BaAl 4 derivative phases in the sections {La,Ce}-Ni 2 Si 2 – {La,Ce}Zn 2 Si 2 : phase relations, crystal structures and physical properties †‡

Phase relations and crystal structures have been evaluated within the sections LaNi 2 Si 2 – LaZn 2 Si 2 and CeNi 2 Si 2 – CeZn 2 Si 2 at 800 °C using electron microprobe analysis and X-ray powder and single crystal structure analyses. Although the systems La – Zn – Si and Ce – Zn – Si at 800 °C do not reveal compounds such as “ LaZn 2 Si 2 ” or “ CeZn 2 Si 2 ” , solid solutions {La,Ce}(Ni 1 − x Zn x ) 2 Si 2 exist with the Ni/Zn substitution starting from {La,Ce}Ni 2 Si 2 (ThCr 2 Si 2 -type; I 4/ mmm ) up to x = 0.18 for Ce(Ni 1 − x Zn x ) 2 Si 2 and x = 0.125 for La(Ni 1 − x Zn x ) 2 Si 2 . For higher Zn-contents 0.25 ≤ x ≤ 0.55 the solutions adopt the CaBe 2 Ge 2 -type ( P 4/ nmm ). The investigations are backed by single crystal X-ray di ﬀ raction data for Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 ( P 4/ nmm ; a = 0.41022(1) nm, c = 0.98146(4) nm; R F = 0.012) and by Rietveld re ﬁ nement for La(Ni 0.56 Zn 0.44 ) 2 Si 2 ( P 4/ nmm ; a = 0.41680(6) nm, c = 0.99364(4) nm; R F = 0.043). Interestingly, the Ce – Zn – Si system contains a ternary phase CeZn 2 (Si 1 − x Zn x ) 2 of the ThCr 2 Si 2 structure type (0.25 ≤ x ≤ 0.30 at 600 °C), which forms peritectically at T = 695 °C but does not include the composition “ CeZn 2 Si 2 ” . The primitive high temperature tetragonal phase with the CaBe 2 Ge 2 -type has also been observed for the ﬁ rst time in the Ce – Ni – Si system at CeNi 2+ x Si 2 − x , x = 0.33 (single crystal data, P 4/ nmm ; a = 0.40150(2) nm, c = 0.95210(2) nm; R F = 0.0163). Physical properties (from 400 mK to 300 K) including speci ﬁ c heat, electrical resistivity and magnetic susceptibility have been elucidated for Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 and La(Ni 0.56 Zn 0.44 ) 2 Si 2 . Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 exhibits a Kondo-type ground state. Low temperature speci ﬁ c heat data of La(Ni 0.56 Zn 0.44 ) 2 Si 2 suggest a spin ﬂ uctuation scenario with an enhanced value of the Sommerfeld constant.


Introduction
Since its discovery in 1935 by Andress and Alberti, 1 the BaAl 4 structure type and its derivatives have been found in more than 200 intermetallic compounds, particularly the three tetragonal ternary variants: the ThCr 2 Si 2 -type by Ban and Sikirica 2 (or CeAl 2 Ga 2 -type discovered independently by Zarechnyuk et al. 3 in the same year), CaBe 2 Ge 2 by Eisenmann et al. 4 and the noncentrosymmetric variant BaNiSn 3 by Dörrscheidt and Schäfer. 5 The BaAl 4 structure type furthermore is one of the building blocks of various structure types, such as U 3 Ni 4 Si 4 , CeNiSi 2 (in combination with AlB 2 -type slabs) and many others. 6 Although phase equilibria in the Ce-Ni-Si system were investigated in the 70s by Bodak et al. 7,8 more ternary phases were discovered afterwards: Ce 2 Ni 3 Si 5 (U 2 Co 3 Si 5 -type, orthorhombic superstructure variant of BaAl 4 ), 9 Ce 14 Ni 6 Si 11 , 10 Ce 3 NiSi 3 , 11 etc. Being the last member of the first row of transition metals, Zn containing ternary rare earth silicon systems had been one of the least investigated types of systems. Only some reports on the formation of ternary compounds could be found in the literature. 12 Recently our report 13 on the Ce-Zn-Si system at 800°C revealed the formation of several ternary phases. Surprisingly neither BaAl 4 nor its derivative structure could be found in the system at 800°C, instead a far off-stoichiometric ThCr 2 Si 2 -type CeZn 2+x Si 2−x (x ∼ 0.5, labelled as τ 6 ) was found to be stable at temperatures below 695 ± 5°C. 14 Compounds crystallizing in the BaAl 4 type or its derivatives are often associated with various exotic superconducting phenomena, starting with the discovery of heavy fermion superconductivity in CeCu 2 Si 2 by Steglich et al. in 1979, 15 which breaks the previous belief of non-coexistence between magnetism and superconductivity. Spin density wave transition was found in BaFe 2 As 2 , 16 followed by the discovery of superconductivity in K-doped 17 and Co-doped BaFe 2 As 2 . 