The system Ce–Zn–Si for <33.3 at.% Ce: phase relations, crystal structures and physical properties

Institute of Physical Chemistry, University Vienna, Austria. E-mail: fai.failamani@ raimund.podloucky@univie.ac.at; peter. 142779524; Tel: +43 1427752456 Institute of Solid State Physics, Vienn Hauptstraße 8-10, A-1040 Vienna, Aus bauer@ifp.tuwien.ac.at; Fax: +43 15880113 Masaryk University, Faculty of Science, Dep 61137, Czech Republic Masaryk University, Central European Ins 753/5, Brno 62500, Czech Republic. E549492443; Tel: +420 549493299 Institute of Mineralogy and Crystallography 1090 Vienna, Austria. E-mail: gerald.gieste Tel: +43 1427753235 Christian Doppler Laboratory for Thermoele Wiedner Hauptstraße 8-10, A-1040 Vienna, † Electronic supplementary informa 10.1039/c5ra02789f Cite this: RSC Adv., 2015, 5, 36480


Introduction
Ternary compounds Ce-T-Si (T is one of the late transition metals) have been known for their interesting physical properties, such as heavy fermion and unconventional superconductivity, 1,2 Kondo-behaviour and quantum criticalities, 3 intermediate valency, 4 thermoelectric features, 5 etc.Most ternary Ce-T-Si systems have been explored, 6 except for group 12 elements (Zn, Cd, Hg).The high vapor pressure of these metals complicates sample preparation, and requires careful control of compositions.Therefore conventional preparation methods such as arc melting or induction melting in open crucibles cannot be used.However, a few investigations were already concerned with the Ce-Zn-Si system.Kido et al. 7 reported paramagnetism and metallic behavior of REZnSi compounds (RE ¼ Ce, Nd, Sm, Gd, Tb, Ho) in the temperature range of 77-300 K. Recently, phase equilibria for the Ce-Zn-Si system have been derived at 800 C by Malik et al. 8 and revealed the existence of 4 ternary compounds, labeled as s 1 to s 4 .Whilst the crystal structures of s 1 and s 2 and their La-homologues have been elucidated from single crystal X-ray data, the crystal structures of the other compounds remained unresolved.A recent study of RE 7 Zn 21 Tt 2 -phases (Tt is a tetrel element) by Nian-Tzu Suen and Bobev, 9 prompted among other rare earth elements (La-Nd) the formation of novel cerium compounds Ce 7 Zn 21 {Ge,Sn,Pb} 2 crystallizing with the structure type rst determined by Malik et al. 8 for {La,Ce} 7 Zn 21 (Zn 1Àx Si x ) 2 .In their latest publication, they also investigated the single crystals of {Ce-Pr} 7 Zn 21 (Zn 1Àx Si x ) 2 and their magnetic properties. 10Their result, especially on the crystal structure of Ce 7 Zn 21.95 Si 1.05 conrms the work of Malik et al. 8 The absence of ternary compounds in the Ce-poor part (<33 at.%Ce) of the isothermal section Ce-Zn-Si seems unusual, particularly ternary compounds with ThCr 2 Si 2 structure or derivative types are encountered in most Ce-T-Si systems (T is a transition metal from Cr to Cu). 11 Therefore also the possibility of compound formation at lower temperature needs to be explored.Indeed the investigation of the Zn/Si-rich part of the Ce-Zn-Si phase diagram at 800 C (ref.8) revealed hints for a ternary compound (labelled as s 5 ) with composition close to Ce(Zn 1Àx Si x ) 3 ; x z 0.5.Our further attempts to investigate this phase at 700 C prompted another ternary compound (labelled as s 6 ) with composition of Ce 20 Zn 53 Si 27 , which is also formed from the melt.An electron count on s 5 -CeZn 1.5 Si 1.5 , considering the valencies of Ce ¼ +3, Zn ¼ +2 and Si ¼ À4 yields balanced electronic charges suggesting a Zintl behaviour interesting for thermoelectric application.
Therefore this work focuses on the investigation of phase equilibria and crystal structures of s 5 and s 6 , as well as their mechanism of formation and stability.Furthermore the magnetic ground state of cerium in these compounds was of interest.Particularly the small amount of tetrel elements (Tt) to stabilize {La,Ce} 7 Zn 21 (Zn 1Àx Tt x ) 2 was investigated by DFT calculations for Tt]Ge to get insight into the electronic DOS, bonding behavior and ground state energies of hypothetical binary Ce 7 Zn 23 in comparison with ternary Ce 7 Zn 23Àx Ge x (x ¼ 0.5, 2).

