Bhabha Atomic Research Centre, Mumbai , India.

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1 High pressure phase transitions in ZrMo 2 O 8 and HfMo 2 O 8 : an electrical conductivity study G.D. Mukherjee a *, A.S. Karandikar a, V. Vijayakumar a, A.K. Tyagi b and B.K. Godwal a a High Pressure Physics Division, b Applied Chemistry Division, Bhabha Atomic Research Centre, Mumbai , India. gdm@apsara.barc.ernet.in Summary The ac resistance measurements on trigonal (α-phases) of ZrMo 2 O 8 and HfMo 2 O 8 carried out up to 5 GPa using the toroid anvil apparatus are reported. The ac resistance in both the materials is found to be strongly frequency dependent due to the strong lattice response to the movement of the ions. For both the compounds slope changes and anomalies are observed in both the resistance data at the structural transition pressures. The activation volumes at room temperature are obtained by analyzing the conductance data in terms of the pressure dependent activation volume model. The different pressure evolution of ac conductance observed for both the systems are due to the different mechanisms responsible for conduction process at low and high frequencies, which are mediated by the structural evolution with pressure. Introduction Over the last few decades investigations on frame work structured materials of the type MX 2 O 8 (M = Zr, Hf and X = W, Mo) have drawn considerable interest due to their negative thermal expansion behaviour, which may have important technological applications in e.g. composites with tunable thermal expansion (Achary, 2002). ZrMo 2 O 8, which belongs to the above group, has shown promises for possible use in nuclear fuel processes, as ionexchangers and catalysts (Prinetto, 1995). Therefore high pressure studies of these materials have acquired a significant importance for both basic and applied sciences. ZrMo 2 O 8 and its isostructural compound HfMo 2 O 8 stabilize in a trigonal symmetry (α - phase) at ambient condition. High pressure structural investigations on α - ZrMo 2 O 8 has shown two successive phase transformations by the displacive movement of oxygen atoms: α - δ (monoclinic) phase at GPa and δ - ε (triclinic) phase at GPa followed by amorphization above 10 GPa (Anderson, 2001 and Carlson, 2000). α -HfMo 2 O 8 has been found to transform to a 20% denser monoclinic (β) phase at 2.15 GPa and 560 o C (Achary, 2002). But to our knowledge no other reports on the high pressure studies of α -HfMo 2 O 8 are available till date. The structure of α-zrmo 2 O 8 (α-hfmo 2 O 8 ) consists ZrO 6 (HfO 6 ) octahedra, which share all the corners with the MoO 4 tetrahedra. While only three oxygen atoms at the apices of the tetrahedra form part of the three adjacent octahedra, the oxygen atom at the fourth apex is `non-bridged' and points towards the interlayer region. This kind of framework arrangement gives rise to a two-dimensional layered structure perpendicular to c-axis. The interlayer

2 oxygen can hop to adjacent defect sites leading to dynamic oxygen disorder and ionic conduction. Therefore structural transitions will be reflected in the ionic (ac) conductivity. Such conductivity variation can also reveal the feasibility of these materials as pressure sensing elements. In view of the above more detailed investigations of the phase transformations under pressure in these systems is desired. In order to gain more insight about the phase transitions and to obtain its significance, we carried out high pressure ac resistance measurements on ZrMo 2 O 8 and HfMo2O8 respectively up to 5.5 GPa, which is reported here. Experimental Trigonal (α) phases of ZrMo 2 O 8 and HfMo 2 O 8 were prepared by the conventional solid-state synthesis. The high pressure ac electrical conductance measurements were carried out up to 5 GPa in a modified pressure cell of the toroid anvil apparatus (TA). The 2-probe technique was used for the resistance measurements, in which, the pressurizing rams of the TA apparatus themselves act as probes for voltage measurement and sourcing the current. A cylindrical sample assembly and the graphite electrodes along with the solid pressuretransmitting medium are arranged inside the cylindrical central hole (ID 6 mm) of the toroid shaped pyrophillite gasket. The sample assembly was prepared as follows. The powder sample was pressed by hand to form a pellet (thickness: 1 mm, dia: 6 mm), and was sandwiched between two thin graphite plates (thickness: 1.8 mm, dia: 6 mm). The faces of graphite plates facing the sample were insulated leaving a tiny circular area exposed at one corner (diagonally opposite for the upper and lower graphite plates) for good electrical contact to the sample. The exposed faces of the graphite plates were painted with silver paste for good electrical contact. Then the gasket containing the sample is placed in between the toroid shaped anvils and slowly compressed to an initial pressure of 0.4 GPa. The TA is kept locked at that pressure for some time. This ensures a good ohmic contact between the sample and the electrodes. The initial thickness of the hand pressed sample pellet reduces (irreversibly) to about 0.46 mm at this pressure. Further compression to 6 GPa and decompression back to ambient pressure does not change the sample thickness from the above-mentioned value. This ensures a reproducible data in the pressure range GPa not affected by the irreversible densification of the hand-pressed powder sample. The TA apparatus is pressure calibrated using Bi I - II and Yb hcp - bcc transitions at 2.65 GPa and 4 GPa respectively. The ac resistance measurements were carried out using the GR 1689 Precision RLC Digibridge in the frequency range of 12 Hz to 100 khz with an accuracy of about 1%. The pressure variation of the leakage resistance, coming mainly from the pyrophillite gasket, was found to be within the precision of the bridge and can be considered practically constant. The

