Chem. Mater. 2005, 17, 2255-2261
2255
New Quaternary Barium Copper/Silver Selenostannates: Different Coordination Spheres, Metal-Metal Interactions, and Physical Properties Abdeljalil Assoud, Navid Soheilnia, and Holger Kleinke* Department of Chemistry, UniVersity of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ReceiVed January 17, 2005. ReVised Manuscript ReceiVed February 16, 2005
BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10 were prepared by directly reacting the elements in stoichiometric ratios at 800 °C, followed by long heating between 600 and 650 °C. BaAg2SnSe4 crystallizes in the BaAg2SnS4 type, space group I222, BaCu2SnSe4 in the SrCu2GeSe4 type, space group Ama2, and Ba3Cu2Sn3Se10 in a new structure type, space group P21/n. All three structures comprise almost undistorted SnSe4 tetrahedra and pairs of the group 11 elements (M ) Cu and Ag). While both the M atoms are bonded to four Se atoms in each case, the deviations from an MSe4 tetrahedron are severe, and distinctly different within this series. BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10 are black semiconductors, with computed band gaps of 0.2, 0.7, and 1.2 eV, respectively. The experimental gaps for the former two are 0.24 and 0.48 eV, respectively. The electrical conductivities consistently decrease with increasing band gap.
Introduction Various researchers are investigating new materials for use in the thermoelectric energy conversion.1-5 There is a general consensus that thermoelectrics should be narrow-gap semiconductors comprising heavy elements,6,7 with gaps between 6 and 10 kBT, with kB ) Boltzmann constant and T ) operating temperature, and hence 0.16-0.26 eV at room temperature.8 We have recently commenced to investigate mixed-valent selenostannates (SrSn2Se49) as well as tin polychalcogenides (Sr2SnSe5,9 Ba2SnSe5,10 and Ba2SnTe511). These materials exhibit (calculated) band gaps between 0.2 and 1.2 eV. We observed the expected tendency toward smaller molecular units with increasing ratio of cation size (Sr, Ba) to anion size (Se, Te). Since extended structural units are essential for good mobility, and hence vital for thermoelec* To whom correspondence should be addressed. E-mail: kleinke@ uwaterloo.ca.
(1) Sales, B. C.; Mandrus, D.; Williams, R. K. Science 1996, 272, 13251328. (2) Chung, D.-Y.; Hogan, T.; Brazis, P.; Rocci-Lane, M.; Kannewurf, C.; Bastea, M.; Uher, C.; Kanatzidis, M. G. Science 2000, 287, 10241027. (3) Venkatasubramanian, R.; Slivola, E.; Colpitts, T.; O’Quinn, B. Nature 2001, 413, 597-602. (4) Hsu, K. F.; Loo, S.; Guo, F.; Chen, W.; Dyck, J. S.; Uher, C.; Hogan, T.; Polychroniadis, E. K.; Kanatzidis, M. G. Science 2004, 303, 818821. (5) Chung, D.-Y.; Hogan, T. P.; Rocci-Lane, M.; Brazis, P.; Ireland, J. R.; Kannewurf, C. R.; Bastea, M.; Uher, C.; Kanatzidis, M. G. J. Am. Chem. Soc. 2004, 126, 6414-6428. (6) Rowe, D. M. CRC Handbook of Thermoelectrics; CRC Press: Boca Raton, FL, 1995. (7) DiSalvo, F. J. Science 1999, 285, 703-706. (8) Sofo, J. O.; Mahan, G. D. Phys. ReV. 1994, B49, 4565-4570. (9) Assoud, A.; Soheilnia, N.; Kleinke, H. Chem. Mater. 2004, 16, 22152221. (10) Assoud, A.; Soheilnia, N.; Kleinke, H. J. Solid State Chem. 2005, 178, in press. (11) Assoud, A.; Derakhshan, S.; Soheilnia, N.; Kleinke, H. Chem. Mater. 2004, 16, 4193-4198.
