LiSr2âxEuxGe3: Light on the Europium Site Preferences - The Journal

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LiSr2-xEuxGe3: Light on the Eu Site Preferences Eduardo Cuervo-Reyes, Christian Mensing, and Adam Slabon J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06144 • Publication Date (Web): 20 Sep 2016 Downloaded from http://pubs.acs.org on September 22, 2016

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The Journal of Physical Chemistry

LiSr2−xEuxGe3: Light on the Eu Site Preferences Eduardo Cuervo-Reyes,∗,†,‡ Christian Mensing,‡ and Adam Slabon∗,¶ Materials for Energy Conversion, EMPA-Dübendorf, Überlanderstrasse 129, CH-8600, Laboratory of Inorganic Chemistry, ETH-Zurich, Vladimir-Prelog-Weg 1, CH-8093, and Laboratory of Inorganic Chemistry, RWTH-Aachen, Landoltweg 1, D-52074 E-mail: [email protected]; [email protected]

Phone: +41 (0)58 765 49 95. Fax: –

Abstract Quaternary Li/Sr/Eu/Ge-compounds display a rich variety of structural modifications and magnetic phases. In LiSr2 Ge3 , the Sr atoms can be substituted with Eu and this leads to only one of the three structure types of the parent compound. Previous evidence indicates that in the solid solution, LiSr2−x Eux Ge3 , Sr and Eu atoms are not evenly distributed over the two inequivalent crystallographic sites. Here we present a model that accounts quantitatively for this site-preference, combining electronic structure calculations and statistical mechanics. Alongside we report on a new exemplar, LiSr1.5 Eu0.5 Ge3 , which becomes the eighth obtained within the LiSr2−x Eux Ge3 system. We also measured the magnetic susceptibility of LiSr1.5 Eu0.5 Ge3 , which shows evidence of mixed ferromagnetic and antiferromagnetic interactions. Ab initio calculations reveal that the electronic structure of LiSr2−x Eux Ge3 exhibits, beneath the intermetallic appearance, traces of a Zintl anion.

Figure 1: The crystal structure of LiSr2−x Eux Ge3 (structure type LiCa2 Ge3 ).

Its lowest energy form, known as α-LiSr2 Ge3 , adopts the LiCa2 Tt3 (Tt = Si, Ge) structure (space group Pnnm), which contains ecliptically stacked planar Ge-chains (in [tttctc]∞ conformation) running along the a direction (see Figure 1). 5 The second modification, γ-LiSr2 Ge3 , is obtained upon quenching of the reaction products; therefore, it is considered a high-temperature modification. It crystallizes in the space group Fddd and is isostructural to LiBa2 Tt3 , containing slightly puckered boat-like Ge6 -rings. 6 The third (and most recently synthesized) form, 3,4 the β LiSr2 Ge3 featuring planar Ge6 -rings, adopts the AgCa2 Si3 structure in the space group Fmmm and seems to be stabilized by a small deficit of

Introduction LiSr2 Ge3 is a polytypic compound of which three structural modifications are known at present. 1–4 ∗ To

whom correspondence should be addressed for Energy Conversion, EMPA-Dübendorf, Überlanderstrasse 129, CH-8600 ‡ Laboratory of Inorganic Chemistry, ETH-Zurich, Vladimir-Prelog-Weg 1, CH-8093 ¶ Laboratory of Inorganic Chemistry, RWTH-Aachen, Landoltweg 1, D-52074 † Materials

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lithium. Basic electronic structure analyses have shown, 3,4,7 in agreement with the trends in similar compounds, 8–10 that the α-form has rather metallic features where the extended and ecliptically stacked anions are responsible for the formation of the conduction band. On the other hand, the β and γ modifications resemble more a classical Zintl structure with a [Ge6 ]−10 polyanion (although a small overlap between HOMO and LUMO bands could not be discarded).

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age Eu-occupation than the M1 site. Occupancy fractions from the literature 3,4,7 are given in Table 1. The atomic coordination of both sites are shown in Figure 2. An explanation based on sterichindrance, which applies well to the Ca/Eu substitution, 12 is not conclusive in the present case owing to the similar size of strontium and europium. Most likely, subtle influences coming from the interplay of electronic structure and local coordination 13 also play a role here. Table 1: Fractional Eu-occupancies, p1 and p2 , of the two inequivalent crystallographic sites, M1 and M2, in LiSr2−x Eux Ge3 for each of the up to date synthesized composition, x. Entry in bold fonts corresponds to a composition reported in this article.

Figure 2: Coordination spheres of the two different crystallographic sites in LiSr2−x Eux Ge3 , M1 and M2, occupied by divalent metals. The first coordination sphere of M2 is tighter and contains less anions than the one of M1. Note that Eu (which prefers the M2 site) is slightly more electronegative than Sr.

