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Order–disorder transition in clathrate Ba6Ge25 studied by positron annihilation
Applied Surface Science 342 (2015) 42–46
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Order–disorder transition in clathrate Ba6 Ge25 studied by positron annihilation X.F. Li a , B. Zhao a , T. Zhang a , H.F. He a , Q. Zhang b , D.W. Yang b , Z.Q. Chen a,∗ , X.F. Tang b,∗∗ a b
Hubei Nuclear Solid Physics Key Laboratory, Department of Physics, Wuhan University, Wuhan 430072, PR China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, PR China
a r t i c l e
i n f o
Article history: Received 21 October 2014 Received in revised form 4 March 2015 Accepted 5 March 2015 Available online 14 March 2015 Keywords: Thermoelectric materials Clathrate Phase transition Positron annihilation
a b s t r a c t Clathrate Ba6 Ge25 is prepared by melt method and spark plasma sintering. Structural transition below room temperature is studied by positron annihilation and X-ray diffraction measurements. There is a pronounced transition in the temperature range of 200–250 K which might be involved with the movement of Ba atoms in Ge cages and result in disordered structure. This transition is further confirmed by the theoretical calculation of positron annihilation states. Thus our results confirm the structural models proposed by Carrillo-Cabrera et al. (2005). The measured specific heat capacity, electric resistivity and magnetic susceptibility all show anomalous transition in the same temperature range, indicating that the movement of Ba atoms in the cage has influence on the thermal, electric as well as magnetic properties of Ba6 Ge25 . © 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to the energy crisis, thermoelectric material has attracted great interest in recent years. A large variety of waste heat can be converted to useful electric energy by the thermoelectric materials [1–6]. The efficiency of a thermoelectric generator is related to a dimensionless figure of merit ZT = S2 T/, where T denotes the absolute temperature, S is the Seebeck coefficient, is the electric conductivity, is thermal conductivity. Therefore a good thermoelectric material is characterized by a high power factor S2 and/or a low thermal conductivity , which should share the characteristics of both “phonon glasses” and “electron crystals” (PGEC) [7–9]. Nevertheless, the above three parameters (S, and ) are not independently controllable. In most cases, they are closely interconnected. For example, with increase in the free carrier concentration of thermoelectric materials, the electric conductivity will increase. However at the same time, the Seebeck coefficient S will decrease, which leads to a complex behavior of the power factor S2 . In addition, the electronic thermal conductivity E , which is one of the contribution to , will also increase with increasing . Since is constituted by the electronic contribution E and lattice
∗ Corresponding author. Tel.: +86 13986130578. ∗∗ Corresponding author. E-mail addresses: [email protected] (Z.Q. Chen), [email protected] (X.F. Tang). http://dx.doi.org/10.1016/j.apsusc.2015.03.025 0169-4332/© 2015 Elsevier B.V. All rights reserved.
contribution L , while L has the major contribution to the total and is not determined by the electronic structure, one effective way to improve ZT is to adjust the microstructure of thermoelectric materials, so as to decrease the lattice thermal conductivity and enhance the performance of the thermoelectric devices [10]. Clathrates, in particular Ba6 Ge25 , have received considerable scientific interest and initiated intense experimental activity because of their potential as thermoelectric materials [11–14]. In Ba6 Ge25 clathrates, the Ba atoms are enclosed within cages which are formed by covalently bonded Ge atoms. Since the cages are much larger than the Ba guest atom, Ba atom can rattle inside the cages, which creates conditions for extensive phonon scattering that leads to a low thermal conductivity of about 1.2 W/K m [12]. Moreover, the cages can also provide a high electric conductivity [14]. Therefore, the two characteristics, low thermal conductivity and high electric conductivity, are both realized in this compound. It was found that the electric and thermal conductivity of Ba6 Ge25 will both change below room temperature due to a phase transition occurred at around 180–215 K [9]. Such transition deteriorates the thermoelectric properties of materials. It was speculated that the locking-in of rattling Ba atoms below the transition temperature is responsible for the lowering of electric conductivity. The structural modifications at the phase transition temperatures also influence magnetic and optical properties [15]. Understanding the change of properties of Ba6 Ge25 with temperature obviously requires a detailed study of the microstructure change during the phase transition
X.F. Li et al. / Applied Surface Science 342 (2015) 42–46
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process. However, information about the atomic-scaled disorder is difficult to obtain by usual crystallographic analysis such as X-ray diffraction which relies only on the Bragg scattering. Positron annihilation spectroscopy (PAS) has been proven to be a powerful tool for the study of structural transformation, especially the order–disorder transition in liquid crystals, polymers and other materials [16–19]. The positron annihilation characteristics such as positron lifetime change according to the local chemical and physical properties of the annihilation environment. Positron is also very sensitive to open-volume defects such as vacancies, and the positron annihilation parameters at defects are different from the perfect lattice site [20]. So if there is a local structure modification during phase transition, it can be also detected by positrons.
