Lattice Dynamics Study of Thermoelectric Oxychalcogenide BiCuChO

Article pubs.acs.org/JPCC

Cite This: J. Phys. Chem. C 2019, 123, 16046−16057

Lattice Dynamics Study of Thermoelectric Oxychalcogenide BiCuChO (Ch = Se, S) R. Viennois,*,† P. Hermet,† M. Beaudhuin,† J.-L. Bantignies,‡ D. Maurin,‡ S. Pailhes̀ ,§ M. T. Fernandez-Diaz,∥ M. M. Koza,∥ C. Barreteau,⊥ N. Dragoe,⊥ and D. Beŕ ardan*,⊥

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†

Institut Charles Gerhardt Montpellier, UMR 5253, CNRS-UM-ENSCM, Université de Montpellier, cc 1504, Place Eugène Bataillon, F-34095 Montpellier Cedex 5, France ‡ Laboratoire Charles Coulomb, UMR 5221, CNRS-UM, Université de Montpellier, cc 1504, Place Eugène Bataillon, F-34095 Montpellier Cedex 5, France § Institut Lumière Matière, UMR 5306, CNRS-UCBL, Université Claude Bernard Lyon 1, Campus La Doua, F-69622 Villeurbanne, France ∥ Institut Laue Langevin, rue Jules Horowitz, F-38042 Grenoble, France ⊥ SP2M-ICMMO (UMR 8182 CNRS), Univ. Paris-Sud, Univ. Paris-Saclay, 91405 Orsay, France S Supporting Information *

ABSTRACT: The BiCuSeO-based compounds with very low thermal conductivity are among the most promising thermoelectric materials recently discovered. Their lattice dynamics, which remains mostly unexplored experimentally, is investigated in this paper. We report Raman experiments on BiCuSe1−xSxO solid solutions and infrared experiments on BiCuSeO and BiCuSO alloys coupled to first-principles-based calculations. We have observed that the high-energy A1g Raman-active mode strongly depends on the chalcogen content. We also report the density functional theory calculations of the dielectric and elastic constants, the phonons in the whole Brillouin zone, and the thermodynamic properties. We have determined the thermal expansion of BiCuSeO at room temperature from neutron diffraction experiments and evaluated its thermodynamic Grüneisen parameter and found a quite large value compared to other thermoelectric materials, which confirms the large anharmonicity of BiCuSeO. conductivity, and κ the thermal conductivity (electronic and vibrational).13 The most efficient thermoelectric materials currently used in applications exhibit ZT ∼ 1 and are constituted by toxic and rare elements (such as Te in alloys based on Bi2Te3 and PbTe) or very expensive ones (such as Ge as in Si−Ge alloys).13 The discovery of ZT as high as 1.5 at T ∼ 900 K in BiCuSeO-based alloys sets them among the most promising thermoelectric materials of the latest generation.11,12 The main reason for such very good thermoelectric properties is the intrinsically very low thermal conductivity of BiCuSeO and its alloys.10−12 Many theoretical works have been dedicated to the lattice dynamics of BiCuSeO8,14−25 and some of them to the case of BiCuSO.8,16,20,21,24,25 More particularly, only the Supporting Information of one of these studies reported the symmetry of the BiCuSO transverse optical (TO) zone-center modes, but these authors neither discussed the nature of these modes in detail nor reported the longitudinal optical (LO) modes.8 Although several calculations of thermal conductivity

1. INTRODUCTION Since the initial discovery of the layered tetragonal structure of ZrCuSiAs type by Johnson and Jeitschko in 1974,1 many compounds sharing this structure have attracted attention.2−10 These materials have been mainly highlighted because of the discovery of the new high-temperature iron-based superconducting compounds among the oxypnictide family (doped RFeAsO, R = rare-earth) with superconducting temperature as high as 56 K, the largest among bulk materials at room pressure outside the cuprate compound family.2−4 The oxychalcogenides of 1111 stoichiometry have attracted the interest for the properties of some of them (RMChO with R = rare-earth or Bi; M = Cu, Ag; and Ch = chalcogen) as ionic conductors (when M = Ag),5 as transparent conductors, and for their optoelectronic properties6,7 or for photovoltaic applications (when M = Cu).8 More recently, the large potential of some moderate band gap doped semiconducting BiCuChO oxychalcogenides (see Figure 1 for the crystal structure) for the thermoelectric energy conversion has been evidenced.10−12 The thermoelectric performance of a material can be evaluated using the dimensionless figure of merit, ZT = S2σT/κ, with T the temperature, S the Seebeck coefficient, σ the electrical © 2019 American Chemical Society

Received: May 21, 2019 Revised: June 12, 2019 Published: June 12, 2019 16046

DOI: 10.1021/acs.jpcc.9b04806 J. Phys. Chem. C 2019, 123, 16046−16057

Article

The Journal of Physical Chemistry C

Fletcher−Goldfarb−Shanno algorithm until the residual stresses and forces were less than 2 × 10−5 GPa and 6 × 10−5 Ha/Bohr, respectively. Our relaxed structures obtained from DFT calculations are compared to prior and present experimental data in Table S1 of the Supporting Information (SI). They are in very good agreement with experimental data, especially between the relaxed structure of BiCuSeO (at 0 K) and the neutron data at low temperature (4 K). Density functional perturbation theory (DFPT) calculations32 were performed for calculating the dynamical matrix, Born effective charges, and thermodynamic properties. Phonon dispersion curves, including the dipole−dipole interactions, were interpolated according to the scheme described by Gonze et al.33 We considered a 4 × 4 × 2 q-points grid for the calculations of the phonon band structure, whereas a denser 250 × 250 × 140 qpoints grid was used for the calculations of the phonon density of states and heat capacity. The infrared absorbance and infrared reflectivity spectra were, respectively, calculated as described in refs 34 and 35. The BiCuSe1−xSxO solid solutions with x = 30 and 70% were calculated by the virtual crystal approximation (VCA)36,37 and using the same computational parameters as for the parent compounds.

