Supporting Information for: Ag2Se to KAg3Se2: Suppressing order-disorder transitions via reduced dimensionality

Transcription

1 Supporting Information for: Ag2Se to KAg3Se2: Suppressing order-disorder transitions via reduced dimensionality Alexander J. E. Rettie 1, Christos D. Malliakas, 2 Antia S. Botana 1, James M. Hodges, 2 Fei Han, 3,4 Ruiyun Huang, 5 Duck Young Chung 1, Mercouri G. Kanatzidis 1,3 1. Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA 2. Department of Chemistry, Northwestern University, Evanston, IL, 60208, USA 3. Center for High Pressure Science and Technology Advanced Research, Shanghai , China 4. HPSynC, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, United States 5. Department of Materials Science, Northwestern University, Evanston, IL, 60208, USA S1

2 S1 Room temperature Rietveld refinement Room temperature refinements were in excellent agreement with the reported single crystal data from Bensch and Duriche. 1 The model became unstable if anisotropic displacement parameters were refined, so isotropic displacement parameters were used. Negligible improvements in refinement statistics (< 0.1% in weighted residuals (wr)) occurred when the isotropic displacement parameters were refined starting from the reported single crystal solution, thus these were used in the final solution (Table S2). As no significant deviation from stoichiometry was detected in EDX analysis the occupancy of all atoms was fixed at unity. Table S1. Powder diffraction data and structure refinement for β-kag 3Se 2 at 300 K. Empirical formula K Ag3 Se2 Formula weight Temperature Wavelength Crystal system 300 K Å monoclinic Space group C 2/m Unit cell dimensions Volume (1) Å 3 Z 4 Density (calculated) g/cm 3 a = (1) Å, α = 90 b = (7) Å, β = (2) c = (4) Å, γ = 90 2θ range for data collection to [Step ] Refinement method Rietveld Goodness-of-fit 1.47 Profile R indices R p = , wr p = Table S2. Atomic coordinates ( 10 4 ) and equivalent isotropic displacement parameters (Å ) for β - KAg 3Se 2 at 300 K with estimated standard deviations in parentheses. Label x y z Occupancy U iso Se(1) 2028(4) (7) 1 19 Se(2) 5130(4) (7) 1 20 Ag(1) 5941(3) (5) 1 33 Ag(2) 6881(4) (6) 1 49 Ag(3) 562(4) (6) 1 35 K 1352(11) 0 450(3) 1 28 S2

3 Figure S1. a) Rietveld refinement of synthesized KAg 3Se 2 at room temperature. Vertical ticks represent the simulated reflection positions. The broad feature at ~22 is due to the fused-silica capillary and carbon powder used for dilution. b) SEM image of a KAg 3Se 2 crystal isolated from a boule grown by the Bridgman technique. S3

4 Figure S2. a) Carbon-coated fused-silica tube (9 mm o.d.) for Bridgman crystal growth. b) KAg 3Se 2 boule after growth. c) Cleaved crystals used for transport measurements. xy ( -cm) 4 5 K 25 K 75 K K 225 K 300 K 2 1 Hall resistance vs. field B (T) Figure S3. Hall effect data for the β-kag 3Se 2 polycrystal presented in the main text versus applied field. S4

5 Figure S4. a) Temperature-dependent conductivity and b) Hall effect data for a second β-kag 3Se 2 polycrystal with carbon paint contacts from 2 to 300 K. Figure S5: Brillouin zone used in for band structure path of monoclinic β-kag 3Se 2 in Figure 3 in the main text with principal axes labelled. S5

6 Figure S6. a) DTA of KAg 3Se 2 showing the melting and the crystallization temperatures as well as a reproducible set of exo/endothermic peaks below the melting point. Temperatures were estimated from the peak onsets. The broad shape of the first crystallization peak was anomalous. b) XRD patterns of DTA residue and pristine material at room temperature. Grey ticks indicate the simulated powder pattern for KAg 3Se 2. Figure S7. Crystal structure of a) orthorhombic β-ag 2Se showing two unique Ag-Se environments: bent trigonal planar (labelled tri-ag, shaded in purple) and distorted tetrahedral (labelled tet-ag, shaded in magenta). 2 b) An isolated [Ag 3Se 2] - layer from β-kag 3Se 2, illustrating similar structural motifs to the parent compound in a). K and Se atoms have been omitted for clarity. The unit cell of β-ag 2Se is shown with black lines in a). S2 High temperature (T = 823 K) Rietveld refinement The capillary used for room temperature data collection (Section S1) was heated to 823 K and XRD data were collected under the same conditions. These data were refined using the crystal structure of NaCu3S2 (R-3m) as a starting point. Refinement results can be found in Tables 1-4 in S6