18 More recently, BCS-like superconductivity was found in noncentrosymmetric BaPtSi 3 (BaNiSn 3 -type) 19 and isotypes. 20 In cerium and actinoid compounds the hybridization of the Ce-f electrons with the conduction band gives rise to various kinds of interesting physical phenomena. Systematic studies of the transport, magnetic and calorimetric properties and Ce L III X-ray absorption spectra and XPS measurements characterized CeNi 2 Si 2 as an intermediate valence (valence fluctuation) system with a characteristic Kondo-lattice temperature T* ∼ 600 K. [21][22][23][24][25][26] The positive Seebeck coefficient, decreasing with the Si content in CeNi 2−x Si 2+x was taken as a decrease of the electronic DOS particularly of the Ni-3d-states at the Fermi level concomitant with a narrowing of the Ce-4f level and a decreasing Ce-valence. 27 The replacement of Ni by Pd, Cu, Au drives the Ce from an intermediate valence (IV) to a non-IV ground state. [21][22][23][24][25][26][27] Probably because of the non-existence of compounds "LaZn 2 Si 2 " and "CeZn 2 Si 2 ", the corresponding isopleths {La,Ce}Ni 2 Si 2 -{La,Ce}Zn 2 Si 2 have not attracted interest.
Therefore the present work intends to provide detailed information on the phase equilibria, crystal structures and physical properties of the novel BaAl 4 -derivative phases in the systems {La,Ce}-Ni-Si as well as in the isopleths {La,Ce}Ni 2 Si 2 -{La,Ce}Zn 2 Si 2 .
Polycrystalline bulk samples for the analysis of the quaternary isopleths {La,Ce}(Ni 1−x Zn x ) 2 Si 2 and for physical property studies were prepared from intimate blends of powders of arc melted master alloys {La,Ce}Ni 2−x Si 2 (various x; powdered under cyclohexane) and fine Zn-filings in appropriate compositional ratios. These blends were cold compacted in a steel die without lubricants, vacuum-sealed in quartz tubes, heated from 420°C to 800°C at the rate of 1°C min −1 and then annealed at this temperature for 7 days. After water quenching the samples were re-powderized (under cyclohexane) in order to ensure homogeneity. The samples were loaded into 10 mm diameter graphite dies for hot pressing under Ar in a uniaxial hot press system (HP W 200/250-2200-200-KS) at 800°C for 1 hour employing a pressure of 56 MPa. Densities of the samples have been calculated from their dimensions and masses after removing a 0.5 mm thick surface layer (grinding with SiC paper). X-ray powder diffraction data were collected from each alloy employing a Guinier-Huber image plate system with monochromatic CuK α1 radiation (8°< 2θ < 100°). Precise lattice parameters were calculated by least squares fits to the indexed 2θ values calibrated with Ge as the internal standard (a Ge = 0.565791 nm). Quantitative Rietveld refinements of the X-ray powder diffraction data were performed with the FULLPROF program. 28 Single crystals from the systems {La,Ce}-Ni-Si were picked from crushed reguli. Quaternary single crystals were grown from Zn flux starting from a cold compacted pellet (Ce 2 Ni 4 Si 8 + Zn-filings = Ce 2 Ni 4 Si 8 Zn 86 (in at.%)), which was heated to 900°C at the rate of 1°C min −1 and then cooled to 800°C at the same rate. After annealing for 4 days at this temperature the sample was subsequently quenched in water and then boiled with 15% aqueous solution of HCl in a water bath in order to dissolve the extra Zn. Crystals were carefully washed with distilled water and dried.