2. Experiment and calculation Ba6 Ge25 was prepared from elemental germanium (Ingot, 99.99% purity, Tianjin Jinbolan Fine Chemical Co. Ltd) and barium (Ingot, 99.2% purity, Alfa Aesar). They were mixed together in the molar rate of 1.15:4 in an argon-filled glove box (p(O2 /H2 O) < 1 ppm). Excess Ba was added in order to compensate the loss during reaction [21]. The mixture was placed in a graphite crucible and sealed in quartz tube under a vacuum of ∼1 ×10−2 Torr, then it was put into a melting furnace. The sealed quartz tube was heated slowly to 1273 K at a heating rate of 2 K/min and subsequently heated to 1353 K at a heating rate of 1 K/min. Then it was maintained at this temperature for 8 h. After that, the sample was cooled to 873 K at 2 K/min and further cooled to room temperature in the furnace. The obtained ingot was ground into fine powder, and then it was treated by the spark plasma sintering (SPS) at 923 K for 10 min under uniaxial pressure of 45 MPa. The relative density of the obtained bulk sample was higher than 96%. X-ray diffraction (XRD, Bruker D8 Advance) was measured using Cu K˛ radiation. Positron lifetime spectrum was measured using a fast–fast coincidence system with time resolution of about 220 ps. A 20 Ci 22 Na positron source was sandwiched between two pieces of identical sample for measurements. Doppler broadening spectrum of the annihilation radiation was measured simultaneously using a high purity Ge detector with energy resolution of about 1.1 keV at 511 keV. The Doppler spectra were characterized by the S parameter, which is defined as the ratio of central region (511 ± 0.76 keV) to the total area of the 511 keV annihilation peak. Electric conductivity measurements were performed on a Lakeshore 7704 system by applying an external magnetic field of 6 T using the van der Pauw’s method. Magnetization behavior and the specific heat capacity (Cp ) were measured by a Physical Property Measurement System (PPMS, Quantum Design). In order to clarify that the positron lifetime is due to annihilation of positrons in the crystal lattice or vacancy clusters or any other extended defects and to support directly the interpretation of experimental data, we constructed the structure model of Ba6 Ge25 according to the result of Carrillo-Cabrera et al. [22] and calculated the positron lifetimes at different temperatures. The structure model for the positron lifetime calculations was a 1 × 1 ×1 unit cell of Ba6 Ge25 (space group P41 32) with different lattice constants and atomic positions for Ba6 Ge25 at different temperatures which are given by Carrillo-Cabrera [22]. The number of atoms in the unit cell varies from 128 to 168 which also depends on the temperature. The positron annihilation calculations are performed using atomic superposition (ATSUP) method proposed by Puska and Nieminen [23], which is simple enough to be used in complex systems while keeping the computational requirements method for modeling positron states and annihilation in solids. In the calculations, non-self-consistent electron density and coulomb potential
Fig. 1. XRD pattern for Ba6 Ge25 measured at different temperatures.
are considered to be within each isolated atom electron density and coulomb potential superposition. To solve the needed electron and positron densities, we used the conventional scheme of the two-component density-functional theory, based on the wellestablished Boronski–Nieminen parameterization, to calculate the positron–electron correlation potential as well as the enhancement factor of positron annihilation [24]. The positron wave function at the point (k = 0) is obtained by solving the positron Kohn–Sham equation in reciprocal space with use of the numerical diagonalization technique [25].
3. Results and discussion Fig. 1 shows the XRD spectra for the Ba6 Ge25 sample measured at different temperatures. At room temperature of 303 K, all the diffraction peaks are in agreement with the standard pattern of Ba6 Ge25 (ISCD collection code no. 414371) [22]. This confirms that Ba6 Ge25 is single phase with cubic symmetry. The primary peak is at around 31.329◦ . The diffraction pattern of Ba6 Ge25 in the 2 range from 25◦ to 60◦ remains almost unchanged in the whole temperature range of 123–303 K. However, when the temperature decreases to 243 K, three additional peaks appear at around 11.94◦ , 17.05◦ and 21.99◦ . These three peaks show strongest intensity at around 233 K. This clearly indicates structural transformation upon cooling of the Ba6 Ge25 . Fig. 2 shows the relative intensity of the three additional peaks as a function of temperature. The three peaks are all enhanced in the temperature range of 203–253 K. Below 203 K, these peaks still remain, but with very low intensity. The appearance of three anomalous peaks in the XRD pattern at low temperatures indicates that the lattice structure of Ba6 Ge25 has changed. It has been reported that the lattice parameter of Ba6 Ge25 exhibits an anomaly in the temperature range of 200–240 K [21], which indicates phase transition in this temperature range. However, the three anomalous peaks appeared in our measurements have not been reported. It can be noted that the three anomalous peaks are located at lower degrees. This suggests that during the phase transition, some ordered superstructure may have formed due to the movement of either Ba or Ge atoms.
