Jan
Rothballer
a,
Frederik
Bachhuber
ab,
Stefan M.
Rommel
a,
Tilo
Söhnel
*bc and
Richard
Weihrich
*a
aUniversität Regensburg, Institute of Inorganic Chemistry, Universitätsstraße 31, 93040 Regensburg, Germany. E-mail: richard.weihrich@ur.de; Web: http://www.uni-regensburg.de/chemie-pharmazie/anorganische-chemie-weihrich/ Fax: +49-941-943-4983
bSchool of Chemical Sciences, The University of Auckland, Private Bag, 92019, Auckland, New Zealand. E-mail: t.soehnel@auckland.ac.nz; Web: http://www.science.auckland.ac.nz/people/t-soehnel
cCentre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University, Auckland, New Zealand
First published on 29th August 2014
The solid solution In2−xSnxCo3S2 is attractive due to a variety of interesting properties depending on the In/Sn content, i.e. half metal ferromagnetic Sn2Co3S2, low dimensional metal In2Co3S2, and semiconducting thermoelectric InSnCo3S2. For the latter, crystal structure effects and a metal to insulator transition are not only related to electron counting but also to ordering of In and Sn within and between Co Kagomé nets. These observations have not been adequately understood to date. The degree of ordering is now evaluated from neutron diffraction data to distinguish In and Sn. The origin and effects on crystal and electronic structures are studied by DFT calculations on a superstructure model. Relations of local bonding (electron localization function ELF and Bader's AIM theory), In/Sn site preference, crystal structure distortions, and the opening of the gap are explored. Results are generalised from predictions on isoelectronic compounds.
The behaviour of the mentioned A2Co3S2 compounds is ostensibly understood by electron counting. For InSnCo3S2 (46 valence electrons, VE), the Fermi energy (EF) is found in a band gap. For the pure A = In (45 VE) and Sn (47 VE) compounds, it is shifted above or below EF and causes metal and magnetic properties. However, in case of InSnCo3S2 the semiconducting properties were not only found to be sensitive to electron counting. Due to DFT calculations ordering of In and Sn on crystallographic sites between and within the Co Kagomé lattices opens and closes the gap.11 A completely ordered semiconducting ground state is predicted to be preferred in energy by 0.11 eV with respect to the ordered metallic state. This prediction is in line with the observation of semiconducting and thermoelectrical properties.7,8 However, non-Vegard like behaviour of crystal structure data, trigonal distortion in the solid solution In2−xSn2Co3S2, and 119Sn-Mößbauer spectroscopy on powder samples indicate incomplete ordering and site preference for In and Sn.11 These observations are not yet understood and raise the question on the real structure and origin and effects of partial In/Sn disorder on electronic and crystal structure in InSnCo3S2. If a general principle applies, substitution effects should allow for a systematic design of novel exciting HAP compounds.
As In and Sn cannot be distinguished by X-rays, high resolution neutron powder diffraction measurements were performed as the method of choice on the ECHIDNA instrument at the OPAL reactor12 on In2Co3S2, InSnCo3S2, and Sn2Co3S2. From refined diffraction data a supercell model was obtained for DFT modelling. The origin of crystal and electronic structure effects on bonding of In and Sn were analysed in direct space using the Electron Localization Function (ELF)13 and Bader's theory of atoms in molecules (AIM).14 Special attention is spent on the question of multicenter metal bonds as found for Laves phases.15 Finally, effects on crystal structures and band gaps upon substitution are probed by DFT modelling to conclude on general rules for novel promising materials.
