Crystal structure and physical properties of new

Journal of Solid State Chemistry 243 (2016) 95–100

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Crystal structure and physical properties of new Ca2TGe3 (T ¼ Pd and Pt) germanides T. Klimczuk a,n, Weiwei Xie b, M.J. Winiarski a, R. Kozioł a, L.S. Litzbarski a, Huixia Luo b, R.J. Cava b a b

Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80–233 Gdansk, Poland Department of Chemistry, Princeton University, Princeton, NJ 08544, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 16 June 2016 Received in revised form 28 July 2016 Accepted 30 July 2016 Available online 9 August 2016

The crystallographic, electronic transport and thermal properties of Ca2PdGe3 and Ca2PtGe3 are reported. The compounds crystalize in an ordered variant of the AlB2 crystal structure, in space group P6/mmm, with the lattice parameters a ¼ 8.4876(4) Å/8.4503(5) Å and c ¼ 4.1911(3) Å/4.2302(3) Å for Ca2PdGe3 and Ca2PtGe3, respectively. The resistivity data exhibit metallic behavior with residual-resistivity-ratios (RRR) of 13 for Ca2PdGe3 and 6.5 for Ca2PtGe3. No superconducting transition is observed down to 0.4 K. Specific heat studies reveal similar values of the Debye temperatures and Sommerfeld coefficients: ΘD ¼ 298 K, γ ¼ 4.1 mJ mol 1 K 2 and ΘD ¼ 305 K, γ ¼ 3.2 mJ mol 1 K 2 for Ca2PdGe3 and Ca2PtGe3, respectively. The low value of γ is in agreement with the electronic structure calculations. & 2016 Elsevier Inc. All rights reserved.

Keywords: AlB2-type structure Intermetallic compounds Germanides

1. Introduction The discovery of superconductivity with Tc near 40 K in MgB2 [1] has caused significant excitement and renewed interest in the study of compounds with the AlB2 crystal structure type. Although more than one hundred ternary intermetallic compounds that possess this structure type have been reported [2] not many of them are superconducting. The hexagonal AlB2-type structure can be described by alternating graphite-like honeycomb layers of B atoms and hexagonal layers of Al atoms, as shown in Fig. 1(a). Replacing aluminum by a rare-earth metal, and boron by silicon or germanium generates a large family of rare-earth disilicides and digermanides. In this system, superconductivity has been reported under ambient pressure for β-ThSi2 (Tc ¼ 2.4 K) [3], and above 16 GPa for CaSi2 (Tc ¼ 14 K) [4]. Partial chemical substitution leads to superconductivity in the disordered ternary compounds Sr (Ga0.37Si0.63)2 with Tc ¼ 3.4 K [5], Ca(Al0.5Si0.5)2 with Tc ¼ 7.7 K [6]. In the ternary variants, the honeycomb layer can consist of an ordered array of atoms in a 1:1 ratio, forming a KZnAs-type crystal structure, as seen for example in superconducting SrPtAs [7] presented in Fig. 1(b), or can consist of transition metal atoms (T) and Si or Ge atoms in the ratio of 1:3. In this sub-family, the rare-earth metal (R) between the layers forms a triangular lattice and the formula is R2TX3 (R ¼ rare-earth metal and X ¼ Si or Ge). Both