7 the main text. As no significant deviation from stoichiometry was detected by EDX analysis in the starting material, the occupancy of all atoms was fixed to stoichiometric KAg3Se2. Using this crystal structure, electronic band structure calculations were performed (Figure S8). The band structure bears similarity to β-kag3se2, but the conduction and valence bands have flattened and the band gap is larger (~1.3 ev) and direct. Figure S8. a) Electronic band structure and b) orbital-projected density of states plots for the high temperature, hexagonal α-phase of KAg 3Se 2. S3 In situ synchrotron X-ray diffraction (XRD) with a 2D detector Temperature-dependent synchrotron X-ray diffraction (SXRD) data from room temperature to 600 C were collected on beamline 11-ID-C at the Advanced Photon Source (APS) at Argonne National Laboratory. Undiluted KAg3Se2 powder was loaded into a fused-silica capillary (0.3 mm o.d.) and flame-sealed in under < 10-4 mbar. The sample was stationary during collection. Integration of the 2D images was performed using Dioptas software (version 0.2.4) using CeO2 as a standard. Le Bail refinements were carried out using GSAS-II software (version 0.2.0). S7

8 Figure S9. Synchrotron XRD pattern of pristine β-kag 3Se 2 at 303 K. A small K 2Ag 12Se 7.11 impurity with strong preferred orientation was present that was not observable in laboratory PXRD measurements. Figure S10: a) X-ray diffraction pattern post-in situ XRD compared with a simulated β-kag 3Se 2. The β phase returns, but the peak intensities were mismatched, consistent with preferred orientation and grain growth after heating and cooling. b) Raw 2D diffraction pattern illustrating the smeared spot pattern postmeasurement. S8

9 The relative peak intensities varied as a function of temperature and time. Thus, Rietveld refinements to obtain atomic information could not be performed. The sample was static during collection, so we attribute this behavior to ionic mobility and grain growth on heating. Le Bail fits were performed at each temperature to extract the unit cell parameters as functions of temperature. As shown in Figure S8, the thermal expansion of KAg3Se2 was approximately linear over the temperature range studied. Linear fits yielded linear coefficients of thermal expansion (CTEs) of 2.3, 3.3 and K -1 in the a, b and c axes respectively for the low temperature phase. Linear CTEs for α-kag3se2 were 2.8 and K -1 for a and c respectively. Volumetric CTEs were determined from the evolution of cell volume with T and measured to be 8.6 and K -1 for β- KAg3Se2 and α-kag3se2 respectively. Figure S11: Evolution of unit cell parameters with temperature for a) β-kag 3Se 2 and b) α-kag 3Se 2. In all cases the error bars were smaller than the symbols and so were omitted. The linear fits are represented as dashed lines and the corresponding fit quality is noted. The slight non-linearity of the curves in b) is attributed to poor coupling of the sample and heater at higher temperatures. Sequential Le Bail refinements were used to extract the lattice parameters. Refinement was considered complete when the wr were less than 5%. S9

10 S4 Ionic conductivity experiments Polycrystalline pellet samples were prepared by cold pressing followed by annealing in a fusedsilica ampule under < 10-4 mbar at 500 C for 12 hrs. Subsequently the pellets were air quenched to room temperature, resulting in >90% relative density (ρpellet/ρsingle crystal). Ionic conductivity measurements were conducted in a horizontal tube furnace from room temperature to 500 C on pressed and annealed KAg3Se2 pellets under Ar gas flowing at 50 sccm. Two-point AC impedance measurements were accomplished using a Solartron impedance analyzer with a frequency range from 1 MHz to 1 Hz and voltage amplitude of 20 mv. The impedance spectra were measured at room temperature and 500 C. Several contact materials were trialed: sputtered Pt metal (~40 nm thick), cold-pressed AgI pellets (Alfa Aesar) and Ag:β -alumina. Na: β -alumina polycrystalline pellets were acquired from Ionotec and subsequently ion-exchanged with molten AgNO3 at 350 C for 24 hrs using the method of Yao and Kummer 3 to produce Ag:β -alumina. The degree of ion exchange was monitored by weight change. The moderate conductivity of the material at room temperature and below suggested that KAg3Se2 might be a mixed ionic-electronic conductor and so electron-blocking, Ag + ion-specific electrodes would be required to measure the partial Ag + ion conductivity with either AC 4 or DC 5 techniques. AgI is commonly selected as an electrode material as it possesses high Ag + ion conductivity and low electronic conductivity, however it was found to react with KAg3Se2 at T > 300 C in vacuum to produce KAg4I5 and Ag2Se by PXRD. Ag + :β -alumina was subsequently identified as a potential electrode material, having been applied to silver-containing oxides at high temperature. 6 However, after heating an Ag + :β -alumina disk in contact with a pressed, annealed KAg3Se2 pellet at 500 C for several hours, the pellet was found to have converted entirely to Ag2Se by PXRD. A plausible reaction mechanism is that Ag + was exchanged for K + at high temperature. Figure S12: a) Photograph and b) SEM image of an Ag metal filament observed on a melted KAg 3Se 2 boule. EDX spectra yielded only Ag with minor O and Se peaks. S10

