fm3̄m	a = 5.313(1)
8	Dy5.5MoO11.25−δ	1600 °C-3 h	Speckled brown	96.38	Fm3̄m	a = 5.313(1)
9	Ho6MoO12−δ	1400 °C-3 h	Yellow with separate spots	74.26	Ia3̄	a = 10.579(2)
10	Ho6MoO12−δ	1600 °C-3 h	Yellow with separate spots	85.2	Ia3̄	a = 10.583(4)
11	Ho5.5MoO11.25−δ	1400 °C-3 h	Speckled yellow	82.65	Fm3̄m	a = 5.292(3)
12	Ho5.5MoO11.25−δ	1500 °C-3 h	Speckled yellow	89.27	Fm3̄m	a = 5.291(2)
13	Ho5.5MoO11.25−δ	1600 °C-3 h	Speckled yellow	94.44	Fm3̄m	a = 5.291(2)
14	Er6MoO12	1200 °C-40 h	Pink	—	R3̄	a = 9.695(4)
						c = 9.242(4)
15	Er6MoO12	1400 °C-3 h	Pink	78.76	R3̄	a = 9.697(4)
						c = 9.249(6)
16	Er6MoO12−δ	1600 °C-3 h	Orange with separate spots	77.64	Ia3̄	a = 10.526(4)
17	Er5.5MoO11.25−δ	1600 °C-3 h	Speckled orange	96.25	Fm3̄m	a = 5.267(2)
18	Tm6MoO12	1400 °C-3 h	Lemon	71.32	R3̄	a = 9.69(3)
						c = 9.234(15)
19	Tm6MoO12−δ	1600 °C-3 h	Yellow with separate spots	76.58	Ia3̄	a = 10.474(14)
20	Yb6MoO12	1200 °C-3 h	Lemon	65.86	R3̄	a = 9.614(2)
						c = 9.170(2)
21	Yb6MoO12	1400 °C-3 h	Lemon	75.06	R3̄	a = 9.610(2)
						c = 9.169(2)
22	Yb6MoO12	1500 °C-3 h	Lemon	78.12	R3̄	a = 9.612(2)
						c = 9.166(2)
23	Yb6MoO12−δ	1600 °C-3 h	Yellow with separate spots	81.19	Ia3̄	a = 10.421(5)
24	Yb5.5MoO11.25	1200 °C-3 h	Lemon	65.86	R3̄	a = 9.618(2)
						c = 9.172(2)
25	Yb5.5MoO11.25	1400 °C-3 h	Lemon	75.06	R3̄	a = 9.615(2)
						c = 9.168(2)
26	Yb5.5MoO11.25	1500 °C-3 h	Lemon	85.21	R3̄	a = 9.616(2)
						c = 9.168(2)
27	Yb5.5MoO11.25−δ	1600 °C-3 h	Yellow with separate spots	87.2	Ia3̄	a = 10.439(6)
28	Lu6MoO12	1400 °C-3 h	Lemon	64	R3̄	a = 9.594(6)
						c = 9.127(4)
29	Lu6MoO12	1600 °C-3 h	Light yellow	66.42	R3̄	a = 9.594(13)
						c = 9.123(8)

---

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 ≈ 4 × 10⁻⁶ mbar). To prevent shifts 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.

Table 2 Microanalysis data of the samples under investigation

Sample no.	Composition	Synthesis temperature	Average nominal Ln/Mo atomic ratio	Average measured Ln/Mo atomic ratio
2	La5.5MoO11.25	1600 °C-3 h	5.5	5.7 ± 0.6
3	Gd6MoO12−δ	1600 °C-3 h	6	6.5 ± 0.2
6	Dy6MoO12−δ	1500 °C-3 h	6	6.4 ± 0.5
9	Ho6MoO12−δ	1400 °C-3 h	6	6.5 ± 0.6
10	Ho6MoO12−δ	1600 °C-3 h	6	6.3 ± 0.9
11	Ho5.5MoO11.25−δ	1400 °C-3 h	5.5	6.1 ± 0.5
12	Ho5.5MoO11.25−δ	1500 °C-3 h	5.5	5.5 ± 0.2
15	Er6MoO12	1400 °C-3 h	6	6.5 ± 0.5
16	Er6MoO12−δ	1600 °C-3 h	6	6.3 ± 0.2
17	Er5.5MoO11.25−δ	1600 °C-3 h	5.5	6.1 ± 0.3
19	Tm6MoO12−δ	1600 °C-3 h	6	6.3 ± 0.4
21	Yb6MoO12	1400 °C-3 h	6	5.8 ± 0.2
23	Yb6MoO12−δ	1600 °C-3 h	6	5.3 ± 0.4
A	Er5.5MoO11.25	1200 °C-40 h	5.5	6.6 ± 0.7
B	Tm6MoO12	1200 °C-40 h	6	6.6 ± 0.3

---

The electrical conductivity of Ln_6−xMoO_12−δ (Ln = La, Yb; x = 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 fired at 1000 °C for 30 min.