Inspections on an AXS-GADDS texture goniometer assured the high crystal quality, unit cell dimensions and Laue symmetry of the specimens prior to the X-ray intensity data collections on a four-circle Nonius Kappa diffractometer equipped with a CCD area detector employing graphite monochromated MoKα radiation (λ = 0.071069 nm). Orientation matrices and unit cell parameters were derived using the program DENZO. 29 Besides the general treatment of absorption effects using the multi-scan technique (redundancy of integrated reflections >8) no additional absorption corrections were performed because of the rather regular crystal shapes and small dimensions of the investigated specimens. The structures were solved by direct methods and were refined with the SHELXL-97 program 30 within the Windows version WinGX. 31 After the reaction during annealing the samples had almost a powder-like consistency, too soft to be polished by standard procedures. This problem was overcome by casting the sample powder along with conducting glue into a cylindrical mould of ∼5 mm diameter. After hardening several of the powder cylinders were hot compacted in conductive resin and were ground and polished under glycerine instead of water in order to avoid oxidation of the samples. Microstructures and compositions were examined by light optical microscopy (LOM) and scanning electron microscopy (SEM) via Electron Probe Micro-Analyses (EPMA) on a Zeiss Supra 55 VP equipped with an EDX system operated at 20 kV.
Physical property measurements (magnetic susceptibility, electrical resistivity, and specific heat) were performed on the hot pressed samples with methods described in our previous publications, e.g. ref. 32.

Results and discussion
3.1. The BaAl 4 -type derivative phases in the systems La-Ni-Si and Ce-Ni-Si systems contain a compound {La,Ce}Ni 2 Si 2 which was reported to crystallize in the ThCr 2 Si 2 type 34 with a practically negligible homogeneity range. A thorough check on these findings prompted us to prepare samples with the nominal composition {La,Ce} 20 Ni 40 Si 40 (in at.%). As-cast alloys as well as samples annealed at 800°C for 4 days revealed nearly a single phase condition with the ThCr 2 Si 2 type, thus suggesting a congruent or a degenerate peritectic formation of these phases, and furthermore confirmed the crystal structure data from Bodak et al. 34 Levin et al. 27 studied the homogeneity range of CeNi 2 Si 2 (ThCr 2 Si 2 -type) at a relatively low temperature of 727°C and discovered a rather large homogeneity range of 8 at.% ranging from 36 to 44 at.% Si. Our reinvestigation (EPMA) of the phase relations around CeNi 2 Si 2 at 800°C reveals a smaller homogeneity range for the ThCr 2 Si 2 type of ∼4 at.% from 38.3 to 42.3 at.% Si. Our lattice parameters (see Fig. 1), however, agree well with the result of Levin et al. 27 In general the Ni/Si substitution does not affect the a-axis much, however one can see that the c-axis decreases almost linearly with increasing Ni content. In an attempt to investigate the crystal structure of CeNi 4 Si 35 we discovered a Ni-rich phase CeNi 2+x Si 2−x (x ∼ 0.3). EPM analysis of an as-cast alloy with a slightly higher Ni-content (Ce 20 Ni 43 Si 37 ) showed primary crystallization of Ce 20 Ni 41 Si 39 followed by a peritectic-like formation of a thin layer of Ce 20 Ni 46 Si 34 (see Fig. 2). The remaining liquid crystallized as CeNi 4 Si and a novel phase   20 Ni 60 Si 20 a single crystal suitable for X-ray structure analysis (see below) was selected.
3.1.1. The crystal structure of CeNi 2+x Si 2−x , x = 0.33 with the CaBe 2 Ge 2 -type. A single crystal, extracted from an as-cast alloy with a nominal composition of Ce 20 Ni 60 Si 20 revealed unit cell parameters (a = 0.40150(2) and c = 0.95210(2) nm) consistent at first glance with a body centred ThCr 2 Si 2 type, but additional weak reflections could be satisfactorily indexed on the basis of a primitive Bravais cell. Systematic extinctions suggested the space group type P4/nmm for the highest crystal symmetry. Direct methods indicated Ce, Ni, Si atoms in positions typical for the CaBe 2 Ge 2 -type, where the electropositive atom occupies the 2c site (1/4, 1/4, ∼0.75), the transition metal atoms occupy a 2c site (1/4, 1/4, ∼0.1) and a 2b site (3/4, 1/4, 1/2), and the tetrel atoms occupy the sites 2c (1/4, 1/4, ∼0.35) and 2a (3/4, 1/4, 0). Refinement with anisotropic atom displacement parameters (ADPs) converged to R F = 0.0163 and residual electron densities smaller than ±1.53 e − Å −3 with fully occupied metal sites but for a statistical occupation of 0.33Ni + 0.67Si in site 2a of P4/nmm, which was fixed after the EPMA value. Thus, a structure formula CeNi 2+x Si 2−x , x = 0.33, results, which corresponds to the composition Ce 20 Ni 46.5 Si 33.5 close to the ThCr 2 Si 2 -type phase. Crystal data for CeNi 2+x Si 2−x along with the ADPs are summarized in Table 1. Although attempts to refine the Ni/Si ratio at the 2a site yield a lower R F of 0.011 and a residual electron density less than 0.87 e − Å −3 , the resulting Ni content (0.22(1)Ni + 0.78Si) corresponds to the composition Ce 20 Ni 44.5 Si 35.5 deviating significantly from the EPMA derived composition. Thus we prefer the EPMA value and the corresponding formula CeNi 2+x Si 2−x , x = 0.33.