Investigations on the Si/Ge and Eu/Sr miscibility in LiSr2 Ge3 3,4,7 have revealed that doping with Si results exclusively in the formation of the γ modification, while partial Eu/Sr replacement only gives the α-form. This trend resembles the situation found for Li(Sr/Eu)2 Si3 11 where the subtle difference in electron affinities play a similar directing role: i.e., the Sr and Si combination allows the formation of “closed-shell”alike anions, while higher content of Eu and Ge leads to structural arrangements with more delocalized electronic states. It turns out that, despite the large difference in size between Si and Ge atoms, the γ-form manages to accommodate them with no preferences over the two crystallographic sites (for all synthesized compositions LiSr2 Ge3−x Six ). In contrast with this, the much more similar cations, Eu2+ and Sr2+ , are well differentiated in the LiSr2−x Eux Ge3 solid solution. For all obtained compositions, the structure refinement indicates that the M2 site has a higher aver-

x

p1

p2

p1 /p2

0 0.06 0.25 0.50 0.61 1.43 1.82 2

0 0.02 0.08 0.18 0.19 0.60 0.86 1

0 0.04 0.17 0.32 0.42 0.83 0.96 1

0.50 0.47 0.54 0.45 0.72 0.90 1

Continuing the investigation on LiSr2−x Eux Ge3 , we were able to find a simple statistical model which describes quantitatively the differences in Eu/Sr occupation in all (up to date) obtained compositions (x = 0.06, 0.25, 0.5, 0.61, 1.43, 1.82). Presenting this model is one of the subjects of the present paper. Among the entries in Table 1, there is a newly synthesized composition, LiSr1.5 Eu0.5 Ge3 , which had not been obtained at the time when the preceding work 3 was published. Therefore, we report here its synthesis and basic characterization, for the sake of completeness. We also performed calculations of the electronic structure employing density functional theory codes. Numerical results are consistent with the site preference. The electron localizability indicator reveals small differences among the Ge-Ge bonds, suggesting an interpretation of this intermetallic compound as a relaxed Zintl-phase.


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Methods Synthesis and preparation All sample handling was performed in argon-filled gloveboxes (H2 O < 1ppm; O2 < 1ppm). This includes storage of chemicals and sealing of metal ampoules with an arc welder, too. LiSr2−x Eux Ge3 (x = 0.5) was synthesized from pure elements (lithium granules 99.9 wt% ALDRICH; europium pieces 99.9 wt% SMART ELEMENTS; strontium pieces 99.9 wt% SMART ELEMENTS; germanium lumps 99.999 wt% ALDRICH). In order to ensure high purity of starting materials, strontium and europium were redistilled twice under highvacuum conditions and transferred to the glovebox. 2.59 mmol (18.0 mg) of lithium, 3.89 mmol (340.9 mg) of strontium, 1.30 mmol (197.1 mg) of europium and 7.78 mmol (564.9 mg) of germanium were placed in a niobium (PLANSEE GmbH, Germany) ampoule inside the glovebox. The niobium ampoule was sealed and subsequently enclosed additionally in a steel ampoule by using an arc welder. This steel ampoule was enclosed inside an evacuated quartz tube and heated at 1200 K for 6 h. After the reaction, the ampoule was opened inside the glovebox for further characterization. No mass difference of the closed niobium ampoule, before and after the reaction, was detected. The product is silvery-metallic and very sensitive to air and moisture. The purity of the sample was confirmed by powder x-ray diffraction measured in transmission mode with Cu Kα1 radiation (Figure 3). Magnetic measurements were performed on selected single crystals of around 30 mg, by means of a Superconducting Quantum Interference Device (SQUID) from Quantum Design. 14 We measured the susceptibility over a temperature range from 2 K to 300 K. The reproducibility and stability of the measurement is warranted by making several temperature scans, and measuring each point of a scan several times. Statistical errors are well below 1 % of the reported average values.

Figure 3: Powder x-ray diffraction patterns of LiSr2−x Eux Ge3 (x = 0.5). Red (black) line corresponds to the calculated (measured) pattern. Note the fitting and sharpness of the measured pattern indicating that it corresponds to a single phase with europium distributed homogeneously over the whole volume. Even within the same structure type, the formation of domains with different europium content would cause a significant broadenning of the peaks, which is absent in this case. poses: 1) the estimation of the energy involved in the M1-M2 site exchange of a Sr-Eu pair and 2) analysis of the chemical bonding. We employed the modern CASTEP 15,16 package within Materials Studio. For a consistency test, we took first ultra-soft pseudo-potentials and then normconserving ones (obtaining equivalent results for the total energy difference). The calculation settings were the following. Pseudo-atomic calculations were done for the configurations Ge 4s2 4p2 , Sr 4s2 4p6 5s2 , Li 1s2 2s1 and Eu 5s2 5p6 4 f 7 6s2 . For the periodic system, we then included the Ge 4d, Sr 4d, Eu 5d and Eu 6p orbitals. Upand down-spin occupations were considered independent and each europium atom was given the 8 S7/2 configuration as initial guess. The exchange-correlation functional due to PerdewBurke-Erzenhof (PBE) 17 was used in the generalized gradient approximation. Effective eigenvalues were calculated on a Monkhorst-Pack 18 grid of 5 × 4 × 11 points in reciprocal space (equivalent to a separation of 0.02 Å−1 ). Broyden density

Computational methods Electronic structure calculations within density functional theory were employed with two pur-


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Table 2: Crystal structure data and refinement.

mixing was employed in the self-consistency algorithm, with energy tolerance of 0.5 × 10−6 eV per atom and plane wave cut-off energy of 660 eV. We complement the band structure analysis with the visualization of the chemical bonding in real space provided by the electron localizability indicator 19 (ELI-D). The ELI-D was calculated using an adaptation of Savin’s implementation for the electron localization function (ELF) 20–22 within the tight- binding linear-muffin-tin-orbitals method (TB-LMTO-ASA) 23–28 v47. Definition and interpretation of the ELI-D, and the ELF can be found elsewhere. 19,21,22,29–32 Within the LMTO method, we solved the scalar relativistic wave equation with the non-local exchange-correlation due to Langreth-Mehl-Hu. 33 Broyden mixing was used in the SCF algorithm, with a tolerance of 10−5 Ry for the total energy, 10−5 e for the atomic charges and 10−6 Ry for the Fermi energy. We took as valence basis set the muffin-tin orbitals with the following dominant character: 4s, 4p and 4d, for Ge; 2s and 2p for Li; 5s, 5p and 4d for Sr; and for Eu, 6s, 6p, 5d and 4 f . The k-space integration was done following the tetrahedral method, 34,35 on a grid of 16 × 16 × 16 points.