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Fig. 2. Relative intensity of the three anomalous peaks as a function of temperature for Ba6 Ge25 .
Clathrate Ba6 Ge25 has a complex chiral structure, with cages formed by Ge atoms, in which Ba atoms are located. There are three sites for the Ba guest atoms. Each site has different coordination environment. The first site for Ba(1) is in the center of Ge20 polyhedra [21,22,26,27]. The other two sites, Ba(2) and Ba(3), occupy a chiral network with large cavities which lie along the channels that are interconnected throughout the unit cell. The large space in the cage for Ba(2) and Ba(3) and the weak bonding of Ba atom to the cage allow these Ba atoms to rattle inside the cages. So during the movement of the Ba atoms, a new ordered superstructure is possible to appear, which has larger units than that of Ba24 Ge100 . In order to study the structural transition of Ba6 Ge25 , positron lifetime and Doppler broadening spectra were measured. Variation of positron lifetime and Doppler broadening S parameter as a function of temperature is shown in Fig. 3. In the whole temperature range of 20–300 K, only one positron lifetime can be resolved from the lifetime spectrum. At room temperature, the positron lifetime is about 292 ps. Such relatively long positron lifetime is generally believed to be due to positron trapping in the cage structure of Ba6 Ge25 . However, the cages are filled with Ba guest atoms, so the free space will be limited inside the cages. It is not sure whether it can still trap positron or not.
Fig. 3. (a) Positron lifetime and (b) Doppler broadening S parameter measured for Ba6 Ge25 as a function of temperature.
As can be seen in Fig. 3, with decreasing temperature, positron lifetime shows monotonous decrease. At 20 K, the positron lifetime decreases to about 265 ps. However the decreasing rate is different at different temperatures. There is a sharp decrease of lifetime in the temperature range of 210–250 K, while the slope is much smaller in the other temperature range. This anomaly coincides well with the XRD results, indicating the occurrence of structural transition. Variation of the Doppler broadening S parameter as a function of temperature is also shown in Fig. 3. It reveals completely the same trends as that of the positron lifetime. The Doppler broadening spectrum reflects local electron momentum distribution where positron annihilates. When positrons are trapped at openvolume defects, the probability of positron annihilating with high momentum core electrons is reduced, thus results in a narrowing of Doppler broadening spectrum. On the other hand, existence of guest atoms at or near the positron annihilation site will also vary the electron momentum distribution seen by positrons. In this case, positron lifetime and Doppler broadening S parameter will probably show divergent results since positron lifetime is not sensitive to the chemical environments. In our results, the positron lifetime and Doppler broadening S parameter show the same trends, indicating that the change is due to structural transition. We have performed the temperature dependent positron annihilation measurements during both heating and cooling process. It can be seen from Fig. 3 that the cooling curves of either positron lifetime or Doppler broadening S parameter almost overlap with the heating curves. This shows that the structural transition is reversible and has no hysteresis. The drastic decrease of positron lifetime and S parameter in the temperature range of 210–250 K indicates increasing of the electron density. This is most probably due to the displacement of Ba atoms inside the cages. It has been suggested that upon cooling to below the transition temperature, the Ba(2) and Ba(3) atoms move off their position and get locked in well-separated positions (split sites) [9]. Carrillo-Cabrera et al. also suggested that the phase transition involves Ge Ge bond breaking and Ba cation displacements. The structural transformation results in disorder of Ba(2) and Ba(3), which has influence on the local electron density in the cages [22]. This will definitely affect the positron annihilation parameters. The positron lifetime and S parameter increase slightly with increasing temperature below 200 K, which is most probably due to the lattice thermal expansion. To confirm the above interpretation of experimental data, the theoretical positron lifetimes of Ba6 Ge25 at selected temperatures are also calculated. The lattice positions of Ba and Ge atoms at different temperatures are from the data of Cabrera et al. [22]. Fig. 4 shows calculated positron density distribution in Ba6 Ge25 at selected temperatures of 90, 190, 257 and 295 K. It can be observed that the positrons are in delocalized state, which are distributed in the interstitial region outside of the Ge cages. There are no localization of positrons in the Ge cages. This might be due to the occupation of Ba atoms in the cages. The calculated positron lifetimes are plotted as a function of temperature in Fig. 5. Comparing Fig. 5 with Fig. 3, the change trend of positron lifetime is very similar between theoretical calculation and experiment results, which could lead to a conclusion that the temperature dependence of the positron lifetime mainly originates from the movement of Ba and Ge atoms. According to the X-ray diffraction measurements by Cabrera et al. [22], the phase transition involves Ge Ge bond breaking and Ba cation displacements. They further observed an anomaly in the change of lattice parameter a due to the movement of Ba and Ge atoms. Our abnormal change of the positron lifetime from both experiment and theoretical calculation thus confirms the movement of Ba and Ge atoms during phase transition. The calculated positron lifetimes are different from the experimental ones, which is probably due to the reason that positrons annihilate not only
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Fig. 4. Calculated positron density distribution in Ba6 Ge25 at selected temperatures of 90, 190, 257 and 295 K. Yellow clouds represent the calculated positron density distribution. Green and violet spheres are Ba and Ge atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 5. Calculated positron lifetime for Ba6 Ge25 as a function of temperature.
