An investigation of the structural dynamics in the fast ionic conductor Cu 2 −δ Se using neutron scattering

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An investigation of the structural dynamics in the fast ionic conductor Cu ₂ _−δ Se using neutron scattering

S.A. Danilkin

^∗

Bragg Institute, Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, NSW 2234 Australia

Received 9 November 2007; received in revised form 10 December 2007; accepted 11 December 2007 Available online 26 December 2007

Abstract

Energy resolved neutron diffraction measurements were performed on Cu1.75Se and Cu1.98Se samples for both␣- and␤-phases. In-situ measurements of the Cu_1.98Se compound during heating show that the␤–␣phase transition takes place at 420 K and has noticeable temperature hysteresis.

In addition to Bragg reflections, the diffraction patterns of the␣-Cu1.75Se at RT and␣-Cu1.98Se at 435 K samples taken in conventional two-axis geometry show a broad maximum related to diffuse scattering. This diffuse background is suppressed in the energy resolved experiment which indicates a strong contribution from inelastic scattering coming from correlated thermal displacements of the ions in the super-ionic phase. On the other hand, the diffraction pattern of the non super-ionic␤-phase shows only minor differences between spectra measured with and without the analyser crystal.

Keywords: Ionic conduction; Crystal structure; Neutron scattering; Diffraction

1. Introduction

The compound Cu2−δSe (0≤δ≤0.25) is a mixed ionic–electronic conductor. For stoichiometric Cu2Se, the phase transition temperature to the super-ionic ␣-phase is 414 K, but transition temperature depends on the composition and decreases with increasing values forδ. At room temperature, the super-ionic␣-phase exists over the composition range from δ= 0.15 to 0.25[1].

The structures of␣- and␤-phases are basically of antifluorite- type with Se atoms in fcc positions and Cu atoms distributed over the large number tetrahedral, trigonal and octahedral sites many of which being vacant. In the low-temperature␤-Cu2-␦Se, the Cu cations form an ordered structure in distorted fluorite unit cell. According to Kashida and Akai[2],␤-phase has a triclinic unit cell with Cu sites forming a√

3×√

3 network in the [1 1 1]

plane. The vacant Cu layers stack at every fourth metal layer along the [1 1 1] axis. Another description given by Vuˇci´c and

∗Tel.: +61 2 9717 3338; fax: +61 2 9717 3603.

E-mail address:[email protected].

co-workers [3] assumes the monoclinic unit cell with lattice parametersam= 7.12,bm= 12.34,cm= 13.81 andβm= 80^◦. The characteristics of the proposed structures for the ␤-phase are the ordered distribution of the Cu atoms and large unit cells. A review of the structural data of␤-phase can be found in papers [3–5].

The high-temperature ␣-phase is considered to have ran- domly distributed Cu ions over interstitial sites, but information about the location of Cu in the lattice is controversial. For instance in split-site model of Heyding and Murray [6], 72%

of Cu ions are located in tetrahedral 8(c) (1/4, 1/4, 1/4) positions and the remaining Cu cations are in trigonal 32(f) (xxx) (x= 0.33) sites. Sakuma[7]suggests that 88% of Cu is in 32(f1) (x= 0.297) positions with the rest Cu in 32(f2) (x= 0.471) sites.

However, Yamamoto and Kashida [5]found that the split-site model with most of Cu atoms located in tetrahedral and trigonal sites and small fraction of Cu atoms (5%) in octahedral 4(b) sites had the same order of R-factor as the anharmonic model with Gram–Charlier expansion for the atoms located in the tetrahedral sites. In the anharmonic model, the 95% of Cu atoms are in tetrahedral sites with small fraction in octahedral positions. The Fourier map of the average structure of

doi:10.1016/j.jallcom.2007.12.064

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␣-Cu2Se at 160^◦C shows that the electron density of the Cu atoms has a long tail toward the octahedral site[5]. Yamamoto and Kashida [8] also perform analysis of the cation distribution in Cu2Se using the maximum entropy method. They found that in␤-Cu2Se at room temperature, the Cu ions occupy the tetrahedral 8(c) and trigonal 32(f) (1/3 1/3 1/3) sites. At elevated temperature in the␣-phase, the Cu ions are concentrated in the tetrahedral sites with a noticeable population of the octahedral 4(b) positions. In Cu1.8Se, the situation is different: the Cu ions are already concentrated at the tetrahedral sites at room temperature and population of the octahedral sites increases with temperature.