The temperature dependence of the total (electronic and ionic) conductivity of La_5.5MoO_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, Yb₆MoO₁₂ bixbyite (Ia3̄) and Yb₆MoO₁₂ rhombohedral (R3̄), 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 flow rate is 130 ml min⁻¹.

Results and discussion

Room-temperature synthesis of heavy rare-earth molybdate Yb₆MoO₁₂ and intermediate rare-earth molybdate Ho₆MoO₁₂ from oxides

Fig. 1a shows XRD patterns illustrating the mechanochemical synthesis of Yb₆MoO₁₂ from its constituent oxides. Scan 1 in Fig. 1a represents the XRD pattern of unmilled Yb₂O₃, which has the bixbyite structure (Ia3̄) (ICDD PDF 18-1463). Its lattice parameter was determined to be a = 10.402(2) Å. Scans 2 and 3 in Fig. 1a represent XRD patterns of MoO₃ before and after grinding for 4 min in an Aronov vibrating ball mill. It is seen that the layered oxide MoO₃ 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 3Yb₂O₃ + MoO₃ (after 4 min of grinding (Aronov mill)). Since the mixture contains a considerable amount of ytterbium oxide, the relative amount of MoO₃ is not very large. After 40 min of subsequent grinding in a SPEX 8000 mill, we observed complete dissolution of the molybdenum oxide in Yb₂O₃ with the bixbyite structure (Ia3̄). The resultant solid solution also had the bixbyite structure (Ia3̄), and its lattice parameter was a = 10.423(2) Å, i.e. it considerably exceeded that of the parent Yb₂O₃. Thus, it is reasonable to believe that an Yb₂O₃-based solid solution (Yb₆MoO₁₂) forms even during grinding, so this process can be thought of as the room-temperature mechanochemical synthesis of Yb₆MoO₁₂ with the bixbyite structure (Ia3̄). Note also that subsequent annealing at 1600 °C for 3 h had no significant effect on its lattice parameter a = 10.421(5) Å (Table 1). A similar situation was observed for Tm₆MoO₁₂ with parameter a = 10.465(2) Å, which exceeded that of the parent Tm₂O₃ (a = 10.459(1) Å).

Fig. 1 (a) XRD patterns of (1) unmilled Yb₂O₃ with the bixbyite structure, (2) unmilled MoO₃, (3) MoO₃ after grinding for 4 min in an Aronov mill, (4) a 3Yb₂O₃ + premilled MoO₃ (4 min) mixture, (5) the 3Yb₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 40 min in a SPEX 8000 mill, and (6) the 3Yb₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 60 min in the SPEX 8000; (b) XRD patterns of (1) unmilled Ho₂O₃ with the bixbyite structure after annealing at 1000 °C for 1 h, (2) unmilled MoO₃, (3) MoO₃ after grinding for 4 min in the Aronov mill, (4) a 3Ho₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 10 min in the SPEX 8000, (5) the 3Ho₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 20 min in the SPEX 8000, (6) the 3Ho₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 40 min in the SPEX 8000, (7) the 3Ho₂O₃ + premilled MoO₃ (4 min) mixture after grinding for 60 min in the SPEX 8000, and (8) the 3Ho₂O₃ + MoO₃ precursor (represented in scan 7) after heat treatment at 1100 °C for 4 h.

Fig. 1b shows the XRD pattern of unmilled Ho₂O₃ with the bixbyite structure ((Ia3̄); a = 10.583(2) Å) after annealing at 1000 °C for 1 h (scan 1) and the XRD patterns of MoO₃ before and after grinding for 4 min in the Aronov vibrating ball mill (scans 2 and 3). Also shown in Fig. 1b is the XRD pattern of a 3Ho₂O₃ + MoO₃ mixture after 10 min of grinding in the SPEX mill (scan 4). It is seen that MoO₃ almost completely disappeared and that the reflections from Ho₂O₃ became markedly weaker and broader. Scans 5–7 in Fig. 1b represent the XRD patterns of the 3Ho₂O₃ + MoO₃ mixture after 20, 40, and 60 min of grinding. It is seen that the superstructure reflections from the parent Ho₂O₃ (bixbyite structure, (Ia3̄)) (Fig. 1b, scan 7) completely disappeared and that the strongest reflections remaining in the XRD pattern are due to a fluorite-like phase with a = 5.301(2) Å and are markedly broadened.

Thus, the mechanochemical synthesis of heavy rare-earth molybdates (Yb₆MoO₁₂) differs from that of intermediate rare-earth molybdates (Ho₆MoO₁₂), which can be accounted for in terms of the nature of the starting oxide Ln₂O₃ (Ln = Yb, Ho).