3 precision was improved by taking the mean value of few successive measurements at every pressure point. The contact resistance due to the graphite plates, rams etc. was estimated by replacing the sample with another graphite plate of thickness 0.5 mm. This yielded a resistance value of 15 Ω, which remained almost constant with respect to frequency and pressure. Results and Discussion The pressure variation of ac resistance of α-zrmo 2 O 8 and α-hfmo 2 O 8 for a few frequencies normalized with respect to 0.4 GPa is shown in FIG. 1. The data show different pressure behaviour at different frequencies, with large changes mainly at the low frequencies, 12 Hz and 1 khz. Though the pressure evolution of ac data for both the samples are different, they show similar trend at similar frequencies, like, continuous increase in resistance above 33 khz, a peak at 1 khz and initial decrease at 12 Hz. A careful investigation of ac resistance data of α-zrmo 2 O 8 shows anomalies at about 1 GPa, 2 GPa (only for 12 Hz) and 2.5 GPa. Since α-zrmo 2 O 8 undergoes two structural transitions in the frequency ranges GPa and GPa respectively, the above anomalies in the ac resistance data can be related to the above structural transitions. Therefore initially we present and discuss the results of the high pressure ac electrical resistance measurements on α-zrmo 2 O 8 on the basis of known pressure evolution of its structure and then compare the results of the measurements on α-hfmo 2 O 8 with the above. It is well known that under the application of ac electric field, the ionic conduction in solids take place by the hopping of the conducting ions to neighbouring equivalent vacant sites or defects. At ambient conditions, universal frequency dependent conductivity (σ(ω) vs ω) behaviour is established for solids, where m ( ω) = σ 0 Aω (1) σ + Fig. 1. Pressure evolution of change in ac resistance data with respect to 0.4 GPa for (a) α- ZrMo 2 O 8 and (b) α-hfmo 2 O 8. At very low frequencies and ambient temperature the random diffusion of ionic charge carriers via activated hopping gives rise to the frequency independent conductivity, σ 0.