Figure 1. Crystal structure of BiCuSeO (left) and Brillouin zone (from the Bilbao crystal server9) of the crystal structure with P4/nmm space group including high-symmetry points (right).

and anharmonic properties have been published, there is presently no clear consensus about the origin of the low thermal conductivity in these materials. Although it is clear that the anharmonicity in BiCuSeO is quite large as shown by its large calculated Grüneisen parameters, the origin of these large values is controversial. Depending on the authors, this origin can be attributed to (i) the lone pairs of the Bi atoms,7,26 (ii) the Cu vibrations,16 (iii) both,15,19,22 or (iv) the layered nature of the crystal structure of the BiCuChO compounds with weakly bonded [Bi2O2] and [Cu2Se2] layers, which could give interlayer interactions decreasing the thermal conductivity.20 To discriminate between these different possibilities and understand the origin of the intrinsically low thermal conductivity in BiCuSeO and related compounds, the study of the experimental lattice dynamics in BiCuChO compounds is of fundamental interest. However, to our knowledge, there is only one infrared spectroscopic study of the lattice vibrations of BiCuSeO27 and one very recent Raman spectroscopic study of the lattice vibrations of both compounds;28 both have been reported at room temperature. In this Raman study, the assignment of the Raman modes of BiCuSeO is made following the calculations of Saha,14 whereas that of BiCuSO was made without the support of any theoretical study. This lack of a theoretical support led to incorrect assignment for some Raman modes, as will be discussed later. Here, we report the experimental and the density functional theory (DFT)-based calculations of the infrared and Raman spectra of BiCuChO (Ch = Se, S) compounds. We compare the thermodynamic properties and atomic displacement parameters (ADPs) of BiCuChO compounds obtained from lattice dynamics calculations in the whole Brillouin zone with the literature data and our own experimental data obtained from neutron diffraction experiments for BiCuSeO (as a function of temperature) and with prior literature experimental data for both compounds.

3. EXPERIMENTAL DETAILS The samples were synthesized by the solid-state reaction route, and their purities were checked using X-ray diffraction as described in details in ref 38. Infrared experiments were performed on pellets constituted by few milligrams of BiCuChO powders dispersed in polyethylene. The infrared absorption experiments were performed with a Brucker IFS 66 V Fourier transform infrared spectrometer using a Si bolometer cooled at 10 K with liquid He. The spectral resolution was 2 cm−1, and 64 scans were recorded for each spectrum. The absorption spectra were corrected for the background. The Raman scattering experiments were performed using different experimental setups. The resonant effect for the two parent compounds BiCuSeO and BiCuSO was studied using a T64000 spectrometer from Horiba-Jobin-Yvon in triple-monochromator configuration to probe the low-energy vibrational mode between 20 and 100 cm−1. We used a backscattering geometry, and the beam was focused using a 50× lens. Two different wavelengths were used for probing the possible resonant effect: 514.5 nm (from an Ar−Kr laser) and 633 nm (from a laser diode). No significant differences were found for the Raman spectra recorded with these two different wavelengths. Different powers were tested to check heating of the sample, and we choose a power set to 2 mW. The Raman spectra of the solid solutions BiCuSe1−xSxO were studied using a LabRam HR Evolution spectrometer from Horiba Scientific using an excitation wavelength of 532 nm and a power set to 5 mW to avoid heating. The beam was focused on the sample using a 50× lens. The scattered light was collected in backscattering geometry using the same lens. For both Raman spectrometers, the spectral resolution was about 2 cm−1. The neutron diffraction experiments were performed at the ILL facility using the D2B beamline. The neutron diffraction experiments were performed using 1.594 Å wavelength and an “orange” cryostat. The Rietveld refinements were performed with the Fullprof software.39 Specific heat measurements were performed using a Quantum Design Physical Properties Measurement System (PPMS) from 300 to 2 K with Apiezon N grease.

2. COMPUTATIONAL DETAILS The DFT calculations were carried out using the ABINIT code.29 We used the local density approximation (LDA) with optimized norm-conserving pseudopotentials.30 The Bi (5d, 6s, 6p), Cu (3d, 4s), S (3s, 3p), Se (4s, 4p), and O (2s, 2p) electronic states are considered as valence states. A cutoff kinetic energy of 60 Ha and a grid of 12 × 12 × 6 k-points obtained according to the Monkhorst−Pack scheme were used.31 The structural relaxation was performed using the Broyden− 16047


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4. ZONE-CENTER PHONON MODES As discussed in the Introduction, several studies reported the calculations of the lattice dynamics of BiCuSeO and BiCuSO.8,14−25 Among these studies, the zone-center TO phonons and their symmetries have been poorly explored with only two (one) article(s) dealing with BiCuSeO14,22 (BiCuSO)8 (see the Supporting Information). Similarly, the LO modes have only been calculated by Saha14 in BiCuSeO, leaving the frequencies of these modes presently unidentified in BiCuSO. This missing information is detrimental for a good understanding of the lattice vibrations in these materials and for the interpretation of the experimental observations. The zone-center optical modes of the BiCuChO compounds can be classified according to the irreducible representations of the D4h point group into Γopt = 3 A2u ⊕ 3 Eu ⊕ 2 A1g ⊕ 2 B1g ⊕ 4 Eg. The three gerade representations (A1g, B1g, Eg) are Raman active, and the two remaining representations (ungerade) are infrared active. No silent mode is expected. Thus, the group theory predicts eight distinct Raman lines and six distinct infrared bands. Calculated frequencies and symmetries of the BiCuSO and BiCuSeO phonon modes are listed in Tables 1

Supporting Information for more details). In the case of BiCuSO, the calculations by Le Bahers et al.8 using the HSE06 hybrid exchange−correlation functional are also farther from the experimental results than our LDA calculations as well as the PBEsol calculations by Ji et al.20 It results from the calculated lattice parameters, which are only slightly smaller than the experimental one using the PBEsol exchange−correlation functional14,19,20 but much larger at the PBE level.21,22 We also report in Table 2 the Raman frequencies of BiCuSe1−xSx solid solutions from both experiments and DFT calculations based on the VCA. 4.1. Raman Spectra. Figure 2 shows a comparison of the experimental Raman spectra of BiCuSeO and BiCuSO recorded

Table 1. Experimental and Calculated Zone-Center Phonon Frequencies (in cm−1) of the Infrared-Active TO Modes in BiCuSO and BiCuSeOa mode symmetry

BiCuSO (exp.)

Eu TO1 (LO1) A2u TO1 (LO1) Eu TO2 (LO2) A2u TO2 (LO2) Eu TO3 (LO3) A2u TO3 (LO3)

BiCuSO (DFT)

BiCuSeO (exp.)

BiCuSeO (DFT)

54

56.3 (62.2)

59, 59.5*

56.3 (63.4)

100.5

91.3 (102)

91, 92*

78.4 (91.1) 106 (145.7)

123

131.2 (202.2)

127, 116.5*

177

168.9 (224.4)

178

151.2 (179)

310.5

304.3 (388.7)

293, 262*

284.4 (369.3)

478.5

436.4 (510.8)

455, 475*

408.4 (486.1)

a

The calculated LO modes are within the parenthesis. Asterisks: TO modes of BiCuSeO observed by Berdonosov et al.27

Figure 2. Experimental Raman spectra of polycrystalline BiCuSe1−xSxO samples with x = 0, 10, 30, and 70%. The ticks correspond to the position of the calculated Raman lines using the DFT calculations.