It is worth mentioning that although the primitive reflections in CaBe 2 Ge 2 -type CeNi 2+x Si 2−x are relatively small, they are still visible in the single-phase powder diffraction spectra. Interestingly, neither a Ni-rich composition nor primitive reflections could be observed at 800°C in alloys at the Ni-rich side of the 1 : 2 : 2 stoichiometry. This strongly suggests that the primitive CaBe 2 Ge 2 -type phase CeNi 2+x Si 2−x is a high temperature phase. Alloys at the Ni-rich side of 1 : 2 : 2 annealed at 1000°C indeed show the Ni-rich composition Ce 20 Ni ∼46 Si ∼34 in equilibrium with CeNi 4 Si and Ce(Ni 1−x Si x ) 3 . Consequently, the X-ray powder diffraction spectra show two sets of BaAl 4type reflections (see Fig. 2). As the sample is multiphase, it is rather difficult to identify the primitive peaks, however, the lattice parameters of one of the BaAl 4 derivative phases show a shorter c-axis, which is closer to the value of CeNi 2+x Si 2−x with the primitive CaBe 2 Ge 2 -type as obtained from the single crystal data. The other set of BaAl 4 derivative reflections give similar unit cell parameters as for CeNi 2 Si 2 with the ThCr 2 Si 2 -type. These observations, together with the fact that a single crystal was obtained from an as-cast alloy led us to conclude that CeNi 2+x Si 2−x with the primitive CaBe 2 Ge 2 -type is a high temperature phase (1000°C ≤ T stability < 1615°C). 36 Polymorphism between ThCr 2 Si 2 -and CaBe 2 Ge 2 -types is often encountered in various systems, particularly for ternary rare earth silicides containing Ir and Pt. 12 In some cases, e.g. in the La-Ir-Si system, 37 the CaBe 2 Ge 2 -type is the high temperature form, whilst the ThCr 2 Si 2 -type is stable at lower temperatures. Therefore CeNi 2+x Si 2−x with the primitive CaBe 2 Ge 2type is hitherto the first example of ThCr 2 Si 2 -CaBe 2 Ge 2 polymorphism found in ternary rare earth silicides with 3d transition metal elements. The slight flattening of the unit cell, i.e. the shorter length of the c-axis observed in CeNi 2+x Si 2−x (CaBe 2 Ge 2 -type), is also commonly found in many systems exhibiting such polymorphism. 12 Besides the temperature effect, the substitution of Si by Ni at the 2a-site may act as a driving force for the structural change from a body centred to a primitive atom arrangement in terms of a group-subgroup relation. This idea comes from the fact that an alloy with stoichiometric composition CeNi 2 Si 2 does not show any changes in the powder diffraction spectra in the as-cast state, and after annealing at 1000°C for 4 days. An example of structural evolution at a constant temperature can be found in the Sr-Au-Ge system 38 where at 700°C, increasing the Ge content in SrAu 2−x Ge 2+x led to a series of structural changes from the ThCr 2 Si 2 -type to the BaCu 2 Sb 2type and finally to the CaBe 2 Ge 2 -type, where all structure types are variants of the BaAl 4 -type.