La_6−xMoO_12−δ (x = 0, 0.5) formation from mechanically activated precursors

The ICDD PDF database of La₆MoO₁₂ presents data on low-temperature phases, with broad diffraction lines,²⁶ whereas data on well-crystallized fluorite La₆MoO₁₂ at high temperatures, T ∼ 1500–1600 °C, are missing. Previously, rare-earth molybdates were studied as a rule at temperatures no higher than 1400 °C. However, the qualitative transpiration tests²⁷ indicated that the compounds R₆WO₁₂ (R = Y, Tm, Lu) and Ln₆MoO₁₂ (Ln = Tm–Lu) with a rhombohedral (R3̄) structure demonstrate high thermal stability. After annealing for 2 h at 1750 °C in air, pellets of pure oxides, R₂O₃ (R = Y, Tm–Lu), had completely volatilized while both of the rhombohedral (R3̄) Y₆MO₁₂ (M = Mo, W) compounds showed only a small loss (0.1–0.3%) in weight.

Fig. 2 shows XRD patterns illustrating the phase formation process in La_5.5MoO_11.25 at 900, 1200, 1600, and 1650 °C (scans 1–4). When comparing the XRD patterns of La_5.5MoO_11.25 synthesized at 1600 and 1650 °C (Fig. 2, scans 3 and 4) to that of La₆MoO₁₂ prepared at 1600 °C (Fig. 2, scan 5), it is important to note that, like La₆WO₁₂,⁸ La₆MoO₁₂ does not exist as a distinct compound but is a mixture of La_6−xMoO_12−δ and La₂O₃ (ICDD PDF-2, no. 74-144) (*) as also are La(OH)₃ (ICDD PDF-2, no. 83-2034) (^), and La₂O(CO₃)₂ × H₂O (ICDD PDF-2, no. 28-512) (v), which are La₂O₃ hydration and carbonation products.

Fig. 2 XRD patterns, showing the process of phase formation of La_5.5MoO_11.25 from the mechanically activated oxide mixture under various conditions, (1) 900 °C-4 h, (2) 1200 °C-4 h, (3) 1600 °C-3 h, and (4) 1650 °C-3 h, in comparison with (5) La₆MoO₁₂, synthesized at 1600 °C-3 h. The XRD pattern of La₆MoO₁₂ (curve 5) contains not only lines of La₂O₃ (ICDD PDF-2, no. 74-144) (*) but also those of La(OH)₃ (ICDD PDF-2, no. 83-2034) (^), and La₂O(CO₃)₂ × H₂O (ICDD PDF-2, no. 28-512) (v), which are La₂O₃ hydration and carbonation products.

Given this, we synthesized not only Ln₆MoO₁₂ but also Ln_5.5MoO_11.25 (Ln = La, Gd, Dy, Ho, Er, Yb) in order to prevent the final material from being multiphasic.

When analyzing the La_5.5MoO_11.25 formation process, it is worth noting the formation of a metastable, low-temperature fluorite phase at 900 °C, which then transforms into a rhombohedral (R3̄) phase at 1200 °C (Fig. 2, scans 1 and 2). The formation of a metastable, low-temperature fluorite phase was also observed in lutetium molybdate (Lu₆MoO₁₂) synthesis⁶ and was reported for Y₆WO₁₂ and Ln₆WO₁₂ (Ln = 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_5.5MoO_11.25 from 1200 to 1600 and 1650 °C led to the formation of a new phase that was also rhombohedral to a first 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 La₆MoO₁₂ (Fig. 2, scan 5). Comparison of XRD data of the zirconium-substituted molybdate La_5.8Zr_0.2MoO_12.1,¹⁰ the La_5.5MoO_11.25 synthesized in this study, and a molybdenum-rich La_28−y(W_1−xMo_x)_4+yO_54+δ tungstate²⁸ 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 × 28 × 9.8 Å), and with an unusually large volume of 6600 ų. Thus, further research is needed, with the use of neutron and synchrotron X-ray diffraction, to accurately determine the complex structure of La_5.5MoO_11.25.

Gd_6−xMoO_12−δ (x = 0, 0.5) formation from mechanically activated precursors

Fig. 3a and b show XRD patterns illustrating the phase formation process in Gd₆MoO₁₂ and Gd_5.5MoO_11.25, respectively, at 900, 1200, 1500, and 1600 °C. For Gd₆MoO₁₂ XRD of the sample after 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 Eu₆WO₁₂ 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_5.5MoO_11.25−δ sample consists of a pure fluorite (Fm3̄m) phase (Fig. 3b, scans 3 and 4), whereas the Gd₆MoO_12−δ sample contains impurity phases (Fig. 3a, scans 4 and 5). After 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 fluorite Gd₆MoO_12−δ by annealing at 1600 °C because of the partial reduction of the material.

Fig. 3 (a) XRD patterns, demonstrating the process of phase formation of Gd₆MoO₁₂ after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 900 °C-4 h, (2) 1100 °C-4 h, (3) 1200 °C-3 h, (4) 1500 °C-3 h, and (5) 1600 °C-3 h. (b) XRD patterns, demonstrating the process of phase formation of Gd_5.5MoO_11.25 after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 900 °C-4 h, (2) 1200 °C-3 h, (3) 1500 °C-3 h, and (4) 1600 °C-3 h.