disordered and ordered variants of R2TX3 ternary compounds with this hexagonal (P6/mmm) crystal structure are known. The disordered version is characterized by the lattice parameter ratio c/ aE 1, e.g. R2CuSi3 (R ¼ Ce, Nd, Gd, Y) and La2TSi3 (T ¼ Fe, Ni) [8]. For these disordered compounds, superconductivity has been reported for Y2PtGe3 (Tc ¼ 3.3 K) [9] and Y2PdGe3 (Tc ¼3 K) [10]. The ordered variant of the structure is found e.g. for U2IrSi3 [11], Ce2CoSi3 [12,13] and U2RhSi3 [14]. The view of the a-b plane for the ordered version of R2TX3 is presented in Fig. 1(c), The a lattice parameter is doubled compared to AlB2and the disordered variant of R2TX3, and therefore the ratio c/a E 0.5. More complex R2TX3 intermetallics are also known, crystallizing in the Er2RhSi3 structure type (c/a E 1), e.g. R2RhSi3 (R ¼ Y, La, Ce, Nd, Sm, Gd- Er) [15], and in the CaIn2 structure type (c/a E 1.5), e.g. R2AgIn3 (R¼Pr, Nd, Tb, Ho, Er) [16]. The crystal structures and physical properties of general R2TX3 systems were reviewed in ref [17]. Here we describe synthesis, crystal structure and physical properties of the new intermetallic compounds Ca2PdGe3 and Ca2PtGe3. Although Ca2NiSi3 and Sr2NiSi3 are reported as disordered AlB2-type compounds, to the best of our knowledge, ordered-variant Ae2TX3 AlB2-type compounds containing alkali earth (Ae) metals have not been reported.

2. Experimental n

Corresponding author. E-mail address: [email protected] (T. Klimczuk).

http://dx.doi.org/10.1016/j.jssc.2016.07.029 0022-4596/& 2016 Elsevier Inc. All rights reserved.

The synthesis of Ca2TGe3 (T ¼ Pd and Pt) was performed via a

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T. Klimczuk et al. / Journal of Solid State Chemistry 243 (2016) 95–100

Fig. 1. Crystal structure of three compounds in the AlB2 family. (a) AlB2 – small and large balls stand for boron and aluminum; (b) KZnAs – large balls represent potassium, small orange and grey balls are arsenic and zinc; (c) Ca2PtSi3 – large balls represent calcium, small red and blue balls are platinum and silicon; atomic ordering on the honeycomb layers is emphasized. (d) Alternatively, the structure of Ca2PtGe3 can be represented by small rings of silicon atoms and larger rings formed by platinum atoms. Drawings were made using the VESTA software [27]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

multistep reaction method. First, stoichiometric amounts of Pd or Pt (both 99.95%, Alfa Aesar) and Ge (99.999%, Alfa Aesar) were arcmelted together under a high purity, Zr-gettered argon atmosphere; weight loss was less than 0.5 wt%. The as-melted shiny metallic droplets were then thoroughly ground and the resulting fine powders were combined with Ca pieces (99.8%, Alfa Aesar) in 15% molar excess in an alumina crucible. Due to the air sensitivity of elemental calcium, this step was done in an Ar-filled glovebox. The crucible was enclosed in a quartz glass ampoule partially backfilled with Ar ( 50 kPa). The ampoule was heated to 700°C for 3 h, ramped to 880°C at 10 deg h 1, held there for 12 h, and then cooled by an air quench. The ampoule was opened inside a glovebox and the product was ground and put into the same alumina crucible. This treatment was repeated two more times at maximum temperatures of 900°C and 920°C. In the last heating step the powder was cold pressed (applied pressure p 300 MPa) into a hard pellet with a size of approx. 5 mm diameter and 2 mm thickness. Powder XRD measurements were conducted on a Bruker D8 diffractometer with Cu Kα radiation and a Lynxeye detector. The results were processed by means of Rietveld refinement [18] using the FULLPROF 5.30 software [19]. Ca2PtGe3 was also examined at room temperature by the single crystal diffraction method on a Bruker Apex Duo diffractometer with Mo Kα radiation (the details are included in the supplemental information). Energy-dispersive X-ray spectroscopy (EDS) measurements were conducted using an Apollo-X SDD detector inside a FEI Quanta 250 FEG scanning electron microscope in high-vacuum conditions with the electron energy set to 30 keV. EDS spectra were collected on 10 points with an acquisition time of 200 s. Data were analyzed using EDAX TEAM™ software by means of a standardless method with the eZAF quantization approach. The density of the samples was estimated by the Archimedes method using a dedicated balance setup (Radwag, Poland) and employing p-xylene as an immersion liquid. Resistivity measurements were performed using a standard

four probe technique employing a Quantum Design Physical Property Measurement System (PPMS) equipped with 3He refrigerator. The contacts were made by spot welding platinum wires (50 mm diameter) on the sample surface. Heat capacity was measured in the temperature range 1.9 K o T o 300 K using the standard relaxation technique of the PPMS system.