trics, we are interested in working with smaller cations, while retaining heavy elements. This might be achieved by adding Cu+ (or Ag+) cations into the Ba/Sn/Se system, noting that high-lying d states of Cu might contribute to small band gaps. Moreover, the expected d10-d10 interaction of the coinage metals12 might lead to extended motifs with good conductivities. Also, materials based on K2BaCu8Te1013 appear to exhibit good thermoelectric properties.14 The sulfide BaCu2SnS4 is reported to crystallize in such a three-dimensional structure, with the Ba cations filling one-dimensional channels,15 and we computed its band gap to be 0.6 eV. Subsequently, we prepared the new selenides (selenostannates) BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10 with calculated band gaps between 0.2 and 1.2 eV, which are being introduced with this paper. Experimental Section Syntheses. The reactions started from the elements (Ba, 99% nominal purity, pieces, Aldrich; Cu, 99.5%, powder, -150 mesh, Alfa Aesar; Ag, 99.9995%, powder, -22 mesh; Sn, 99.8%, powder, -325 mesh, Alfa Aesar; Se, 99.8%, powder, -200 mesh, Aldrich), with masses of all elements combined of around 500 mg. The isoelectronic compounds BaCu2SnSe4 and BaAg2SnSe4 were prepared during attempts to form the Se variants of the sulfides BaCu2SnS4 and BaAg2SnS4. The new compound Ba3Cu2Sn3Se10 was first found as one of two major products (besides Cu2SnSe316) in a reaction starting from the elements in a ratio of 1Ba:2Cu:2Sn:6Se. (12) Pyykko¨, P. Chem. ReV. 1997, 97, 597-636. (13) Zhang, X.; Park, Y.; Hogan, T.; Schindler, J. L.; Kannewurf, C. R.; Seong, S.; Albright, T.; Kanatzidis, M. G. J. Am. Chem. Soc. 1995, 117, 10300-10310. (14) Patschke, R.; Zhang, X.; Singh, D.; Schindler, J.; Kannewurf, C. R.; Lowhorn, N.; Tritt, T.; Nolas, G. S.; Kanatzidis, M. G. Chem. Mater. 2001, 13, 613-621. (15) Teske, C. L.; Vetter, O. Z. Anorg. Allg. Chem. 1976, 426, 281-287. (16) Marcano, G.; Rinco´n, C.; de Chalbaud, L. M.; Bracho, D. B.; Sa´nchez Pe´rez, G. J. Appl. Phys. 2001, 90, 1847-1853.
10.1021/cm050102u CCC: $30.25 © 2005 American Chemical Society Published on Web 03/25/2005
2256 Chem. Mater., Vol. 17, No. 9, 2005 This ratio was chosen in an attempt to increase the Sn content, compared to that of BaCu2SnSe4, to increase the covalent part of the network. In each case, the elements were placed into a silica tube, which was then sealed under vacuum. The tube was put into a programmable muffle furnace. The BaM2SnSe4 samples were heated to 800 °C within 24 h, kept at 800 °C for 6 h, slowly cooled (within 100 h) to 650 °C, and then annealed at 650 °C for 100 h. Thereafter, the furnace was switched off, to allow for rapid cooling to room temperature. The temperature profile was chosen to initially exceed the expected melting points (at about 700 °C), to cool slowly through the melting points to obtain crystals, and then to anneal below the melting points to allow for homogenization. Phase-pure Ba3Cu2Sn3Se10 was obtained by using the elements in a stoichiometric ratio. The temperature profile applied was heat to 800 °C within 1 day, keep at 800 °C for 6 h, cool to 600 °C within 6 h, heat at 600 °C for 200 h, and finally finish by switching off the furnace. Our preliminary attempts to synthesize the Ag-containing variant of this new type failed. Analyses. An INEL powder diffractometer with a positionsensitive detector utilizing Cu KR radiation was used to verify the quantitative yields of BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10. Selected crystals of BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10 were investigated via energy-dispersive analysis of X-rays (EDX) using an electron microscope (LEO 1530) with an additional EDX device (EDAX Pegasus 1200). The crystals were scanned with an acceleration voltage of 21 kV under high dynamic vacuum. No heteroelements (e.g., stemming from the