Experimental methods and density functional theory calculation
Most samples were prepared by mixing and cold pressing proper blends of ball milled powders of CeSi x master alloys with Zn lings inside an Ar lled glove box.Master alloys CeSi x were prepared by argon arc melting of Ce and Si pieces on a watercooled copper hearth with a tungsten electrode, while Zn lings were prepared from puried Zn drops.Samples in the Zn-rich corner were then sealed under vacuum or argon and annealed at 600 C for 4 to 14 days.Samples with low Si(Ge) content (close to binary Ce-Zn) were prepared in a different way.Ce lings, Zn lings, and Si(Ge) powder were mixed in proper ratio, cold pressed, sealed and then subjected to the same heat treatment.All starting materials had a purity of better than 99.9 mass%.
Aer heat treatment, samples were quenched by submersing the quartz capsules in cold water and analyzed by X-ray powder diffraction with Ge-monochromated CuKa 1 -radiation employing a Guinier-Huber image plate recording system.X-ray powder diffraction analyses were performed via Rietveld renement using the FULLPROF program. 12Precise lattice parameters were determined referring to Ge as internal standard (a Ge ¼ 0.565791 nm).Special treatments were needed to prepare samples for Electron Probe Microanalysis (EPMA) due to their powder-like consistency.Coarse powders of samples were mixed and cold pressed with ne powders of conductive resin in a small steel die (5-6 mm in diameter) prior to hot compacting them together into a coarse powder/ granule of conductive resin.Samples were ground and polished under glycerin in order to avoid oxidation and/or hydrolysis.Microstructures and compositions were examined by light optical microscopy (LOM) and scanning electron microscopy (SEM) and EPMA on a Zeiss Supra 55 VP equipped with an energy dispersive X-ray analysis (EDX) detector operated at 20 kV.Single crystals of s 5 and s 6 were grown from Zn ux.Powders of a multiphase alloy with nominal composition Ce 20 Zn 50 Si 30 were mixed and cold pressed with Zn lings in a weight ratio of 1 : 45 and 1 : 57 for s 5 and s 6 , respectively.The sample billets were sealed under vacuum in quartz capsules, heated to 800 C, kept at this temperature for 1 hour, and were then slowly cooled with a rate of 6 C h À1 to 735 C and 670 C for s 5 and s 6 , respectively.Aer quenching in cold water, the Zn ux matrix was dissolved in cold diluted HCl.No reaction of the single crystal material with HCl was observed during leaching.
Single crystals of {La,Ce} 7 Zn 21 (Zn 1Àx Ge x ) 2 were prepared from cold pressed mixtures of La/Ce lings, Zn lings and Ge powder with nominal composition of La 25 Zn 73 Ge 2 and Ce 25 Zn 70 Ge 5 , respectively.The Ce-containing pellet was sealed under vacuum into a quartz ampoule, heated to 600 C with a rate of 60 C h À1 , kept at this temperature for 12 h, further heated to 1050 C at 600 C h À1 , and then slowly cooled to 800 C with a rate of 10 C h À1 .A slightly different heat treatment was performed to grow single crystals of La 7 Zn 21 (Zn 1Àx Ge x ) 2 heating the pellet to 600 C at 60 C h À1 , keeping this temperature for 12 h, followed by further heating to 900 C at a rate of 600 C h À1 , resting at this temperature for 30 minutes, and then slowly cooling to 800 C at a rate of 6 C h À1 .Single crystals were then mechanically isolated and selected from the crushed regulus.