Similar results were obtained in another single crystal study of Oliveria et al.[9]. The proposed anharmonic model shows large anharmonic coefficients for displacements of Cu atoms located in trigonal sites (x= 0.295) so that Cu atoms are displaced from the tetrahedral site towards the face of the tetrahedron by approximately 0.5 ˚A. From the analysis of the temperature dependence of anharmonic coefficients of Cu atoms, authors show that the chosen model describes the positional disorder of Cu atoms from the tetrahedral position rather than time averaged anharmonic displacements.

These results demonstrate the difficulty in standard analysis of crystallographic data from disordered systems due to high correlation between parameters, in particular in separa- tion of the positional disorder and vibrational displacements.

At the same time disorder gives rise to broad diffuse maxima observed in neutron diffraction patterns of polycrystalline and single crystal samples of copper selenide [7,10,11]. The diffuse background generally contains both elastic and inelastic scattering components which originate from the static disorder and dynamic correlations. These contributions could be separated in neutron diffraction experiments with the use of energy analysis. This could be achieved using a triple- axis spectrometer in E≈0 mode with the analyser crystal adjusted to reflect elastically scattered neutrons from the sample. In such an experiment conducted by Sakuma et al. [10]

the contribution of inelastic scattering processes related to thermal vibrations was estimated by the comparison of the data measured with the analyser crystal and without it, in conventional double-crystal mode. However, in spite of the indication of the considerable vibrational/anharmonic motions in Cu2Se [8,9], the strong diffuse background was observed from both two-axis and E≈0 mode measurements probably due to insufficient energy resolution of the spectrometer [10].

In order to clarify the role of static disorder versus low- energy phonons in the diffuse scattering, we performed energy resolved neutron scattering measurements at higher resolution.

This paper presents the results of these neutron diffraction measurements taken in E≈0 mode together with conventional diffraction data from the super-ionic␣-phase (Cu1.98Se at 435 K and Cu1.75Se at 300 K) and the ordered ␤-Cu1.98Se at 300 K.

In addition to diffraction patterns taken at 300 and 435 K, we also performed in-situ study of the modification of the crystal structure during heating/cooling to obtain information about the kinetics of the phase transformation.

2. Experimental

The samples were prepared by solid-state reaction of high purity Cu and Se powders in evacuated (p< 10⁻⁵mbar) sealed quartz ampoules. The mixed components were heated up to 720 K for about 100 h with subsequent annealing for 48 h at 420–520 K. After slow cooling to room temperature, the product was ground and then homogenised under vacuum for 100 h at 670 K.

Neutron diffraction patterns of the samples were measured with the E1 triple-axis spectrometer (HMI, Berlin[12]) using a HOPG monochromator and analyser at a wavelength of 2.42 ˚A. The collimation of the spectrometer was 40–40–40–80with a resolution at the elastic line ofE≈0.7 meV. The cylindrical samples of Cu1.75Se and Cu1.98Se, with masses of 4.8 and 8.5 g, respectively, were measured in a standard cryofurnace at ambient temperature and at 435 K (Cu1.98Se only). The diffraction patterns of Cu1.98Se in the range of scattering angle2Θ= 60–75^◦(Q= 2.6–3.2 ˚A⁻¹) were also measured in-situ during heating and cooling in order to obtain information about the structure transformation during the phase transition.

The diffraction patterns of the Cu1.75Se and Cu1.98Se are plotted in Figs. 1 and 2on an enlarged scale to show diffuse background in detail. The data were taken both with and without the analyser crystal, using otherwise identical experimental conditions. After subtraction of the flat background, the spectra of Cu1.75Se and Cu1.98Se were normalised to the sample mass and the counts of the incident neutron beam monitor. Spectra measured with and without the analyser crystal, were normalised to the area intensity of the Bragg reflections.

Fig. 3shows the contour plot of the diffraction patterns of Cu1.98Se in coordi- natesT−Qin the vicinity of fcc reflection (2 2 0) measured during heating (a) and cooling (b).