3.2. The quaternary solution phases La(Ni 1−x Zn x ) 2 Si 2 and Ce(Ni 1−x Zn x ) 2 Si 2 As neither stoichiometric CeZn 2 Si 2 nor off-stoichiometric CeZn 2+x Si 2−x (x ∼ 0.5) exists in the Ce-Zn-Si system at 800°C, it is interesting to investigate the extent of solubility of Zn in the CeNi 2 Si 2 phase at 800°C. Stoichiometric body centred CeNi 2 Si 2 is found to substitute for Ni up to 18% Zn, i.e. Ce(Ni 1−x Zn x ) 2 Si 2 , x = 0.18. The substitution of Zn for Ni is also reflected in the gradual increase of the unit cell parameters (Fig. 1). For further Zn substitution the Bravais lattice changes from body centered to primitive, as indicated by the appearance of additional weak reflections that violate the systematic extinction of a body-centred cell. The samples remain single phase up to x = 0.55 at 800°C. On further Zn substitution the samples became multiphase, indicating that the solubility limit has been reached. Since the primitive CaBe 2 Ge 2 -type phase also exists in the Ce-Ni-Si end member system at a high temperature in the Nirich side, and the body centred ThCr 2 Si 2 -type phase extends slightly to both the Ni-and Si-rich sides at 800°C, we suspected that a slight deviation from the stoichiometric 1 : 2 : 2 composition could stabilize/destabilize one of these structure types with the incorporation of Zn. Such a situation is often found in various systems, e.g. in the Ce-Zn-Si system at 800°C 13 or Ce-Ag-Si at 500°C 40 where two compositional polymorphic modifications of CeSi 2 with the α-ThSi 2 type and the α-GdSi 2 type dissolve transition metal elements, however, the α-GdSi 2 -based solid solutions end prematurely while the α-ThSi 2 -based solid solutions extend further up to ∼20 at.% transition metal content.
In order to check the possibility of such a scenario we prepared several alloys with off-stoichiometric compositions. Although the nominal compositions deviate far (∼5 at.%) from the 1 : 2 : 2 composition, only a small variation (±1 at.%) in the homogeneity range could be observed in the quaternary 122 phase. A variation of unit cell parameters of alloys in both the Si-poor and rich parts of the 122 stoichiometry shows good agreement with those from the stoichiometric 122 alloys. This suggests that there is no parallel solid solution running beside the one shown in Fig. 1. 3.2.1. The crystal structures of {La,Ce}(Ni 1−x Zn x ) 2 Si 2 with the CaBe 2 Ge 2 -type. In order to get details on the primitive unit cell, a single crystal has been selected from the flux residuals of an alloy with the composition Ce 2 Ni 4 Si 8 Zn 86 (in at.%), slowly cooled from 900°C. A SEM analysis performed directly on the crystals separated from the flux (shown in Fig. 3), defined the composition as Ce 19.4 Ni 25.3 Zn 16.1 Si 39.2 (at.%). Unit cell, systematic extinctions (indicating P4/nmm as the space group type of highest symmetry) as well as the X-ray intensity pattern confirmed a structure solution in terms of  the CaBe 2 Ge 2 -type. It should be mentioned, however, that six reflections with I obs > 4σ(I) violated the space group extinction rules: (010), (210), (210), (230), (230) and (340). In comparison with the highest intensity observed (12 000 counts), the (210), (210), (230), (230) reflection intensities are below 2 counts and can be disregarded, whereas the (010) intensity (below 7 counts) may stem from a 'Renninger enhancement' effect. Interestingly, the site occupation of the transition metal and tetrel atoms is exchanged, i.e. the tetrel atoms occupy sites 2c (1/4, 1/4, ∼0.1) and 2b, whilst the transition metal atoms occupy sites 2c (1/4, 1/4, ∼0.35) and 2a. This site exchange configuration gives rise to the intensity of the primitive reflections, therefore the CaBe 2 Ge 2 -type phases can be identified easily in the quaternary system by X-ray powder diffraction.
Although the small differences in the X-ray scattering power of Ni and Zn make it difficult to unambiguously differentiate between these atom types, it was possible to define the site occupation of Zn by analyzing site ADPs. As the ADPs of the two Si sites did not show any anomalies, it was certain that Zn occupied one or both of the Ni sites. Among all remaining combinations of Zn site occupations, the lowest R F was found when Zn substituted Ni at the 2a site. Although it was possible to refine the Ni/Zn occupancy at this site, the resulting value (0.48(3)Ni + 0.52Zn) deviates far from the value obtained by EPMA: 0.22Ni + 0.78Zn. Therefore, in the final refinement the Ni/Zn occupancy was fixed according to EPMA, resulting in the structure formula Ce(Ni 1−x Zn x ) 2 Si 2 , x = 0.39 (i.e. Ce 20 Ni 24.4 Zn 15.6 Si 40 ).