Inspections on an AXS D8-GADDS texture goniometer assured high crystal quality, unit cell dimensions and Laue symmetry of the single crystal specimens prior to X-ray intensity data collections at room temperature on a Bruker APEXII diffractometer equipped with a CCD area detector and an Incoatec Microfocus Source ImS (30 W, multilayer mirror, Mo-Ka, l ¼ 0.071069 nm).Orientation matrices and unit cell parameters were derived using the Bruker APEXII soware suite. 13No 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 (SHELXS-97) and were rened with the SHELXL-97 (ref.14) program within the Windows version WINGX. 15Crystal structure data were standardized using program STRUCTURE-TIDY. 16n order to investigate the thermal stability of s 5 and s 6 and to determine the corresponding ternary reaction isotherms, DTA measurements were performed using a Netzsch STA 409 CD/3/ 403/5/G apparatus.Due to the high vapor pressure of Zn, measurements were performed in closed thin-walled quartz crucibles.Single-phase material of s 5 and s 6 was measured from room temperature to 900 C with a heating/cooling rate of 5 C min À1 .Isothermal annealing served to conrm the phase elds related to the four-phase reactions observed in DTA: for this purpose two alloys in the Zn rich part with nominal compositions, Ce 5.9 Zn 59.8 Si 34.3 and Ce 7.6 Zn 78.4 Si 14 , were prepared from powders of CeSi x and Zn lings and annealed at 500 C for 4 days.Aer rst reaction, the alloys were powderized to a grain size below 53 mm inside the glove box and were then cold compacted in a steel die (diameter ¼ 10 mm).The pellets were dry-cut into several pieces and sealed in quartz tubes under about 300 mbar Ar and annealed at 400 C, 650 C, 710 C, 750 C, 770 C, 790 C, 810 C, 850 C, 860 C, 870 C, 880 C and 900 C for 1 day each.Single phase samples of s 5 and s 6 were prepared in a similar way.The second annealing temperature was 700 and 600 C for s 5 and s 6 , respectively.The furnaces were calibrated with standard thermocouples and Sb (melting point ¼ 631 C).
Dc magnetic susceptibility measurements were performed with a SQUID magnetometer for s 5 and s 6 from 2-300 K with various magnetic elds from 0.006 to 6 T on freely rotating single crystals with a total mass of 0.80 mg (individual crystals with a typical mass of 100 mg) and on sintered polycrystalline samples of about 20 mg.Ac susceptibility measurements were carried out on sintered polycrystalline samples of about 200 mg with a Lakeshore 7000 ac susceptometer applying an ac-eld with amplitude of 325 A m À1 and a frequency of 100 Hz.Specic heat measurements were performed on a commercial Quantum Design PPMS calorimeter on a sintered s 6 sample and on s 5 single crystals.Parts of a sintered sample of s 5 were also used for resistivity and Seebeck coefficient measurements.Resistivity measurements were performed from 2-300 K in a home-made equipment using the ac bridge resistance technique, while the high temperature part (300-673 K) was measured simultaneously with the Seebeck coefficient in a ZEM-3 ULVAC.
The density functional theory (DFT) calculations were performed by using the Vienna ab initio simulation package (VASP) 17,18 and applying the pseudopotential construction according to the projector-augmented-wave method. 19For the exchange-correlation functional the generalized gradient approximation according to Perdew et al. (PBE) 20 was chosen.The VASP calculations were done with high precision using the predened/default values as provided by the VASP package.The energy cutoff was chosen at 350 eV.Spin polarized calculations were done assuming ferro/ferrimagnetic ordering.For the k space integration the Gaussian smearing method with a value for s of 0.1 eV was taken.k space grids were constructed by the method outlined in ref.21  .No additional many-body treatment was made for the localized character of the f-like states of Ce, since the compounds under study are all in a metallic state with f-occupation of $1 per Ce atom.PBE is considered to reasonably capture the localization properties in terms of spin-polarization as it does for 3d transition metals.Assuming the experimental structure as starting point for all cases, the atomic positions as well as the unit cell parameters were fully relaxed.The Ge substitution was made according to Table 3 at the experimentally dened M1 sites.

Binary boundary systems
The Zn-Si system (calculated) and the Ce-Zn system were accepted aer Massalski 22 taking also into account a more recent investigation on the low temperature modication of ) with TbCu 7 -type. 23For the Ce-Si system we rely on the version of Malik et al., 8 which essentially is based on the investigation by Bulanova et al. 24 but also includes further phases such as Ce 2 Si 3Àx (ref.25) and the high pressure phases CeSi 5 and Ce 2 Si 7 . 26The La-Zn system was taken from the latest experimental investigation by Berche et al. 27 with recent data on the crystal structure of LaZn 4 . 28Detailed crystallographic data for unary and binary boundary phases are summarized in Table S1 (ESI †), those for ternary compounds are listed in Table 1, respectively.