3. Results and discussion

3.1. Crystal structure and phase transition

The diffraction pattern of␣-Cu1.75Se (Fig. 1) corresponds to an fcc structure in general agreement with previous papers[5–7], showing that about 73% copper cations are concentrated in the tetrahedral 8c positions with the rest of the Cu distributed over 4b and 32(f1) (x= 0.39) sites. At room temperature, the diffraction pattern of Cu1.98Se (Fig. 2b) is consistent with the pattern No 29-575 of the PDF2 database[13]calculated from the orig- inal crystallographic data of De Montreuil for bellidoite[14].

This unit cell has tetragonal symmetry P42/nwith parameters a= 11.52,c= 11.74 with the Cu atoms distributed over the interstitial sites forming the ordered superstructure. A more detailed

Fig. 1. Diffraction pattern of Cu1.75Se in the␣-phase at 300 K. () double-axis scan, (䊉) triple-axis (E≈0) scan.

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Fig. 2. Diffraction patterns of Cu1.98Se in the␣-phase at 435 K (a) and the

␤-phase at 300 K (b). () double-axis scan, (䊉) triple-axis (E≈0) scan.

analysis of the diffraction pattern was not performed because of the limited number of observed reflections in our experiment.

At 435 K, the diffraction pattern of␣-Cu1.98Se (Fig. 2a) corresponds to the cubic phase, although the intensities of the (2 0 0) and (2 2 2) reflections (Q≈2.2 and 3.8 ˚A⁻¹, respectively) are lower than the intensities observed for␣-Cu1.75Se (Fig. 1). In addition to the peaks from the fcc structure,␣-Cu1.98Se at 435 K

also has two small additional maxima atQ≈2.6 and 4.2 ˚A⁻¹ which are probably related to ordering of the Cu atoms even at a temperature above the reported phase transition. Note that our previous diffraction experiments with a single crystal of Cu1.85Se performed at ambient temperature, which according to literature [1] is the “disordered”␣-phase, in fact show the presence of superstructure reflections at the G±1/2 <1 1 1>

andG±1/3 <2 2 0> positions of reciprocal space[11]. Another important experimental condition is that the diffraction pattern of␣-phase (Fig. 2a) was taken immediately upon reaching the temperature of 435 K so that the disordering process could not be fully completed. As mentioned by Yamamoto and Kashida [8], the order–disorder transition in Cu–Se compound is so grad- ual that the ordering of the low-temperature phase persists into the high-temperature phase. This manifests itself as the hysteresis observed in the differential scanning calorimetry (DSC) experiments[15]and the temperature dependence of some phys- ical properties[16]. However, Frangis et al.[4]on the basis of electron diffraction data, consider that the ␤–␣ transition is a reversible one without thermal hysteresis.

In this respect, it is of interest to follow the changes in the diffraction pattern of Cu1.98Se during heating from room temperature to 435 K and the subsequent cooling. Fig. 3a shows the modification of the (4 0 3), (5 1 0) and (4 0 4) peaks of the

␤-phase during transition into the fcc␣-phase. During heating, the intensity of (4 0 3) and (5 1 0) peaks decrease gradually up to a temperature of about 400 K, followed by a sharp drop in intensity and extinction at 420 K. On cooling, the first indication of ␤-phase appears at a much lower temperature. From Fig. 3b this temperature is estimated to be 375 K. The phase transition was also be observed by a change in the slope of the temperature dependence ofd-spacing of (2 2 0) reflection, this have been seen at temperature of T= 380 K. These results are in general agreement with DSC measurements by Chrissafis et al.[15]. The authors pointed out that on cooling the transformation begins gradually, far from the DSC peak temperature,

Fig. 3. Contour plot of neutron scattering intensity collected from Cu1.98Se on heating (a) and cooling (b).

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while the transformation is completed relatively fast. During cooling, the opposite was observed. However, contrary to paper [15]the hysteresis observed in this experiment (∼40 K) is well above the values determined by DSC measurements, despite the lower rates of heating and cooling (0.35 K/min and 0.2 K/min, respectively).