reaction container) were detected, and the Ba:M:Sn:Se ratios obtained could be rounded to the expected values of 1:2:1:4 and 3:2:3:10, respectively. Temperature-dependent combined differential scanning calorimetry (DSC) and thermogravimetry (TG) measurements with the computer-controlled NETZSCH STA 409PC Luxx were performed between room temperature and 700 °C starting from 25-30 mg of the phase-pure samples. The measurements were carried out under a constant flow of argon (80 mL/min), which also protected the balance (flow of 50 mL/min). The heating rate was 20 °C/min. The weight losses remained under 1% in each case. No phase transformations occurred below the melting points, whose onsets were found to be 680 °C for BaAg2SnSe4, 670 °C for BaCu2SnSe4, and 645 °C for Ba3Cu2Sn3Se10. Structure Determinations. Single crystals were studied by X-ray diffraction utilizing a Bruker Smart APEX CCD diffractometer with graphite-monochromatized Mo KR1 radiation (crystal-to-detector distance 4.550 cm), performed by scans of 0.3° in ω in two groups of 606 frames (each with an exposure time of 40-60 s) at φ ) 0° and 60°. The data were corrected for Lorentz and polarization effects. Absorption corrections were based on fitting a function to the empirical transmission surface as sampled by multiple equivalent measurements using SADABS.17 The structure solution and refinements were carried out with the SHELXTL program package.18 The lattice parameters, and systematic extinctions, indicated that BaCu2SnSe4 forms the SrCu2GeSe4 type,19 and BaAg2SnSe4 the BaAg2SnS4 type.20 Subsequent refinements confirmed these assumptions, converging to Rw(Fo2) ) 0.049 for the copper and Rw(Fo2) ) 0.073 for the silver selenide. The small Flack parameters of 0.07(1) and 0.10(2), respectively, are indicative of correctly determined absolute structures. In both (17) SAINT, version 4; Siemens Analytical X-ray Instruments Inc.: Madison, WI, 1995. (18) Sheldrick, G. M. SHELXTL, version 5.12; Siemens Analytical X-ray Systems: Madison, WI, 1995. (19) Tampier, M.; Johrendt, D. Z. Anorg. Allg. Chem. 2001, 627, 312320. (20) Teske, C. L.; Vetter, O. Z. Anorg. Allg. Chem. 1976, 427, 200-204.
Assoud et al. Table 1. Crystallographic Data for BaAg2SnSe4, BaCu2SnSe4, and Ba3Cu2Sn3Se10 refined empirical formula fw T of measurement (K) λ (Å) space group a (Å) b (Å) c (Å) β (deg) V (Å3) Z µ (mm-1) Fcalcd (g/cm3) R(Fo)a/Rw(Fo2)b
BaAg2SnSe4
BaCu2SnSe4
Ba3Cu1.941(5)Sn3Se1 0
787.61 298(2)
698.95 298(2)
1681.02 298(2)
0.71073 I222 (No. 23) 7.1154(7) 7.4994(7) 8.3375(8)
0.71073 Ama2 (No. 40) 11.1215(13) 11.2373(13) 6.7531(8)
444.90(7) 2 27.75 5.88 0.028/0.073
843.97(17) 4 29.65 5.501 0.026/0.049
0.71073 P21/n (No. 14) 6.6246(7) 13.6012(14) 23.097(2) 94.723(2) 2074.0(4) 4 28.63 5.384 0.050/0.089
a R(F ) ) ∑||F | - |F ||/∑|F |. b R (F 2) ) [∑[w(F 2 - F 2)2]/ o o c o w o o c ∑[w(Fo2)2]]1/2.
Table 2. Atomic Coordinates and Equivalent Displacement Parameters of BaAg2SnSe4 atom
site
x
y
Ba Sn Ag Se
2a 2c 4j 8k
0 0 0 0.20515(6)
0 0 1/ 2 0.19588(5)
z
Ueq/Å2
0.19269(11) 0.32798(6)
0.01792(12) 0.01466(12) 0.04206(19) 0.01770(12)
0 1/
2
Table 3. Atomic Coordinates and Equivalent Displacement Parameters of BaCu2SnSe4 atom
site
Ba Sn Cu Se1 Se2 Se3
4a 4b 8c 8c 4b 4b
y
z
Ueq/Å2
0.35264(4) 0.21466(6) 0.24775(4) 0.55889(6) 0.38993(6)
0.13985(7) 0.72714(6) 0.22667(11) 0.88233(9) 0.88517(11) 0.35947(10)
0.01472(8) 0.01219(9) 0.02332(14) 0.01365(9) 0.01334(12) 0.01331(12)
x 1/
0 1/
4
0.12848(6) 0.07158(4) 1/ 4 1/ 4
2