Empirical Formula

LiSr2−x Eux Ge3 (x = 0.5)

Formula Weight (a.u.)

432.12

Space group

Pnnm (no. 58)

Lattice parameters (Å)

a = 11.078(2) b = 11.862(2) c = 4.6170(9)

Cell Volume (Å3 ) Formula units/cell Density (g cm−3 )

606.7(2) 4 4.73

Diffractometer

APEX CCD

Radiation (λ )

MoKα (0.71073 Å)

Indices range

−16 < h < 16 −17 < k < 17 −6 < l < 6

Refined parameters

40

Results and discussion

Measured reflections

7860

Experimental characterization

Unique reflections

1173

Structure refinement

Rint

0.0313

Well-shaped single crystals were selected under the optical microscope and sealed into double walled glass capillaries under argon atmosphere. The primary tests were performed using a single crystal diffractometer equipped with a CCD detector (Bruker SMART Platform, monochrome MoKα radiation). The data were integrated with the SAINT program 36 and corrected for Lorentz factor, polarization, air absorption, and absorption due to the path length through the detector face plate. The structure was derived from direct methods. 37 Details of the X-ray diffraction experiments and data handling are presented in Tables 2 to 4. Interatomic distances are given in Table 5. The crystal structure of LiSr2−x Eux Ge3 (x = 0.5) exhibits

R1

0.0189

wR2

0.0393

Residual electron density

+1.05/−1.16

three independent crystallographic sites of germanium. These form infinite chains showing different Ge-Ge distances within the chain, which are in the range between 2.49 and 2.60 Å and indicate germanium single bonds. The shortest bonds of 2.49 Å and 2.50 Å can be found for Ge3-Ge3 and Ge2-Ge3, respectively. Ge1-Ge2 and Ge1-Ge1 display longer contact distances of 2.60 Å and 2.62


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Table 3: Coordinates (xx, y , and z , in fractions of the lattice parameters), Wyckoff position, Isotropic displacements (pm2 ), and occupancy factor of the atoms in LiSr2−x Eux Ge3 (x = 0.5). Atom

Wyckoff position x

Li M1 (Eu/Sr) M2 (Eu/Sr) Ge1 Ge2 Ge3

4g 4g 4g 4g 4g 4g

0.1409(6) 0.17853(2) 0.54977(2) 0.10973(3) 0.24572(3) 0.46764(3)

Table 4: Anisotropic displacement parameters in pm2 . U13 = U23 = 0. Atom U11

U22

U33

Li M1 M2 Ge1 Ge2 Ge3

240(30) 162(2) 114(1) 128(2) 141(2) 121(2)

250(30) 131(2) 121(1) 140(2) 148(2) 188(2)

240(30) 115(1) 124(1) 105(2) 107(2) 106(2)

y

z

Uiso

Occupancy

0.7834(6) 0.07278(2) 0.15028(2) 0.54168(3) 0.36310(3) 0.39967(3)

0 0 0 0 0 0

240(14) 136(1) 120(1) 124(1) 132(1) 138(1)

1 0.176(2)/0.824(2) 0.325(2)/0.675(2) 1 1 1

Table 5: Interatomic distances in (Å); m denotes the number of such pairs for the corresponding atom.

U12 Pair

−30(3) 9(3) 1(1) 1(1) 1(1) −1(1)

Li

d

m

Pair

d

m

Ge2 2.79(1) 2 Ge2 2.60(1) 1 Ge3 2.95(1) 2 Ge1 Ge1 2.62(1) 1 M1 3.46(1) 2 Li 2.89(1) 1

Ge3 3.30(1) 2 Ge3 2.50(1) 1 M1 Ge1 3.31(1) 2 Ge2 Li 2.79(1) 2 Li 3.46(1) 1 M2 3.17(1) 2

Å, respectively. The infinite chains running along the a direction (the Ge-polyanions) are ecliptically stacked at a typical stacking distance of 4.61 Å (the length of the b crystallographic axis). Each germanium atom appears inside a triangular prism (with cations as corners), whose rectangular faces are perpendicular to the chain-forming Ge-Ge bonds or in-plane Ge-Li branches. This is a very common arrangement in main-group metal tetrelides. Each cation in the structure is coordinated by anions from three distinct germanium chains (a situation also related to the n-glide planes being among the symmetry operations of this structure). Strontium and europium atoms on the crystallographic M2 site display shorter distances to germanium atoms than the corresponding cations occupying the M1 site. The shortest Sr/Eu-Ge distance of 3.09 Å can be found for the M2-Ge3 atoms.