3.2.Crystal structure of ternary compounds in the Ce-Zn-Si system 3.2.1.Crystal structure of s 5 -CeZn(Zn 1Àx Si x ) 2 , x ¼ 0.71.The X-ray diffraction pattern of a suitable ux grown single crystal of s 5 was fully indexed in orthorhombic symmetry (a ¼ 0.42079(1), b ¼ 1.76522(3), c ¼ 0.41619(1) nm).Analysis of systematic extinctions suggested three possible space group types Cmcm, Cmc2 1 , C2cm (non-standard setting) and consequently structure solution employing direct methods was attempted in the space group type Cmcm of highest symmetry (see Table 2).In order to nd mixed Zn/Si sites, renements were rst performed with Ce and Zn only.Two of the three Zn sites (M1, M2) were found to have an unusually high atomic displacement parameter (ADP), indicating partial substitution by Si atoms.
Further renement with anisotropic ADPs for all atoms converged to R F ¼ 0.020 and residual electron densities smaller than AE3.04 e À ÅÀ3 .The nal formula obtained, CeZn(Zn 1Àx Si x ) 2 with x ¼ 0.71 corresponds to the composition Ce 25.0 Zn 39.7 Si 35.3 (in at.%), which perfectly ts to the value derived from EPMA (Ce 24.9 Zn 39.6 Si 35.5 ).Details on crystal data along with ADPs are summarized in Table 2.A Rietveld X-ray powder diffraction renement conrms the structure model for s 5 .Furthermore, lattice parameters, crystal symmetry, and Wyckoff positions proved that this compound is isotypic with the structure type of CeNiSi 2 (see Fig. 1).
Interatomic distances are given in Table S2 (ESI †).Comparing atom distances with the sum of atomic radii, direct bonding is neither revealed between M1-Zn3 nor for M2-M2.However, stronger bonding is inferred from the distances among M1-M1, M1-M2 and M2-Zn3 atoms, particularly taking into account the Zn/Si random occupancy.At 600 C the phase s 5 -CeZn(Zn 1Àx Si x ) 2 exhibits a compositional range, 0.68 # x #  0.76, excluding any stoichiometric composition (for details see Section 3.4).
Compounds with the CeNiSi 2 type are known in many Ce-T-Si systems (T ¼ Fe to Cu, Rh, Ir, Pt, and Sn) and exist in both stoichiometric and non-stoichiometric forms. 11For s 5 -CeZn(Zn 1Àx Si x ) 2 , however, only the non-stoichiometric composition could be found, whereas the Ce-Cu-Si system, 29 which is the closest homologous system, contains two individual phases of same symmetry (isotypic with CeNiSi 2 ), namely CeCu 1.6 Si 1.4 (^CeCu(Cu 0.6 Si 0.4 )Si) and stoichiometric CeCuSi 2 , both separated by a two-phase equilibrium: Ce(Cu 1Àx Si 1+x ) 2 (AlB 2 -type) + CeCu 2 Si 2 .It should be noted that the atom preference in the mixed sites in s 5 -CeZn(Zn 0.26 Si 0.74 )-(Zn 0.31 Si 0.69 )where Zn/Si randomly ll two 4c-sites with y ¼ 0.03338( 5) and y ¼ 0.16921(5)differs from non-stoichiometric CeCu(Cu 0.6 Si 0.4 )Si where Cu and Si atoms only share the 4c-site with y ¼ 0.038.However, we have to note here that the reliability of the X-ray single crystal study on photographs for CeCu 1.6 Si 1.4 is low, as R F was only 17.7%. 30The discussion on TbFe 0.5 Si 2 being a site exchange variant of the CeNiSi 2 -type has been solved from neutron diffraction data on HoFe 0.5 Si 2 , 31 which clearly revealed isotypism with the CeNiSi 2 -type.From the good correspondence of the composition rened from X-ray data with the composition derived from EDX, we can safely conclude that the structure of s 5 -CeZn(Zn 1Àx Si x ) 2 does not contain any defect sites like HoFe 0.5 Si 2 .