cases, the M atom exhibited larger thermal displacement parameters than the other atoms, by factors between 2 and 3. While this is not uncommon for Cu and Ag sites, we refined their occupancies to check for deficiencies. The refined values of 1.008(3) for Cu and 0.996(3) for Agswithout changes in the residual valuessshow that these sites are indeed fully occupied. Thus, the high displacement parameters stem from the asymmetric environment of the Cu and Ag sites. In the case of Ba3Cu2Sn3Se10, the systematic absences (0k0 reflections absent for all odd k, h0l absent for all odd l) were indicative of the space group P21/n, centrosymmetric in accord with the Ehkl statistics. SHELXS with TREF (“direct methods”) found 18 atomic sites to which the different atoms Ba, Cu, Sn, and Se were readily assigned. Subsequent refinements against F2 converged to satisfactory residual values, e.g., Rw(Fo2) ) 0.090. Since the Cu2 atom stood out with high (albeit almost) isotropic displacement parameters, i.e., Ueq(Cu2)/Ueq(Cu1) ) 1.9, we refined its occupancy factor. That resulted in a significant deficiency, i.e., an occupancy of 94.1(5)%, and possibly insignificant decreases of the residual factors, to, e.g., Rw(Fo2) ) 0.089. We summarize the crystallographic data in Table 1, and the atomic parameters are given in Tables 2-4. Calculations of the Electronic Structures. We utilized the LMTO method (LMTO ) linear muffin tin orbital), with the atomic spheres approximation (ASA),21,22 for the electronic structure calculations. In the LMTO approach, the density functional theory is used with the local density approximation (LDA) for the (21) Andersen, O. K. Phys. ReV. 1975, B12, 3060-3083. (22) Skriver, H. L. The LMTO Method; Springer: Berlin, Germany, 1984.
Quaternary Barium Copper/SilVer Selenostannates
Chem. Mater., Vol. 17, No. 9, 2005 2257
Table 4. Atomic Coordinates and Equivalent Displacement Parameters of Ba3Cu2Sn3Se10 atom
site
x
y
z
Ueq/Å2
Ba1 Ba2 Ba3 Sn1 Sn2 Sn3 Cu1 Cu2a Se1 Se2 Se3 Se4 Se5 Se6 Se7 Se8 Se9 Se10
4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e 4e
0.54207(7) 0.97679(7) 0.46879(8) 0.53898(7) 0.54637(7) 0.45057(7) 0.44806(16) 0.5365(2) 0.70146(11) 0.30288(11) 0.03199(11) 0.30512(11) 0.29114(11) 0.76959(11) 0.46749(11) 0.76772(11) 0.90105(11) 0.53191(12)
0.14122(3) 0.96363(3) 0.85268(3) 0.33991(3) 0.16541(3) 0.81294(3) 0.55099(9) 0.44638(11) 0.35278(6) 0.23282(5) 0.17290(5) 0.96158(5) 0.25216(5) 0.05772(5) 0.01414(5) 0.44638(5) 0.15009(5) 0.30847(5)
0.22353(2) 0.10304(2) 0.41272(2) 0.90339(2) 0.04269(2) 0.24109(2) 0.79245(5) 0.04765(7) 0.28576(3) 0.95913(3) 0.18788(3) 0.28638(4) 0.34454(3) 0.34999(3) 0.09754(3) 0.97005(3) 0.01455(3) 0.11255(3)
0.02010(9) 0.02135(10) 0.02368(10) 0.01576(10) 0.01449(9) 0.01370(9) 0.0321(3) 0.0558(6) 0.01928(15) 0.01715(14) 0.01710(14) 0.01922(15) 0.01746(14) 0.01755(14) 0.01886(15) 0.01582(14) 0.01844(14) 0.01659(14)
a
Occupancy 94.1(5)%. Table 5. Selected Interatomic Distances (Å) of BaAg2SnSe4
Ba-Se Ba-Se Sn-Se
4× 4× 4×
3.4147(5) 3.4302(5) 2.5191(4)
Ag-Se Ag-Se Ag-Ag
2× 2×
2.5670(5) 2.9334(6) 3.2130(19)
Table 6. Selected Interatomic Distances (Å) of BaCu2SnSe4 Ba-Se1 Ba-Se2 Ba-Se3 Ba-Se1 Sn-Se3 Sn-Se1 Sn-Se2
2× 2× 2× 2× 2×
3.3266(6) 3.3356(5) 3.3853(5) 3.4195(6) 2.5180(8) 2.5348(6) 2.5516(8)
Cu-Se1 Cu-Se2 Cu-Se1 Cu-Se3 Cu-Cu
2.4384(10) 2.4569(9) 2.4967(9) 2.5515(9) 2.7030(14)
determination of the exchange correlation energy.23 The integrations in k space were performed by an improved tetrahedron method24 on grids of 3492 (BaAg2SnSe4), 1026 (BaCu2SnSe4), and 104 (Ba3Cu2Sn3Se10) independent k points. The crystal orbital Hamilton population (COHP) curves,25 together with the integrated COHP values (ICOHPs),26 were used to extract information about the bond strengths of selected interactions, most importantly the Ag-Ag and the Cu-Cu contacts, respectively. Physical Property Measurements. Cold-pressed bars of dimensions 6 × 1 × 1 mm were used for the transport measurements. Silver paint (Ted Pella) was used to create the electric contacts. A homemade device using a four-point method was used to determine the voltage drops ∆V over a distance of 2 mm under dynamic vacuum between 320 and 180 K. The Seebeck coefficients (thermopower) of BaAg2SnSe4 were determined with a commercial thermopower system (MMR Technologies).
