Ge2 and the Influence of the Valence ... - ACS Publications

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First-Order Phase Transition in BaNi2Ge2 and the Influence of the Valence Electron Count on Distortion of the ThCr2Si2 Structure Type Viktor Hlukhyy,*,† Dmytro Trots,‡ and Thomas F. Fas̈ sler† †

Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany Hamburger Synchrotronstrahlungslabor, DESY, Notkestrasse 85, 22607 Hamburg, Germany

‡

S Supporting Information *

ABSTRACT: Structural instability has a strong influence on the understanding of superconductivity in iron-containing 122 phases. Similar to the 122 iron-based high-temperature superconductors, the intermetallic compound BaNi2Ge2 undergoes an orthorhombic-totetragonal structural phase transition. The compound was prepared by arc-melting mixtures of the elements under an argon atmosphere. Single crystals were obtained by a special heat treatment in a welded tantalum ampule. The crystal structure of the compound was investigated by powder and single-crystal X-ray diffraction. Differential thermal analysis of BaNi2Ge2 showed a reversible phase transition at ca. 480 °C. In situ temperature-dependent synchrotron powder X-ray diffraction studies revealed that below 480 °C the crystal structure of BaNi2Ge2 is orthorhombic [own structure type, space group Pnma, a = 8.3852(4) Å, b = 11.3174(8) Å, and c = 4.2902(9) Å at 30 °C] and the high-temperature phase above 510 °C belongs to the tetragonal ThCr2Si2-type structure [space group I4/mmm, a = 4.2664(1) Å, and c = 11.2537(3) Å at 510 °C]. The reversible first-order low-temperature ↔ hightemperature phase transition around 480 °C is associated with distortion of the [Ni2Ge2] layer of low-temperature modification. The anisotropy of thermal expansion of the unit cell in BaNi2Ge2 was analyzed. The crystal chemistry and chemical bonding are discussed in terms of linear muffin-tin orbital band structure calculations and a topological analysis using the electron localization function. In related compounds, the level of distortion of the uncollapsed tetragonal ThCr2Si2-type structure depends on the valence electron count (VEC).

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application of external pressure.10 Such structural instabilities play an important role in material science and especially in the occurrence of superconductivity.11,12 Usually the 122 superconductors are located at the border of structural instabilities. The structural phase transition in the parent compounds of 122 FeAs superconductors is widely believed to be driven by the magnetic component, whereas in Fe-free 122 compounds, the charge density wave (CDW) or Peierls instability may be responsible for distortion of the square layers of the transition metals.13−16 The bonding situation in the ThCr2Si2-type structures also has an important impact on the origin of the structural transition. The structures can be described as two-dimensional [T2X2] networks that are separated by A atoms (uncollapsed structure). In the so-called collapsed structures, the [T2X2] slabs form interlayer X−X bonds, leading to three-dimensional [T2X2] networks. The rearrangement of the T/X atoms in every second [T2X2] slab results in a structural transformation from the collapsed ThCr2Si2 type to the CaBe2Ge2 type.14,16−18 The instability is influenced by the atomic size of the T and X atoms and their electronegativity.19

INTRODUCTION In order to get a better understanding of the high-temperature (HT) superconductivity in Fe-122 phases such as Ba1−xKxFe2As2,1,2 crystallizing in the ThCr2Si2 type, an investigation of other isostructural compounds is highly desirable. The search for 122 compounds with closely related structures and the investigation of their physical properties will allow for deeper insight into the structure−property relationship and thus the potential of such compounds for HT superconductivity. Compounds of the general composition AT2X2 (A = rare-earth or alkaline-earth metal; T = transition metal; X = p-block element) most commonly crystallize in the ThCr2Si2-type structure, which represents an ordered variant of the BaAl4 type.3,4 The structures of ternary intermetallics derived from the BaAl4-type structure represent one of the most frequent families of compounds and comprise more than 2000 representatives.5,6 The parent compounds of the iron− arsenic HT superconductors AeFe2As2 (Ae = Ca, Sr, Ba) are itinerant antiferromagnetic semimetals that undergo a structural phase transition from a tetragonal (I4/mmm) to an orthorhombic (Fmmm) structure upon cooling.7−9 In these compounds, superconductivity emerges upon suppression of the phase transition and antiferromagnetic ordering either by partial chemical substitution at the Ae, Fe, or As sites or by © XXXX American Chemical Society

Received: September 14, 2016

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DOI: 10.1021/acs.inorgchem.6b02190 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Very recent investigations20 have shown the interplay between the valence electron counts (VECs) per formula unit and the phase stability of three types of BaAl4 derivatives: ThCr2Si2, CaBe2Ge2, and BaNiSn3. In the uncollapsed structures of the ThCr2Si2 type (also known as the BaZn2P2 type), containing two-dimensional polyanionic networks without interlayer X−X bonds, no rearrangement of the T/X atoms during the phase transition is observed, but distortion of the square-planar transition-metal lattice occurs.14−16 The 122 superconducting iron selenides with the uncollapsed tetragonal (ucT-)ThCr2Si2-type structure are also located at the border of structural instability, and an order−disorder situation of the Fe vacancies in the square-planar lattice without any distortion is observed.21,22 Despite the great interest in the 122 superconducting family documented in a huge number of theoretical and experimental investigations, there are still surprises such as the recently discovered superconductivity in the 122 germanides SrPd2Ge2 and SrNi2Ge2 with ThCr2Si2-type structure,23 and there are still many open questions concerning the phenomenon of the phase transition. In the course of our recent investigations of such phases, we have discovered and characterized the ThCr2Si2-type representatives CaCo 2Si2, SrCo2Si2, CaRh2Si2, CaFe2Si2, CaFe2−xRhxSi2, and BaCo2Ge2.24,25 The 122 nickel-based compounds are of special interest because quite a number of them show superconductivity similar to that of AFe2As2 (A = K, Rb, Cs). The nickel-based pnictides SrNi2P2, SrNi2As2, BaNi2P2, and BaNi2As2 have recently been found to be superconducting (Tc = 1.4,26 0.62,27 2.5−3,28,29 and 0.7 K,30 respectively), along with the chalcogenides KNi2S2 and KNi2Se2 (Tc = 0.531 and 0.8 K,32 respectively) and the germanide SrNi2Ge2 (Tc = 0.87 K).33 Partial substitution at the p-block element or transition-metal site causes an increase of the critical temperature.33,34 For example, the solid solutions BaNi2P2−xGex and SrNi2P2−xGex show an increase of Tc up to 2.9 and 3.0 K, respectively, upon substitution of P atoms by Ge atoms, which can be regarded as a direct hole doping of the superconducting [Ni2P2] layers.34,35 The substitution of smaller cations by larger cations in the AeNi2Ge2 series may be used to induce a more pronounced layered character in the [Ni2Ge2] network and thereby structural instability. With this idea in mind, the new BaNi2Ge2 has been synthesized. In order to clarify several open issues regarding lattice instabilities in the 122 family, we have studied the temperature dependence of the BaNi2Ge2 crystal structure with the help of high-resolution powder X-ray diffraction (synchrotron radiation). In addition, we present single-crystal measurements, differential thermal analysis, magnetic measurements, and electronic band structure calculations. Preliminary results on the structural phase transition in BaNi2Ge2 have already been briefly reported recently.36