Ge3 3.09(1) 1 Ge3 2.49(1) 1 M2 Ge2 3.17(1) 2 Ge3 Li 2.95(1) 2 Ge1 3.18(1) 2 M1 3.30(1) 2 while warming under 1000 Oe a sample that was previously cooled without and with magnetic field, respectively; i.e., zero-field cooled (ZFC) and field cooled (FC) samples. χ is reported in cm3 mol−1 Eu , rescaled according to the nominal Eu content from the refinement. Above 30 K, χ is accurately described with C + χ0 (1) T −θ where the first term represents the paramagnetic response from localized unpaired spins, and the second (temperature-independent), χ0 , accounts for the paramagnetic (spin) contribution of the conduction electrons and the diamagnetic orbital contribution of conduction electrons and closed shells. The effective magnetic moment per europium ion√resulting from the fit to the data, μeff = 2.82 C, (in units of the Bohr magneton) is 8.1(2) μB , which is very close to the theoretical χ=

Magnetic susceptibility The magnetic susceptibility (χ) of LiSr2−x Eux Ge3 (x = 0.5) is shown in Figure 4 as a function of the temperature, between 2 K and 300 K. Black and red points correspond to measurements done


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value (7.94 μB ) for a 8 S7/2 electronic configuration. Since europium is always found in a divalent state in germanides as well as in silicides, the accuracy of the fitted moment serves to confirm the correctness of refined europium content. The 2.5 % uncertainty of the fitted μeff comes mainly from the error propagation of the composition while the standard deviation in the susceptibility curve is negligible.

ions may be also a source of magnetic frustration. The possibility of domain formation in solid solutions may also contribute to the complexity of the magnetic response. In the present case, the behavior of χ at temperatures below its singularity (featuring a history dependent kink, with a further increase at lower temperatures) is not representative of a simple spin structure. We do not have microscopic information of this structure (e.g., neutron diffraction) at the moment. Therefore, we leave the subject of magnetic phases for future investigations.

1.0 0.9

3

-1

mol ]

0.8

[cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ZFC FC

0.8

0.6

Theoretical results

0.7

0.4

0.6 0

Statistical model for site preferences 5

10

15

In all synthesized compositions of LiSr2−x Eux Ge3 , we find that p2 ≥ p1 (see Table 1). Local coordination of atoms on sites M1 and M2 (shown in Figure 2) differ not only in geometrical arrangement but also in total formal charge. The M1 (M2) position has nine (seven) germanium atoms among its ten neighbors. The rest of the neighbors are lithium ions in both cases. As such, site M1 is surrounded by more negative charges than M2 and it is therefore expected to be a better place for a more electropositive element; i.e., strontium. In addition to this, the coordination sphere of the M2 site is slightly tighter than the one of M1, as can be seen from the interatomic distances in Table 5, fitting to the preferential allocation of a slightly smaller atom (europium). However, this are simply qualitative arguments. It should be checked whether this preference is supported by accurate calculations using currently available computational methods. Furthermore, a finite fraction of Eu atoms appear on site M1 (also for x < 1) when there are still M2 sites available. We cannot know a-priory whether this corresponds to an equilibrium distribution, or to a casual and out of equilibrium arrangement. In order to answer these questions, we develop a statistical model for the site occupancies and compare it with the experimental data, and with the results with firstprinciples energy calculations. It should be noted that although there are significant differences in the lattice parameters of the parent compounds, LiSr2 Ge3 and LiEu2 Ge3 , 3,4

T

0.2 0.0

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0

100

200

300

T [K]

Figure 4: Susceptibility (χ) vs temperature (T ) per mol of Eu. Inset: low-T magnification. The high temperature susceptibility χ0 = 6.7(3) 10−4 cm3 mol−1 simply indicates that the spin contribution of the conduction electrons dominates over the diamagnetic background. For the Weiss constant (average exchange coupling) we obtain θ = 2.38(4) K. Its positive value corresponds to a surplus of ferromagnetic interactions, but the fact that it is smaller that the temperature (Tc ≈ 9 K) at which the singularity in χ occurs indicates the presence of both positive (ferromagnetic) and negative (anti-ferromagnetic) exchange couplings between Eu-magnetic centers. 38 Evidence of different (and in some cases frustrated) exchange couplings have been previously reported in several Zintl-related europium compounds 11,39–42 and can result in complex magnetic structures. 43,44 This is highly probable for metallic systems with certain degree of disorder in the distribution of the magnetic centers, as in the present case. The triangular prismatic arrangement of europium in this type of compounds with exchange couplings mediated by the (silicide/germanide) an-


6

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the peaks in the powder XRD patterns of the solid solution are very sharp. This indicates that the formation of nano- or micro-clusters with varying composition can be neglected and we can assume that x, as well as the fractional Eu occupancies p1 and p2 = x − p1 , are good intensive variables. In the following we derive the expressions for p1 and p2 as a function of x. Later, we show that this model represents the experimental data well. Atomic positions labelled as M1 and M2 have equal multiplicity; thus, a macroscopic sample of LiSr2−x Eux Ge3 contains in average as many M1 as M2 sites. Let us call this number g; then n1 ≡ gp1 (n2 ≡ gp2 ) denotes the number of Eu atoms on M1 (M2). The total number of europium atoms in the sample, n = n1 + n2 , is n = gx, with 0 ≤ x ≤ 2. Global variables g, n1 and n1 always scale linearly with the sample size. In the thermodynamic limit, the entropy also scales linearly and the intensive variables p1 and p2 are size-independent. Thus, the actual value of g is irrelevant; g is simply an integer number formally introduced for the counting of configurations. We obtain p1 and p2 by constructing the appropriate thermodynamic potential Ω and finding the (n1 ; n2 ) set that minimizes it. As it is commonly done for macroscopic systems, we formulate our problem in the grand-canonical ensemble, which makes the derivations simpler. We need expressions for the entropy, and the energy of a (n1 ; n2 ) configuration. The number of ways in which ni sites (for europium atoms) can be chosen out of g Mi sites (i = 1, 2) is Γi =