Results and Discussion Crystal Structures. Since the structure types of the two new selenides BaAg2SnSe4 (BaAg2SnS4 type) and BaCu2SnSe4 (SrCu2GeSe4 type) are known, and described elsewhere,19,20 we will keep their description short. Both structures comprise BaSe8 square antiprisms with Ba-Se bonds between 3.33 and 3.43 Å (Tables 5 and 6), connected via opposite faces to linear chains running along [100] in (23) Hedin, L.; Lundqvist, B. I. J. Phys. 1971, 4C, 2064-2083. (24) Blo¨chl, P. E.; Jepsen, O.; Andersen, O. K. Phys. ReV. 1994, B49, 16223-16233. (25) Dronskowski, R.; Blo¨chl, P. E. J. Phys. Chem. 1993, 97, 8617-8624. (26) Landrum, G. A.; Dronskowski, R. Angew. Chem., Int. Ed. 2000, 39, 1560-1585.
Table 7. Selected Interatomic Distances (Å) of Ba3Cu2Sn3Se10 Ba1-Se4 Ba1-Se1 Ba1-Se6 Ba1-Se7 Ba1-Se10 Ba1-Se3 Ba1-Se3 Ba1-Se5 Ba3-Se9 Ba3-Se8 Ba3-Se8 Ba3-Se4 Ba3-Se3 Ba3-Se10 Ba3-Se10 Ba3-Se6 Ba3-Se2 Sn3-Se1 Sn3-Se4 Sn3-Se3 Sn3-Se5 Cu2-Se10 Cu2-Se8 Cu2-Se8 Cu2-Se6
3.3040(9) 3.3483(9) 3.3717(9) 3.3857(9) 3.4235(9) 3.4385(9) 3.4405(9) 3.6902(9) 3.3044(9) 3.3503(9) 3.3597(8) 3.3710(10) 3.3728(9) 3.3742(10) 3.4584(10) 3.7845(9) 3.941(3) 2.4955(9) 2.5051(9) 2.5103(8) 2.5764(9) 2.4029(14) 2.4519(15) 2.4938(15) 3.006(2)
Ba2-Se9 Ba2-Se1 Ba2-Se9 Ba2-Se7 Ba2-Se5 Ba2-Se7 Ba2-Se3 Ba2-Se2 Sn1-Se6 Sn1-Se8 Sn1-Se2 Sn1-Se5 Sn2-Se7 Sn2-Se9 Sn2-Se10 Sn2-Se2 Cu1-Se6 Cu1-Se1 Cu1-Se4 Cu1-Se10 Cu2-Cu2
3.2699(9) 3.2808(9) 3.2841(9) 3.3351(9) 3.4345(9) 3.4352(9) 3.4579(9) 3.4923(9) 2.5065(9) 2.5258(9) 2.5606(9) 2.5652(9) 2.4941(8) 2.4976(9) 2.5347(8) 2.5795(9) 2.3682(13) 2.3797(13) 2.3872(13) 2.9047(15) 2.652(3)
BaAg2SnSe4 and [001] in BaCu2SnSe4 (Figure 1). The smaller cationic elements, Cu, Ag, and Sn, are 4-fold coordinated, wherein only the SnSe4 tetrahedra are quite regular. The MSe4 polyhedra are pairwise interconnected, and isolated SnSe4 tetrahedra connect them via corner-sharing to a three-dimensional network. As discussed for BaCdSnS4,27 one can describe these structures as TlSe28 variants. The new structure type of Ba3Cu2Sn3Se10 is more complex than the structures of BaM2SnSe4. It shares in part the local coordination spheres, namely, the SnSe4 tetrahedra, and the 4-fold coordination of the Cu atoms. On the other hand, the three independent Ba atoms show irregular coordination by seven (Ba1, Ba3) and eight (Ba2) Se atoms, if only bonds 1 eV, reasonable conductivity of appropriately n- and p-doped BaAg2SnSe4 may be expected. The calculation of the electronic structure of BaCu2SnSe4 reveals this material to be a direct semiconductor with Egap ) 0.7 eV. Again the lowest unoccupied states have mostly Sn s character, two bands in this case (Figure 6) because of the two Sn atoms in the primitive cell, and the valence band between -5.5 and 0 eV is dominated by Cu d and Se p states. Compared to that of BaAg2SnSe4, the highest occupied band is very flat, disadvantageous for high (p-type) conductivity. With respect to the CuII discussion, we note that all Cu d bands occur below the Fermi level, indicative of CuI. Their maximum contribution is closer to the Fermi level than in (32) Jepsen, O.; Andersen, O. K. Z. Phys. 1995, 97, 25. (33) Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry in Solids; Clarendon Press: Oxford, U.K., 1972.