(infrared modes) and 2 (Raman modes) along with the experimental frequencies. The values reported in these tables show reasonable agreement between our calculated frequencies and the experimental ones. This agreement is as good as with the other sets of calculations previously reported using the PBEsol exchange−correlation functional,14,19,20 but a stronger deviation can be observed at the Perdew−Burke−Ernzerhof (PBE) level21,22 with respect to the experimental ones (see the

at room temperature between 30 and 500 cm−1. These spectra are in good agreement with the spectra at ambient conditions in the recent work of Zhang et al.28 In the case of BiCuSeO, four strong lines can be observed located at 55, 85, 147, and 177 cm−1. They correspond to the four Raman M1−M4 modes found by Zhang et al.28 The two tiny features at 102 and 113 cm−1 are not significant because their magnitudes are comparable to the background noise. In contrast, the Raman

Table 2. Experimental and Calculated Zone-Center Phonon Frequencies (in cm−1) of the Raman-Active Modes in BiCuSe1−xSxO Solid Solutions (x = 0, 0.3, 0.7, 1) mode symmetry

x = 1: exp. (DFT)

x = 0.7: exp. (DFT)

x = 0.3: exp. (DFT)

x = 0: exp. (DFT)

Eg Eg B1g A1g Eg A1g B1g Eg

58 (76) (90.8) (101.5) 154.5 (160.8) (231) 275.5 (283.6) (374.2) (454.2)

57.7 (74) (86.7) (105) 153.2 (158) (199.2) 261.5 (237) (370.8) (446.8)

54.7 (69.4) 93 (83.4) (108.7) 147.5 (154.5) (173.9) 177 (198.8) (365.2) (437.9)

55.4 (65.5) 85.3 (81.9) (111.5) 147 (152.1) (161.6) 177.2 (179.7) (360.7) (432)

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The Journal of Physical Chemistry C spectrum of BiCuSO is simpler with only three dominant lines that can be observed at 58, 155, and 276 cm−1. Only the two last lines were observed by Zhang et al.,28 and they correspond to the M4 and M6 modes in ref 28. As will be seen below, contrary to their proposed assignment, these two lines at 155 and 276 cm−1 should correspond to the M3 and M4 modes of BiCuSeO at 147 and 177 cm−1, respectively. The position of the two M1 and M3 lines have a small evolution when substituting selenium by sulfur atoms, suggesting that they are weakly linked to the chalcogen atoms. Raman spectra of BiCuSe1−xSxO solid solutions with x = 10, 30, and 70% are shown in Figure 2. These spectra highlight that the intensity of the line centered at 177 cm−1 in BiCuSeO smoothly decreases as the sulfur concentration increases and is almost null for x = 70%. At the same time, its position only slightly upshifts. Similarly, the intensity of the broad line at 276 cm−1 in BiCuSO is correlated with the sulfur concentration as this line is not observed in BiCuSeO and its intensity strongly decreases until being almost null for x = 30%. At the same time, a significant downshift of its position can be observed. As will be seen later from the comparison with the calculations, these modes correspond to the same atomic motions. Our calculations enable us to go further into the analysis by identifying the symmetry of the Raman lines (Table 2). In the case of BiCuSeO, the frequency of the experimental lowest M1 line at 55 cm−1 is located about 10 cm−1 higher in our calculations, whereas the experimental M2 line at 85 cm−1 is in rather good agreement with the position of the line predicted at 82 cm−1. These experimental modes have Eg symmetry. The experimental M3 and M4 lines centered at 147 and 177 cm−1 are assigned to the calculated lines at 152 and 180 cm−1, respectively, and have the A1g symmetry. The two Raman lines expected from the calculations above 300 cm−1 are too weak to be observed on the experimental spectra; see below. We believe that the M5 line, which appears at high pressure in the Raman experiments of Zhang et al.,28 corresponds at room pressure to the Raman mode located between the M3 and M4 lines because it has much larger pressure dependence than the M3 and M4 lines. From our DFT calculations, we assign this mode to the Eg line calculated at 161.6 cm−1. In the case of BiCuSO, the lowest frequency M1 line at 58 cm−1 in the experiment could be assigned to the calculated Eg mode at 76 cm−1 even if it has much lower energy. This should be related to the smaller c lattice parameter found in our calculations as compared to the experiment, which implies stronger bondings and hence larger force constants. The position of this Raman line increases by about 8% as the sulfur content increases (see Figure 2). There is good agreement between calculations and experiments for the frequency position of the experimental M3 line at 155 cm−1 and the calculated A1g mode at 161 cm−1. Its position slightly increases by ∼6% with sulfur content (see Figure 2). The last Raman mode observed in our experiment at 276 cm−1 can be well explained by our calculations and corresponds to the high-energy A1g mode predicted at 284 cm−1. We conclude therefore that the assignment made by Zhang et al.28 for this mode is not correct. In contrast with the two other M1 and M3 modes, this mode is very strongly upshifted in BiCuSO as compared to BiCuSeO by ∼55% and correspond therefore to the M4 mode. For this vibrational mode, the frequency ratio, ω(BiCuSO)/ω(BiCuSeO) = 1.56, is in excellent agreement with the mass ratio, M(Se)/M(S) = 1.57.