4 However, in many ionic conductors low frequency dispersion is observed, which is related to the strong dielectric response of the lattice to the movement of the ions (Almond, 1984). By increasing the measuring frequency the hopping paths of the mobile ions become shorter in terms of numbers of consecutive hops, and the conduction increases in a power law form (Aω m ). Electrical transport measurements under pressure can probe the volume changes, which take place by the relaxation or distortion of lattice induced by the mobile ions. This volume change is known as the activation volume, V act = ( g act / P) T, where g act is the activation Gibbs free energy governing the transport process. For ionic conductors the activation volume can be determined from the conductance measurements in the vicinity of room temperature through the following equation (Papathanassiou, 1996 and 1998): V act ln G = k BT P T where k B is the Boltzmann's constant, and G is the ionic conductance. Generally the measured conductance values can be fitted to the second order polynomial equation, ln G = ln G 0 + ap + bp 2 and then V act is calculated from the fitted parameters by, V act = -k B T(a + 2bP) (Papathanassiou, 1996 and 1998). The logarithm of the ac conductance data of α- ZrMo 2 O 8 and α-hfmo 2 O 8 with respect to pressure are shown in FIG. 2 and Fig. 3 respectively for frequencies at 12 Hz, 1 khz and 100 khz. The ac conductance values increase by orders of magnitude as the frequency is increased from 12 Hz to 100 khz, indicating a strong frequency dependence coming from different conduction mechanisms at different frequencies (diffusion at 12 Hz and hopping of ions at 1 khz and above). At room temperature ionic conduction in the polycrystalline samples is expected to take place by a few available thermally activated vacancies and other small number of intrinsic defects and impurities. Therefore with increasing pressure, the decrease in volume and changes in the available hopping sites due to the pressure induced structural evolution, will restrict movement of the mobile ions and defects and the ac conduction is expected to decrease. However in contrast to the above scenario in α-zrmo 2 O 8 the ac conductance at 12 Hz increases rapidly up to 1 GPa by a large amount (about 16%). The zero pressure activation volume is calculated to be -3.1 cm 3 /mol. If the diffusion of defects is mainly responsible for conduction at 12 Hz, the negative activation volume indicates that either the vacancy formation volume is extremely low or the energy of vacancy migration is unexpectedly high. This indicates a more complicated conduction mechanism, which is not entirely mediated by point defect mechanisms (i.e. formation and migration of vacancies), but is related to an inherent property of the crystal lattice. Similar negative activation volumes were observed for O 2- ion self-diffusion (~ -2.8 to -3.3 cm 3 /mol) in network-structured silicate melts (Poe, 1997). In MX 2 O 8 compounds dynamic oxygen atom disorder is observed to be (2)

5 present even up to very low temperatures and the activation energy of oxygen atom migration in one of the compound of the above class has been estimated to be 34 kj/mol (0.35 ev) (Allen, 2003 and 2004), which is at the lower range of the activation energies in ionic solids. In view of the above facts the diffusion of oxygen ions assumes importance in α- ZrMo 2 O 8. Therefore the sharp increase in ionic conductance up to 1 GPa can be related to the α - δ pre-transition effect in the sample. The α-phase is loosely packed and open for the anions to move and also the α - δ structural transition in ZrMo 2 O 8 is driven by the displacement of the non-bridging oxygen anions. Therefore it can be inferred that the displacive movement of (non-bridging) oxygen ions due to the α - δ pre-transition effect facilitates ionic diffusion in α-zrmo 2 O 8 and is reflected in the sharp increase in ionic conductance up to 1 GPa. Above 1 GPa, the sample stabilizes in the δ-phase. Therefore the decreasing conductance in the region 1 2 GPa, indicate to the absence of any contribution from the co-ordinated displacement of oxygen anions. XRD studies have shown that the δ - ε transition in ZrMo 2 O 8 takes place in the pressure region GPa with displacive movement of O atoms. This is reflected in the increase in ionic conductance in the range GPa. However as the δ - ε phase transition gets completed at 2.5 GPa, the ac conductance decreases as expected with pressure due to the absence of the displacive motion of oxygen anions. Fig. 2. Typical ln G vs. P plot for α-zrmo 2 O 8 at frequencies (a) 12 Hz, (b) 1 khz and (c) 100 khz. The solid lines are the 2 nd order polynomial fit to the data points. Fig. 2. Typical ln G vs. P plot for α-hfmo 2 O 8 at frequencies (a) 12 Hz, (b) 1 khz and (c) 100 khz. The solid lines are the 2 nd order polynomial fit to the data points.