Figure 6. Densities of states (left) and band structure (right) of BaCu2SnSe4. The Sn 5s contributions are emphasized via the fat band representation.
Figure 7. Densities of states (left) and band structure (right) of Ba3Cu2Sn3Se10. The Sn 5s contributions are emphasized via the fat band representation.
the Ag compound, namely, around -1.5 eV instead of -4.5 eV. The largest gap of these selenides is found in Ba3Cu2Sn3Se10 with Egap ) 1.2 eV (Figure 7). The empty conduction band consists of 12 Sn s bands, in accord with the 12 Sn atoms per unit cell. This gap is too large for thermoelectric applications. Qualitatively one understands that Ba3Cu2Sn3Se10 exhibits the largest gap, namely, because of its highest Ba content (16.7 atom %, compared to 12.5 atom % in BaM2SnSe4). BaAg2SnSe4 has a smaller band gap than BaCu2SnSe4 because of the one disperse Ag-Se band at the top of the conduction band, hence caused by the crystal structure. The two Cu-Cu contacts of 2.65 and 2.70 Å as well the Ag-Ag contact of 3.21 Å (dashed lines in Figure 4) are all on the order of twice the respective Slater radii (rCu ) 1.35 Å, rAg ) 1.60 Å34). Therefore, they most likely correspond to bonding interactions, but not to regular single bonds, which would be significantly shorter. To verify whether the M-M contacts are bonding, we plotted their crystal orbital Hamilton populations (Figure 8). While some antibonding states are filled, in particular in the case of BaCu2SnSe4, the filled bonding states outweigh the antibonding ones in all three (34) Slater, J. C. J. Chem. Phys. 1964, 41, 3199-3204.
2260 Chem. Mater., Vol. 17, No. 9, 2005
Assoud et al.
Figure 8. Crystal orbital Hamilton populations for the M-M interactions of BaAg2SnSe4 (left), BaCu2SnSe4 (middle), and Ba3Cu2Sn3Se10 (right).
Figure 9. Electrical conductivity measurements of BaAg2SnSe4 (left) and BaCu2SnSe4 (right).
M-M interactions. Despite formally being closed-shell (d10-d10) interactions, this finding is not surprising because of the hybridization with the energetically higher lying s and p orbitals.35,36 Their integrated COHP values (ICOHPs)26 are significant, with -0.24 eV for the Ag-Ag bond, -0.32 eV for the Cu-Cu bond of BaCu2SnSe4, and -0.75 eV for the Cu-Cu bond of BaCu2SnSe4 (noting that negative energies correspond to bonding interactions). Since these M-M bonds have very little, if any, contribution at the vicinity of the Fermi level, their existence has little impact on the band gap sizes. Moreover, an analysis of the ICOHP values of the different M-Se interactions is instructive. The ICOHPs for the two shorter Ag-Se bonds (2.57 Å, -1.85 eV) are almost 3 times higher than those of the longer ones (2.93 Å, -0.63 eV), supporting the proposed [2 + 2] coordination of the Ag atom. Similarly, the two different kinds of Cu-Se distances in Ba3Cu2Sn3Se10 (