This means that this M4 mode should involve mainly chalcogen atoms, as will be confirmed below by the calculations. In both compounds, we were not able to observe experimentally the high-energy B1g and Eg modes predicted by the calculations above 300 cm−1. There are different reasons that could explain why we do not observe all of the eight lines predicted by the group theory. In particular, we cannot exclude that some of these lines have too weak Raman intensity to be detected or/and that they are very broad due to larger anharmonic effect or because of defects. The analysis of the eigen displacement vectors obtained from the diagonalization of the dynamical matrix shows that: • both low-energy M1 and M2 modes of Eg symmetry are out-of-phase bending modes involving mainly the three different metallic atoms moving in the ab-plane, but for the lower-energy mode, the interlayer motions are out of phase with the largest contribution from the Cu−Se layer in BiCuSeO and the largest contribution from Bi in BiCuSO, whereas in the higher-energy mode, they are inphase with the largest contribution from the Cu−S layer in BiCuSO; • the low-energy mode of B1g symmetry involves only Cu and O atoms in the different layers with the largest contribution from Cu atoms; • both M3 and M4 modes of A1g symmetry involve some kind of scissoring-bending motion of both the Bi atoms and the chalcogen atoms along the c-direction, with the lower-energy mode involving mainly the Bi atoms whereas the higher-energy mode involving mainly the chalcogen atoms, which explains why it is most sensitive to chalcogen substitution; • the M5 mode of Eg symmetry located between the two A1g modes involves mainly some kind of bending motion of Cu and chalcogen atoms in the ab-plane. Our DFT calculations indicate that the higher-energy modes of B1g and Eg symmetry involve almost only oxygen atom motions along the c-direction and in the ab-plane, respectively. 4.2. Infrared Spectra and Dielectric Constant. Figures 3 and 4 report the experimental and calculated infrared absorbance spectra of BiCuSeO and BiCuSO, respectively (the artifacts in both spectra are related to the low transmittance between 370 and 460 cm−1 of the polyethylene). In the case of BiCuSeO, our experimental spectrum shows six bands at 59, 91, 127, 178, 293, and 455 cm−1. Their numbers, frequencies, and relative intensities are in excellent agreement with the calculated spectrum. Except the experimental band at 178 cm−1, the other five bands have also been observed by Berdonosov et al.,27 which make their assignments quite reliable. However, we think that the band at 178 cm−1 is real as its presence is supported by our calculations. The assignment of the six polar transverse optical (TO) modes of BiCuSeO and their symmetries are listed in Table 1. The infrared reflectivity spectrum has also been calculated up to 600 cm−1 (i) to estimate the LO−TO splitting of polar modes and (ii) to provide benchmark theoretical spectra for future experiments. This calculation is shown at the bottom of Figure 3 at normal incidence. The reflectivity related to the A2u-modes is observed when the electric field is collinear to the caxis. Similarly, the Eu-modes can be observed when the electric field is perpendicular to this axis. Since our approach neglects the damping of the phonon modes, the calculated reflectivities saturate to 1. The LO−TO splitting is significant (more than 40 cm−1) for the modes above 200 cm−1. Usually, only TO phonon 16049


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Figure 4. Infrared absorbance spectra of the powdered BiCuSO sample dispersed in a polyethylene pellet; theoretical infrared absorbance spectra of the powder-averaged BiCuSO compound; theoretical infrared reflectance spectra of the single-crystalline BiCuSO compound with polarized light in the ab-plane and c-direction.

Figure 3. Infrared absorbance spectra of the powdered BiCuSeO sample dispersed in a polyethylene pellet; theoretical infrared absorbance spectra of the powder-averaged BiCuSeO compound; theoretical infrared reflectance spectra of the single-crystalline BiCuSeO compound with polarized light in the ab-plane and cdirection.

The analysis of the eigen displacement vectors gives additional information on the atoms involved in a given normal mode. This analysis shows that:

modes are evidenced in absorbance. However, in a sufficiently thick pellet, LO modes can be observed, which could explain the width of the modes above 200 cm−1 observed in the experimental absorbance spectrum. In the case of BiCuSO, six bands can also be observed in the experimental spectrum. They can be assigned using our calculated spectrum as listed in Table 1. Similar to that of BiCuSeO, the two bands above 200 cm−1 are quite wide. This width is correlated to the importance of the LO−TO splitting as evidenced in the calculated reflectivity spectrum shown at the bottom of Figure 4. When Se is substituted by S atoms, the calculated frequencies of the A2u(TO1), A2u(TO3), and Eu(TO3) modes increase between 5 and 10% in good agreement with our experiments. However, for the three other polar modes, this trend is not so clear. Indeed, the frequency of the lowest energy mode, Eu(TO1), decreases from 59 to 55 cm−1 in our experiments, whereas its frequency is the same in our calculations. The frequency of the A2u(TO2) mode is more or less the same for both compounds in our experiments, whereas it increases by ∼10% in our calculations. The case of the remaining mode, Eu(TO2), is unclear as we observe a frequency decrease from 127 to 124 cm−1 in our experiments, whereas our calculations predict an opposite trend. However, considering the experimental frequency of 117 cm−1 observed by Berdonosov et al.,27 our calculations are consistent with this upshift.

• the two modes of Eu and A2u symmetry below 100 cm−1 involve all of the atoms (although the contribution of O is weaker) for motions in the ab-plane and along the cdirection, respectively; • the two modes of Eu and A2u symmetry, respectively, at 106 and 151.2 cm−1 in the DFT calculations involve mainly copper, selenium, and oxygen atom motions in the ab-plane and along the c-direction respectively; • the two modes of Eu and A2u symmetry above 200 cm−1 involve essentially the motions of the oxygen atoms because these are about 2 orders of magnitudes larger than the motions of other atoms. For the lower-energy Eu polar infrared-active mode, the atoms of each layer move in the same x- or y-direction and the motions are in the opposite direction between each layer, which makes it a shearing-like mode. For the lower-energy A2u polar infraredactive mode, all of the atoms of one layer move in the same direction, along the c-direction, but the interlayer motion is in out-of-phase translation. For the case of the two higher-energy Eu polar infrared-active modes, the motions of atoms are of scissoring type within the layers with out-of-phase interlayer motions in the case of the mode at about 106 cm−1 and with inphase interlayer motions in the case of the higher-energy mode. 16050


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Table 3. Contribution to the Ionic Dielectric Constant εion of the Zone-Center Polar Phonons of Eu Symmetry (ε⊥ion) and A2u Symmetry (ε//ion) Obtained from DFPT Calculations for BiCuSO and BiCuSeO compound dielectric component ionic contribution TO1 TO2 TO3 total phonon εion electronic contribution ε∞ (corrected ε∞) total ε0 = ε∞ + εion (corrected ε0)

BiCuSO

BiCuSeO

⊥

//

⊥

//

13.3 31.5 5.8 50.6

8.25 11.3 3.6 23.15

16.65 23.2 9.4 49.25

10.7 7 5.25 22.95

16.15 (13.7)

13.15 (11.86)

13.59 (11.67)

11.48 (10.06)

66.75 (64.3)

36.3 (35.01)

62.84 (60.92)

34.43 (33.01)

Table 4. Calculated Elastic Constants Cij (in GPa) in BiCuSeO and BiCuSO from DFPT Calculations