Ln_6−xMoO_12−δ (Ln = Dy, Ho, Er, Tm, Yb, Lu; x = 0, 0.5) formation from mechanically activated precursors

Fig. 4a and b show XRD patterns illustrating the phase formation process in Dy₆MoO₁₂ and Dy_5.5MoO_11.25. Annealing at 900 °C leads to the formation of metastable bixbyite (Ia3̄), 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 Dy₆MoO_12−δ (Fig. 4a, scan 3) and at 1600 °C of Dy_5.5MoO_11.25−δ (Fig. 4b, scan 5), leads to the formation of a pure fluorite (Fm3̄m) phase. After annealing at 1600 °C, the Dy₆MoO_12−δ sample contains impurities (Fig. 4a, scan 4), in contrast to Dy_5.5MoO_11.25−δ (Fig. 4b, scan 5). The Dy-containing samples with the fluorite structure have a non-uniform coloration (with black inclusions). The samples with the bixbyite structure have a more uniform coloration.

Fig. 4 (a) XRD patterns, showing the process of phase formation of Dy₆MoO₁₂ after heat treatment of the mechanically activated oxide mixture under various conditions: (1) 900 °C-4 h, (2) 1200 °C-3 h, (3) 1500 °C-3 h, and (4) 1600 °C-3 h. (b) XRD patterns, showing the process of phase formation of Dy_5.5MoO_11.25 after heat treatment of the mechanically activated oxide mixture under various conditions: (1) 900 °C-4 h, (2) 1100 °C-4 h, (3) 1200 °C-3 h, (4) 1500 °C-3 h, and (5) 1600 °C-3 h.

Fig. 5a and b present XRD patterns illustrating the phase formation process in Ho₆MoO₁₂ and Ho_5.5MoO_11.25. Here, low-temperature (∼900–1100 °C) annealing also leads to the formation of a mixture of a metastable bixbyite phase (Ia3̄), a tetragonal, and a rhombohedral phase (tracks) (Fig. 5a and b, scan 1; Fig. 1b, scan 8). After heat treatment at 1600 °C, Ho₆MoO_12−δ has the bixbyite structure (Ia3̄) and Ho_5.5MoO_11.25−δ has the fluorite structure (Fm3̄m). The Ho-containing samples with the fluorite structure also have a non-uniform coloration, which seems to be evidence of partial reduction.

Fig. 5 (a) XRD patterns, demonstrating the process of phase formation of Ho₆MoO₁₂ after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 1100 °C-4 h, (2) 1200 °C-3 h, (3) 1400 °C-3 h, and (4) 1600 °C-3 h. (b) XRD patterns, demonstrating the process of phase formation of Ho_5.5MoO_11.25 after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 900 °C-4 h, (2) 1100 °C-4 h, (3) 1200 °C-3 h, (4) 1400 °C-3 h, (5) 1500 °C-3 h, and (6) 1600 °C-3 h.

In the case of Er₆MoO₁₂ (Fig. 6a), at 900 °C we observe the formation of a metastable bixbyite (Ia3̄) 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 Er₆MoO₁₂ (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 (Ia3̄) phase Er₆MoO_12−δ (Fig. 6a, scan 5). Fig. 6b compares the XRD patterns of Er₆MoO_12−δ and Er_5.5MoO_11.25−δ after annealing at 1600 °C. The former material has the bixbyite structure (Ia3̄) and the latter has the fluorite (Fm3̄m) structure. To examine the influence of annealing time on the phase formation process at a low temperature (1200 °C), the mechanically activated mixture of the oxides 3Er₂O₃ + MoO₃ was sintered at 1200 °C for 4 and 40 h, respectively (Fig. 6c). We observed the formation of an Er₆MoO_12−δ bixbyite cubic phase (metastable) (Fig. 6c, scan 1) in the thermodynamic stability region of the rhombohedral (R3̄) Er₆MoO₁₂ phase with the same composition under the effect of kinetic factors.¹⁹ The transformation into the stable rhombohedral (R3̄) Er₆MoO₁₂ 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 (R3̄) Er₆MoO₁₂ at 1200 °C. A similar process (from metastable fluorite to the stable rhombohedral (R3̄)) was recently reported as an irreversible, first order diffusional ordering process for the Ln₆WO₁₂ (Ln = Y, Ho, Er, Yb).²⁹

Fig. 6 (a) XRD patterns, showing the process of phase formation of Er₆MoO₁₂ after heat treatment of the mechanically activated oxide mixture under various conditions: (1) 1100 °C-4 h, (2) 1200 °C-3 h, (3) 1400 °C-3 h, (4) 1500 °C-3 h, and (5) 1600 °C-3 h. (b) XRD patterns of the (1) Er₆MoO_12−δ (Ia3̄) and (2) Er_5.5MoO_11.25 (Fm3̄m), synthesized at 1600 °C-3 h. (c) XRD patterns of the Er₆MoO₁₂ after thermal annealing at 1200 °C for (1) 4 h and (2) 40 h.