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turned upside down three times in order to ensure homogenization. After these melting procedures, samples of only low crystallinity but of high purity were obtained. These samples were used for differential thermal analysis (DTA) and magnetic and high-resolution synchrotron diffraction measurements. The growth of larger crystals suitable for single-crystal X-ray diffraction analysis was realized by heat treatment and subsequent slow cooling. For this purpose, the barium, nickel, and germanium pieces of stoichiometric amounts were sealed in a tantalum ampule (total mass = 0.5 g) and placed in a silica glass tube, which was evacuated. The silica tube was then inserted into a vertical resistance tube furnace (LOBA, HTM Reetz GmbH), heated at a rate of 120 °C h−1 to 1000 °C, kept at this temperature for 24 h, and subsequently cooled to room temperature at a rate of 6 °C h−1. The sample, which exhibits a metallic luster, could easily be separated from the tantalum crucible. BaNi2Ge2 is stable against air and moisture. From the sample, platelike single crystals could be separated. X-ray Investigations. The purity of the sample was checked using a Stoe Stadi P powder diffractometer with a Cu Kα1 source. The lattice parameters determined from the powder patterns and from the singlecrystal data agreed well. The powder pattern (Supporting Information, Figure S1) showed the presence of a single-phase sample of orthorhombic BaNi2Ge2. An in situ powder X-ray diffraction experiment was carried out on a high-resolution synchrotron powder diffractometer B2 (HASYLAB, Hamburg, Germany). The experiment was performed in Debye− Scherrer geometry, and the data were collected using an image-plate OBI detector. In order to minimize the absorption and fluorescence of the sample, the wavelength used for this experiment was equal to 0.49966 Å (as determined from the position of the reflections of the LaB6 standard material SRM 660a). The diffraction patterns were collected at constant temperatures in the range of 30−810 °C and at a temperature increment of 30 °C. Because of the presence of small amounts of air in the sealed quartz capillary, partial oxidation of BaNi2Ge2 was observed starting at 420 °C. Four separate phases were detected and identified as BaNi2Ge2, BaO, Ni2−xGe, and BaGe2. The results of quantitative phase analyses as a function of the temperature during this partial oxidation of BaNi2Ge2 are summarized in Figure S2 in the Supporting Information. First, we noticed a decrease in the amount of the BaNi2Ge2 phase, accompanied by an increase in the phases BaO, Ni2−xGe, and BaGe2, which starts at 420 °C and continues to 700 °C. Beyond 700 °C, the composition of the sample remains almost constant, indicating the complete exhaustion of oxygen in the sample. For determination of the crystal structure parameters, implementation of the full profile Rietveld method in the FullProf program package was used.37 The lattice parameters, atomic coordinates, and space group of the low-temperature (LT) orthorhombic structure from the single-crystal data (see below) were chosen as starting models for Rietveld refinement. The reflections of the HT phase were indexed in a tetragonal unit cell, and the structure of BaCo2Ge225 was chosen as a starting model for the refinement (Table 2 and Figure S3 in the Supporting Information). In order to model the shape of the peak profile, the pseudo-Voigt function was used. The background contribution was determined using a linear interpolation between selected data points in nonoverlapping regions. The scaling factor, zero angular shift, profile shape parameters, half-width (Caglioti) parameters, asymmetry, and lattice parameters as well as the fractional coordinates of the atoms and overall isotropic temperature factors were varied during the fitting procedures. Single-crystal data for BaNi2Ge2 were collected at room temperature using a Stoe IPDS-IIT image-plate diffractometer with graphitemonochromatized Mo Kα (0.71073 Å) radiation. A numerical absorption correction was applied using the X-Red and X-Shape software.38,39 Table 1 shows the relevant crystallographic data for the data collection and refinement procedures. The starting atomic parameters for BaNi2 Ge 2 were deduced from an automatic interpretation of direct methods using SHELXS-2014.40 Subsequently, the structures were refined (SHELXS-2014 and full-matrix least squares on Fo2)41 with anisotropic atomic displacement parameters for all atoms. In order to check for the correct composition, the occupancy

EXPERIMENTAL SECTION

Syntheses. The synthesis of BaNi2Ge2 was carried out starting from commercially available elements with high purity: ingots of the barium (ChemPur, 99.3%), nickel wire (Alfa Aesar, 99.9%) and germanium pieces (ChemPur, 99.999%). All manipulations were performed in an argon-filled glovebox. In order to prevent extensive evaporation of barium, at first nickel and germanium pieces of stoichiometric amounts (total mass = 0.5 g) were arc-melted on a water-cooled copper hearth (Mini Arc Melting System, MAM-1, Johanna Otto GmbH, placed in an argon-filled glovebox). Subsequently, barium was added, and the arc melting was repeated using a lower current. For both steps, the resulting regulus was arc-melted and B


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Inorganic Chemistry Table 1. Crystal Data and Structure Refinement for LTBaNi2Ge2 at Room Temperature (Single-Crystal Data) empirical formula fw (g mol−1) space group, Z unit cell dimens (powder X-ray diffraction data) a (Å) b (Å) c (Å) V (Å3) calcd density (g cm−3) abs coeff (mm−1) F(000) cryst size (mm3) θ range (deg) range in hkl reflns collected indep reflns reflns with I > 2 σ(I) data/param GOF on F2 final R indices [I > 2 σ(I)] R indices (all data) largest diff peak and hole (e Å−3)

Table 3. Atomic Coordinates and Isotropic Equivalent Displacement Parameters for LT- and HT-BaNi2Ge2

BaNi2Ge2 399.94 Pnma, 4

atom Ba Ni Ge

8.3901(3) 11.2949(4) 4.2950(2) 408.10(3) 6.51 32.88 704 0.01 × 0.04 × 0.12 4.9−27.5 ±10, ±14, ±5 5955 492 (Rint = 0.099) 456 (Rσ = 0.034) 492/25 1.136 R1 = 0.035, wR2 = 0.085 R1 = 0.040, wR2 = 0.087 1.516 and −1.369