3.2.2.Crystal structure of s 6 -CeZn 2 (Si 1Àx Zn x ) 2 , x ¼ 0.30.Complete indexation of the X-ray single crystal diffraction data for s 6 prompted a tetragonal unit cell.The systematic analysis of extinctions suggested I4, I 4, I4/m, I422, I4mm, I 42m, I 4m2 and I4/mmm, as possible space group types.Structure solution and renement employing direct methods in the highest symmetry space group type I4/mmm converged to R F ¼ 0.008 with residual electron densities smaller than AE0.81 e À ÅÀ3 .Details on crystal data along with ADPs are summarized in Table 2. Unit cell parameters, crystal symmetry, and Wyckoff sites conrm isotypism with the ThCr 2 Si 2 structure type (see Fig. 2).
Interatomic distances are given in Table S2 (ESI †).As the Msite is mainly occupied by Si, distances M-M and M-Zn1 are much smaller than distances Zn1-Zn1.Taking into account the random occupancy Zn/Si in the 4e site, the M-M distance is smaller than the sum of radii 33 and is a good indication for dumbbell formation.Comparing the M-M and M-Zn1 distances with those in YbZn 2 (Si 1Àx Zn x ) 2 ; x ¼ 0.25, 34 which is hitherto the only far off-stoichiometric REZn 2 Si 2 crystallizing in the ThCr 2 Si 2 type, no signicant difference can be found.Consistent with the mixed atom site, s 6 -CeZn 2 (Si 1Àx Zn x ) 2 exists  at 600 C in a small homogeneity range 0.25 # x # 0.30 (for details see Section 3.4).Similar to s 5 also the phase s 6 does not include the stoichiometric composition CeZn 2 Si 2 , although rst row transition metals mostly form ordered, stoichiometric compounds CeT 2 Si 2 (T ¼ Cr to Cu), some with only a small deviation from 1 : 2 : 2 stoichiometry.3b and c).
Indexing of the X-ray diffraction data from a suitable single crystal of Ce 7 Zn 21 (Zn 1Àx Ge x ) 2 was complete for an orthorhombic unit cell corresponding to the structure type of Ce 7 Zn 21 (Zn 1Àx Si x ) 2 .The structure solution, employing direct methods in space group Pbam with the highest symmetry, compatible with the set of systematic extinctions, resulted in the same atom arrangement as for Ce 7 Zn 21 (Zn 1Àx Si x ) 2 .Despite the small difference in the X-ray scattering power of Zn and Ge atoms, one mixed Zn/Ge site could unambiguously be identied from the rest of the fully occupied Zn sites.It is the same site as in the parent Ce 7 Zn 21 (Zn 1Àx Si x ) 2 type revealing a slightly smaller ADP and thus requests the presence of an atom with a slightly higher scattering power.
Even though it was possible to rene the occupancy of Zn/Ge (yielding 0.45(5) Zn1 + 0.55(5) Ge1), the ratio Zn/Ge was xed in accord with the composition obtained from EPMA (0.25 Zn1 + 0.75 Ge1).A nal renement with anisotropic ADPs converged to R F ¼ 0.0215 with a residual electron density less than 1.7 e À ÅÀ3 .Detailed crystal data and atomic displacement parameters are summarized in Table 3.The structure renement essentially conrmed the data obtained by Suen et al. 9 but here for an even lower Ge-content.
Although EPM analyses in the La-Zn-Ge system prompted a phase with composition of La 23.3 Zn 71.6 Ge 5.1 (see Fig. 3b), attempts to grow a single crystal with this Ge content were unsuccessful.However, for lower Ge-contents a suitable single crystal could be obtained (see Fig. 3a).Following the same steps and arguments as for Ce 7 Zn 21 (Zn 1Àx Ge x ) 2 , structure solution and renement of the single crystal data clearly showed isotypism with Ce 7 Zn 21 (Zn 1Àx Si x ) 2 .However, due to the low amount of Ge atoms in the unit cell, it was not possible to identify the Zn/Ge mixed site from the rest of the Zn sites.Therefore Ge atoms were placed at the corresponding Si-site as in Ce 7 Zn 21 (Zn 1Àx Si x ) 2 with the occupancy taken from EPMA (La 23.3 Zn 76.0 Ge 0.7 in at.%).