lent cations can be neglected, which is supported in this case by the evidence of composition homogeneity. The third term in the thermodynamic potential contains the Lagrange multiplier, λ , which is introduced in the grand-canonical representation to control the europium content via the equation ∂ Ω/∂ λ = n. The effective temperature of the distribution, T ∗ , should not be the room temperature as the permutation of Sr and Eu atoms should be already frozen at higher temperatures. Since there is no structural distortion between synthesisand room-temperature, T ∗ can be anywhere in this range, probably closer to the melting point. In the macroscopic limit, one can replace the factorials with an easier to handle function using Stirling’s formula, m! ≈ (m/e)m . Solving ∂ Ω/∂ n1 = 0 and ∂ Ω/∂ n2 = 0 for p1 ≡ n1 /g and p2 ≡ n2 /g, we obtain p1 = p2 = with β ∗λ

e

1 β ∗ [λ +Δ/2]

e

+1

1 ∗ eβ [λ −Δ/2] + 1

,

(3)

,

(4)

∗ β Δ 1−x cosh (5) = x 2 ∗ 2 β Δ 1−x 2−x cosh , + + x 2 x

where β ∗ = (kB T ∗ )−1 . We find that p1 and p2 satisfy the relation

g! . (g − ni )!ni !

η≡

The multiplicity of a (n1 ; n2 ) configuration is Γ = Γ1 Γ2 , and the configurational entropy, kB ln Γ, where kB is the Boltzmann constant. For a given (fixed) x, the configuration energy will depend on the difference n1 − n2 . We can express the thermodynamic potential as

p2 (1 − p1 ) ∗ = eβ Δ , p1 (1 − p2 )

(6)

which does not contain x explicitly. This implies that if neither T ∗ nor Δ depends on the composition, η should take the same value for all x. Since there is no direct M1-M2 contact in this structure type, the permutation energy, Δ, should be in first approximation independent of the composition, x. Higher order corrections may show a small increase with the europium content due to a contraction of the interatomic distances and a similar behavior is expected for the melting point. Thus, β ∗ Δ could only depend very weakly on x. In contrast with this, the l.h.s. of Eq. (6) is a strongly varying function of its arguments, as it can be seen

Δ Ω = −kB T ∗ ln Γ + [n1 − n2 ] + λ [n1 + n2 ] . (2) 2 where Δ is the energy cost of exchanging a Sr-Eu pair on sites M1 and M2. This linear approximation is valid as long as the interaction among diva-


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energy cost Δ ≈ 0.05 eV. In order to fit the value of η obtained from the experiments, it is required that T ∗ ≈ 528 K, which falls (as it should) in the range between room- and synthesis-temperature.

from the linearized variation |δ p1 | 1 |δ p2 | 1 δη = + . η p1 1 − p1 p2 1 − p2

(7)

Complementary electronic structure analysis

This is specially relevant for close to extreme compositions. For example, a change in one percent of p2 (i.e., |δ p2 |/p2 = 0.01) around p2 = 0.9, results in a 10 % of change in η. Small uncertainties in the occupations have then a strong effect on the resulting η. This means that if the model does not represent the actual europium distribution (i.e., if Eq. (6) is not valid), a plot of η vs. x should be rather scattered. If the model is correct, the data points should appear along a horizontal line.

In contrast with many binary-, 9,39 and ternarymetal tetrelides, 38,40–44 LiSr2−x Eux Ge3 does not seem to follow the Zintl rules according to its electron count. Assigning formal valences leads to 5/3− 2+ Li1+ Sr2+ , with a lack of 1/3e per 2−x Eux Ge3 germanium atom to complete the filling of the “non-bonding” Ge-pz -states. The possibility of having Eu3+ can be excluded since the latter is a non-magnetic ion, which would be in contradiction with the magnetic response of the samples. Furthermore, all evidence in the literature indicates that europium adopts a divalent state in germanides and silicides. In Zintl compounds containing planar polyanions the highest occupied (and full) band is generally made of non-bonding orbitals 9,39–42 (the pz orbitals in our coordinate system). The metallic behavior, when present, is due to a small energyoverlap of this pz -band with the conduction band (usually formed by anti-bonding states of the Zintl anion). This overlap (closure of the indirect gap) is aided by the ≈ 1 eV of dispersion of the pz -band due to the weak σ -overlap of the pz -orbitals along the anion-stacking direction. In LiSr2−x Eux Ge3 , on the other hand, the pz bands are only partially occupied even without charge transfer to other states, placing LiSr2−x Eux Ge3 out of the Zintl group and into the (generally more complex) intermetallic phases. Yet, with an additional examination we find that LiSr2−x Eux Ge3 does show traces of a Zintl anion in a relaxed fashion. The difference of 0.13 Å (5%) in bond length made us suspect a somewhat non-even share of electrons among the Ge1-Ge1 and Ge3-Ge3 bonds. To look for a footprint of bonding differences in real-space, we computed the ELID shown in Figure 6. It displays a better defined attractor in the Ge3-Ge3 contact when compared to the worse defined features as one moves along the chain towards the Ge1-Ge1 bond. In the present context, this suggests a different balance in the occupation of the symmetric and anti-

102 101 100 10-1 0.0

0.5

1.0

1.5

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2.0

Eu content per f.u.