Ba Ni Ge

x/a

y/b

z/c

Ueq × 103 (Å2)

LT-BaNi2Ge2 (Pnma and Single-Crystal Data at RT) 1 4c 0.14120(9) /4 0.2528(2) 8d 0.3549(1) 0.0016(1) 0.1568(3) 8d 0.0992(1) 0.58069(9) 0.1663(2) HT-BaNi2Ge2 (I4/mmm, Powder Data at 510 °C) 2a 0 0 0 1 1 4d 0 /2 /4 4e 0 0 0.3384(2)

21.1(3) 17.9(3) 17.9(3) 20.7(7) 42.7(12) 46.8(11)

Table 4. Interatomic Distances (Å) Calculated with the Lattice Parameters Taken from Powder X-ray Data and Corresponding −iCOHPsa distance (Å)

−iCOHP (eV)

LT-BaNi2Ge2 (Pnma and Single-Crystal Data at RT) Ba−Ge (2×) 3.314(1) 0.440 Ba−Ge (2×) 3.402(1) 0.245 Ba−Ni (2×) 3.336(1) 0.254 Ba−Ni (2×) 3.362(1) 0.245 Ni−Ni (2×) 2.777(2) 0.516 Ni−Ni (1×) 2.783(2) 0.770 Ge−Ni (1×) 2.322(2) 1.960 Ge−Ni (1×) 2.339(2) 1.864 Ge−Ni (1×) 2.376(2) 1.677 Ge−Ni (1×) 2.396(2) 1.851 Ge−Ge (1×) 2.855(1) 0.324 LT-BaNi2Ge2 (Pnma and Powder Data at 480 °C) Ba−Ge (2×) 3.391(4) 0.390 Ba−Ge (2×) 3.461(4) 0.365 Ba−Ni (2×) 3.372(4) 0.249 Ba−Ni (2×) 3.387(4) 0.198 Ni−Ni (2×) 2.818(5) 0.418 Ni−Ni (1×) 2.818(5) 0.275 Ge−Ni (1×) 2.295(4) 1.890 Ge−Ni (1×) 2.325(5) 1.787 Ge−Ni (1×) 2.377(5) 1.338 Ge−Ni (1×) 2.393(4) 1.679 Ge−Ge (1×) 2.930(4) 0.199 HT-BaNi2Ge2 (I4/mmm and Powder Data at 510 °C) Ba−Ge (8×) 3.523(1) 0.554 Ba−Ni (8×) 3.531(1) 0.330 Ni−Ni (4×) 3.017(1) 0.422 Ge−Ni (4×) 2.354(1) 2.500

Table 2. Crystal Data and Structure Refinement for HTBaNi2Ge2 at 510 °C (Rietveld Refinement) empirical formula fw (g mol−1) space group, Z unit cell dimens a and b (Å) c (Å) V (Å3) calcd density (g cm−3) wavelength λ (Å) step scan increment 2θ (deg) 2θ range (deg) program no. of profile points shape param η Caglioti param U V W no. of reflns no. of refined param RB RP Rexp Rwp χ

Wyckoff position

BaNi2Ge2 399.94 I4/mmm, 2 4.2665(1) 11.2544(2) 204.868(7) 6.48 0.499966 0.004 3−35° FullProf 11751 0.4825 0.2179 −0.0516 0.0117 192 80 5.89 5.01 1.79 6.32 12.43

a Values at EF are within LT- and HT-BaNi2Ge2. All −iCOHP values are in electronvolts per bond per cell.

observed. Elemental analysis revealed the compositions of the crystals (in atomic percentages): Ba, 21(2); Ni, 41(4); Ge, 38(3). These values are in agreement with the compositions determined by the X-ray structure refinement methods. Thermal Analysis. DTA was carried out in the temperature range of 25−1000 °C using custom-made niobium containers for the sample and as a reference crucible (Netzsch DSC 404C). The niobium crucible was loaded with about 100 mg of a powdered sample of pure BaNi2Ge2. The crucible was then closed by pressing niobium in the upper part of the crucible using a pipe tong and subsequent welding. The DTA curves were recorded under a continuous flow of argon (50 mL min−1) to prevent corrosion of the crucibles at high temperatures. The obtained thermograms were evaluated with the software ProteusNetzsch Analysis.42 Four cycles involving heating to 1000 °C and

parameters of both compounds were refined in a separate series of least-squares cycles, showing that all sites are fully occupied. Thus, the ideal occupancies were assumed in the last cycles. A final difference electron-density (Fourier) synthesis did not reveal any significant residual peaks (see Table 1). The positional parameters and interatomic distances for both modifications are listed in Tables 3 and 4. After data collection the single crystal was analyzed by energydispersive X-ray measurement with a JEOL 5900LV scanning electron microscope. No impurity elements heavier than sodium have been C


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Inorganic Chemistry subsequent cooling to room temperature using a heating rate of 5 °C min−1 were performed. After the DTA experiments, the crucible was opened, and the product was again analyzed by powder X-ray diffraction. The powder X-ray diffraction data after the experiment revealed no changes within the single-phase BaNi2Ge2 (Pnma) sample. The thermal effects of the DTA experiment can be assigned to a reversible first-order phase transition. Magnetic Measurements. The magnetic measurements were carried out on a polycrystalline sample held in a gelatin capsule inside a plastic straw using a MPMS XL5 SQUID magnetometer (Quantum Design). The temperature-dependent data were obtained by measurement of the magnetization from 1.8 to 300 K in an applied magnetic field of 500 Oe. Field-dependent measurements were carried out at 2 and 300 K. Corrections were applied to the measured susceptibilities for the sample holder and for the diamagnetic contributions of the core electrons. Electronic Structure Calculations. For electronic structure calculations, the linear muffin-tin orbital (LMTO) method in the atomic sphere approximation (ASA) was employed using the tightbinding (TB) program TB-LMTO-ASA.43 The exchange-correlation term was calculated within the local density approximation and parametrized according to von Barth and Hedin.44 For the radii of the atomic spheres, the automatically determined values were used, whereas the positions and radii of the empty spheres were determined after Jepsen and Andersen.45 The basis set of short-range atomcentered TB-LMTOs contained s and d valence functions for barium, s−d valence functions for nickel, and s and p valence functions for germanium. Ba 6p and 4f and Ge 3d orbitals were included using a downfolding technique.46 Analysis of the chemical bonding is based on the theoretical partial and total density of states (DOS) curves, on plots of the crystal orbital Hamilton populations (COHPs),47 and on band structures with fat bands and contour-line diagrams of the electron localization function (ELF).48 From COHP analyses, the contribution of the covalent part of a particular interaction to the total bonding energy of the crystal can be obtained. All COHP curves presented here are in the following format: positive values are bonding and negative antibonding. In the fat-band analysis, the atomic orbital character is represented as a function of the bandwidth.