3. Results and discussion A hard pellet of synthesized Ca2PtGe3 was studied by EDS spectroscopy. A standardless analysis gave a composition of Ca2.21(4)Pt0.94(1)Ge3 which is within error of the composition Ca2PtGe3 determined in the structural studies. The 10% excess of calcium observed may be due to experimental error, or due to elemental Ca remaining in the intergrain regions. The same observation has been made for Ca2PdGe3. The space group P6/mmm was found for Ca2PtGe3 by successful structural refinement from single crystal (see Supplemental material) and powder X-ray diffraction (PXRD) data. Both methods give similar values of the lattice parameters for Ca2PtGe3. The Rietveld refinements of the PXRD patterns for Ca2PdGe3 and Ca2PtGe3 are presented in Fig. 2 (a) and (b), respectively. The structural parameters are gathered in Table 1. Comparing the lattice parameters we can conclude that replacing Pd by Pt in Ca2TGe3 causes a shrinkage of the unit cell in the a direction and expansion in the c direction. Such lattice parameter changes cause the unit cell volumes for both compounds to be almost the same: V ¼ 261 Å3 for Ca2PdGe3 and 262 Å3 for Ca2PtGe3. The crystal structure of Ca2PdGe3 (which is also a good general representation of the structure of Ca2PtGe3) is illustrated in Fig. 1 (c). The figure emphasizes the similarity of the honeycombs found in this and other AlB2-type compounds (Fig. 1(a)). The AlB2-type structure may be regarded as a fully intercalated graphite, in the sense that all of the available hexagonal prismatic sites between


97

Table 2 Selected physical properties data for Ca2PdGe3 and Ca2PtGe3.

ρ0 (μΩ cm) ΘD (K) RRR γ (mJ mol 1 K 2)

Fig. 2. Rietveld refinement of the room temperature powder X-ray (Cu Kα radiation) diffraction data for (a) Ca2PdGe3 and (b) Ca2PtGe3. Observed data and calculated intensity are represented by the black circles and the solid red line, respectively. The difference is shown in the lower part by a solid black line. The blue vertical ticks correspond to the Bragg peaks for the space group P6/mmm (no. 191). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1 Refined structural parameters for Ca2PdGe3 and Ca2PtGe3, as refined from room temperature powder x-ray diffraction data. Ca2PdGe3 Space group Pearson symbol Z (number of formula units per unit cell) a (Å) c (Å) Cell volume (Å3) Molar weight (g mol 3) Density (g cm 3) Ca1 (3g) Ca2 (1b) T (Pd or Pt) (2c) Ge (6l)

Ca2PtGe3 P6/mmm (No. 191) hP12 2

8.4921(1) 4.1922(1) 262 404.5 5.13

d (Ge-Ge) (Å) d (T-T) (Å)

8.4520(1) 4.2188(1) 261 493.2 6.27 x ¼ z ¼ ½, y ¼ 0 x ¼ y ¼ 0, z ¼ ½ x ¼ 1/3, y ¼ 2/3, z ¼ 0 x ¼ 0.1662(1), y ¼ x ¼ 0.1650(2), y ¼ 0.3324(1), z ¼ 0 0.3300(2), z ¼ 0 2.401 2.459 4.880 4.903