For the case of the two higher-energy A2u polar infrared-active modes, the motions of atoms are of wagging type within the layers with out-of-phase interlayer motions in the case of the mode at about 151 cm−1 and with in-phase interlayer motions in the case of the higher-energy mode. For a nonmagnetic centrosymmetric material, the dielectric constant can be separated into an electronic (ε∞) and a vibrational (εion) contribution. These contributions have been calculated according to ref 35. Our calculated values at the LDA level of the electronic contribution are ε⊥∞ = 16.1 and ε//∞ = 13.6 for BiCuSeO, whereas for BiCuSO, these values slightly decrease to ε⊥∞ = 13.6 and ε//∞ = 11.5. These calculated values are quite reliable because they are not significantly altered when the calculations are performed at the GGA level. Indeed, using the PBEsol functional in standard DFT14,20 or the PBE functional in DFT + U,22 the results reported in the literature for BiCuSeO show that14,20,22 14.2 ≤ ε⊥∞ ≤ 18.6 and 12 ≤ ε//∞ ≤ 14. Similarly, our calculated LDA values of ε∞ in BiCuSO are consistent with the PBEsol values reported by Ji et al.:20 ε⊥∞ = 12.7 and ε//∞ = 11.5. Nevertheless, standard DFT usually overestimates the experimental values of ε∞ due to the lack of the polarization dependence of LDA exchange−correlation functionals. To overcome this problem, it is a common practice to apply the so-called scissors correction,40 in which we use an empirical rigid shift of the conduction bands to adjust the LDA band-gap value [E g L D A (BiCuSeO) = 0.29 eV and E g LDA (BiCuSO) = 0.52 eV] to the experimental one [Egexp(BiCuSeO) = 0.8 eV and Egexp(BiCuSO) = 1.1 eV].7 By comparing our calculated LDA band-gap value, the scissor corrections are fixed to 0.51 and 0.58 eV for BiCuSeO and BiCuSO, respectively. With this correction, the values of the optical dielectric tensor decrease as expected and we get ε⊥∞ = 13.7 and ε//∞ = 11.9 for BiCuSeO and ε⊥∞ = 11.7 and ε//∞ = 10.06 for BiCuSO. For the latter compound, Le Bahers et al.8 found lower values (ε⊥∞ = 10.0 and ε//∞ = 7.5) using a hybrid functional, but their band-gap prediction was a little bit overestimated (1.22 eV). The total ionic contributions of both materials reported in Table 3 are very close and much larger than those of their electronic counterpart, in agreement with the prior works of Saha for BiCuSeO14 and Le Bahers et al. for BiCuSO.8 The mode-by-mode decomposition shows that the contribution of polar modes for both materials is similar (Table 3). Indeed, the two first Eu-modes represent more than 80% of the ε⊥ion component, whereas there is no A2u-mode that clearly dominates ε//ion. 4.3. Acoustic Phonons. Table 4 lists our calculated isothermal elastic constants. They are strongly anisotropic and

compound

C11

C33

C12

C13

C44

C66

BiCuSeO BiCuSO

163.8 180.2

105.3 118.7

72.3 82.6

69.7 77.5

33.2 40.3

43.8 48

have quite low values because of the relatively soft bonding in BiCuSeO and BiCuSO. For both compounds, the mechanical stability criteria are fulfilled:41 C11 > 0, C33 > 0, C44 > 0, C66 > 0. (C11 − C12) > 0, (C11 + C33 − 2C13) > 0, and [2(C11 + C12) + C33 + 4C13] > 0. In Table 5, we report different elastic parameters (bulk, shear, Young’s, and Poisson’s moduli) calculated on a polycrystalline powder using the Hill approximation41 together with the sound velocities and the Debye temperature. The elastic constants as well as the sound velocity are about 10% smaller in BiCuSeO than in BiCuSO. They follow the same trend as that of most optical modes. Interestingly, the difference between the sulfide and the selenide is larger (about 15%) for the shear moduli (C12, C13, C23, and G), whereas both the Poisson coefficient and the Debye temperature are very close. For the latest, this is because the larger sound velocity in BiCuSO is compensated by its smaller average molar mass due to lighter sulfur. Regarding BiCuSeO, the calculations are in good agreement with the experimental transverse velocity (1900 m/s) but to a lesser extent with the experimental longitudinal velocity (3200 m/s), which is about 20% lower.26 This disagreement can explain why the experimental Young modulus (E = 76.5 or 78.8 GPa) and the experimental Poisson coefficient (ν = 0.25)26,42 are much smaller than the calculated ones by about 20 and 25%, respectively. Note that because these experimental values were obtained using polycrystalline samples that may be not fully dense, one cannot exclude that they could be underestimated. However, recent measurements of X-ray diffraction under pressure have led to an experimental isothermal bulk modulus B = 83 ± 3 GPa, which is about 10% lower than the calculated bulk modulus BH. However, despite these differences, the experimental sound velocity (v = 2107− 2112 m/s) and Debye temperature (θD = 243−245 K)26,42,43 are only 5% smaller than our calculated values. The previous calculations using GGA/PBESol functional19,20 found only slightly smaller elastic constants Cij than in the present calculations for both compounds (with the exception of the C44 in the case of ref 19), which is related to the close values of the lattice parameters.19,20 In contrast, the prior calculations performed using the GGA/PBE functional gave elastic constants much smaller than our LDA calculations, which is related to the larger lattice parameters and hence weakest bondings in the case 16051


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Table 5. Calculated Powder-Averaged Bulk Modulus B (in GPa), Shear Modulus G (in GPa), Young’s Modulus E (in GPa), Poisson’s Coefficient ν, Longitudinal Velocity vl (in m/s), Transverse Velocity vt (in m/s), Sound Velocity v (in m/s), and Debye Temperature θD (in K) in BiCuSeO and BiCuSO Using the Hill Formalism compound

B

G

E

ν

vl

vt

v

θD

BiCuSeO BiCuSO

92.7 103.4

35.3 41.1

94 108.8

0.331 0.325

3921 4298

1970 2224

2210 2490

257 297

Figure 5. Phonon dispersion curves of (a) BiCuSeO and (b) BiCuSO. Partial and total density of states of (c) BiCuSeO and (d) BiCuSO.