Yb₆MoO₁₂ and Yb_5.5MoO_11.25 have identical phase formation sequences (Fig. 7a and b). A metastable bixbyite phase (Ia3̄) is formed at 900 °C (Fig. 7a and b, scans 1). The stability range of the rhombohedral (R3̄) phase, 1200 to 1500 °C, is broader in comparison with that of Er₆MoO₁₂ (Fig. 7a, scans 2–4; Fig. 7b, scans 3–5). After annealing at 1600 °C, both Yb₆MoO_12−δ and Yb_5.5MoO_11.25−δ have the high-temperature bixbyite structure (Ia3̄) (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 (rhombohedral–bixbyite) phase transitions for Ln₆MoO₁₂ (Ln = Er, Yb).

Fig. 7 (a) XRD patterns, demonstrating the process of phase formation of Yb₆MoO₁₂ after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 900 °C-4 h, (2) 1200 °C-4 h, (3) 1400 °C-3 h, (4) 1500 °C-3 h, and (5) 1600 °C-3 h. (b) XRD patterns, demonstrating the process of phase formation of Yb_5.5MoO_11.25 after heat treatment of the mechanically activated oxide mixture at the different temperatures: (1) 900 °C-4 h, (2) 1100 °C-4 h, (3) 1200 °C-4 h, (4) 1400 °C-3 h, (5) 1500 °C-3 h, and (6) 1600 °C-3 h.

Tm₆MoO₁₂ was also found to undergo an order–disorder (rhombohedral–bixbyite) phase transition, like Ln₆MoO₁₂ (Ln = Er, Yb) (Fig. 8, scans 1 and 2). At the same time, Lu₆MoO₁₂ seems to undergo an order–disorder transition at higher temperatures, like La_5.5MoO_11.25, as evidenced by the fact that, in the range 1400–1600 °C, Lu₆MoO₁₂ retains the rhombohedral structure (Fig. 8, scans 3 and 4). A metastable fluorite phase (Fm3̄m) was obtained previously for Lu₆MoO₁₂ 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 fluorite phase, rather than as a bixbyite phase.

Fig. 8 XRD patterns of Tm₆MoO₁₂ and Lu₆MoO₁₂, synthesized (1 and 3) at 1400 °C-3 h and (2 and 4) at 1600 °C-3 h.

Thus, in this study, Ln₆MoO₁₂ (Ln = Er, Yb, Tm) and solid solutions based on these compounds were shown for the first time to undergo high-temperature order–disorder (rhombohedral–bixbyite) phase transitions (T_PT ≥ 1500 °C), and we identified metastable bixbyite phases forming below 1000 °C.

Morphotropic and thermodynamic order–disorder (fluorite–rhombohedral phase–bixbyite) transitions

Fig. 9 shows the unit-cell parameter a as a function of the Ln ionic radius of the Ln_5.5MoO_11.25−δ (Ln = Er–Gd) molybdates with the fluorite structure after 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 fluorite phase La_5.5MoO_11.25−δ synthesized at 900 °C. Fitting the dependence of a on the Ln ionic radius of the Ln_5.5MoO_11.25−δ (Ln = Er–Gd) molybdates at 1600 °C by a straight line, we find that the a of high-temperature La_5.5MoO_11.25 markedly exceeds that of metastable fluorite La_5.5MoO_11.25.

Fig. 9 Unit-cell parameter as a function of the Ln³⁺ ionic radius of fluorite Ln_5.5MoO_11.25 (Ln = Er–Gd) after annealing at 1600 °C for 3 h.

The data in Fig. 10 illustrate the morphotropic fluorite–bixbyite phase transition in the Ln₆MoO_12−δ molybdates after annealing at 1600 °C for 3 h. Fig. 10 and Table 1 present the unit-cell parameter as a function of the Ln³⁺ ionic radius of Ln₆MoO_12−δ (Ln = Yb, Tm, Er, Ho, Dy, Gd). The heavy rare-earth molybdates Ln₆MoO_12−δ (Ln = Ho, Er, Yb, Tm) crystallize in the bixbyite structure (Ia3̄) and the intermediate rare-earth molybdates Ln₆MoO_12−δ (Ln = Dy, Gd) crystallize in the fluorite structure (Fm3̄m). The Ho_6−xMoO_12−δ (x = 0, 0.5) molybdates were shown to exist in two phases, with the fluorite and bixbyite structures, and the heavy rare-earth molybdates Ln₆MoO₁₂ (Ln = Er, Tm, Yb) exist as rhombohedral and bixbyite phases.

Fig. 10 Fluorite–bixbyite morphotropic transition in Ln₆MoO_12−δ after annealing at 1600 °C for 3 h: unit-cell parameter as a function of the Ln³⁺ ionic radius of Ln₆MoO_12−δ (Ln = Yb, Er, Ho, Dy, Gd).