in the perfect lattice structure but also at some vacancy defects, which leads to the results that the experimental values of positron lifetime are longer than the theoretical calculated ones at selected temperatures. Temperature dependence of the specific heat capacity Cp of Ba6 Ge25 is presented in Fig. 6. There is a distinct symmetric anomaly between 200 and 260 K with a peak at around 230 K. The abnormal
Fig. 6. Specific heat capacity Cp as a function of temperature for Ba6 Ge25 . The inset shows an enlarged view of the specific heat capacity of Ba6 Ge25 in the temperature range between 180 and 285 K. The line is drawn to guide the eye.
change of specific heat capacity near 230 K indicates a first-order phase transition. Paschen et al. observed the same anomaly in Cp for Ba6 Ge25 , and he reported that the entropy per mole Ba6 Ge25 of this anomaly is 1.47 R, where R is the universal gas constant. This is an abnormally large entropy release for a first-order structural transition which may indicate that a second-order phase transition goes hand in hand with the structural transition [9]. This structural change results in the greater expansion of the lattice parameter, which is in good agreement with the data of the neutron powder diffraction [21] and the X-ray diffractometry [22]. The resistivity of Ba6 Ge25 as a function of temperature is presented in Fig. 7. Between 325 and 260 K, the resistivity shows negligible change with decreasing temperature. The expected decreasing of resistivity with decreasing temperature is not observed, which is a sign of metallic conduction. This might be due to the small change of resistivity in the narrow temperature range between 260 and 325 K. When the temperature decreases to the range between 240 and 180 K, the resistivity increases dramatically. Below 180 K, continues to increase slowly and reaches a final value of more than 1.4 m cm at 10 K, which increases by a factor of about 4. The resistivity of Ba6 Ge25 exhibits transition from metallic behavior to semiconductor-like behavior over the whole temperature range. The abrupt change of resistivity in the temperature range of 180–240 K coincides with the results of XRD, positron
Fig. 7. Electrical resistivity of Ba6 Ge25 measured as a function of temperature.
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the structural transition, which enhanced the structural disorder and causes change of the local electron density and reconstruction of lattice structure. The specific heat capacity, electrical resistivity and magnetic susceptibility all show abnormal transition in the same temperature range, suggesting that the Ba guest atoms play important role on the thermal, electric and magnetic properties in clathrate Ba6 Ge25 . Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11275143 and 11305117, and the “973 Program” of China under Grant No. 2013CB632502. Fig. 8. Temperature dependence of the total magnetic susceptibility for Ba6 Ge25 in a magnetic field of 6 T.
annihilation and specific heat capacity measurements. This suggests that the change of resistivity is also caused by the structural transition. Fig. 8 shows the temperature dependence of magnetic susceptibility of Ba6 Ge25 measured in a magnetic field of 6 T. The magnetic susceptibility is negative over the whole temperature range which may be due to a predominant Larmor diamagnetic susceptibility of filled electronic shells [9]. Upon cooling down from room temperature, first decreases slowly up to 250 K and then decreases very sharply between 240 and 180 K. Again, the transition temperature range is nearly the same as revealed by all the above measurements. The anomalies of both electrical resistivity and magnetic susceptibility can be explained by the movement of Ba atoms. The locking-in of rattling Ba atoms to the split sites in the Ge cages leads to the reduction of the mobility of conduction electrons, which results in increase of the electrical resistivity. At the same time, the conduction electrons together with the lattice deformation build large bipolarons, so even though the conduction electrons are virtually unaffected, the spin carriers are lost due to formation of spinless bipolarons [9]. Thus the magnetic susceptibility decreases drastically during structural transition, i.e. the locking-in of Ba atoms. There is one feature in common for the temperature dependence of resistivity and magnetic susceptibility. It can be seen in Figs. 7 and 8 that the cooling-down curve is obviously different from the warming-up curve near the transition temperature, i.e. there is a hysteresis in the change of the above two quantities with varying temperature. Such thermal hysteresis effect upon coolingdown and warming up is typical for first-order phase transitions. 4. Conclusion In summary, the structural transition of Ba6 Ge25 is observed in the temperature range of 200–250 K through positron annihilation and XRD measurements. Breaking of the Ge Ge bonding and movement of the Ba atoms to the off-center split sites is responsible for
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Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Order–disorder transition in clathrate Ba6 Ge25 studied by positron annihilation X.F. Li a , B. Zhao a , T. Zhang a , H.F. He a , Q. Zhang b , D.W. Yang b , Z.Q. Chen a,∗ , X.F. Tang b,∗∗ a b