Figure 5: η calculated using the p1 and p2 values from the structure determination, for different refined compositions (x). The alignement of the data points indicates the validity of the statistical model. The corresponding graph η vs x obtained with the nominal compositions from Table 1 is shown in Figure 5. Error bars for η, calculated with Eq. (7) taking the δ p values from the structure refinements, are also displayed in the plot. All η values lie between 2 and 3.9 and can be considered very similar within the error margins of a strongly varying function, indicating that the data is qualitatively well represented by the statistical model. We calculated the total energy within the DFT approximation for two configurations with x = 1: one with europium on site M1 and strontium on site M2; the other with the cations exchanged. Comparing the total energies we find that europium indeed prefers the M2 site with a Sr-Eu permutation


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2 0 Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-2 -4 -6 -8 -10 Γ

Figure 6: Planar cut, covering one unit cell at z = 0, of the ELI-D calculated with all electrons. The density of colored pixels is proportional to the valence electron density. Numbers 1, 2, and 3 correspond to Ge1, Ge2, and Ge3 atoms.

ZT

YS X

UR

Figure 7: Band structure of LiSr2 Ge3 within DFT showing the valence states. The lower 12 bands are mainly derived from Ge-4s orbitals and those above -4 eV have dominant Ge-4p contribution. Notice the dispersion of the bands crossing the Fermi energy in the segments Γ−Z, T−Y and X−U indicating transport along the stacking direction. The main contribution to the transport comes from the four bands of dominant (Ge3)-4pz origin.

symmetric combinations of pz states. Therefore, this real-space indicator is suggestive of 5/3− 2+ a compromise between Li1+ Sr2+ 2−x Eux Ge3 and an alternative formal charge partitioning −2 2+ −1 Li1+ Sr2+ 2−x Eux Ge Ge2 , with a double Ge3Ge3 bond and a “closed-band” structure. This interpretation is also consistent with the oval shape in the ELF cross-section of the Ge3-Ge3 attractor found within the extended-Hückel approximation. 7 We also performed a Mulliken analysis and found that Ge3 (Ge1) is the least (most) negatively charged site in the chain, which supports the required trend for the occupation of the pz states. It is known that small polarizing cations (like Li1+ and Mg2+ ) generally prefer to branch off the most negatively charged or terminal atoms in Zintl polyanions. 7,10,11 In agreement with this, Li cations are located closer to the Ge1 and Ge2 sites than to the Ge3. It should be noted that in the cited work 7 the authors employ a different numbering scheme for the atoms, in which Ge1 and Ge3 appear interchanged. The band structure of LiSr2 Ge3 (shown in Figure 7) predicts a very anisotropic electron trans-

port, mainly along the stacking direction (indicated by the bands crossing the Fermi level mainly in the Γ−Z, T−Y and X−U segments). This is a typical feature of metallic Zintl compounds too. The block of bands between -4 eV and the Fermi energy contains 12 (mainly p-derived) bands per chain. The lower six are related to the σ -bonds along the chain; the higher six, to the “non-bonding” pz -orbitals. All the bands are actually double (see segment Γ−Z), and two fold degenerate in most of the k-space, since there are two (bond-disconnected) chains in the unit cell. The highest partially occupied band has a dominant contribution from the π ∗ (anti-symmetric) combination of neighboring Ge3pz -orbitals. The ideal case of a double Ge3-Ge3 bond would have this band completely empty. The actual situation is subtler, since there is a considerable overlap with the next (lower) band, resulting in an effective bonding order that gradually changes along


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(0 < x < 1). Z. Anorg. Allg. Chem. 2011, 637, 846-852.

the chain from highest at the Ge3-Ge3 bond to lowest at the Ge1-Ge1 bond. Mulliken bondpopulation analysis confirms this trend and the resulting charge gradient is stabilized with the surrounding cations. The europium site preference is consistent with a higher Eu-occupancy around bonds with higher effective order.

(4) Qinxing, X. Syntheses, Structures, and Properties of Multinary Zintl Phases and their Decomposition Reactions. Ph.D Dissertation 2004, ETH-Zürich, no. 15626. (5) Müller, W.; Schäfer, H.; Weiss, A. Die Struktur der Phasen Ca2 LiSi3 und Ca2 LiGe3 . Z. Naturforsch. 1971, 26, 5–7.

Summary

(6) von Schnering, H.G.; Bolle, U.; Curda, J.; Peters, K.; Carillo-Cabrera, W.; Somer, M.; Schultheiss, M.; Wedig, U. Hückel Arenes with Ten π Electrons: Cyclic Zintl Anions [Si6 ]10− and [Ge6 ]10− , Isosteric to [Si6 ]4− and [As6 ]4− . Angew. Chem. Int. Ed. Engl. 1996, 35, 984–986.