unsuccessful. Therefore, in situ powder X-ray diffraction experiments were carried out. Crystal Structure of the LT Modification of BaNi2Ge2. The crystal structure of the LT modification of BaNi2Ge2 was determined by single-crystal X-ray diffraction. The compound crystallizes in a new structure type in the space group Pnma (Pearson symbol oP20). The structure of LT-BaNi2Ge2 reflects a distorted variant of the ThCr2Si2 structure and contains two-dimensional [Ni2Ge2] layers, which are separated by Ba atoms (Figure 2a). In these

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Figure 2. Views of the structures of LT-BaNi2Ge2 (single-crystal data at room temperature) (a) along the c axis and (b) along the b axis and of HT-BaNi2Ge2 (powder data, 510 °C) (c) along the a axis and (d) along the c axis. The Ni−Ge, Ni−Ni, and Ge−Ge contacts within the [Ni2Ge2] layers are emphasized. The Ba, Ni, and Ge atoms are drawn as red, blue, and white spheres, respectively. The displacement ellipsoids in the LT-BaNi2Ge2 structure are drawn at the 90% probability level.

Figure 1. DTA heating (red line) and cooling (blue line) curves in the temperature range of 70−1000 °C (5 K min−1 heating/cooling rate) showing a reversible phase transition of BaNi2Ge2.

layers, the distorted squares of a planar network of Ni atoms are alternatingly capped above and below the plane by Ge atoms. Similar to the ThCr2Si2-type structure, the layers can also be described as being constructed from highly distorted NiGe4 tetrahedra, which share edges in the ab plane. The interatomic distances of LT-BaNi2Ge2 at room temperature are summarized in Table 3. The deviation from tetragonality of this orthorhombic structure arises from the deviation of the nickel tetragons of the planar nickel network from squares: each Ni atom has three Ni-atom neighbors at shorter distances in the range between 2.777(2) and 2.783(2) Å and a fourth Ni atom at a much longer distance of 3.824(2) Å (Figure 2b). As a consequence, also a short intralayer Ge−Ge distance of 2.855(1) Å appears. However, this latter distance is significantly longer than a typical covalent Ge−Ge bond observed in the cubic germanium structure (2.45 Å) or than those reported for the Zintl phases BaGe and BaGe2 (2.63 and 2.59−2.63 Å, respectively).49−51 The shortest interatomic distances in LTBaNi2Ge2 occur between the Ni and Ge atoms [2.322(2)− 2.396(2) Å], which are similar to those observed in CaNi2Ge2 and SrNi2Ge2.52,53 Because of orthorhombic distortion, two sets of Ge−Ni−Ge angles with values of 129.02(6)° and 131.12(6)°

RESULTS AND DISCUSSION A single-phase sample of BaNi2Ge2 can easily be obtained by fusion of the elements in a stoichiometric ratio at high temperatures. The structure of this phase was determined by single-crystal X-ray diffraction analysis at room temperature. DTA of BaNi2Ge2 shows endothermic (at 476.5 °C) and exothermic (at 452.7 °C) events upon heating and cooling, respectively (Figure 1). These peaks hint for a reversible structural phase transition. Several attempts to obtain the HT phase by thermal quenching in water or liquid nitrogen were

D


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Inorganic Chemistry

between those of the orthorhombically distorted LT-BaNi2Ge2 [129.02(6)−131.12(6)°] but is significantly larger than those in SrNi2Ge2 (122.3°) and CaNi2Ge2 (119.1°). The shortest interlayer distance between the Ge atoms in HT-BaNi2Ge2 [d(Ge−Ge) = 3.638(3) Å] is significantly shorter compared to that of LT modification [3.835(1) Å]. Thermal Expansion and Structural Phase Transition in BaNi2Ge2. In order to investigate the HT behavior of BaNi2Ge2, we analyzed the high-resolution X-ray diffraction data in the temperature range from 30 to 810 °C (Figure 3). Because the orthorhombic Pnma structure is a distorted variant of the basic ThCr2Si2-type structure (I4/mmm), in the tetragonal setting, the lattice parameters of the orthorhombic structure (aorth, borth, and corth) are related to the pseudotetragonal (*) subcell parameter (atetr* = btetr* and ctetr*) as atetr* = aorth/2, btetr* = corth, and ctetr* = borth. Figure 4 shows the temperature dependence of the lattice parameters of BaNi2Ge2 determined by Rietveld refinements (data collected upon heating). Discontinuous changes in the diffraction pattern and thus in the values of the lattice parameters are observed between 480 and 510 °C, which correlates well with the DTA signals around 476 °C. This is clear evidence for an abrupt transition from the LT-distorted Pnma structure to the HT basic I4/mmm ThCr2Si2-type structure. The changes in the lattice parameters are anisotropic with a linear increase of the atetr lattice parameter with temperature (Figure 4a), while the ctetr parameter increases only slightly and remains almost constant in the Pnma structure before the transition but grows enormously after the transition to I4/mmm (Figure 4b). A volume reduction of 1.4% upon transformation from the Pnma structure to the I4/mmm structure is a very strong indication of a first-order phase transition (Figure 4c). From the temperature dependence of the unit cell volume, the linear coefficient of thermal expansion has been defined as (V2 − V1)V1−1(T2 − T1)−1, where V2 and T2 are the final unit cell volume and sample temperature and V1 and T1 are the initial unit cell volume and sample temperature, respectively. For the LT Pnma and HT I4/mmm modifications, the coefficients of thermal expansion are 3.55 × 10−5 and 5.21 × 10−5 K−1, respectively. The anisotropic changes in the lattice parameters are mirrored in the pseudotetragonal axial ratio ctetr*/atetr* (Figure 4d). A decrease and increase of this ratio is revealed within the Pnma and I4/mmm polymorphs of BaNi2Ge2, respectively. The difference between aorth and corth can be taken as a measure for the orthorhombic distortion of the pseudotetragonal subcell. The temperature dependence of the orthorhombic order parameters P = (atetr* − btetr*)/(atetr* + btetr*) presented in Figure 4e are in the range of ∼(1.0−1.2) × 10−2 for the LT structure and lie between those of FmmmBaFe2As2 (0.4 × 10−2)57 and Fmmm-SrRh2As2 (3.3 × 10−2).58 Rietveld refinements at various temperatures reveal that the distance of the Ge atoms from the plane of Ni atoms does not change with the temperature for each modification but abruptly increases during the phase transition [0.879(1) Å for LTBaNi2Ge2 at 480 °C to 1.000(1) Å for HT-BaNi2Ge2 at 510 °C]. Because the [Ni2Ge2] layers are not interconnected along the z direction, the abrupt decrease of the ctetr* parameter can be explained by a geometric effect. Because of transformation of the distorted [Ni2Ge2] layers of the orthorhombic modification into the square layers of the tetragonal modification, the Ba atoms get more space between them in HT-BaNi2Ge2: the shortest Ba−Ge and Ba−Ni distances change from 3.941(4)