The final refinement converged to R F = 0.0134 and residual electron densities were less than ±1.48 electrons per Å 3 for three metal and two Si positions with a Wyckoff sequence     Table 2; interatomic distances are presented in Table 3; coordination polyhedra for all atom sites and a three-dimensional view on the crystal structure are presented in Fig. I Fig. 4 clearly reveals an atom site exchange in the tetrahedron-layers sandwiching the Ce-atoms: Ni-and Si-layers are exchanged. However, it is interesting to see that the random substitution of Ni/Si and Ni/Zn always occurs at the same site (2a site).
Several examples of such site exchange variants of the CaBe 2 Ge 2 -structure type can be found in the literature, particularly for ternary stannides and antimonides, e.g. Ce{Ni,Cu,Pd, Ir,Pt} 2 Sn 2 . 12 For ternary silicides, only the high temperature modification LaIr 2 Si 2 37 is known to exhibit such a site exchange arrangement. A similar situation is also encountered in quaternary Ce(Cu 1−x Ag x ) 2−y Sb 2 . 41 In contrast to primitive Ce(Ni 1−x Zn x ) 2 Si 2 , where the occupation of Zn/Si sites is inverted with respect to primitive CeNi 2+x Si 2−x , body centred Ce(Ni 1−x Zn x ) 2 Si 2 as well as offstoichiometric CeZn 2+x Si 2−x (x ∼ 0.5) do not exhibit such a site exchange.
The Rietveld refinement performed on single-phase body centred Ce(Ni 1−x Zn x ) 2 Si 2 (x = 0.18) shows that Zn substitutes Ni at the 4d site, while the 4e site remains fully occupied by Si. In the case of ternary CeZn 2+x Si 2−x (x = 0.5), due to the higher Zn-content, Zn and Si share the 4e site with a ratio of 3 : 7 whereas the 4d site is fully occupied by Zn. 14 A detailed groupsubgroup diagram relating the parent BaAl 4 structure to the ThCr 2 Si 2 and CaBe 2 Ge 2 for the various phases in the Ce-Ni-Zn-Si system is presented in terms of a Bärnighausen tree, depicted in Fig. II of the ESI. ‡ In analogy to the section Ce(Ni 1−x Zn x ) 2 Si 2 , phase relations have also been explored for the isopleth La(Ni 1−x Zn x ) 2 Si 2 (see Fig. 1). Combined EPM and X-ray powder intensity data analyses revealed a solid solution with the ThCr 2 Si 2 -type for 0 ≤ x ≤ 0.125, followed by a change to a primitive tetragonal symmetry typical for the CaBe 2 Ge 2 -type for 0.25 ≤ x ≤ 0.55. The solid solution terminates at x = 0.55 as for higher Zn-concentrations multiphase X-ray spectra were observed. Rietveld refinement data for La(Ni 0.56 Zn 0.44 ) 2 Si 2 are summarized in Table 2  3.3.1. La(Ni 1−x Zn x ) 2 Si 2 . La(Ni 1−x Zn x ) 2 Si 2 , x = 0.44 was studied down to 400 mK, but no phase transition, indicating e.g., superconductivity was observed. The temperature dependent heat capacity, C p , of La(Ni 0.56 Zn 0.44 ) 2 Si 2 is shown in Fig. 6(a) and plotted as C p /T vs. T. Unexpectedly, C p /T (T ) exhibits a minimum around 2.5 K below which the electronic con-  tribution tends towards 20 mJ mol −1 K −2 for T ∼ 0, a value larger than what is likely for simple intermetallic compounds. The overall shape, however, reminds one of spin fluctuation systems like YCo 2 or UAl 2 . 42 In order to prove such a proposition, the standard spin fluctuation ansatz, C p (T ) = γT + βT 3 + δT 3 ln(T/T*) is employed to the experimental data, revealing excellent agreement for γ = 13 mJ mol −1 K −2 and T* = 8.7 K (solid line, inset Fig. 6(a)). This agreement would suggest spin fluctuations in the nearly localized regime present in La(Ni 0.56 Zn 0.44 ) 2 Si 2 . The fit parameter β = 0.13 mJ mol −1 K −4 allows the estimation of a Debye temperature of about 460 K, referring to the rather stiff lattice of this system. The resistivity, ρ, of La(Ni 0.56 Zn 0.44 ) 2 Si 2 was studied within the temperature range 4.2-300 K. At elevated temperatures (T > 100 K) ρ(T ) behaves metallic-like. The almost linear slope of ρ(T ) refers predominantly to electron-phonon interactions. A shallow minimum is observed at about 25 K and below this temperature the resistivity increases with decreasing temperature (see Fig. 6(b)). A plot of the resistivity on a logarithmic temperature scale (inset, Fig. 6(b)) for various externally applied magnetic fields reveals, unexpectedly a logarithmic behaviour, indicating Kondo-type interactions, which might be attributed to a small amount of uncompensated Ni spins. These features were reproduced in several independently prepared samples and comply with the enhanced value of the Sommerfeld constant deduced from the specific heat experiment.