We have reported the synthesis and characterization of a new composition, LiSr1.5 Eu0.5 Ge3 , which becomes the number eight in the quaternary LiSr2−x Eux Ge3 solid solution. The powder x-ray diffraction pattern indicates a quite homogeneous composition of the reaction products. The refined x value is consistent with our interpretation of magnetic susceptibility measurements in terms of localized f 7 electrons at Eu-sites. We found a statistical model that accounts for the uneven distribution of europium over the two inequivalent crystallographic sites, in all up to date reported compositions. First-principles calculations are in good agreement with the observed site preference. The crystal and electronic structure of this intermetallic solid solution was shown to exhibit features of Zintl phases.

(7) Qinxing, X.; Nesper, R. Structural and Electronic Characterization of Eu2 LiSi3 , Eu2 LiGe3 and Eux Sr2−x LiGe3 Mixed Crystals. Z. Anorg. Allg. Chem. 2006, 632, 1743– 1751. (8) Nesper, R. Structure and Chemical Bonding in Zintl–phases Containing Lithium. Prog. Solid State Chem. 1990, 20, 1–45. (9) Cuervo Reyes, E; Nesper, R. Electronic Structure and Properties of the Alkaline Earth Monosilicides. J. Phys. Chem. C, 2012, 116, 2536–2542. (10) Wengert, S. Experimentelle und theoretische Lösungsansätze zu grundlegenden Problemen in Zintlverbindungen–planare Zintlanionen, Kationenfunktionalitäten und Aufbauprinzipien sowie eindimensionale Metallizität und Ionenleitung in festen Siliciden. Ph.D Dissertation 1997, ETH no. 12070.

Acknowledgement This work has been supported by the Swiss National Science Foundation under project no. 2-77937-10 and by the SCCER storage/mobility funds. A.S. thanks the Fonds der Chemischen Industrie (FCI).

(11) Cuervo-Reyes, E.; Slabon-Turski, A.; Mensing, C; Nesper, R. Spin-Glass Behavior and Electronic Structure of LiEu2 Si3 . J. Phys. Chem. C 2012, 116, 1158–1164.

References (1) Bolle, U.; Carillo-Cabrera, W.; Peters, K.; von Schnering, H.G. Crystal Structure of Tetrastrontium Dilithium Hexasilicide(10−), Sr4 Li2 Si6 . Z. Kristallogr., NCS 1998, 213, 689.

(12) Hyungrak, K.; Olmstead, M. M.; Klavins, P.; Webb, D. J.; Kauzlarich, S. M. Structure, Magnetism, and Colossal Magnetoresistance (CMR) of the Ternary Transition Metal Solid Solution Ca14−x Eux MnSb11 (0 < x < 14). Chem. Mater. 2002, 14, 3382–3390.

(2) Cardoso-Gil, C.; Carillo-Cabrera, W.; Schultheiss, M.; Peters, K.; von Schnering, H.G.; Grin, Y. New Examples for the Unexpected Stability of the 10π-Electron Hückel Arene [Si6 ]10− . Z. Anorg. Allg. Chem. 1999, 625, 285–293.

(13) Deringer, V. L.; Goerens, C.; Esters, M.; Dronskowski, R.; Fokwa, B. P. T. Chemical Modeling of Mixed Occupations and Site Preferences in Anisotropic Crystal Structures: Case of Complex Intermetallic Borides. Inorg. Chem. 2012, 51, 5677–5685.

(3) Xie, Q.; Cuervo-Reyes, E.; Wörle, M.; Nesper, R. Polytypism of LiSr2 Ge3 and the Solid Solutions LiSr2 Six Ge3−x and LiSr2−x Eux Ge3


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(14) Mc Elfresh, M. Fundamentals of Magnetism and Magnetic Measurements. Featuring Quantum Design’s Magnetic Property Measurement System. (Quantum Design NY 1994).

(27) Nowak, H. J.; Andersen, O. K.; Fujiwara, T, Jepsen, O.; Vargas, P. Electronic-Structure Calculations for Amorphous Solids Using the Recursion Method and Linear Muffin– Tin Orbitals: Application to Fe80 B20 . Phys. Rev. B 1991, 44, 3577–3598.

(15) Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. First–Principles Simulation: Ideas, Illustrations and the CASTEPcode. J. Phys.: Cond. Matt. 2002, 14, 2717–2744.

(28) Lambrecht, W. R. L.; Andersen, O. K. Minimal Basis Sets in the Linear Muffin-Tin Orbital Method: Application to the DiamondStructure Crystals C, Si, and Ge. Phys. Rev. B 1986, 34, 2439–2449.

(16) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I. J.; Refson, K.; Payne, M. C. First Principles Methods Using CASTEP. Z. Kristallogr. 2005, 220, 567– 570.

(29) Savin, A. The Electron Localization Function (ELF) and its Relatives: Interpretations and Difficulties. Journal of Molecular Structure: THEOCHEM 2005, 727, 127–131.

(17) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868.

(30) Silvi, B.; Savin, A. Classification of Chemical Bonds based on Topological Analysis of Electron Localization Functions. Nature 1994, 371, 683–686.

(18) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188-5192.

(31) A very informative review of the ELF and applications, as well as a very complete list of references can be found at the web page http://www.cpfs.mpg.de/ELF/ of the Max Plank Institute for Chemical Physics of Solids.

(19) Wagner, F. R.; Bezugly, V.; Kohout, M.; Grin, G. Charge Decomposition Analysis of the Electron Localizability Indicator: A Bridge between the Orbital and Direct Space Representation of the Chemical Bond. Chem. Eur. J. 2007, 13, 5724–5741.