Fig. 11 plots the unit-cell parameters against the Ln³⁺ ionic radius of rhombohedral Ln₆MoO₁₂ (Ln = Er, Tm, Yb, Lu) prepared at 1400 °C (3 h). Both a and c increase with the Ln³⁺ ionic radius. Note that the temperature stability range of the rhombohedral phase increases with decreasing Ln³⁺ ionic radius. In particular, the rhombohedral phase of Er₆MoO₁₂ exists only after a short 3 h annealing at 1400 °C, whereas that of Yb_6−xMoO_12−δ (x = 0, 0.5) exists after annealing in the range 1200–1500 °C (Table 1; Fig. 7a and b). However the true stability region of the Er₆MoO₁₂ rhombohedral phase starts from 1200 °C as shown by long temperature annealing (40 h) at 1200 °C (Fig. 6c, scan 2). Rhombohedral (R3̄) Tm₆MoO₁₂ also exists below 1600 °C (Table 1; Fig. 8). The rhombohedral phase of Lu₆MoO₁₂ persists at 1600 °C, and it seems to undergo disordering at a higher temperature.

Fig. 11 Unit-cell parameters as functions of the Ln³⁺ ionic radius of rhombohedral (R3̄) Ln₆MoO₁₂ (Ln = Er, Tm, Yb, Lu) prepared at 1400 °C (3 h).

In this study, using brief annealing (3 h) of mechanically activated oxide mixtures, we were able to obtain high-temperature bixbyite Ln₆MoO_12−δ (Ln = Ho, Er, Tm, Yb) in the range 1400 to 1600 °C. The stability of the heaviest rare-earth molybdates and tungstates, Ln₆Mo(W)O₁₂ (Ln = Tm, Yb, Lu), was studied qualitatively by Aitken et al.²⁷ and was shown to be even higher than that of Ln₂O₃ (Ln = 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 R₆MoO₁₂ (R = 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 Yb₆MoO_12−δ (Table 2, no. 23) (Fig. 12a and b) and Ho₆MoO_12−δ (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.

Fig. 12 (a and c) SEM image and (b and d) Mo X-ray map of Yb₆MoO_12−δ and Ho₆MoO_12−δ, respectively, synthesized at 1600 °C.

Given this, using mechanochemical synthesis, we were able to produce rather dense ceramics with fluorite and related (rhombohedral (R3̄) and bixbyite (Ia3̄)) structures, and it is of obvious interest to study not only the structure but also the electrical properties of these polymorphs. Indeed, as shown earlier, La_5.8Zr_0.2MoO_12.1 and Ln_6−xZr_xMoO_12+δ (Ln = Nd, Sm, Dy; x = 0.6) zirconium-doped materials have oxygen ion conductivity in a dry atmosphere and proton conductivity in a wet atmosphere below 700, 500, and 425 °C.^10,11 These materials have ionic conductivity at low and medium temperatures, whereas at higher temperatures electronic conductivity prevails. Thus, it is important to evaluate the conductivity of the zirconium-free Ln_6−xMoO_12−δ (Ln = La, Yb; x = 0, 0.5) rare-earth molybdates with the rhombohedral and bixbyite structures.

Total conductivity of La_5.5MoO_11.25 in dry and wet air

The impedance spectra obtained for the rhombohedral La_5.5MoO_11.25 (T_syn. = 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 specific bulk and electrode capacitances extracted via non-linear least squares fitting (C_b ∼ 10⁻¹² F cm⁻¹ and C_el ∼ 10⁻⁵ F cm⁻²) are consistent with the aforementioned interpretation. Fig. 14 presents the total conductivity of La_5.5MoO_11.25 (T_syn. = 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_5.5MoO_11.25 shows an inflection point at ∼600 °C in a wet atmosphere. A shift 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_5.5MoO_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.

Fig. 13 Impedance spectra of rhombohedral La_5.5MoO_11.25 (T_syn. = 1600 °C) in dry air and wet air at difference temperatures.

Fig. 14 Arrhenius plots of the total conductivity of La_5.5MoO_11.25 in dry and wet air.

Table 3 Activation energy for bulk conduction in the solid solutions in dry and wet air

Composition	Activation energy of bulk conductivity Ea, eV in dry air		Activation energy of bulk conductivity Ea, eV in wet air
	Below 600 °C	Above 600 °C	Below 600 °C	Above 600 °C
La5.5MoO11.25	0.71	1.3	0.68	1.15
Yb6MoO12−δ bixbyite (Ia3̄)	1.16	1.37	1.07	1.32
Yb6MoO12 rhombohedral (R3̄)	0.53	0.98	0.58	0.98

---

Even though the conductivity of La_5.5MoO_11.25 (2 × 10⁻⁴ at 600 °C) is lower than that of La_6−xWO_12−δ,^7–9 the more complex structure of La_5.5MoO_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 Yb₆MoO₁₂ polymorphs: bixbyite (Ia3̄) and rhombohedral (R3̄) in dry and wet air

Fig. 15 shows the typical impedance spectra of bixbyite Yb₆MoO_12−δ (Ia3̄) 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.