of PBE calculations.44−46 However, they found slightly and much larger Debye temperature than in our calculations for BiCuSeO46 and BiCuSO.44,45 For BiCuSO, in the recent work of Zhang et al.,28 the experimental isothermal bulk modulus obtained using X-ray diffraction under pressure was determined to be 129 ± 5 GPa, a value much larger than for BiCuSeO. This contrasts with our calculations using LDA and the calculations of Ji et al. using PBESol20 showing that the bulk modulus is about 10% larger in BiCuSO than in BiCuSeO. Our calculated isothermal bulk modulus for BiCuSO is about 20% smaller than the experimental values, and it is closer to the experimental values than the calculated isothermal bulk modulus by Ji et al. using PBESol20 and by other groups using PBE,44,45 which are slightly smaller and much smaller than our results, respectively. At this stage, it is difficult to understand why our results agree rather well for BiCuSeO whereas not for BiCuSO. Therefore, to get a definitive conclusion about the elastic properties, new experiments for both compounds are strongly suggested. Our calculated Poisson’s coefficients are rather large, and we also find rather large and positive values for the Cauchy pressures Px = C13 − C44 = 36.5 GPa and Pz = C13 − C44 = 28.5 GPa. These values are more typical of rather ionic materials. Indeed, covalent semiconductors with bonding of angular character have negative Cauchy pressures and rather small Poisson coefficients.47 This agrees well with the prior electronic structure calculations showing that the charges are located around Bi, O, and Se atoms; the bonds between Bi and O are mostly ionic, whereas the Cu−Se bonding has a significant covalent character and the interlayer has mainly an ionic character with some weak covalent bonds between Bi and Se,

which thus means that BiCuSeO has a mixed covalent and ionic character.46,48 One can find a more unusual feature in BiCuSeO and BiCuSO. Pugh has defined a criterion separating brittle from ductile materials from the B/G ratio, which must be lower than 1.75.47,49 Most of the semiconductors are brittle and have B/G < 1.75.47 One finds a large B/G ratio of 2.58 and 2.515 for BiCuSeO and BiCuSO, respectively. In other studies, large B/G ratios (although smaller than ours) were also found for both BiCuSO (2.17,44 2.19,45 2,1620) and BiCuSeO (1.84,46 2.51,19 2.1320). The measurements of elastic constants on singlecrystalline samples would be interesting to confirm these unusually large B/G ratios for semiconducting compounds.

5. LATTICE DYNAMICS IN THE WHOLE BRILLOUIN ZONE AND THERMODYNAMIC PROPERTIES 5.1. Lattice Dynamics in the Whole Brillouin Zone. We report now on the calculated lattice dynamics in the whole Brillouin zone of BiCuSeO and BiCuSO. The phonon dispersion curves and the total and partial density of states (DOS) are displayed in Figure 5. Our results are in good agreement with prior calculations in the literature.8,14−25 As expected, the modes involving O atoms have the largest energies, whereas the modes involving Bi atoms have the lowest energies. The average energy of the Cu vibrations is lower than that of Se, despite the lower mass of the Cu atoms. As expected, the vibrational energies of the S atoms are much larger than those of Se atoms. In the case of BiCuSeO, there is an energy band gap between the high-energy modes dominated by the vibrations of O atoms above 250 cm−1 and the lower-energy modes below 16052


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The Journal of Physical Chemistry C 180 cm−1. In contrast, within this energy range, there are vibration modes in BiCuSO dominated by sulfur vibrations. These characteristics can also be highlighted by plotting the cumulative spectral weight of the different atoms as a function of the frequency (see Figure S1). For both compounds, the acoustic vibrations at the Brillouin zone boundary have much lower energies in the Γ−Z direction than in other directions. Close to the Z high-symmetry point, the transverse acoustic branches significantly flatten and are at the origin of a shoulder (labeled A) in the DOS at 30−35 cm−1, which mainly involves Bi atoms. In both compounds, the second shoulder (labeled B) in the DOS at 50−60 cm−1 is due to (i) the two lower optic modes (of Eu and Eg symmetry at Γ point) around the Γ and Z points, (ii) the flattening of the longitudinal acoustic mode around Z and in the Z−R direction, and (iii) the flattening of the transverse acoustic modes around the X and R points. The last contribution is by far the most important and involves mainly the Bi atoms, whereas the first two contributions involve mainly both the Cu and Bi atoms. In the case of the first intense peak (labeled C) between 70 and 75 cm−1, the largest contribution is coming from Cu and Se in the case of BiCuSeO and from Cu in the case of BiCuSO combined with a significant contribution from Bi in both cases. For the next peaks at 85−95 cm−1 (labeled D), the main contributions are coming from Cu and Bi atoms. It is difficult to see what the main phonon branches contributing to these peaks are, but in Figure 5, one can see that some phonon branches are flattening along the X−M and R−A directions for both compounds. The next peak (labeled E) of the phonon DOS of both compounds at 140−150 cm−1 involves mainly Bi atoms. In the case of BiCuSO, it clearly corresponds to the flattening along the X−M and R−A directions of the phonon branch with A1g symmetry at Γ point and is observed in the above Raman spectroscopy experiments at about 150 cm−1. By analogy to the sulfide, in the case of BiCuSeO, we can reasonably think that the same phonon branch gives the main contribution to this DOS peak despite the presence of other phonon branches in this energy region. The two next features of the DOS (labeled F) are located at very different positions in both compounds: at 160 and 180 cm−1 for BiCuSeO and at 200−220 and 275 cm−1 for BiCuSO. In both cases, chalcogen atoms are mainly involved with some contribution from Cu. The higher-energy peak at 180 (BiCuSeO) and 275 (BiCuSO) cm−1 is mainly due to the quite flat phonon branch with A1g symmetry at Γ point, which strongly depends on the chalcogen atom and was observed in Raman spectroscopy experiments. Above 300 cm−1, the DOS is mainly due to O atoms and the different phonon branches are highly dispersive, as already noted by Shao et al.17 who showed that these optical branches have a significant contribution to the thermal conductivity. The large peak (labeled G) observed in the DOS between 350 and 365 cm−1 is due to the flattening around X and R and along the Γ−Z direction of the high-energy phonon branches with B1g symmetry at Γ point. 5.2. Neutron Diffraction, Thermal Expansion, and Debye−Waller Factors. To have better insight into the dynamics of the different atoms in BiCuSeO through their Debye−Waller factor, we have studied the structural properties at low temperature by neutron diffraction. The detailed results of the Rietveld refinements are given in the Supporting Information (Figures S2−S7 and Table S4). From the thermal variation of the lattice parameters of BiCuSeO (see Figure S4 of SI), we have determined the thermal expansion close to the room temperature by linear fitting of the