In2Co3S2 | InSnCo3S2 | Sn2Co3S2 | |
---|---|---|---|
Diffractometer | Echidna | ||
Temperature [K] | 298 | 298 | 298 |
Space group |
R![]() |
R![]() |
R![]() |
a hex [Å] | 5.3129(7) | 5.3124(6) | 5.3638(4) |
c hex [Å] | 13.652(2) | 13.478(2) | 13.166(1) |
a sup [Å] | 7.6384(8) | 7.6035(5) | 7.5909(3) |
α sup [°] | 88.143(1) | 88.642(1) | 89.919(1) |
Z(S) | 0.2791(3) | 0.2808(3) | 0.2818(2) |
B iso Co on 9d [Å2] | 0.68(5) | 0.51(4) | 0.49(5) |
B iso In/Sn on 3a [Å2] | 1.59(8) | 0.90(9) | 0.70(7) |
B iso In/Sn on 3b [Å2] | 1.36(9) | 0.65(8) | 0.26(6) |
B iso S on 6c [Å2] | 0.77(7) | 0.77(6) | 0.37(7) |
ρ calc [g cm−3] | 7.017 | 7.175 | 7.261 |
V [Å]3 | 333.72(9) | 329.42(7) | 328.06(4) |
R p | 3.70 | 3.65 | 3.40 |
R wp | 4.83 | 4.90 | 4.62 |
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Fig. 2 (a) Hexagonal crystallographic cell (ahex, chex) and primitive supercell (asup, αsup), (b) occupation of 75% of A1 sites by In, (c) of 75% A2 sites by Sn. |
Occupation scheme | SI | SII | SIII | SIV | SV |
---|---|---|---|---|---|
In on 3a [%] | 100 | 75 | 69(4) | 25 | 0 |
In on 3b [%] | 0 | 25 | 31(4) | 75 | 100 |
R p | 3.78 | 3.67 | 3.67 | 3.88 | 4.15 |
R wp | 5.08 | 4.94 | 4.93 | 5.20 | 5.68 |
Mixed occupation of In and Sn on inter-A1 and intralayer A2 sites in InSnCo3S2 is modelled within a trigonal supercell (Fig. 2a–c). It is obtained by a klassengleiche supergroup-relation from the crystallographic cell by doubling the ahex axis (ahsup = 2 × ahex).6 The related primitive cell pictures the 8-fold perovskite-related superstructure of the HAP concept4,9 as deduced from antiperovskites like MgNi3C.11,24 The trigonal distortion therein is reflected by the deviation of the supercell angle αsup = 90° for Sn2Co3S2 to 88° for In2Co3S2. The primitive A site substructure is now split into two A1 sites, i.e. 1a (0,0,0) and 3d (0,0,1/2), and two A2 sites, i.e. 1b (1/2,1/2,1/2) and 3e (1/2,0,1/2). In the hexagonal setting A1 sites are 3a and 9e (1/2,0,0), and A2 sites 3b and 9e (1/2,0,1/2). The occupation of A1 and A2 sites by In and Sn is modelled similar to partial substitution in the solid solution In2−xSnxCo3S2 (x = 1/4, 3/4, 1¼, 1¾).6 However, here we focus on the effect of A site occupation for the InSnCo3S2 composition. According to the refinements a scheme with 75% Sn on A2 and 75% In on A1 sites (SII, Fig. 2b and c) serves as an appropriate model with R values close to the SIII scheme, while the opposite occupation (SIV) is less preferred.
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Fig. 3 Electronic band structure for different supercell occupation schemes (SV, SIV–SII, SI from left to right). |
One can conclude now on the relation of A site occupation and the closing of the gap looking again at the electronic structures of Sn2Co3S2, InSnCo3S2, and In2Co3S2 (Fig. 4). At first sight, semiconducting behaviour of InSnCo3S2 (46 VE) is only the result of Fermi level shifting. In Sn2Co3S2 (47 VE, type IA HFM) one electron per formula unit is found in a conduction band like state which is completely spin polarized in the electronic ground state. The resulting characteristics of a semiconductor for one spin channel and a metal for the second is interesting for spintronics.25
InSnCo3S2 has one electron less. The Fermi energy (EF) is shifted into the gap for both spin channels. This is only true for preferred occupation of In on A1 sites. On A2 sites they cause metallic behaviour as previously seen. Accordingly, for In2Co3S2 not only a shift of EF below the gap is observed, but also a closing of the gap due to an electronic structure distortion. This was not understood from partial substitution of Sn by In.6 With the new results, one must conclude that the gap is not closed when In partially occupies A2 sites and Sn the A1 sites. As a content of 75% Sn on A2 sites keeps the gap open it seems mandatory that continuous Sn–Co–Sn–Co chains are maintained within the Co layers.
Next, the relations of A site occupation and crystal structure distortions are addressed by comparison of experimental data4,8 for In2Co3S2, InSnCo3S2, and Sn2Co3S2 with DFT predictions for ordered schemes of InSnCo3S2. According to the results (Fig. 5, see also ESI†) the asup and chex lattice parameters are continuous functions of In/Sn ordering on A1 and A2 sites that explain the kink of the curves.4,8 The experimental parameters deviate from values predicted for the fully ordered semiconducting SI scheme, but they are close to the results for the SII model. Towards the SIV and SV schemes calculated lattice parameters are closer to values known for Sn2Co3S2. Thus, replacing Sn by In causes huge changes in chex and ahex on the A1 site, but only minor effects on the A2 site. Similarly, a large contraction of chex and an enlargement of ahex are found, when In1 in In2Co3S2 is replaced by Sn. When all A2 sites in InSnCo3S2 are occupied by Sn, a contraction of the ahex axis is predicted (S1). Predicted structures are thus similar to In2Co3S2 for A1 = In, but similar to Sn2Co3S2 for A1 = Sn. One must conclude that the trigonal distortion is mainly driven by the A1 site. A1 = In causes longer chex and shorter ahex axis, A1 = Sn the contrary. A hint on the responsible bonds is given as ahex = 2dA2–Co = 2dCo–Co determines metal distances within the Kagomé layers, while the chex axis mainly affects the interlayer metal distances dA1–Co.