Hubei Nuclear Solid Physics Key Laboratory, Department of Physics, Wuhan University, Wuhan 430072, PR China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, PR China
a r t i c l e
i n f o
Article history: Received 21 October 2014 Received in revised form 4 March 2015 Accepted 5 March 2015 Available online 14 March 2015 Keywords: Thermoelectric materials Clathrate Phase transition Positron annihilation
a b s t r a c t Clathrate Ba6 Ge25 is prepared by melt method and spark plasma sintering. Structural transition below room temperature is studied by positron annihilation and X-ray diffraction measurements. There is a pronounced transition in the temperature range of 200–250 K which might be involved with the movement of Ba atoms in Ge cages and result in disordered structure. This transition is further confirmed by the theoretical calculation of positron annihilation states. Thus our results confirm the structural models proposed by Carrillo-Cabrera et al. (2005). The measured specific heat capacity, electric resistivity and magnetic susceptibility all show anomalous transition in the same temperature range, indicating that the movement of Ba atoms in the cage has influence on the thermal, electric as well as magnetic properties of Ba6 Ge25 . © 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to the energy crisis, thermoelectric material has attracted great interest in recent years. A large variety of waste heat can be converted to useful electric energy by the thermoelectric materials [1–6]. The efficiency of a thermoelectric generator is related to a dimensionless figure of merit ZT = S2 T/, where T denotes the absolute temperature, S is the Seebeck coefficient, is the electric conductivity, is thermal conductivity. Therefore a good thermoelectric material is characterized by a high power factor S2 and/or a low thermal conductivity , which should share the characteristics of both “phonon glasses” and “electron crystals” (PGEC) [7–9]. Nevertheless, the above three parameters (S, and ) are not independently controllable. In most cases, they are closely interconnected. For example, with increase in the free carrier concentration of thermoelectric materials, the electric conductivity will increase. However at the same time, the Seebeck coefficient S will decrease, which leads to a complex behavior of the power factor S2 . In addition, the electronic thermal conductivity E , which is one of the contribution to , will also increase with increasing . Since is constituted by the electronic contribution E and lattice
∗ Corresponding author. Tel.: +86 13986130578. ∗∗ Corresponding author. E-mail addresses: [email protected] (Z.Q. Chen), [email protected] (X.F. Tang). http://dx.doi.org/10.1016/j.apsusc.2015.03.025 0169-4332/© 2015 Elsevier B.V. All rights reserved.
contribution L , while L has the major contribution to the total and is not determined by the electronic structure, one effective way to improve ZT is to adjust the microstructure of thermoelectric materials, so as to decrease the lattice thermal conductivity and enhance the performance of the thermoelectric devices [10]. Clathrates, in particular Ba6 Ge25 , have received considerable scientific interest and initiated intense experimental activity because of their potential as thermoelectric materials [11–14]. In Ba6 Ge25 clathrates, the Ba atoms are enclosed within cages which are formed by covalently bonded Ge atoms. Since the cages are much larger than the Ba guest atom, Ba atom can rattle inside the cages, which creates conditions for extensive phonon scattering that leads to a low thermal conductivity of about 1.2 W/K m [12]. Moreover, the cages can also provide a high electric conductivity [14]. Therefore, the two characteristics, low thermal conductivity and high electric conductivity, are both realized in this compound. It was found that the electric and thermal conductivity of Ba6 Ge25 will both change below room temperature due to a phase transition occurred at around 180–215 K [9]. Such transition deteriorates the thermoelectric properties of materials. It was speculated that the locking-in of rattling Ba atoms below the transition temperature is responsible for the lowering of electric conductivity. The structural modifications at the phase transition temperatures also influence magnetic and optical properties [15]. Understanding the change of properties of Ba6 Ge25 with temperature obviously requires a detailed study of the microstructure change during the phase transition
X.F. Li et al. / Applied Surface Science 342 (2015) 42–46
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process. However, information about the atomic-scaled disorder is difficult to obtain by usual crystallographic analysis such as X-ray diffraction which relies only on the Bragg scattering. Positron annihilation spectroscopy (PAS) has been proven to be a powerful tool for the study of structural transformation, especially the order–disorder transition in liquid crystals, polymers and other materials [16–19]. The positron annihilation characteristics such as positron lifetime change according to the local chemical and physical properties of the annihilation environment. Positron is also very sensitive to open-volume defects such as vacancies, and the positron annihilation parameters at defects are different from the perfect lattice site [20]. So if there is a local structure modification during phase transition, it can be also detected by positrons.