are observed. The alteration of the alkaline-earth metal from Ca to Ba in AeNi2Ge2 leads to a flattening of the NiGe4 tetrahedra; i.e., substitution with larger cations enforces an expansion of the unit cell, while the Ni−Ge distances remain unchanged.25 The shortest distance between the [Ni2Ge2] layers is found between two Ge atoms of adjacent slabs with d(Ge−Ge) = 3.835(1) Å. The large interlayer distance supports the view of a twodimensional character of these structures. This distance is drastically reduced to 2.83 Å in SrNi2Ge2,25 with the smaller Sr atoms located between the layers. However, this Ge−Ge distance is still too long to be considered as a covalent Ge−Ge bond, but further Ae atom substitution by even smaller Ca atoms leads to the formation of such covalent Ge−Ge interactions of 2.62 Å between the [Ni2Ge2] layers in CaNi2Ge2.52 LT-BaNi2Ge2 (Pnma) is structurally related to the homologous BaNi2Si2 with distorted two-dimensional [Ni2Si2] layers, which contain, however, covalent Si−Si intralayer bonds of 2.54 Å.54 The structure of another homologue, BaPt2Ge2, has recently been reported to adopt an inverse BaCu2Sb2-type structure with fragments of both the ThCr2Si2 and CaBe2Ge2 structure types.55 Two other polymorphs of BaPt2Ge2, which crystallize in LaPt2Ge2 (space group P21/c) and BaNi2Ge2 (space group Pnma), have been reported.56 Crystal Structure of the HT Modification of BaNi2Ge2. In situ powder X-ray diffraction experiments in the temperature range from 30 to 810 °C (Figure 3) were carried out on a high-

Figure 3. Stack of in situ synchrotron diffraction patterns of BaNi2Ge2 collected upon heating.

resolution diffractometer (synchrotron radiation). These studies revealed that the crystal structure of BaNi2Ge2 remains orthorhombic (Pnma) in the temperature range between 30 and 480 °C. However, at 510 °C BaNi2Ge2 undergoes a structural transition to HT modification, which can be indexed with the tetragonal structure of ThCr2Si2 at 510 °C: I4/mmm, Z = 2, a = 4.2666(1) Å, and c = 11.2545(2) Å. The structural details for HT-BaNi2Ge2 were obtained from a Rietveld refinement of the powder synchrotron X-ray diffraction data. The interatomic distances of HT-BaNi2Ge2 at 510 °C are summarized in Table 3. Similar to LT-BaNi2Ge2, the structure 2 of HT modification contains two-dimensional ∞ [Ni2Ge2] layers, which are separated by Ba atoms (Figure 2c,d). The Ni atoms form a network of regular squares with a Ni−Ni distance of 3.0169(1) Å, which is significantly longer than that in LT-BaNi2Ge2 [2.777(2)−2.783(2) Å] and in the homologous SrNi2Ge2 (2.95 Å) and CaNi2Ge2 (2.82 Å).52,53 The Ni− Ge distances of 2.354(1) Å are in the same range as those in LT-BaNi2Ge2 and other AeNi2Ge2 compounds. The value of the “vertical” tetrahedral Ge−Ni−Ge angle of 130.00(5)° lies E


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Inorganic Chemistry

turn, induces the abrupt decrease of the ctetr* parameter during the phase transition from the Pnma modification to the I4/ mmm modification. The increase of the lattice parameter c with temperature is much more pronounced in the tetragonal HT modification. It is most probably induced by the repulsive force of the lone pairs at the Ge atoms oriented toward each other, which corroborates with the shortening of the interlayer Ge− Ge distances along the ctetr* axis: 3.913(3) Å at 480 °C for LT modification versus 3.627(3) Å at 510 °C for HT modification. Interestingly, unlike to LT-BaNi2Ge2, in BaNi2Si2, no phase transition up to 900 °C has been observed by in situ temperature-dependent powder X-ray diffraction investigations (Supporting Information, Figure S4), most probably because of the existence of strong covalent intralayer Si−Si bonding [d(Si−Si) = 2.54 Å], which stabilizes this orthorhombic distortion. As mentioned above, the other isoelectronic homologue BaPt2Ge2 has recently been reported to be structurally unstable as well.55,56 Symmetry Breaking Driven by Valence Electrons in the Uncollapsed ThCr2Si2 Type. In general, intermetallic compounds are less sensitive to electronic changes compared to salt-like Zintl phases. However, in classes like Hume−Rothery or Laves phases, an influence of the VECs on the structural properties is well-known.59−61 Other intermetallics, for example, BaAl4-type derivatives, also show a VEC dependence on the structure: for specific compositions and VEC values, BaNiSn3, ThCr2Si2, and CaBe2Ge2 types occur in the BaAuxSn4−x solid solution.20 The ThCr2Si2-type structure is relatively stable toward electronic changes, which is mirrored in a large number and variety of AT2X2 compounds for many different element combinations.4 This is mainly true for collapsed AT2X2 structures with X−X interlayer bonds, which play a significant role in stabilization of the structure. However, the uncollapsed AT2X2 structures seem to be more sensitive to electronic changes, as will be shown in the following discussion. The influence of the electron count on T−X and X−X bonding in the ThCr2Si2-type representatives has theoretically been investigated for phosphides.62 Furthermore, in some of the 122 compounds, electronic changes suppress the structural instability, which, in turn, can induce superconductivity. Therefore, the study and systematization of knowledge about the structural phase transition and its dependence on the electron concentration are very important. In the following, the electron-induced structural distortions will be discussed in more detail on the basis of the group− subgroup scheme, a compact graphical representation that was introduced by Müller and Bärnighausen.63,64 The structural relationships between numerous BaAl4-derived structures on the basis of a group−subgroup scheme were discussed previously.65,66 We have extended these relationships to new members of this large family including the LT-BaNi2Ge2 structure (Figure 5). In Figure 6, only uncollapsed structures (without interlayer X−X bonds), which are more sensitive to electronic changes compared to collapsed structures, have been considered. In these structures, a phase transition associated with distortion of the [T2X2] layers is taking place. As shown in Figures 5, 6, and S5 in the Supporting Information, the distortive symmetry reduction on going from HT to LT modification of the described 122 compounds with uncollapsed (uc) structures is directly dependent on the VEC per formula unit. No structural instabilities have been reported