lattice parameters from 240 to 300 K. The thermal expansion coefficients along the a-direction and along the c-direction are αa = 24.9 MK−1 and αc = 17.6 MK−1. The volume thermal expansion and the linear thermal expansion are αV = 67.4 MK−1 and αlin = αV/3 = 22.5 MK−1, respectively. We can compare these results with the thermal expansion extracted from the thermal variation of the lattice parameters of Vaqueiro et al.,16 αa = 25.7 MK−1 and αc = 21.2 MK−1, obtained by the powder neutron diffraction experiments on BiCuChO compounds between room temperature and 700 K. From their data, one also obtains αV = 72.6 MK−1 and αlin = 24.2 MK−1, values that are larger than ours. The thermal expansion of BiCuSeO is thus rather anisotropic and quite large. From the Vaqueiro’s data,16 one can as well determine the thermal expansion of BiCuSO and one finds αa = 24.96 MK−1 and αc = 22.94 MK−1. This is the same order of magnitude as for BiCuSeO but less anisotropic. Typically, for most of the semiconducting materials, αlin is smaller than 20 MK−1.50,51 The thermal expansion of BiCuSeO is much larger than that observed in most of the thermoelectric materials.51−53 Through the large corresponding Grüneisen parameter, it constitutes the signature of a large anharmonicity in this compound, which could explain its low thermal conductivity, as discussed in several theoretical papers predicting large Grüneisen parameters for BiCuSeO.14−17,21 Even in rather anharmonic thermoelectric materials such as PbTe, the linear thermal expansion αlin = 20 MK−1 is smaller than in BiCuSeO.52,53 To the best of our knowledge, among the thermoelectric materials, only β-Cu2Se and α-Cu2Se have similar linear thermal expansion (αlin ∼ 20−25 MK−1).54,55 Larger thermal expansion can be found only in highly anharmonic and ionic compounds such as NaCl (αlin ∼ 40 MK−1).51 A better insight into the magnitude of the anharmonicity of a material can be obtained from the estimation of its Grüneisen parameter. In the case of anisotropic materials such as BiCuChO, the Grüneisen parameters can be determined for the different directions using51 Γi =

V CP

∑ Cikαk k

with V the volume per mole, CP the heat capacity, Cik the elastic constants, and αk the thermal expansion coefficient along the different directions. As the elastic constants Cik have not been measured to date, we used our calculated elastic constants together with the measured heat capacity CP38 and the thermal expansion from this work and the Vaqueiro’s work.16 This will enable us to estimate the order of magnitude of the Grüneisen parameters Γi for both compounds. One finds Γa = 2.96 or 3.13 and Γc = 2.22 or 2.41 for BiCuSeO using our thermal expansion values or those of Vaqueiro et al.,16 respectively. In the case of BiCuSO, one finds Γa = 3.49 and Γc = 2.76. These values are rather anisotropic and quite large (especially for the adirection). When the experimental bulk modulus B is known, as is the case for BiCuSeO and BiCuSO,28 the experimental average thermodynamic Grüneisen parameter can be calculated using Γexp = BVαV/CP, where αV is the volume thermal expansion. In this case, one finds Γexp = 2.27 or 2.45 using our thermal expansion values or those of Vaqueiro et al.,16 respectively. In the case of BiCuSO, one finds much larger Γexp = 3.79. These values are much larger than in most of the thermoelectric materials, including those with quite low thermal conductivity.50,53,54,56 This supports once more the idea that 16053


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The Journal of Physical Chemistry C there is large anharmonicity in these compounds. We find very good agreement with the different calculations reported in the literature for the average Grüneisen parameter for which ∼2.5 was found in the case of BiCuSeO15,17,23 with the exception of the Saha’s calculations (1.8−1.9).14,19 The present values of the Grüneisen parameters are much larger than the experimental estimation of ∼1.5 for BiCuSeO made previously using a more approximated relation and which did not consider the optical phonons.26 We also note that the anisotropy of our experimental thermal expansion αa/αc is 1.415 and the anisotropy of our estimated Grüneisen parameters Γa/Γc is 4/3. Note that the same anisotropy is found for the thermal conductivity (κa/κc > 1), which has been measured on textured samples by Sui et al.11 This is unexpected from a simple phenomenological model such as the Slack model; the thermal conductivity is proportional to Γ−2.53,56 However, the influence of grain boundaries on textured polycrystalline samples consisting of platelet grains could be larger than the intrinsic contribution to the anisotropy. Therefore, anisotropic thermal conductivity values measured using single crystals would be useful to get a better understanding of this discrepancy. Note, however, that if we use the experimental average Grüneisen parameter obtained above by us or evaluated from the Vaqueiro’s data,16 one can find κav = 1.95 and 1.68 W/m K, respectively, for BiCuSeO. For BiCuSO, one finds κav = 0.92 W/m K. These values are in reasonable agreement with the experimental data of thermal conductivity for BiCuSe1−xSxO.38 Now, we will focus on the temperature dependence of the atomic displacement parameters (ADPs) in BiCuSeO and will compare them to the ADPs in BiCuSO (from ref 16) along with those obtained from our DFPT calculations. From the lowtemperature powder neutron diffraction experiments on BiCuSeO, we have determined the orientational ADPs, Uij, and found that they are almost isotropic in the case of Se atoms but significantly anisotropic for the other atoms. The results are reported in Figure 6 together with results from our DFPT calculations. Our experimental results agree well with the prior results reported by Vaqueiro et al., who obtained isotropic ADPs, Uiso, in BiCuChO for high temperature range16 (see the SI for the comparison). There is rather good agreement between our experiments and our calculations for the values of the ADPs of the different atoms with the Uij of Cu being much larger than

that of the other atoms. However, we note that the U33 of Bi is slightly smaller than that of the other atoms in contrast with the experiments where it is found close to the U33 of Se and larger than the U33 of O. Also, in contrast with the experiments, the calculations predict that U33 is larger than the U11 for the case of Cu. These differences could be due to, e.g., defects and strains, and a more detailed analysis could be done only by analyzing data from single-crystal diffraction experiments. In the case of BiCuSO, our calculated isotropic ADPs Uiso agree rather well with the experimental Vaqueiro’s data16 as for the case of BiCuSeO. The anisotropy of the calculated ADPs Uii is similar in BiCuSO and in BiCuSeO (see the Supporting Information). In both compounds, above 500−600 K in the experimental Vaqueiro’s data,16 there is a deviation from the linear behavior expected with the quasiharmonic model for all atoms and more particularly for the Cu atoms. This could be a sign of the significant anharmonic behavior in these materials. Indeed, Safarik et al. have found similar high-temperature behavior of the ADPs when considering an anharmonic Morse potential well.57 For the different BiCuChO compounds, Vaqueiro et al.16 analyzed the thermal variation of their experimental ADPs using the Einstein model. Thus, we have also analyzed our experimental data for BiCuSeO using both Einstein and Debye models. The results are given in the Supporting Information. From the fit of our experimental data with these models, it was not possible to determine whether the Einstein model was better than the Debye model. When doing the same analysis with ADPs calculated from DFPT, one finds that the Debye model is better for all atoms and in particular for atoms with heavier masses. In both cases, one finds that the Einstein or Debye energy of Cu is always larger than that of Bi atoms and smaller than that of Se atoms (see SI, Table S5). For Bi (Cu) atoms, the Einstein temperatures are θE = 105 (125) and 83 (112) K for x/y and z directions, respectively. These values obtained for Cu atoms are much larger than those reported by Vaqueiro et al.16 and correspond well to the energy range in which the vibrational contribution of Cu is important in the phonon DOS. Vaqueiro et al. have interpreted the rather large values of the ADPs of the Cu atoms as a signature of some kind of rattling modes due to Cu atoms.16 We do not agree with this interpretation. Large ADPs do not necessarily mean that the corresponding atoms behave as rattling atoms. For some detailed discussion of the rattling picture in the case of materials with crystal structure containing cages such as skutterudites or clathrates, see ref 59. Typically, in other thermoelectric materials without rattling atoms, similar values as in BiCuSeO have been found for both the ADPs and for the Einstein temperatures that can be extracted from the fit of the ADPs. ZnSb is a recent example of such material with much higher lattice thermal conductivity (about 2−3 W/m K at RT)53,58 than in pure BiCuSeO (∼1 W/m K at RT).10−12 Some of the authors have observed rather large ADPs for Zn,53 which are similar to those obtained for Cu in BiCuSeO. Also, Einstein temperature of ∼130 K was estimated,53 which is only slightly larger than the values found here for BiCuSeO. However, there is no rattling atom in ZnSb and there is no indication that the situation could be different in the case of BiCuSeO. More importantly, it was even established some time ago using both DFT and inelastic neutron scattering experiments that there is neither rattling nor localized modes in the filled skutterudites LaFe4Sb12 (that was previously described as an archetypal system with rattling modes),59 which has been recently confirmed by measurements