Figures of merit: Rp (%) Rwp (%) Rexp (%) χ2

14.4 14.6 6.93 4.46

17.1 18.8 11.8 2.53

the honeycomb layers are filled. Honeycomb nets containing alternating atoms in a 1:1 ratio are found in the NaBeAs structure type (Fig. 1(b)) while in Ca2TGe3, the honeycomb nets are occupied by Pd/Pt and Ge in an ordered 1:3 ratio. Alternatively, the present

Ca2PdGe3

Ca2PtGe3

4 298(1) 13 4.1(1)

20 305(4) 6.5 3.2(3)

structures can be considered as made from triangular layers of Ca separated by layers that have a Ge6 ring surrounded by 6 Pd or Pt atoms that form a larger T6 ring, as shown in Fig. 1(d). The Ge-Ge near neighbor separation in the Ge6 ring for Ca2PtGe3 (dGe-Ge ¼ 2.459 Å) is larger by 2.4% than that in Ca2PdGe3 (dGe-Ge ¼ 2.401 Å), while the T-T near neighbor separation of the larger T6 ring is different only by 0.4% for the two compounds. The measured density is 4.53(14) and 5.54(30) g/cm3 for Ca2PdGe3 and Ca2PtGe3, respectively, about 12% less than the theoretical density calculated from the crystal structure model (see Table 1). This corresponds to porosity of approximately 14(2)% and 13(4)% for Ca2PdGe3 and Ca2PtGe3, respectively.(Table 2). The temperature dependence of the electrical resistivity ρ(T) of Ca2TGe3 between 0.4 K and 300 K is presented in Fig. 3. The resistivity has metallic-like character (dρ/dT 4 0) with rather low value, ρ(300 K) ¼ 51 μΩ cm for Ca2PdGe3 and 134 μΩ cm for Ca2PtGe3. A sample containing Pd reveals a large residual resistivity ratio RRR ¼ ρ300 K/ρ0.5 K ¼ 13, which is twice as large as is seen for Ca2PtGe3 (RRR ¼ 6.5). For metals in polycrystalline form, where grain boundaries can conduct poorly, and for samples with internal defects, the expected RRR is low (e.g. for polycrystalline Pd-based superconducting Heusler compounds it is about 2 [20]) and therefore the resistivity data for Ca2TGe3 suggests that no gross nonstoichiometries or site interchange is present, consistent with the ordered AlB2 structure determined by diffraction. For a polycrystalline sample of the disordered Y2PtGe3 superconductor, ρ(300 K) ¼ 440 μΩ cm and RRR ¼ 1.6 [9]. The red lines through the experimental data in Fig. 3 represent a fit that combines a Bloch-Grüneisen resistivity ρBG together with a serial resistor ρ0:

ρ(T) = ρ0 + ρBG(T), where

⎛ T ⎞5 ρBG(T) = 4RΘR⎜ ⎟ ⎝ ΘR ⎠

5

∫ (exp(x) − 1)(x1 − exp( − x)) dx.

The latter equation describes the charge carriers scattering on the acoustic phonons, where R is a temperature independent material parameter, ΘR is the Debye temperature estimated from the resistivity measurement [21]. The fit to ρ(T) gives: ρ0 ¼ 3.8 μΩ cm, ΘR ¼ 222 K, and ρ0 ¼ 19 μΩ cm, ΘR ¼ 245 K for Ca2PdGe3 and Ca2PtGe3, respectively. There is no superconducting transition observed down to 0.4 K, as shown in the inset of Fig. 3. The main panels of Fig. 4(a) and (b) illustrate the temperature dependencies of the specific heat (Cp). At room temperature, for both compounds the specific heat Cp(T) reaches the expected Dulong-Petit value (3nR E 150 J mol 1 K 1), where R is the gas constant (R ¼ 8.314 J mol 1 K 1), and n is the number of atoms per formula unit (n ¼ 6). The insets of Fig. 4 show Cp/T versus T2 at temperatures below 6.5 K. The experimental data points for both samples were fitted in the temperature range of 1.9–6.3 K, using the formula Cp/T ¼ γ þ βT2 þ δT4, in which the first term is the electronic contribution and the last two terms are the lattice contribution to the specific heat. The fits yield slightly larger Sommerfeld coefficient γ ¼ 4.1(1) mJ mol 1 K 2 for Ca2PdGe3 than the γ ¼ 3.2(3) mJ mol 1 K 2 obtained for Ca2PtGe3. In a