![]() | ||
Fig. 5 Lattice parameters from neutron data (square symbols) and DFT optimizations (stars) for InSnCo3S2 (SI, SII, SIV, and SV), compared to earlier XRD data from23 (triangles) and8 (circles) for In2−xSnxCo3S2 are shown for the asup (top) and the chex axes (below). |
Metal A–Co bonds appear thus significant in InSnCo3S2 similar to Laves phases.15 Further, ionic A–S interactions must be considered to explain the found results. ELF valence maxima in Fig. 6 appear overloaded for Sn on A1 sites that interlink two Co3A1 tetrahedra. Within the Kagomé nets weak ELF maxima towards the Co neighbours indicate a deficit in valence electron density on A2 sites. Sn seems to have more than enough electrons for bonds on A1 sites, but In only few electrons to form bonds within the Kagomé layers.
The nature of the metal bonds is uncovered by ELF plots perpendicular to the chex axis at approx. 0.1 Å above the atomic positions of A1 and A2 (Fig. 6b, middle). They signal two 4-centre bonds to Co triangles above and below the A1 sites and six 3-centre bonds for A2 to Co neighbours within the Kagomé nets. Similar characteristics were found for Laves phases.15 Accordingly, the Co–A bonds determine crystal and electronic structure properties, as well as site preference in the shandites. On A1 sites In or Sn atoms form two sp-like hybrid orbitals and 4-centre bonds of corner shared tetrahedrons. The A1-5pz orbitals contribute to bonding here. The 5px, 5py-orbitals that point towards S neighbours are shift above EF. On A2 sites, the degenerate 5px and 5py orbitals contribute to bonding within the Kagomé nets. They are lowered in energy while 5pz is shifted above EF. The contrary behaviour of A1- and A2-5p orbitals is visualised by the crystal field like scheme in Fig. 6c. Now, the shortened chex and ahex axis are easily explained by stronger Sn–Co bonds compared to In–Co. This causes shorter chex axis for A1 = Sn and shorter ahex axis for A2 = Sn in InSnCo3S2. Concerning the band gap two effects turn out as significant: Sn has a higher core charge (50) and more valence electrons (4) than In (49, 3). The Sn-5s and 5p orbitals are lowered by 1 eV in shandites compared to A = In.11 On the A1 sites In has enough electrons for bonding with its 5pz orbital. The gap remains, when Sn is replaced by In here. On A2 sites, the degenerate In-5px,y-orbitals seemingly act as a sink for the valence band (VB). The gap to the conduction band (CB) closes. Here, the Sn-5px,y orbitals open the gap. This bonding situation is seen as the reason the for the incomplete preference site. Both, In and Sn can do the bonds on A1 and A2, but the latter is better done by Sn.
This picture is completed by an analyses according to the AIM (atoms in molecules) theory.14 In Fig. 6b (left) bond critical points (BCP) are drawn out. BCP are saddle points, i.e. (3, −1) critical points in the 3D charge density. Within the AIM theory, they indicate atomic interactions along a bond path (BP) for 2 atoms.27 Independent from the occupation scheme applied for InSnCo3S2 BCP are found for A1–Co, A2–Co, and Co–S within occupied tetragonal bipyramides Co[S2A12A22] by numerical analysis. Additional BCP are detected for S–S interactions within the unoccupied bipyramides [S2A12A22] and the shortened A2–S distance due to the shift z(S) along chex. No BCP are found for direct Co–Co or S–A1 interactions.
Extending the analysis to three dimensions, the BCP are situated on faces of zero flux surfaces (ZFS). In Fig. 7 atomic ZFS as obtained for InSnCo3S2 are related to the respective atomic coordination spheres. ZFS determine the surfaces of space filling atomic volumes. Integration of charge density therein reveals atomic volumes (Vat) and atomic charges (Qat). For the Co atoms the close S (dCo–S = 2.18 Å) and A neighbours determine the obtained tetragonally shaped ZFS. Its asymmetry is determined by distances dCo–A2 = ahex/2 and dCo–A1 = arh/2 that depend on the c/a ratio.