Interesting results were also observed for the measurement of full diffraction pattern taken immediately after cooling to temperature of 300–330 K. Compared to the initial pattern measured before heating to 435 K, the pattern after cooling showed different intensities of the Bragg peaks and contained resid- ual reflections characteristic to the fcc high-temperature phase, particularly in vicinity of the (2 0 0) and (4 0 0) peaks. Similar behaviour was observed by Ohtani et al.[16]after cooling of Cu1.75Se samples to liquid nitrogen temperature: samples did not recover entirely to the initial structure, even after successive heating to room temperature and were transformed gradually to ␣-phase upon ageing at room temperature for about 1 week.

3.2. Diffuse scattering

Along with the Bragg peaks, the diffraction pattern of the

␣-phase taken in the conventional two-axis geometry shows a broad maximum related to diffuse scattering centred at Q≈3 ˚A⁻¹, close to the (2 2 0) Bragg reflection (Figs. 1 and 2(a)).

The observed diffuse peak resembles the pattern of␣-Cu2Se at 470 K measured with triple-axis spectrometer by Sakuma et al.

[10]. The authors found the anomalously strong and oscillatory diffuse scattering with two broad maxima atQ≈3 and 5.5 ˚A⁻¹ both in energy resolved and standard two-axis diffraction measurements. Contrary to these findings, our measurements show a drastic suppression of this diffuse component in the pattern measured with the analyser crystal. This clearly indicates a strong contribution to the diffuse scattering in the super-ionic phase from inelastic scattering. On the other hand, the diffraction pattern of the non super-ionic␤-phase (Fig. 2b) shows only minor differences between pattern measured with and without the analyser crystal (Fig. 2b). A similarity of diffuse scattering background in␣-Cu1.75Se at RT and␣-Cu1.98Se at 435 K confirms that observed increase of the diffuse scattering is characteristic of the superionic phase and the changes in diffraction pattern of Cu1.98Se during␤→␣transition are connected with the disordering of the Cu atoms and enhancement of vibrational/anharmonic motions.

As mentioned above, in the previous experiment [10] the pattern taken inE≈0 mode was very similar to the diffraction pattern measured by the conventional double-axis technique in the region of the first diffuse maxima at Q≈3 ˚A⁻¹. This can occur if the contribution from the low-energy phonons and the quasielastic scattering are not filtered by the analyser crystal due to the limited energy resolution of the spectrometer. Such phonons with energies about 2–4 meV were observed in the phonon frequency distribution of Cu2−δSe compounds and in the phonon dispersion curves. The density of states of low- energy phonons is relatively high because of the unusual behaviour of the dispersion curves. According to the mea-

surements of phonon dispersion in ␣-Cu1.85Se, the acoustic transverse branches change slope at wavevectors ofq> 0.2–0.4 and become nearly flat having an energy of about 4 meV[17].

Most probably these phonons give rise to diffuse scattering in Cu–Se compounds. Due to the relatively high spectral density of low-energy phonons, they can play a role in the trans- port of Cu ions. A calculation of diffuse scattering performed in paper [10] shows strong correlations between the thermal displacement of Se and Cu atoms at short distances. This cor- relates with the significant dampening of acoustic phonons observed in␣-Cu1.85Se atq/qm≥0.4[17]that indicates a cou- pling of low-energy phonon modes with displacement of mobile ions.

4. Conclusion

The neutron diffraction measurements show that Cu1.75Se at ambient temperature and Cu1.98Se at 435 K have antifluorite- type structure in agreement with the previous data[3–9]. The diffraction pattern of␤-Cu1.98Se matches the pattern no. 29-575 of the PDF2 database[13]for bellidoite. In-situ measurements of the Cu1.98Se compound during heating show that the␤–␣phase transition takes place at 420 K whereas it is about 40 K lower in successive cooling experiment. This is substantially higher than observed in DSC experiments of Crissafis et al.[15]despite use of lower heating/cooling rates.

The diffraction patterns of the ␣-Cu1.75Se at RT and ␣- Cu1.98Se at 435 K samples taken in two-axis geometry show a broad maximum related to diffuse scattering. This diffuse background is suppressed in the energy resolved experiment clearly indicating a strong contribution from inelastic scattering (dynamic correlations) in the super-ionic phase. On the other hand, the diffraction pattern of the non super-ionic ␤-phase shows only minor differences between spectra measured with and without the analyser crystal.

Acknowledgements

The support of HMI Berlin in providing the neutron facilities used in this work is acknowledged. The author would like to thank N.N. Bickulova for synthesizing the samples studied in this work.

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