98


Fig. 3. Electrical resistivity versus temperature for (a) Ca2PdGe3 and (b) Ca2PtGe3. Applied magnetic field μ0H ¼ 0 T. The solid red lines are fits that combine Bloch Grüneisen resistivity ρBG together with a serial resistor ρ0. Inset: low temperature ρ(T) showing the absence of a superconducting transition above 0.4 K. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Temperature dependence of the heat capacity (Cp) for (a) Ca2PdGe3 and (b) Ca2PtGe3. The solid blue line is a fit to a combined the Debye (solid black line) and the Einstein model (dashed line). Inset shows Cp/T versus T2 in which solid red line is fit by expression Cp/T ¼ γ þ βT2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)


simple Debye model, the

β coefficient is related to the Debye

30

⎛ 12π4 ⎞1/3 temperature (ΘD) through ΘD = ⎜ 5β nR⎟ , and the estimated ⎝ ⎠ Debye temperatures for both compounds are almost identical: 298 (1) K and 305(4) K for Ca2PdGe3 and Ca2PtGe3, respectively. Taking these values of the Debye temperature, the heat capacity based on the Debye model CD (solid black lines) was plotted in the main panel of Fig. 4(a) and (b). Although close to the experimental points, CD is not large enough to reach them above 20 K. Therefore we fitted the data in the temperature range 5–300 K by using following formula: Cp = γT + kCDebye(T) + (1 − k)CEinstein(T), in which higher energy optical vibration modes are considered. The first term (γT) is the electronic contribution, with γ fixed at the values determined from the low temperature fit. The two other terms are phonon contributions to the specific heat given by Debye (CDebye) and Einstein (CEinstein) models:

⎛ T ⎞3 CDebye(T) = 9nR⎜ ⎟ ⎝ ΘD ⎠

∫

99

Ca2PdGe3 Ca2PtGe3

DOS(States/eV)

25 20 15 10 5 0 -6

-5

-4

-3

-2

-1

0

1

2

Energy (eV)

x4exp(x) dx, 2 [exp(x) − 1]

Ca2PdGe3

Ca2PtGe3

2.0

and

The k parameter corresponds to the weight of the Debye term, and ΘD and ΘE are the Debye and Einstein temperatures respectively. The fit represented by solid red lines in Fig. 4, gave the values k ¼ 0.87, ΘE ¼ 124(20) K, ΘD ¼ 292(8) K and k ¼ 0.88, ΘE ¼ 86(17) K, ΘD ¼ 302(10) K for Ca2PdGe3 and Ca2PtGe3, respectively. For both compounds the estimated values are very close, suggesting that the phonon spectra should be very similar.

1.0

Energy (eV)

⎤−2 ⎛Θ ⎞ ⎛ Θ ⎞2 ⎛ Θ ⎞⎡ CEinstein (T) = 3nR⎜ E ⎟ exp⎜ E ⎟⎢exp⎜ E ⎟ − 1⎥ . ⎝ T ⎠ ⎝ T ⎠ ⎝ T ⎠⎣ ⎦