Figure 4. Temperature-dependent evolution of the unit cell dimensions in BaNi2Ge2: (a) pseudotetragonal atetr* parameter; (b) pseudotetragonal ctetr* parameter; (c) scaled unit cell volume V/Z (Z = formula units per unit cell); (d) pseudotetragonal axial ratio ctetr*/ atetr*; (e) values of orthorhombic distortion. The error bars are smaller than the size of the plotted symbols. The pseudotetragonal subcell parameters were obtained from lattice parameters of the orthorhombic cell by atetr* = aorth/2, atetr* = corth, and ctetr* = borth.

and 3.372(4) Å, respectively, for LT-BaNi2Ge2 at 480 °C to 3.523(1) and 3.531(1) Å for HT-BaNi2Ge2 at 510 °C. This, in F


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Inorganic Chemistry

Figure 5. Group−subgroup relationships for structures derived from the ThCr2Si2 type: BaMn2As2, α-SrFe2As2, BaNi2Si2, CeNi2.35Sb1.65, αBaNi2Ge2, α-SrRh2As2, CaGa4, and α-BaNi2As2. The indices for the translationengleiche (t) and klassengleiche (k) transitions and the unit cell transformations are given together with evolution of the atomic parameters. Space group Pmmn and possible atomic coordinates for hypothetical structures are shown in gray (for structural details, see Figure S9 in the Supporting Information).

Figure 6. Dependence of the symmetry of LT modification of the AeT2X2 compounds from the VEC per formula. Structures of HT modification belong to the ucT-ThCr2Si2 type.

Å for HT-BaFe2As2) split into shorter and longer Fe−Fe bonds (2 × 2.79 and 2 × 2.81 Å for LT-BaFe2As2). The order of the phase transition (first or second) in these phases, which seems to be of magnetic origin, has been discussed intensively.71−75 The transition from I4/mmm to Fmmm corresponds to a translationengleiche symmetry reduction of index 2 via decoupling of the tetragonal a lattice parameter. It is interesting to note that, in the system Ba1−xKxFe2As2, superconductivity

for the ucT-ThCr2Si2-type representatives with VEC = 24−27 such as BaCr2As2 (VEC = 24), CsMn2P2 (VEC = 25), BaMn2As2 (VEC = 26), and KFe2As2 (VEC = 27).67−70 Starting from VEC = 28, the tetragonal system becomes instable: BaFe2As2 (VEC = 28) undergoes an I4/mmm to Fmmm structural phase transition associated with only a slight orthorhombic distortion in a square iron network. Because of this distortion, the Fe−Fe distances in the iron square (4 × 2.80 G


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Inorganic Chemistry exists in the range of VEC = 27−27.8, which is in the vicinity of instability (VEC = 28 for BaFe2As2). Two additional electrons in BaNi2Si2 (VEC = 30) cause a further lowering of the symmetry to Cmcm. Distortion of the planar network of Ni atoms in the ab plane (free x parameter) causes a freeing of the y and z parameters for the Si atoms and of the y parameter for the Ba atoms. This corresponds to a klassengleiche symmetry reduction of index 2 from space group Fmmm to Cmcm. A different mechanism of symmetry reduction occurs for LTBaNi2Ge2 (VEC = 30). First, a slight puckering of the square T network (free z parameter) leads to a translationengleiche symmetry reduction of index 2 from space group I4/mmm (ThCr2Si2 type) to Immm of CeNi2.35Sb1.65,5 followed by a klassengleiche symmetry reduction of index 2 to space group Pmmn (hypothetical structure) due to a loss of centering translations. Going from Pmmn to Pnma upon doubling of the subcell c lattice parameter, a klassengleiche symmetry reduction of index 2 takes place, resulting in the freeing of all atomic parameters for Ge and Ba (except of y for Ba) of LT-BaNi2Ge2. Distortion within the nickel squares in both BaNi2Si2 and LT-BaNi2Ge2 (VEC = 30) is more pronounced compared to that in BaFe2As2 with a lower VEC of 28: each Ni atom has three nearest Ni-atom neighbors at distances between 2.65 and 2.74 Å in BaNi2Si2 and at 2.78 Å in LT-BaNi2Ge2. The distance to the fourth Ni atom is much longer, 3.85 and 3.83 Å in BaNi2Si2 and LT-BaNi2Ge2, respectively (Figures S5 and S6 in the Supporting Information). It is worth mentioning that the structures of BaNi2Si2 (Cmcm) and LT-BaNi2Ge2 (Pnma) are not related by a direct group−subgroup relationship as it seems at first glance [with basis vectors a − b, c, (a + b)/2]. For the third representative of the “VEC = 30 group”, SrRh2As2, two phase transitions were reported: P21/c (αSrRh 2 As 2 ) ↔ Fmmm (β-SrRh 2 As 2 ) ↔ I4/mmm (γSrRh2As2).15,58 The intermediate β-SrRh2As2 phase with an incommensurable Fmmm structure only exists in a narrow temperature range (180−282 °C). The structure of α-SrRh2As2 (P21/c) is a direct derivative of LT-BaNi2Ge2 (Pnma) via a translationengleiche symmetry reduction of index 2. The rhodium network in α-SrRh2As2 is further distorted and puckered, whereas the Sr atoms lose their last fixed y atomic parameter. Thus, the 8d sites of the T and X atoms in the Pnma structure of LT-BaNi2Ge2 are each split into two 4e sites in the P21/c structure of α-SrRh2As2. In contrast to three-nickelbonded Ni atoms in Pnma-BaNi2Ge2 and Cmcm-BaNi2Si2, in the α-SrRh2As2 structure, only every second Rh atom of a square-deformed rhodium layer lost one Rh−Rh contact (the distance increases to 3.78 Å). This can be explained by a lower filling degree of antibonding orbitals at the Fermi level of the d9 core of the Rh atoms in contrast to the d10 core of the Ni atoms. The superconducting LT modification of BaNi2As2 (VEC = 32) has been reported to have the lowest symmetry (space group P1̅) among all known ThCr2Si2 superstructures.30,76,77 Within the nickel network in the LT-BaNi2As2 structure, the Ni atoms change from a square lattice to zigzag chains, where short Ni−Ni bonds of 2.77−2.80 Å are separated by longer Ni−Ni distances of 3.10−3.12 Å. Interestingly, the structures of αSrRh2As2 (P21/c) and α-BaNi2As2 (P1̅) are not related by a direct group−subgroup relationship. The structure of αBaNi2As2 (P1̅) is a derivative of α-SrFe2As2 (Fmmm) through the CaGa4 structure (C2/m).5