The ZFS of the A site atoms are clearly determined by bonding to the six Co neighbours. Additionally, the A2–S bonds (dSn2–S = 2.85 Å and dIn2–S) are mirrored by faces of the ZFS for A2 and S. For the S atoms, also three large faces point to the Co neighbours. Integrated atomic charges and volumes (Table 3) for In2Co3S2, Sn2Co3S2, and InSnCo3S2 clearly indicate a Co(0) state as expected from the linear S–Co–S coordination and the covalent [Co3S2] networks. Its atomic volume is comparable to metal Co. The charge of S (−0.6 to −0.7 e) is due to its covalent bonding to Co and ionic behaviour towards In and Sn. Concerning the A sites higher charges, but smaller atomic volumes are determined for the In than for the Sn atoms. Further, a certain disproportion between 3a (+0.75 to +0.83 e) and 3b (+0.67 to +0.70 e) sites is found for indium. In both occupation schemes (SI and SV) tin shows almost similar charges (+0.65 e to +0.69 e). The highest charge is found for In on 3a sites in the SI scheme, while it is lower in scheme SIV and In2Co3S2. Thus, the ordering in InSnCo3S2 is also related to charge balance.
Q/e− | V/Å3 | ||
---|---|---|---|
Sn2Co3S2 | Sn(3a) | 0.638 | 19.49 |
Sn(3b) | 0.646 | 19.00 | |
Co | −0.026 | 11.71 | |
S | −0.612 | 18.05 | |
InSnCo3S2(SI) | In(3a) | 0.830 | 17.54 |
Sn(3b) | 0.689 | 18.93 | |
Co | −0.046 | 11.94 | |
S | −0.686 | 18.68 | |
InSnCo3S2(SV) | Sn(3a) | 0.672 | 19.78 |
In(3b) | 0.767 | 17.47 | |
Co | −0.033 | 12.18 | |
S | −0.658 | 18.53 | |
In2Co3S2 | In(3a) | 0.752 | 18.39 |
In(3b) | 0.699 | 18.07 | |
Co | −0.035 | 12.29 | |
S | −0.670 | 16.06 |
Finally, a generalisation of structural and electronic characteristics found for InSnCo3S2 is concluded by modelling isoelectronic structures where either In or Sn in A1A2Co3S2 is substituted by A = Al, Ga, Tl, Si, Ge, Pb (Table 4). The results clearly show that in all cases semiconducting products are predicted when the main group III element is found on the A1 site and the main group IV element on the A2 site. The reduction of the cell volumes by 10% does not cause closing but larger band gaps for InSiCo3S2, InGeCo3S2, or InSnCo3O2. Inverse occupation closes the gap and causes systematically larger trigonal angles arh (and in turn large c/a values) as seen for PbInCo3S2 and SnTlCo3S2 similar to SnInCo3S2. Smaller band gaps are predicted for the substitution of In by Al and Ga, as well as for the substitution of S by Se. For InSnCo3Te2 a closing of the gap is predicted. These results confirm that the found behaviour of InSnCo3S2 can be generalized to isoelectonic shandites. Besides partial substitution of S by Se7 the mentioned compounds were not yet synthesised. However, the predicted data can give hints for the design of thermoelectric and related interesting properties of InSnCo3S2 based materials upon partial substitution.
A1 | A2 | Ch | V/Å3 | a rh/Å | α/° | z(S) | ΔEgap/eV |
---|---|---|---|---|---|---|---|
In | Si | S | 100.8 | 5.423 | 55.4 | 0.282 | 0.329 |
In | Ge | S | 103.9 | 5.442 | 56.2 | 0.281 | 0.300 |
In | Sn | O | 99.3 | 5.262 | 58.4 | 0.259 | 0.291 |
In | Sn | S | 110.2 | 5.472 | 57.9 | 0.280 | 0.206 |
Sn | In | S | 111.0 | 5.405 | 59.7 | 0.228 | 0 |
In | Pb | S | 114.4 | 5.522 | 58.3 | 0.277 | 0.187 |
Pb | In | S | 114.7 | 5.519 | 58.5 | 0.276 | 0 |
In | Sn | Se | 118.3 | 5.673 | 56.5 | 0.285 | 0.153 |
In | Pb | Se | 122.5 | 5.706 | 57.1 | 0.283 | 0.151 |
In | Pb | Te | 136.9 | 6.017 | 55.2 | 0.288 | 0 |
Al | Sn | S | 103.1 | 5.285 | 59.5 | 0.283 | 0.077 |
Ga | Sn | S | 104.1 | 5.281 | 60.0 | 0.283 | 0.066 |
Tl | Sn | S | 113.4 | 5.529 | 57.8 | 0.277 | 0.197 |
Sn | Tl | S | 114.2 | 5.478 | 59.2 | 0.276 | 0 |
Tl | Sn | Se | 121.3 | 5.702 | 56.8 | 0.283 | 0.163 |
Footnote |
† Electronic supplementary information (ESI) available: Supplementary information is available on VASP and CRYSTAL optimisations and obtained structures. Deposited structure data includes atomic site parameters for the supercells. CCDC 933688, 933689 and 933690. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c4ra03800b |
This journal is © The Royal Society of Chemistry 2014 |