Fig. 15 Impedance spectra of bixbyite Yb₆MoO_12−δ (Ia3̄) (T_syn. = 1600 °C) in dry and wet air.

The real-axis intercept of the high-frequency arc is the bulk resistance of the material, R_bulk. Note that the center of the high-frequency 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 ∼10⁻¹¹ F cm⁻¹, 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 (R3̄) Yb₆MoO₁₂ at low (525 and 570 °C) (Fig. 16a) and higher (650 and 700 °C) (Fig. 16b) temperatures. In contrast to the spectrum of Yb₆MoO_12−δ with the bixbyite structure (Ia3̄), 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 ∼10⁻¹¹ F cm⁻¹.

Fig. 16 Impedance spectra of rhombohedral Yb₆MoO₁₂ (R3̄) (T_syn. = 1500 °C) in dry and wet air.

Fig. 17 presents the temperature dependency of the total conductivity of Yb₆MoO_12−δ (Ia3̄) and Yb₆MoO₁₂ (R3̄) 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 Yb₆MoO_12−δ 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 Yb₆MoO_12−δ has mixed conductivity. Rhombohedral (R3̄) Yb₆MoO₁₂ has no proton conductivity below 600 °C and seems to be an oxygen ion conductor in dry air (E_a = 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 activation energies. For example, as shown by Kiruthika et al.³² some pyrochlore-structured compounds have lower activation energies for bulk conduction. In particular, the activation energy for bulk conduction in Gd_1.8Sr_0.2Hf₂O_6.9 and Nd_1.9Sr_0.1Hf₂O_6.95 is 0.57 and 0.42 eV, respectively.

Fig. 17 Arrhenius plots of the total conductivity in (1 and 3) dry and (2 and 4) wet air of two Yb₆MoO₁₂ polymorphs: (1 and 2) bixbyite (Ia3̄) Yb₆MoO_12−δ and (3 and 4) rhombohedral (R3̄) Yb₆MoO₁₂.

At T > 600 °C the activation energy of rhombohedral (R3̄) Yb₆MoO₁₂ conductivity is E_a = 0.98 eV (Table 3) and we can suppose that ionic conductivity contribution prevails in rhombohedral (R3̄) Yb₆MoO₁₂ at these temperatures.

As shown earlier, the proton conductivity of zirconium-doped 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_5.4Zr_0.6MoO_12.3 has insignificant proton conductivity.¹⁰ The Arrhenius plot of the conductivity of rhombohedral (R3̄) Yb₆MoO₁₂ 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 (R3̄) Yb₆MoO₁₂ seems to have purely oxygen ion conductivity in wet air below 550 °C (Table 3), whereas the conductivity of La_5.5MoO_11.25 has a significant proton contribution (Fig. 14). Above 600 °C, both rhombohedral (R3̄) and bixbyite Yb₆MoO_12−δ have growing electronic conductivity contribution, which increases with temperature (Table 3).

The total conductivity of rhombohedral (R3̄) Yb₆MoO₁₂ is more than an order of magnitude higher than the conductivity of Yb₆MoO_12−δ bixbyite, and is 3 × 10⁻⁵ S cm⁻¹ at 500 °C.

Conclusions

We have investigated the phase formation processes of Ln_6−xMoO_12−δ (Ln = La, Gd, Dy, Ho, Er, Tm, Yb, Lu; x = 0, 0.5) rare-earth 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 fluorite, 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 first time thermodynamic order–disorder (rhombohedral (R3̄)–bixbyite (Ia3̄)) phase transitions in the heavy rare-earth molybdates Ln_6−xMoO_12−δ (Ln = Er, Tm, Yb; x = 0, 0.5). The stability range of the rhombohedral phase increases with decreasing Ln ionic radius.

The total conductivity of La_5.5MoO_11.2 and two Yb₆MoO₁₂ polymorphs, with rhombohedral (R3̄) and bixbyite (Ia3̄) structures, has been determined in dry and wet air using impedance spectroscopy. Below 600 °C, the conductivity of La_5.5MoO_11.25 and bixbyite Yb₆MoO_12−δ (Ia3̄) has a significant proton contribution. Rhombohedral (R3̄) Yb₆MoO₁₂ has oxygen ion conductivity under these conditions (T < 550 °C). At 600 °C in wet air, the conductivity of undoped La_5.5MoO_11.25, which has a complex structure derived from the rhombohedral one, is 2 × 10⁻⁴ S cm⁻¹. The conductivity of rhombohedral (R3̄) Yb₆MoO₁₂ in air at 600 °C is 1 × 10⁻⁴ S cm⁻¹ and that of bixbyite Yb₆MoO_12−δ at 600 °C is 1 × 10⁻⁵ S cm⁻¹. So we have obtained and investigated the first members of oxygen ion- and/or proton-conducting materials with the bixbyite (Ia3̄) and rhombohedral (R3̄) structure in the family of Ln_6−xMoO_12−δ (Ln = Ho, Er, Tm, Yb, Lu; x = 0, 0.5) molybdates.