3.3.2. Ce(Ni 1−x Zn x ) 2 Si 2 . Fig. 7-9 reveal experimental results regarding the magnetic properties of Ce(Ni 1−x Zn x ) 2 Si 2 , x = 0.39. Ce in its atomistic form possesses one electron in the 4f shell, constituting the 4f 1 electronic configuration (EC) and thus carries a total angular momentum j = 5/2. This gives rise to a non-vanishing magnetic moment. In the case of cerium and ytterbium compounds, however, partial hybridisation with the conduction electron system is possible. Its degree depends on the compound's specific electronic structure and in solid solutions on the local chemical environment, i.e., Ce moments varying with the Ni/Zn random occupation in the title compound.
A simple proof of whether or not this EC is preserved in the solid state of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 can be obtained from temperature dependent magnetic measurements. The inverse magnetic susceptibility at 3 T is shown in Fig. 7(a). Phase transitions above 2.5 K are not obtained from this measurement. A quantitative description of the high temperature magnetic susceptibility (50-300 K) can be made by applying a modified Curie Weiss law, revealing a temperature independent Pauli susceptibility (χ 0 = 3.9 × 10 −4 emu mol −1 ), an effective magnetic moment, which is related to the Curie constant (μ eff = 2.20μ B /Ce) and a paramagnetic Curie temperature (θ p = −35 K) from a least squares fit of this model to the experimental data (solid line, Fig. 7(a)).
A negative paramagnetic Curie temperature, in general, refers to antiferromagnetic interactions between conduction electrons and the almost localized Ce 4f electrons. Crystalline electric field (CEF) effects, lifting the 2j + 1 = 6 fold degenerate ground state, as well as the Kondo effect, modify, however, the absolute value of θ p . The effective magnetic moment observed from the Curie Weiss law is below that (2.54μ B ) expected for the free ion Ce 3+ state (EC: 4f 1 ). This reduction may be caused by the fraction of Ce ions in the Ni richer environments, whereas Zn tends to stabilise the Ce 3+ local moment character.
The slight curvature observed in the 1/χ vs. T data-set might result from CEF effects which are simply modelled here by adjusting the parameter χ 0 . At temperatures below about 2 K, the susceptibility, χ(T ), displays a smooth cross-over from the high temperature Curie-Weiss behaviour towards a low temperature Kondo-like flattening of the susceptibility which reaches a value χ LT = 0.054 emu mol −1 at 0.7 K (see inset in Fig. 9b). The inset in Fig. 7(a) shows isothermal magnetization curves, M, for Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 measured at temperatures ranging from 1.2 K to 30 K. Neither spontaneous magnetization nor metamagnetic-like features are obvious from these measurements, thus excluding long range magnetic order in the measured temperature range. A smooth, slightly curvilinear M(H) dependence at low temperatures is observed with relatively small magnetization values near 0.3µ B /Ce at 1.2 K and 6 T. A combination of both, CEF splitting and the Kondo effect (see below) is expected to be responsible for the magnitude of the low temperature magnetic moment. Fig. 7 Fig. 7(b) on a semi-logarithmic temperature scale. Obviously, two temperature ranges can be identified, where ρ mag (T ) behaves in a negative-logarithmic manner (see the solid lines in Fig. 7(b) as a guide for the eyes). Such a behaviour is a hallmark of Kondo-type interactions, as present in a huge amount of cerium based compounds. Following the preposition of   45 Cornut and Coqblin 43 the logarithmic resistivity ranges at low and high temperatures can be understood as derived from the Kondo effect in the CEF ground state and in an excited CEF state, respectively. If these levels are well separated in energy, a pronounced maximum in ρ mag (T ) would be expected as well.
Overall, the present resistivity study strongly indicates a Kondo effect existing in Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 .