(32) Nesper, R.; Wengert, S. Localization Patterns in Interstitial Space: A Special Property of the Electron Localization Function (ELF). Chem. Eur. J. 1997, 3, 985–991.

(20) Savin, A.; Jepsen, O.; Flad, J.; Andersen, O. K.; Preuss, H.; von Schnering, H. G. Electron Localization in Solid-State Structures of the Elements: the Diamond Structure. Angew. Chem. Int. Ed. Engl. 1992, 31, 187–188.

(33) Langreth, D. C.; Mehl, M. J. Easily Implementable Nonlocal Exchange-Correlation Energy Functional. Phys. Rev. Lett. 1981, 47, 446–450.

(21) Savin, A.; Becke, A. D.; Flad, J.; Nesper, R.; Preuss, H.; von Schnering, H. G. A New Look at Electron Localization. Angew. Chem. Int. Ed. Engl. 1991, 30, 409–412.

(34) Jepsen, O.; Andersen, O. K. No Error in the Tetrahedron Integration Scheme. Phys. Rev. B 1984, 29, 5965. (35) Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Improved Tetrahedron Method for BrillouinZone Integrations. Phys. Rev. B 1994, 49, 16223–19232.

(22) Savin, A.; Nesper, R.; Wengert, S.; Fässler, T. F. ELF: The Electron Localization Function. Angew. Chem. Int. Ed. Engl. 1997, 36, 1808–1832.

(36) Bruker AXS Inc., Madison, Wisconsin, USA.

(23) Andersen, O. K. Linear Methods in Band Theory. Phys. Rev. B 1975, 12, 3060–3083.

(37) Sheldrick, G. M. A Short History of SHELX. Acta Cryst. A 2008, 64, 112–122.

(24) Jepsen, O.; Andersen, O. K.; Machintosh, A. R. Electronic Structure of HCP Transition Metals. Phys. Rev. B 1975, 12, 3084–3103.

(38) Slabon, A.; Cuervo-Reyes, E.; Niehaus, O.; Winter, F.; Mensing, C.; Pöttgen, R.; Nesper, R. Evidence of a Mixed Magnetic Phase in EuMgGe: A Semimetallic Zintl Compound with TiNiSi Structure Type. Z. Anorg. Allg. Chem. 2014, 640, 1861–1867.

(25) Andersen, O. K.; Jepsen, O. Explicit, FirstPrinciples Tight–Binding Theory. Phys. Rev. Lett. 1984, 53, 2571–2574. (26) Andersen, O. K.; Pawlowska, Z.; Jepsen, O. Ilustration of the Linear–Muffin–Tin–Orbital Tight–Binding Representation: Compact Orbitals and Charge Density in Si. Phys. Rev. B 1986, 34, 5253–5269.

(39) Cuervo Reyes, E; Stalder, E. D.; Mensing, C.; Budnyk, S.; Nesper, R. Unexpected Magnetism in Alkaline Earth Monosilicides. J. Phys. Chem. C, 2011, 115, 1090-1095.


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(40) Slabon, A.; Mensing, C.; Kubata, C.; Cuervo-Reyes, E.; Nesper, R. Field–Induced Inversion of the Magnetoresistive Effect in the Zintl Phase Eu5+x Mg18−x Si13 (x = 2.2). Angew. Chem. Int. Ed. 2013, 52, 2122-2125. (41) Slabon, A.; Cuervo-Reyes, E.; Kubata, C.; Mensing, C.; Wörle, M.; Nesper, R. Synthesis, Crystal, and Electronic Structure of the New Ternary Zintl Phase Eu2−x Mg2−y Ge3 (x = 0.1; y = 0.5). Z. Anorg. Allg. Chem. 2012, 638, 1417–1423. (42) Slabon, A.; Cuervo-Reyes, E.; Kubata, C.; Mensing, C.; Nesper, R. Exploring the Borders of the Zintl-Klemm Concept: On the Isopunctual Phases Eu5+x Mg18−x Ge13 (x = 0.1) and Eu8 Mg16 Ge12 . Z. Anorg. Allg. Chem. 2012, 638, 2020–2028. (43) Niehaus, O.; Ryan, D. H.; Flacau, R.; Lemoine, P.; Chernyshov, D.; Svitlyk, V.; Cuervo-Reyes, E.; Slabon, A.; Nesper, R.; Schellenberg, I.; and Pöttgen, R. Complex Physical Properties of EuMgSi–a Complementary Study by Neutron Powder Diffraction and 151 Eu Mössbauer Spectroscopy. J. Mater. Chem. C 2015, 3, 7203–7215. (44) Schellenberg, I.; Eul, M.; Schwickert, C.; Kubata, C. M.; Cuervo-Reyes, E.; Nesper, R.; Rodewald, U. Ch.; Pöttgen, R. The Zintl Phases Eu3 Mg5 Si5 and Eu3 Mg5 Ge5 . Z. Anorg. Allg. Chem. 2012, 638, 1976–1985.


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Graphical TOC Entry Reminiscence of a Zintl-anion in the intermetallic LiSr2−x Eux Ge3 . Eu2+ ions take sites 1 and 2 with p (1−p ) η ≡ p2 (1−p1 ) ≈ const. 1

2

102 101 100 10-1 0.0

0.5

1.0

1.5

Eu content per f.u.

2.0


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LiSr2âxEuxGe3: Light on the Europium Site Preferences - The Journal

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