2. Experiment and calculation Ba6 Ge25 was prepared from elemental germanium (Ingot, 99.99% purity, Tianjin Jinbolan Fine Chemical Co. Ltd) and barium (Ingot, 99.2% purity, Alfa Aesar). They were mixed together in the molar rate of 1.15:4 in an argon-filled glove box (p(O2 /H2 O) < 1 ppm). Excess Ba was added in order to compensate the loss during reaction [21]. The mixture was placed in a graphite crucible and sealed in quartz tube under a vacuum of ∼1 ×10−2 Torr, then it was put into a melting furnace. The sealed quartz tube was heated slowly to 1273 K at a heating rate of 2 K/min and subsequently heated to 1353 K at a heating rate of 1 K/min. Then it was maintained at this temperature for 8 h. After that, the sample was cooled to 873 K at 2 K/min and further cooled to room temperature in the furnace. The obtained ingot was ground into fine powder, and then it was treated by the spark plasma sintering (SPS) at 923 K for 10 min under uniaxial pressure of 45 MPa. The relative density of the obtained bulk sample was higher than 96%. X-ray diffraction (XRD, Bruker D8 Advance) was measured using Cu K˛ radiation. Positron lifetime spectrum was measured using a fast–fast coincidence system with time resolution of about 220 ps. A 20 Ci 22 Na positron source was sandwiched between two pieces of identical sample for measurements. Doppler broadening spectrum of the annihilation radiation was measured simultaneously using a high purity Ge detector with energy resolution of about 1.1 keV at 511 keV. The Doppler spectra were characterized by the S parameter, which is defined as the ratio of central region (511 ± 0.76 keV) to the total area of the 511 keV annihilation peak. Electric conductivity measurements were performed on a Lakeshore 7704 system by applying an external magnetic field of 6 T using the van der Pauw’s method. Magnetization behavior and the specific heat capacity (Cp ) were measured by a Physical Property Measurement System (PPMS, Quantum Design). In order to clarify that the positron lifetime is due to annihilation of positrons in the crystal lattice or vacancy clusters or any other extended defects and to support directly the interpretation of experimental data, we constructed the structure model of Ba6 Ge25 according to the result of Carrillo-Cabrera et al. [22] and calculated the positron lifetimes at different temperatures. The structure model for the positron lifetime calculations was a 1 × 1 ×1 unit cell of Ba6 Ge25 (space group P41 32) with different lattice constants and atomic positions for Ba6 Ge25 at different temperatures which are given by Carrillo-Cabrera [22]. The number of atoms in the unit cell varies from 128 to 168 which also depends on the temperature. The positron annihilation calculations are performed using atomic superposition (ATSUP) method proposed by Puska and Nieminen [23], which is simple enough to be used in complex systems while keeping the computational requirements method for modeling positron states and annihilation in solids. In the calculations, non-self-consistent electron density and coulomb potential
Fig. 1. XRD pattern for Ba6 Ge25 measured at different temperatures.
are considered to be within each isolated atom electron density and coulomb potential superposition. To solve the needed electron and positron densities, we used the conventional scheme of the two-component density-functional theory, based on the wellestablished Boronski–Nieminen parameterization, to calculate the positron–electron correlation potential as well as the enhancement factor of positron annihilation [24]. The positron wave function at the point (k = 0) is obtained by solving the positron Kohn–Sham equation in reciprocal space with use of the numerical diagonalization technique [25].
3. Results and discussion Fig. 1 shows the XRD spectra for the Ba6 Ge25 sample measured at different temperatures. At room temperature of 303 K, all the diffraction peaks are in agreement with the standard pattern of Ba6 Ge25 (ISCD collection code no. 414371) [22]. This confirms that Ba6 Ge25 is single phase with cubic symmetry. The primary peak is at around 31.329◦ . The diffraction pattern of Ba6 Ge25 in the 2 range from 25◦ to 60◦ remains almost unchanged in the whole temperature range of 123–303 K. However, when the temperature decreases to 243 K, three additional peaks appear at around 11.94◦ , 17.05◦ and 21.99◦ . These three peaks show strongest intensity at around 233 K. This clearly indicates structural transformation upon cooling of the Ba6 Ge25 . Fig. 2 shows the relative intensity of the three additional peaks as a function of temperature. The three peaks are all enhanced in the temperature range of 203–253 K. Below 203 K, these peaks still remain, but with very low intensity. The appearance of three anomalous peaks in the XRD pattern at low temperatures indicates that the lattice structure of Ba6 Ge25 has changed. It has been reported that the lattice parameter of Ba6 Ge25 exhibits an anomaly in the temperature range of 200–240 K [21], which indicates phase transition in this temperature range. However, the three anomalous peaks appeared in our measurements have not been reported. It can be noted that the three anomalous peaks are located at lower degrees. This suggests that during the phase transition, some ordered superstructure may have formed due to the movement of either Ba or Ge atoms.