Figure 6. Comparison between the thermal variation of experimental anisotropic atomic displacement parameters obtained from Rietveld refinement (symbols) and anisotropic atomic displacement parameters calculated with DFPT (lines). 16054


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Figure 7. Thermal variation of the experimental CP (symbols) and calculated CV (lines) heat capacities of BiCuSeO and BiCuSO (left); the same data plotted in a Debye plot (right).

of its dispersion curves, and finally “true” localized modes or rattling modes exist only in few cage materials.60 Clearly, rather large ADPs values do not constitute a fingerprint of the presence of rattlers. Finally, we note that the sound velocities and Debye temperature for both compounds are only slightly smaller than in ZnSb, a compound where the thermal conductivity is about 2−4 W/m, 53 and thus several times larger than in BiCuSeO.10−12 Moreover, the shape of the phonon dispersion curves is very similar including the energies of the low-energy optical modes, except in the G−Z direction where the acoustic phonons at the zone boundary are located at much lower energy. Therefore, the difference between both kinds of compounds is most probably related to significantly larger anharmonicity in BiCuChO than in ZnSb as indicated by the much larger thermal expansion and Grüneisen parameters in the oxychalcogenide compounds. 5.3. Heat Capacity. The calculated heat capacities of both compounds, BiCuSeO and BiCuSO, are compared in Figure 7 with experimental data.38 Above 50−100 K, the calculated heat capacity at constant volume CV is significantly smaller than the experimental heat capacity at constant pressure CP. The large thermal expansion, αV, of these compounds could be at the origin of these difference as CP − CV = αV2 V B T, where B is the isothermal bulk modulus, V is the volume of the unit cell, and T is the temperature. We can obtain a rough estimate of CP − CV by neglecting the temperature dependence of B and using the experimental value at room temperature from Zhang et al.28 In the case of BiCuSeO, it leads to 4.6 < CP − CV < 5.3 J/mol K at room temperature using αV from our neutron diffraction data (lower bound) or from the data reported by Vaqueiro et al.16 (upper bound). Although these values are a rough estimate, they are in reasonably good agreement with the difference observed in Figure 7 between CV and CP as CP (experiment) − CV (DFT) = 7.63 J/mol K at room temperature. At low temperatures, when plotting the heat capacity as a Debye plot (C/T3 vs T), we find a very good agreement between our calculations and the experiment in the case of BiCuSeO and only a qualitative agreement in the case of BiCuSO. In both cases, one finds a maximum at 15−17 K, which is mainly due to the low-energy optical modes observed both in our Raman and infrared spectroscopy experiments.

absorption experiments on BiCuSeO and on BiCuSO. All of the six infrared-active modes predicted for both compounds are observed. The assignment of the different modes was made by comparing experiments and DFPT calculations. For the BiCuSe1−xSxO solid solutions, DFPT calculations within the VCA of the phonons at Γ point were performed. The highenergy Raman-active A1g mode strongly depends on the chalcogen content. We have also performed DFPT calculations of the dielectric constants, the elastic constants, the phonons in the full Brillouin zone, and the thermodynamic properties of BiCuSeO and BiCuSO. The origin of the different features in the phonon density of states of both compounds is described. We have determined the thermal expansion of BiCuSeO at room temperature from our neutron diffraction experiments and evaluated its thermodynamic Grüneisen parameter using our experimental thermal expansion and heat capacity and our calculated bulk modulus and found a quite large value compared to other thermoelectric materials, which confirms the large anharmonicity of BiCuSeO. The ADPs are also determined by our neutron diffraction experiments, and we have studied their anisotropy. The experimental results have agreed qualitatively with the DFPT calculations. These last calculations also agreed with the experimental isotropic ADPs determined by Vaqueiro et al.16 If the values of the ADPs of Cu atoms are rather large, they are not characteristics of rattling atoms, in contrast with what Vaqueiro et al. claim.16

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b04806. Structures of BiCuSeO and BiCuSO computed by DFT calculations; comparison of the phonon frequencies of BiCuSeO and BiCuSO obtained in this work with prior DFT calculations; normalized cumulative spectral weights of BiCuSeO and BiCuSO computed by DFT calculations; example of Rietveld refinement of the neutron diffraction data of BiCuSeO at room temperature; results of the Rietveld refinement of the neutron diffraction data of BiCuSeO; comparison of the atomic displacement parameters obtained by neutron diffraction with those obtained by DFT calculations and with those obtained with Einstein and Debye models (PDF)

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6. CONCLUSIONS We have reported Raman experiments on thermoelectric BiCuSe1−xSxO compounds. Among the six Raman-active modes predicted, four and three modes were observed for x ≤ 0.3 and x ≥ 0.7, respectively. We have also reported IR

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (R.V.). *E-mail: [email protected] (D.B.). 16055


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The Journal of Physical Chemistry C ORCID

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R. Viennois: 0000-0003-4542-2699 P. Hermet: 0000-0003-3384-2899 Present Address

Université Paris Est, ICMPE (UMR 7182), CNRS, UPEC, F94320 Thiais, France (C.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the Institut Laue Langevin for providing beamtime for the neutron experiments.

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Lattice Dynamics Study of Thermoelectric Oxychalcogenide BiCuChO

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