The next representative of the uc-ThCr2Si2 type is the electron-rich BaZn2As2 (VEC = 36).58 Upon cooling, the structure transforms from tetragonal (I4/mmm) to orthorhombic (Pnma) with almost no relationship to the ThCr2Si2 type. However, the edge- and vertex-sharing Zn@As4 tetrahedra still exist in the three-dimensional [Zn2As2] network of LTBaZn2As2. The Zn atoms in this new network have no or only one Zn-atom neighbor. BaCu2As2 with 34 valence electrons is an exception without any phase transition, which can be explained by the “more stable” collapsed ThCr2Si2-type structure with strong covalent interlayer As−As bonding (2.57 Å).78,79 Thus, by careful examination of the T−T bonding situation in ThCr2Si2 derivatives, we found that, with an increase of the VEC, the degree of distortion within the T networks increases, along with a symmetry reduction. In other words, the excess of electrons gradually destroys the highly symmetrical square network of the transition metals. Within the abtetr plane (T layer), the T-atom arrangement changes from a regular square with four-bonded T atoms (in I4/mmm) to a distorted square with three-bonded T atoms (in Cmcm and Pnma) and further to zigzag chains with two-bonded T (in the triclinic P1̅ structure) and to one-bonded (and zero-bonded) T atoms in the LT-BaZn2As2 structure with a totally destroyed anti-PbOtype substructure. It should be noted that for the phosphorus homologues BaT2 P 228,80,81 as well as for BaRh2 As 2 ,58 BaCo2As2,82 and BaCo2Ge225 with ucT-ThCr2Si2 structure, no phase transition has been reported. An examination of the T−T distances in these compounds reveals that they are shorter than those in the previously discussed compounds, resulting in a higher stability of the structures. These T−T interactions play a crucial role in stabilization of the ThCr2Si2 type, as will be shown in the next section. Chemical Bonding. In order to analyze the electronic structure of both LT and HT modification of BaNi2Ge2 and to gain deeper insight into the origin of the structural instability in BaNi2Ge2 and other related uc-ThCr2Si2-type structures, the band structures including fat-band representations (Figures S7 and S8 in the Supporting Information), total and partial DOSs (Figure 7), and COHPs were calculated (Figure 8). The low-lying bands between −11.0 and −8 eV are predominantly Ge 4s states. The Ni 3d states are located between −5.5 eV up to the Fermi level and hybridize strongly with Ge 4p in the region from −5.5 to −2 eV (Figure 7), indicating covalent Ni−Ge bonds within the [Ni2Ge2] layers. The contribution of the barium states to the valence bands is negligible because these atoms are in the form of Ba2+ cations and thus serve as electron donors. No band gap is observed at the Fermi level of both modifications. However, a pseudogap at 0.25 eV below the Fermi level EF is more pronounced for the orthorhombic LTBaNi2Ge2, but because many bands still cross the Fermi level, the compound is metallic. In tetragonal HT-BaNi2Ge2, this pseudogap has vanished. In other words, the orthorhombic distortion in LT-BaNi2Ge2 “opens” the pseudogap. For a more quantitative bond analysis, we calculated the COHPs, which provide a quantitative measure of the bond strengths. In the presented COHP curves, positive values are bonding and negative values are antibonding (Figure 8). The integrated COHP (−iCOHP) values are given in Table 4. The −iCOHP values are in good accordance with those of other recently published Ae/Ni/Ge compounds. The strongest bonding interactions (i.e., −iCOHP values) are found for the H


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Inorganic Chemistry

Figure 7. DOS and projected DOS calculated for the (a) LTBaNi2Ge2 and (b) HT-BaNi2Ge2 structures. The energy zero is taken at the Fermi level.

shortest Ni−Ge contacts of both BaNi2Ge2 modifications, whereas the Ni−Ni interactions are much weaker. However, their positions around the Fermi energy EF are decisive for the structural stability. The COHP calculations show strongly antibonding Ni−Ni states around the Fermi energy EF for HT-BaNi2Ge2 (Figure 8b). Analysis of the fat bands in this region reveals in-plane d− d σ*-type interactions arising from the interaction of Ni dxy orbitals (Supporting Information, Figure S7), which are capable of Ni−Ni bond formation within the square network of Ni atoms. By contrast, as shown in Figure 8a, most of the Ni−Ni antibonding states in the LT-BaNi2Ge2 modification are shifted to higher-energy values above EF. This is due to the orthorhombic distortion and scission of some Ni−Ni contacts in the nickel squares (4 × 3.017 Å for HT-BaNi2Ge2) to three shorter and one longer Ni−Ni distances (2 × 2.777, 1 × 2.783, and 1 × 3.824 Å for LT-BaNi2Ge2). The −iCOHPs values for the Ni−Ni bonds in the LT modification are much higher than those for the HT modification, in contrast to the Ni−Ge bonds, which are much weaker in the LT modification than in the HT modification. Therefore, the role of the Ni−Ge bonds, which are strongest in both modifications, should not be neglected for the structural stability. Two-electron-poorer BaCo2Ge2 (VEC = 28), which is isoelectronic to BaFe2As2, crystallizes in the ucT-ThCr2Si2 type and shows, however, no structural transition. A reason for the structural stability of tetragonal uc-BaCo2Ge225 can be explained by COHP calculations. As shown in Figures 8c and S8 in the Supporting Information, the bands corresponding to Co dxy antibonding orbitals are shifted to higher-energy values above EF. This indicates a more pronounced depopulation of the antibonding Co dxy orbitals for BaCo2Ge2 (similar to those for orthorhombic LT-BaNi2Ge2), thus leading to a higher structural stability. The filling of antibonding Ni dxy orbitals at the Fermi level in HT-BaNi2Ge2 can be considered as a typical

Figure 8. COHP and −iCOHP curves for the T−T bonds within the T network in the structures of (a) LT-BaNi2Ge2 (Pnma), (b) HTBaNi2Ge2 (I4/mmm), and (c) BaCo2Ge2 (I4/mmm).