6 However the conductance is observed to decrease in the α-phase in 1 khz as well as in 100 khz with about 3% and 2.4% respectively up to 1 GPa. The activation volume is found act to be positive in both the frequencies with V 0 is calculated to be 0.49 cm 3 /mol and 0.19 cm 3 /mol at 1 khz and 100 khz respectively. The positive and decreasing V act 0 with frequency is consistent with orders of magnitude increase in ac conductance with frequency, which can be attributed to the large dielectric response of the lattice to the mobile charge carriers. Since the experiments were done at constant temperature, there is no change in the number of charge carriers. Therefore the large frequency dependence of conductance indicates the hopping of the available free ions is the main conduction mechanism at these frequencies. The decrease in ac conductance with pressure is due to the restrictions on the available hopping sites coming from the reduction in unit cell volume. However unlike for 1 khz where the conductance data show a reversal at 1 GPa, the conductance values at 100 khz continue to decrease up to 5 GPa, the highest pressure of this study with a slope change at 2.5 GPa (corresponding to δ - ε phase transition). Interestingly at 1 khz above 1 GPa the conductance data continue to increase up to 5 GPa, the highest pressure of this study with a slope change at 2.5 GPa, the δ - ε phase transition. The negative values of V act above 1 GPa show that the structural transition at this pressure affects the ionic conduction. It seems that increasing pressure above 1 GPa at 1 khz reduces the residence time of the ion in a vacancy site compared to the flight time between different sites. Therefore above 1 GPa, due to the modified lattice structure, instead of discrete hoping of ions a diffusion of vacancies through the lattice takes place, induced by a relaxation of the lattice surrounding the mobile ion at 1 khz (Sherby, 1970). This may be due to a transition between two power law regimes in the ionic conductivity at a cross over frequency ω c, which is near 1 khz. The cross over frequency is related to a time that is needed to over come a percolation structure, which can be related to the three dimensional frame-work structure of these materials under study. For α-hfmo 2 O 8 the ac conductance data with pressure show a similar trend as observed in the case of α-zrmo 2 O 8. However the pressure evolution of ac conductance data of α-hfmo 2 O 8 do not show sharp anomalies as in the case of α-zrmo 2 O 8. But the pressure derivative of ln G shows small anomalies at about 1.1 GPa and 2.1 GPa as shown in the inset of Fig. 3. However at 12 Hz, in contrast to α-zrmo 2 O 8, for α-hfmo 2 O 8 ln G data continue to increase up to about 2.7 GPa. Also it could be fitted well only up to 2.1 GPa to a second act order polynomial. At this frequency V 0 is calculated to be ( 3.1) cm 3 /mol, which is almost same as in the case of α-zrmo 2 O 8. Comparing the above results with those for α-zrmo 2 O 8, one can infer that migration of non-bridging oxygen ions are the major contributors for ac conduction process in α-hfmo 2 O 8 in the pressure range up to 2.1 GPa. This is not surprising

7 considering the fact the α-hfmo 2 O 8 is isostructural to α-zrmo 2 O 8 and hence is expected to show similar structural evolution with pressure. The decrease in ln G above 2.7 GPa for 12 Hz indicates the absence of any contribution from oxygen ion movement. Similarly the minimum at about 1.2 GPa in the ln G data at about 1.2 GPa can related to the transition from hopping ion conduction to the diffusion of vacancies mediated by the structural evolution in α-hfmo 2 O 8. At 100 khz, the decreasing ac conduction indicate to the presence of hopping conduction of point defects. The ln G data could be fitted well to the second order polynomial function in the frequency ranges GPa and GPa, which returned the V act 0 value to be 0.5 cm 3 /mol. The comparison of the above results with those of α-zrmo 2 O 8 indicate to the possibility of high pressure structural transitions in α-hfmo 2 O 8 in the pressure ranges GPa and GPa. In fact in a very recent high pressure X-ray diffraction measurements in α-hfmo 2 O 8 two successive phase transitions are observed in the pressure range GPa and GPa, which is presented in another paper (Paper no. 107) in the same conference. Conclusion In this paper a detailed study of the effects of hydrostatic pressure on the ac conductivity of the framework structured materials α-zrmo 2 O 8 and α-hfmo 2 O 8 is carried out. It is observed that the pressure evolution of the ac dc conductance is mediated by structural changes in α-zrmo 2 O 8. Two structural phase transitions, similar to the above are predicted for α-hfmo 2 O 8, which are in fact confirmed by a very recent X-ray diffraction investigation. The ionic conductance of both the materials are found to be strongly frequency dependent and show a transition between two power law regimes marked by a crossover frequency, near 1 khz. This behaviour is associated with strong lattice responses to the movement of the ions. The different pressure behaviour of ac conductance at different frequencies in both the compounds are attributed to the different conduction mechanisms mediated by the structural evolution of the materials. References Achary S.N., Mukherjee G.D., Tyagi A.K., and Godwal B.K., 2002, Phys. Rev. B, 66, and references therein. Allen S. and Evans J.S.O., 2003, Phys. Rev. B, 68, Allen S. and Evans J.S.O., 2004, J. Mater. Chem., 14, 151. Almond D.P., Hunter C.C. and West A.R., 1984, J. Mater. Sci., 19, Andersen A.M.K. and Carlson S., 2001, Acta Cryst B. 57, 20. Carlson S. and Andersen A.M.K., 2000, Phys. Rev. B, 61, Papathanassiou A.N. and Grammatikakis J., 1996, Phys. Rev. B, 53,

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