Acknowledgements

This work was supported by the Russian Foundation for Basic Research (grant no. 16-03-00143). We are grateful to Dr Maxim Avdeev from the Bragg Institute, Australian Nuclear Science and Technology Organization for useful discussions in preparing the manuscript.

References

1. J. Wang, X. Jing, C. Yan, J. Lin and F. Liao, J. Lumin., 2006, 121, 57.
2. S. Vishnu, S. Jose and M. L. Reddy, J. Am. Ceram. Soc., 2011, 94, 997.
3. J. Kumar Kar, R. Stevens and C. R. Bowen, J. Alloys Compd., 2008, 461, 77.
4. J. Sun, B. Xue and H. Du, Infrared Phys. Technol., 2013, 60, 10.
5. J. Sun, B. Xue and H. Du, Opt. Commun., 2013, 298–299, 37.
6. H. Li, H. K. Yang, B. K. Moon, B. C. Choi, J. H. Jeong, K. Jang, H. S. Lee and S. S. Yi, Inorg. Chem., 2011, 50(24), 12522.
7. C. Solís, S. Escolástico, R. Haugsrud and J. M. Serra, J. Phys. Chem. C, 2011, 115, 11124.
8. A. Magrasó and R. Haugsrud, J. Mater. Chem. A, 2014, 2, 12630.
9. G. S. Partin, D. V. Korona, A. Ya. Neiman and K. G. Belova, Russ. J. Electrochem., 2015, 51, 381.
10. S. N. Savvin, A. V. Shlyakhtina, A. B. Borunova, L. G. Shcherbakova, J. C. Ruiz-Morales and P. Núñez, Solid State Ionics, 2015, 271, 91.
11. S. N. Savvin, A. V. Shlyakhtina, I. V. Kolbanev, A. V. Knotko, D. A. Belov, L. G. Shcherbakova and P. Nuñez, Solid State Ionics, 2014, 262, 713.
12. K. Kuribayashi, M. Yoshimura, T. Ohta and T. Sata, J. Am. Ceram. Soc., 1980, 63, 644.
13. M. Foex, Bull. Soc. Chim. Fr., 1967, 10, 3696.
14. M. Yoshimura, J. Ma and M. Kakihana, J. Am. Ceram. Soc., 1998, 10, 2721.
15. D. Schildhammer, G. Fuhrmann, L. L. Petschnig, S. Penner, M. Kogler, T. Gotsch, A. Scaur, N. Weinberger, A. Saxer, H. Schottenberger and H. Huppertz, Chem. Mater., 2016, 28(20), 7487.
16. S. Escolastico, V. B. Vert and J. M. Serra, Chem. Mater., 2009, 21, 3079.
17. V. M. Goldschmidt, Usp. Fiz. Nauk, 1929, 6, 811.
18. G. M. Kuz'micheva, Basic Crystal-Chemical Concepts, MITKhT, Moscow, 2001.
19. A. G. Shtukenberg, Yu. O. Punin and O. V. Frank-Kamenetskaya, Usp. Khim., 2006, 75(12), 1212.
20. A. A. Chernov, Usp. Fiz. Nauk, 1970, 100(2), 277.
21. A. A. Chernov, Kinetic phase transitions, Soviet Physics–JETP, 1968, 26(6), 1182–1186.
22. A. V. Shlyakhtina, Crystallogr. Rep., 2013, 58, 545.
23. V. V. Popov, A. P. Menushenkov, A. A. Yaroslavtsev, Ya. V. Zubavichus, B. R. Gaynanov, A. A. Yastrebtsev, D. S. Leshchev and R. V. Chernikov, J. Alloys Compd., 2016, 689, 669.
24. V. M. Vidojikovic, A. R. Brankovic and R. B. Petronijevic, Mater. Lett., 1996, 28, 59.
25. A. F. Fuentes, K. Boulahya, M. Maczka, J. Hanuza and U. Amador, Solid State Sci., 2005, 7, 343.
26. ICDD PDF 24-1087. Mcllvried, McCarthy, Penn State University, University Park, Pennsylvania, USA. 1972.
27. E. A. Aitken, S. F. Bartram and E. F. Juenke, Inorg. Chem., 1964, 3, 949.
28. M. Amsif, A. Magraso, D. Marrero-Lopez, J. C. Ruiz-Morales, J. Canales-Vazquez and P. Nuñez, Chem. Mater., 2012, 24, 3868.
29. Z. D. Apostolov, P. Sarin, R. P. Haggerty and W. M. Kriven, J. Am. Ceram. Soc., 2013, 96, 987.
30. J. S. Mohammed, The Degree Master of Science in Materials Science and Engineering, Georgia Institute of Technology, 2004.
31. A. V. Shlyakhtina, S. N. Savvin, A. V. Knotko, L. G. Shcherbakova and P. Nuñez, Inorg. Mater., 2016, 52, 1055.
32. G. V. M. Kiruthika, K. V. Gavindan Kutty and U. V. Varadarju, Solid State Ionics, 1998, 110, 335.

---