CDW scenario (also called Peierls instability), which provokes the phase transition.83−85 A similar reason for structural instabilities was described recently for the related SrRh2As2 and SrPt2As2 structures.15,16 The formation of Ge−Ge dumbbells within the [Ni2Ge2] layers has been pointed out previously34 as a reason for the phase transition in BaNi2P2−xGex. However, as was mentioned above, the Ge−Ge distance of 2.855(1) Å (as well as the small −iCOHP value of 0.324 eV) is not typical for a covalent Ge− Ge single bond, and thus the role of this intralayer Ge−Ge interaction for the stabilization of orthorhombic LT-BaNi2Ge2 is questionable. Further insight into the nature of the bonding can be provided by the ELF, sketched in Figure 9. The threedimensional ELF plot with an isosurface at η = 0.61 and contour-line diagrams of the ELF clearly highlight the electron lone pairs located at the Ge atoms in LT-BaNi2Ge2 and HTBaNi2Ge2 (parts a and b of Figure 9, respectively). These nonbonding (monotactic) ELF domains are directed from both sides toward each other to the center of the squares of the network of Ba atoms that separate the [Ni2Ge2] layers, underlining a nonbonding interlayer Ge−Ge interaction and I


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the sample holder and the diamagnetic contributions of the core electrons. No indications of either superconductivity or magnetic order were observed down to a temperature of 1.8 K. BaNi2Ge2 exhibits temperature-independent Pauli paramagnetic behavior over 20−300 K with a susceptibility of ∼4 × 10−4 emu mol−1 Oe−1, followed by an upturn of the curve below 20 K. The field dependence of magnetization obtained at 300 K shows a linear increase with the field and no tendency for saturation, clearly indicating the paramagnetic character of BaNi2Ge2. The curved development of the 2 K isotherm shows, however, weakly expressed saturation effects, probably caused by a small amount of ferromagnetic impurities (inset of Figure S10 in the Supporting Information).

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CONCLUSIONS

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ASSOCIATED CONTENT

BaNi2Ge2 has been synthesized and characterized by X-ray diffraction, DTA, electronic structure calculations, and magnetic property measurements. DTA as well as in situ temperaturedependent synchrotron powder X-ray diffraction studies showed a reversible phase transition associated with distortion of the [Ni2Ge2] layer that occurs at ca. 480 °C. The crystal structures of the two BaNi2Ge2 polymorphs are studied in detail. The anisotropy of thermal expansion of the unit cell and the discontinuous change of the lattice parameters dependent on the temperature of the two BaNi2Ge2 polymorphs reflect the strong decrease in the Ge−Ge interlayer distances in HT modification. In addition, the influence of the VEC on the structural stability of the two-dimensional (ucT) representatives of the ThCr2Si2 type has been studied. The increase of the electron number in AeT2X2 (T = transition metal; X = As, Ge, Si) leads to a gradual distortion of the square network of T atoms. In the orthorhombically distorted LT-BaNi2 Ge 2 structure, there are no Ni−Ni antibonding interactions at the Fermi level. By contrast, in HT modification, the antibonding Ni d orbitals contain more electrons at EF, which most probably causes the instability of the tetragonal structure. The shortening of intralayer T−T contacts in BaNi2Ge2 by Ni/Co substitution leads to depopulation of the antibonding d states and, consequently, to stabilization of the tetragonal structure (in BaCo2Ge2). Similarly, substitution of the large Ba2+ cations by smaller congeners could stabilize the tetragonal structure via the formation of interlayer Ge−Ge bonds. The interlayer or intralayer X−X bonds in the ThCr2Si2-type representatives or derivatives play the role of an “inhibitor” for the structural phase transition, as has been shown for the structures of BaCu2As2 and BaNi2Si2. Such tetragonal phases with “oscillating” X−X interactions, which are close to the structural instability, are of great interest, as shown in the recent investigations.34,35,86

Figure 9. Topology of the ELF for LT-BaNi2Ge2 and HT-BaNi2Ge2 calculated from the all-electron density (TB-LMTO-ASA). A threedimensional ELF plot with an isosurface at η = 0.61 and contour-line diagrams (η regions of 0.4−0.7) of the ELF for LT-BaNi2Ge2 in the ab plane (a) and for HT-BaNi2Ge2 in the ac plane (b). Contour-line diagrams of the ELF through the plane of the Ni atoms in the ac plane for LT-BaNi2Ge2 (c) and in the ab plane for HT-BaNi2Ge2 and (d) in the regions of η = 0.2−0.5 chosen for clarity.

the two-dimensionality of both BaNi2Ge2 modifications. Interestingly, the increase of the c lattice parameter with the temperature (dc/dT) is much more pronounced in the tetragonal HT modification, most probably induced by the repulsive force of these lone pairs at opposite Ge atoms. This corroborates with the shortening of the interlayer Ge−Ge distances along the c*tetr axis: 3.913(3) Å at 480 °C for LT modification versus 3.627(3) Å at 510 °C for HT modification. As mentioned before, no phase transition up to 900 °C to a tetragonal form has been observed for the structurally closely related isoelectronic homologue BaNi2Si2, which, however, possesses covalent Si−Si bonds within the [Ni2Si2] layers. This is underlined by the two-dimensional representation of the ELF (Figure S9 in the Supporting Information). The covalent Si−Si bond can easily be recognized, in contrast to the situation in the LT-BaNi2Ge2 structure (Figure 9c). Such strong covalent intralayer Si−Si bonds in BaNi2Si2 stabilize this distorted structure and prevent a structural transition. A similar stabilizing role can be attributed to the covalent interlayer X−X bonds between [T2X2] layers in ThCr2Si2 representatives with collapsed structures. For example, no distortion of the square-planar T lattice has been observed in the BaCu2As2 structure (VEC = 34) with a short As−As interlayer distance of 2.57 Å.78,79 On the other hand, the driving force of distortion of the square T lattice is the T−T d− d σ* interaction, namely, the filling degree of antibonding d orbitals of the transition metal. Magnetic Properties. For BaNi2Ge2, the temperature dependence of the molar magnetic susceptibilities χmol in an external magnetic field of 500 Oe and in the range of 1.8−300 K is presented in Figure S10 in the Supporting Information. The obtained raw magnetization data were converted to molar magnetic susceptibilities (χmol) and subsequently corrected for

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02190. Figures of powder patterns, phase evolution, magnetic susceptibility measurements, band structure calculations for BaNi2Ge2 and related compounds, T-atom networks in BaNi2Ge2 and related compounds, and topology of the ELF for BaNi2Si2 (PDF) X-ray crystallographic information in CIF format (CIF) J


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Viktor Hlukhyy: 0000-0002-7533-2670 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was financially supported by the Deutsche Forschungsgemeinschaft within the priority program SPP-1458 (Project HL 62/1-1). We thank Dr. A. Schier for revision of the manuscript and Dr. A. Senyshyn for his assistance and gratefully acknowledge the HASYLAB for providing access to their experimental facilities.

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