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Fig. 2. Relative intensity of the three anomalous peaks as a function of temperature for Ba6 Ge25 .
Clathrate Ba6 Ge25 has a complex chiral structure, with cages formed by Ge atoms, in which Ba atoms are located. There are three sites for the Ba guest atoms. Each site has different coordination environment. The first site for Ba(1) is in the center of Ge20 polyhedra [21,22,26,27]. The other two sites, Ba(2) and Ba(3), occupy a chiral network with large cavities which lie along the channels that are interconnected throughout the unit cell. The large space in the cage for Ba(2) and Ba(3) and the weak bonding of Ba atom to the cage allow these Ba atoms to rattle inside the cages. So during the movement of the Ba atoms, a new ordered superstructure is possible to appear, which has larger units than that of Ba24 Ge100 . In order to study the structural transition of Ba6 Ge25 , positron lifetime and Doppler broadening spectra were measured. Variation of positron lifetime and Doppler broadening S parameter as a function of temperature is shown in Fig. 3. In the whole temperature range of 20–300 K, only one positron lifetime can be resolved from the lifetime spectrum. At room temperature, the positron lifetime is about 292 ps. Such relatively long positron lifetime is generally believed to be due to positron trapping in the cage structure of Ba6 Ge25 . However, the cages are filled with Ba guest atoms, so the free space will be limited inside the cages. It is not sure whether it can still trap positron or not.
Fig. 3. (a) Positron lifetime and (b) Doppler broadening S parameter measured for Ba6 Ge25 as a function of temperature.
As can be seen in Fig. 3, with decreasing temperature, positron lifetime shows monotonous decrease. At 20 K, the positron lifetime decreases to about 265 ps. However the decreasing rate is different at different temperatures. There is a sharp decrease of lifetime in the temperature range of 210–250 K, while the slope is much smaller in the other temperature range. This anomaly coincides well with the XRD results, indicating the occurrence of structural transition. Variation of the Doppler broadening S parameter as a function of temperature is also shown in Fig. 3. It reveals completely the same trends as that of the positron lifetime. The Doppler broadening spectrum reflects local electron momentum distribution where positron annihilates. When positrons are trapped at openvolume defects, the probability of positron annihilating with high momentum core electrons is reduced, thus results in a narrowing of Doppler broadening spectrum. On the other hand, existence of guest atoms at or near the positron annihilation site will also vary the electron momentum distribution seen by positrons. In this case, positron lifetime and Doppler broadening S parameter will probably show divergent results since positron lifetime is not sensitive to the chemical environments. In our results, the positron lifetime and Doppler broadening S parameter show the same trends, indicating that the change is due to structural transition. We have performed the temperature dependent positron annihilation measurements during both heating and cooling process. It can be seen from Fig. 3 that the cooling curves of either positron lifetime or Doppler broadening S parameter almost overlap with the heating curves. This shows that the structural transition is reversible and has no hysteresis. The drastic decrease of positron lifetime and S parameter in the temperature range of 210–250 K indicates increasing of the electron density. This is most probably due to the displacement of Ba atoms inside the cages. It has been suggested that upon cooling to below the transition temperature, the Ba(2) and Ba(3) atoms move off their position and get locked in well-separated positions (split sites) [9]. Carrillo-Cabrera et al. also suggested that the phase transition involves Ge Ge bond breaking and Ba cation displacements. The structural transformation results in disorder of Ba(2) and Ba(3), which has influence on the local electron density in the cages [22]. This will definitely affect the positron annihilation parameters. The positron lifetime and S parameter increase slightly with increasing temperature below 200 K, which is most probably due to the lattice thermal expansion. To confirm the above interpretation of experimental data, the theoretical positron lifetimes of Ba6 Ge25 at selected temperatures are also calculated. The lattice positions of Ba and Ge atoms at different temperatures are from the data of Cabrera et al. [22]. Fig. 4 shows calculated positron density distribution in Ba6 Ge25 at selected temperatures of 90, 190, 257 and 295 K. It can be observed that the positrons are in delocalized state, which are distributed in the interstitial region outside of the Ge cages. There are no localization of positrons in the Ge cages. This might be due to the occupation of Ba atoms in the cages. The calculated positron lifetimes are plotted as a function of temperature in Fig. 5. Comparing Fig. 5 with Fig. 3, the change trend of positron lifetime is very similar between theoretical calculation and experiment results, which could lead to a conclusion that the temperature dependence of the positron lifetime mainly originates from the movement of Ba and Ge atoms. According to the X-ray diffraction measurements by Cabrera et al. [22], the phase transition involves Ge Ge bond breaking and Ba cation displacements. They further observed an anomaly in the change of lattice parameter a due to the movement of Ba and Ge atoms. Our abnormal change of the positron lifetime from both experiment and theoretical calculation thus confirms the movement of Ba and Ge atoms during phase transition. The calculated positron lifetimes are different from the experimental ones, which is probably due to the reason that positrons annihilate not only
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Fig. 4. Calculated positron density distribution in Ba6 Ge25 at selected temperatures of 90, 190, 257 and 295 K. Yellow clouds represent the calculated positron density distribution. Green and violet spheres are Ba and Ge atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Fig. 5. Calculated positron lifetime for Ba6 Ge25 as a function of temperature.