0.0

-1.0

-2.0

4. Electronic structure Applying simple electron counting rules (i.e. based on the transfer of valence electrons from the most electropositive to the most electronegative elements to fill their valence orbitals) to Ca2TGe3 (T ¼ Pd and Pt) to account for the stability of the AlB2derived structure observed is challenging and likely not valid because it is difficult to assign a formal charge to the T (Pd and Pt) atom [22]. In particular, depending upon the electronegativity scale employed, T can be more electronegative than Ge (i.e. it is more electronegative according to Pauling's scale [23], which uses bond enthalpies and Allen's configuration energies to estimate electronegativities (χPd ¼ 2.20; χPt ¼ 2.28 and χGe ¼ 2.01), and Mulliken's scale or Pearson's absolute electronegativities [24] which are derived from gas-phase ionization energies and electron affinities.) causing a chemically-unclear electron distribution that motivated us to study the electronic structure of Ca2TGe3 computationally. The calculated density of states and band structure of Ca2TGe3 are thus represented in Fig. 5, as obtained by the WIEN2k method [25] with spin-orbit coupling and 10 10 10 k-points. For self-consistency the structural parameters for Ca2PtGe3 and Ca2PdGe3 were taken from the Rietveld refinement of the PXRD patterns. Combining the DOS and fatband calculations, the Ge 4s and Td orbitals can be seen to create a narrow band located 2– 6 eV below the Fermi level. The Fermi level is located at a deep minimum (pseudogap) of the DOS, which is an indication of overall electronic and compound stability. The pseudogap in the DOS provides an explanation for why the Ca2TGe3 structure is stable at 26 e-/f.u.. It can thus can be written in an ionic formula as “2Ca2 þ (TGe3)4-”; i.e. if the electron transfer from the electropositive Ca2 atom layer to the PtGe3 sheet is considered complete, then the sheet itself is nominally isoelectronic with graphite [26]. The fatband calculations for Ge and T show that the hybridization

MK

H

A

MK

H

A

Fig. 5. Calculated electronic structures of Ca2PdGe3 and Ca2PtGe3 using the experimentally determined crystal structures (from powder X-ray diffraction data). Total DOS curves and band structure curves are obtained from non-spin-polarized LDA calculations with spin-orbit coupling.

between Ge 4p and Td orbitals contributes most around the Fermi level.

5. Conclusions In summary, we have successfully synthesized Ca2PdGe3 and Ca2PtGe3, which are the first members of a new Ae2PtGe3 (Ae ¼ alkaline earth metal) family. They form in a hexagonal structure, an ordered variant of AlB2 type, as refined from single crystal and powder X-ray diffraction data. The fit to the low temperature heat capacity reveals rather low values of the Sommerfeld coefficients γ ¼ 4.1 mJ mol 1 K 2 and 3.2 mJ mol 1 K 2 for Ca2PdGe3 and Ca2PtGe3, respectively. Since the density of states at the Fermi energy DOS(EF) is proportional to the Sommerfeld coefficient, we can conclude that DOS(EF) for Ca2PdGe3 and Ca2PtGe3 is low. Both compounds are good metals and superconductivity has not been detected down to 0.4 K. This is in contrast to the observation of superconductivity in Y2PtGe3 (Tc ¼ 3.3 K) [9] and Y2PdGe3 (Tc ¼ 3 K) [10], which form in a disordered variant of AlB2 crystal structure. The electronic structure calculations for Y2TGe3 (T ¼ Pd, Pt) reveal that Y 4d states dominate the Fermi level and hence superconductivity is related to the hexagonal Y layer [10]. Our calculations show that for Ca2TGe3 the Fermi level is located at a deep minimum of the DOS which, while explaining the compound's stability also can explain its lack of superconductivity. Use of chemical methods to vary the size of the lattice or the electron

100


count to induce superconductivity in these phases may be of future interest.

Acknowledgments The research performed at Princeton University was supported by the Gordon and Betty Moore Foundation through its EPiQS program, Grant GBMF-4412. The research performed at the Gdansk University of Technology was supported by the National Science Centre (Poland) Grant (DEC-2012/07/E/ST3/00584).

Appendix A. Supplementary information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jssc.2016.07.029.

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