In general, a lattice of Kondo ions (i.e., a Kondo lattice) is characterised by a drop of the electrical resistivity at lowest temperatures due to coherence. A distribution of Kondo temperatures due to random Ni/Zn occupation may inhibit the formation of a coherent state at low temperatures in the present system (compare Fig. 7b and 8a). Externally applied magnetic fields tend to suppress incoherent scattering processes. Accordingly, for fields above about 6 T, a smooth maximum forms in ρ(T ), which shifts continuously to higher temperatures. Such behaviour can be understood in terms of a Kondo lattice, where the maximum in ρ(T ) is a measure of the Kondo temperature. 44 At lowest temperatures, a Kondo lattice exhibits a Fermi liquid ground state documented by the T 2 behaviour of the electrical resistivity (solid line, Fig. 8(a)). Isothermal resistivity data at various external fields, as presented in Fig. 8(b), reveal a moderate negative magnetoresistance, amounting to about 10% at lowest temperatures and 12 T.
The overall negative magnetoresistance is in line with the Kondo behaviour, where increasing magnetic fields suppress Kondo interactions and as a result decrease resistivity. Although the field dependence of (ρ(B) − ρ(0))/ρ(0) complies with numerical results employing Schlottmann's theory 45 (solid lines, Fig. 8(b)), the Kondo temperature inferred from such fits appears to be unphysically high (about 50 K) which may be a consequence of the aforementioned site-dependent hybridisation/Kondo interaction strength.
In Fig. 9 the heat capacity data of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 , measured down to 400 mK, are displayed as C p vs. T. For com-parison, C p (T ) of La(Ni 0.56 Zn 0.44 ) 2 Si 2 is added, too. Below 2 K, the specific heat of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 shows an anomaly, which is attributed to Kondo-type interactions and is in close correspondence with the smooth cross-over behaviour displayed by the low temperature magnetic susceptibility shown in the inset of Fig. 9b. In order to calculate the magnetic entropy, released at low temperatures, the specific heat data of La(Ni 0.56 Zn 0.44 ) 2 Si 2 are assumed to represent the phonon contribution to this quantity, i.e., C mag = C(Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 ) − C(La(Ni 0.56 Zn 0.44 ) 2 Si 2 ). Results of this procedure are shown in Fig. 9(a) as well. Integrating C mag /T from zero to the upper limit of the present measurements reveals the temperature dependent magnetic entropy, S, shown as a solid line in Fig. 9(a). At 3.9 K, the entropy reaches 0.45R ln2 which according to Desgranges and Schotte, 46 corresponds to a Kondo temperature T K = 3.9 K. As is obvious from Fig. 9(a), S(T ) continuously increases, finally reaching a value of R ln2 around 20 K. The response of the system to the application of magnetic fields is shown in Fig. 9(b), where the heat capacity data are plotted as C p /T vs. log T. The overall observation that C p /T becomes reduced by magnetic fields, concomitant with an entropy transfer to higher temperatures, is in line with a typical Kondo scenario.
Comparing the absolute numbers of the low temperature Sommerfeld coefficient (γ = C p /T ) and of the susceptibility χ LT , the value of the Wilson ratio, R = π 2 k B 2 χ LT /[g J 2 J ( J + 1)µ B 2 γ] ∼ 2, provides a further proof that a Kondo screened ground-state CEF doublet dominates the low temperature physics of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 . Finally, it is interesting to see that the substitution of Ni by Zn in CeNi 2 Si 2 at 800°C supports the ThCr 2 Si 2 -type only up to Ce(Ni 0.82 Zn 0.18 ) 2 Si 2 , where a transition to an atom site occupation variant with the CaBe 2 Ge 2 -type is observed extending up to a composition Ce(Ni 0.45 Zn 0.55 ) 2 Si 2 and maintaining the stoichiometry Ce(Ni,Zn) 2 Si 2 . At higher Zn contents the Fig. 9 (a) Temperature dependent specific heat C p of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 and La(Ni 0.56 Zn 0.44 ) 2 Si 2 . C mag (T ) is derived by subtracting both data-sets. The temperature dependent magnetic entropy S mag (solid line, referring to the right axis) originates from the integration of C mag /T (T ). (b) Field and temperature dependent heat capacity data of Ce(Ni 0.61 Zn 0.39 ) 2 Si 2 plotted as C p /T vs. log T for various externally applied magnetic fields. Data of La (Ni 0.56 Zn 0.44 ) 2 Si 2 are added for the purpose of comparison. The inset shows the low temperature magnetic susceptibility data measured at 0.1 T and temperatures down to 0.7 K.