in the perfect lattice structure but also at some vacancy defects, which leads to the results that the experimental values of positron lifetime are longer than the theoretical calculated ones at selected temperatures. Temperature dependence of the specific heat capacity Cp of Ba6 Ge25 is presented in Fig. 6. There is a distinct symmetric anomaly between 200 and 260 K with a peak at around 230 K. The abnormal
Fig. 6. Specific heat capacity Cp as a function of temperature for Ba6 Ge25 . The inset shows an enlarged view of the specific heat capacity of Ba6 Ge25 in the temperature range between 180 and 285 K. The line is drawn to guide the eye.
change of specific heat capacity near 230 K indicates a first-order phase transition. Paschen et al. observed the same anomaly in Cp for Ba6 Ge25 , and he reported that the entropy per mole Ba6 Ge25 of this anomaly is 1.47 R, where R is the universal gas constant. This is an abnormally large entropy release for a first-order structural transition which may indicate that a second-order phase transition goes hand in hand with the structural transition [9]. This structural change results in the greater expansion of the lattice parameter, which is in good agreement with the data of the neutron powder diffraction [21] and the X-ray diffractometry [22]. The resistivity of Ba6 Ge25 as a function of temperature is presented in Fig. 7. Between 325 and 260 K, the resistivity shows negligible change with decreasing temperature. The expected decreasing of resistivity with decreasing temperature is not observed, which is a sign of metallic conduction. This might be due to the small change of resistivity in the narrow temperature range between 260 and 325 K. When the temperature decreases to the range between 240 and 180 K, the resistivity increases dramatically. Below 180 K, continues to increase slowly and reaches a final value of more than 1.4 m cm at 10 K, which increases by a factor of about 4. The resistivity of Ba6 Ge25 exhibits transition from metallic behavior to semiconductor-like behavior over the whole temperature range. The abrupt change of resistivity in the temperature range of 180–240 K coincides with the results of XRD, positron
Fig. 7. Electrical resistivity of Ba6 Ge25 measured as a function of temperature.
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the structural transition, which enhanced the structural disorder and causes change of the local electron density and reconstruction of lattice structure. The specific heat capacity, electrical resistivity and magnetic susceptibility all show abnormal transition in the same temperature range, suggesting that the Ba guest atoms play important role on the thermal, electric and magnetic properties in clathrate Ba6 Ge25 . Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 11275143 and 11305117, and the “973 Program” of China under Grant No. 2013CB632502. Fig. 8. Temperature dependence of the total magnetic susceptibility for Ba6 Ge25 in a magnetic field of 6 T.
annihilation and specific heat capacity measurements. This suggests that the change of resistivity is also caused by the structural transition. Fig. 8 shows the temperature dependence of magnetic susceptibility of Ba6 Ge25 measured in a magnetic field of 6 T. The magnetic susceptibility is negative over the whole temperature range which may be due to a predominant Larmor diamagnetic susceptibility of filled electronic shells [9]. Upon cooling down from room temperature, first decreases slowly up to 250 K and then decreases very sharply between 240 and 180 K. Again, the transition temperature range is nearly the same as revealed by all the above measurements. The anomalies of both electrical resistivity and magnetic susceptibility can be explained by the movement of Ba atoms. The locking-in of rattling Ba atoms to the split sites in the Ge cages leads to the reduction of the mobility of conduction electrons, which results in increase of the electrical resistivity. At the same time, the conduction electrons together with the lattice deformation build large bipolarons, so even though the conduction electrons are virtually unaffected, the spin carriers are lost due to formation of spinless bipolarons [9]. Thus the magnetic susceptibility decreases drastically during structural transition, i.e. the locking-in of Ba atoms. There is one feature in common for the temperature dependence of resistivity and magnetic susceptibility. It can be seen in Figs. 7 and 8 that the cooling-down curve is obviously different from the warming-up curve near the transition temperature, i.e. there is a hysteresis in the change of the above two quantities with varying temperature. Such thermal hysteresis effect upon coolingdown and warming up is typical for first-order phase transitions. 4. Conclusion In summary, the structural transition of Ba6 Ge25 is observed in the temperature range of 200–250 K through positron annihilation and XRD measurements. Breaking of the Ge Ge bonding and movement of the Ba atoms to the off-center split sites is responsible for
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