11 S5 Low temperature heat capacity In order gain insight into the effect of dimensionality on lattice thermal properties we measured the low temperature heat capacity at constant pressure, Cp, of KAg3Se2 and Ag2Se. Polycrystalline ingots of both materials were obtained by melting and phase purity was confirmed by PXRD. To extract the respective Debye temperatures, ΘD, the Debye model is commonly used: C v = 9NR ( T ) 3 Θ D Θ x 4 e x D /T dx 0 (e x 1) 2 (S1) Where, CV is the heat capacity at constant volume, N number of atoms per mole, R is the gas constant, and T is the temperature. At sufficiently low temperatures (typically T < ΘD/50) 7 the data has a T 3 -dependence and the Debye temperature has a constant, characteristic value: C v C p 12 5 NRπ4 ( T Θ D ) 3 (S2) No values of ΘD have been reported for KAg3Se2. For Ag2Se, ΘD is reported as 80 K, but was obtained from extrapolated heat capacity data where the lowest measured temperature was 16 K. 8 The qualitative trends of our data (Figure S13b and c) indicate that this T 3 regime was not reached even at ~1.8 K (the lowest temperature of our system), consistent with the soft nature of both materials inferred from thermal expansion coefficients. The maxima in the heat capacity (deviations from the Debye model) are typically associated with low energy phonon modes that result in a peak in the phonon density of states (DOS), implying that KAg3Se2 has even lower energy phonon modes than Ag2Se (Figure S13b). Detailed modelling of the phonon DOS would be needed to elaborate on the physical nature of these modes. Figure S13: a) Heat capacity of KAg 3Se 2 (m = 6.5 mg) and Ag 2Se (m = 21.8 mg) polycrystals from 1.8 to 300 K. The error bars were smaller than the symbols and therefore omitted. b) Plot of C p/t 3 vs. T, illustrating that the T 3 -regime has not been reached down to 1.8 K for KAg 3Se 2 and Ag 2Se. Data for SnTe are included to illustrate the T 3 -regime at low T where C p/t 3 has a constant value. Fitting from K (grey dashed line) yields a Debye temperature for SnTe of 171(1) K. c) Numerical integration of eq S1 yields ΘD(T), giving similar results to those presented in b). S11

12 Figure S14: Thermal diffusivity of KAg 3Se 2 from K. The symbols and // represent measurements perpendicular and parallel to the SPS pressing direction respectively. References 1. Bensch, W.; Dürichen, P., Z. Kristallogr. - New Cryst. Struct. 1997, 212 (1), Yu, J.; Yun, H., Acta Cryst. E 2011, 67 (9), i45-i Yao, Y.-F. Y.; Kummer, J., J. Inorg. Nucl. Chem. 1967, 29 (9), 2453IN Ahn, P.-A.; Shin, E.-C.; Kim, G.-R.; Lee, J.-S., J. Korean Ceram. Soc. 2011, 48 (6), Gellings, P. J.; Bouwmeester, H., Handbook of solid state electrochemistry. CRC press: Matsumoto, Y.; Funaki, K.; Hombo, J.; Ogawa, Y., J. Solid State Chem. 1992, 99 (2), Gopal, E., Specific heats at low temperatures. Springer Science & Business Media: Walsh, P. N.; Art, E. W.; White, D., J. Phys. Chem. 1962, 66 (8), S12