Detailed crystal data and atomic displacement parameters are listed in Table 3.As expected from the isotypism with Ce 7 Zn 21 (Zn 1Àx Si x ) 2 , the atomic arrangement in {La,Ce} 7 Zn 21 -(Zn 1Àx Ge x ) 2 also gives a similar zig-zag chain of distorted AuCu 3 and BaAl 4 blocks along the b-axis (see Fig. 4).This arrangement is similar to Ce 3 Zn 11 with La 3 Al 11 -type, which is the neighbouring phase of Ce 7 Zn 21 (Zn 1Àx Ge x ) 2 .Due to the comparable size of Zn and Ge atoms, no signicant difference could be found in the interatomic distances between fully occupied Zn and mixed Zn/Ge sites.
The amount of Ge necessary to stabilize the ternary compounds {La,Ce} 7 Zn 21 (Zn 1Àx Ge x ) 2 is even less than for isotypic {La,Ce} 7 Zn 21 (Zn 1Àx Si x ) 2 and with less than 1 atom percent of Ge infers a rather small degree of thermodynamic instability for the hypothetical binary phases "La 7 Zn 23 " and "Ce 7 Zn 23 ".
As reference energies of the pure phases we dened: , and The DFT energies for the pure phases were calculated for solid nonmagnetic a-fcc-Ce and solid hcp-Zn.It was necessary to adjust the reference energies by E adj (Ce) and E adj (Zn) for a direct comparison with the results of the thermodynamic modeling of Wang et al., 36 and experimental work by Chiotti et al. 37 and Johnson et al., 38 because of the choice of different reference ground states.Then the values for E adj were extracted by linearly tting the DFT results (column DFT in Table 4) to the thermodynamic modeling data (column "model") for the four given compounds, and by that E adj (Ce) ¼ 27.87 and E adj (Zn) ¼ 4.38 kJ mol À1 were obtained.
Table 4 summarizes results of the DFT calculations.The DFT derived adjusted enthalpy of formation compares very well with data of the thermodynamic modelling by Wang et al. 36 Concerning magnetic properties, as taken from the listed magnetic moments, CeZn does not spin polarize, whereas for the other listed compounds Ce x Zn 1Àx the magnetic moment per Ce atom decreases with decreasing Ce content, starting with CeZn 2 which has the largest local moment per Ce atom of 0.71m B .For (hypothetical) Ce 14 Zn 46 (x ¼ 0.23) the local moment is still sizeable amounting to 4.06m B for the total magnetic moment of the unit cell.Replacing Zn by Ge in Ce 14 Zn 46Àx Ge x strongly reduces the magnetic moment to less than 0.07m B for x ¼ 1.The gain in spin-polarization energy is very small being about 0.01 kJ mol À1 per Ce atom, which hints at a spin uctuation system.If x ¼ 4 than there is no spin polarization anymore.
The enthalpy of formation for Ce x (Ge,Zn) 1Àx compounds was derived similarly to the procedure described above.As a reference, solid Ge was taken in its ground state in the diamond structure.Most noticeable for our study is the stability for the Ge-doped compounds.Even for one Ge atom per formula unit, Ce 14 Zn 45 Ge 1 , DH DFT is below the tie-line connecting neighboring Zn-compounds.Here we assume, that in fact the ternary system can be approximately described as a binary one (see Fig. 5).Why Ge stabilizes the compound is analyzed in the following discussing the electronic structure in terms of the density of states (DOS).
3.3.2.DFT phase stabilities for Ce 7 Zn 23Àx Ge x (Z ¼ 2).Panel (a) of Fig. 6 presents the total and atom projected local DOS for Ce 14 Zn 45 Ge 1 .The Fermi energy falls into a sharp uprise of the DOS, which clearly is attributed to the f-states of Ce.At lower energies the DOS is a mixture of Zn and Ce states depending on the energy region.The Ge-DOS features in the range À2.7 < E < À1 eV indicate a more covalent bonding as compared to Zn, which is more pronounced in panel (b) of Fig. 6 showing the local DOS per atom.There the Zn-like DOS is more uniformly spread out in the energy region shown.
The stabilization property of Ge-substitution can be understood by inspecting Fig. 7 showing a reduction of the total DOS at Fermi energy when one Zn is replaced by Ge.This is mainly due to the reduction of the f-like DOS for Ce 14 Zn 45 Ge 1 .The corresponding g values of the electronic specic heat are 3.43 (DOS at E F ¼ 87.3 states per eV for Ce 14 Zn 46 ) and 3.25 mJ mol À1 K À2 (DOS at E F ¼ 82.7 states per eV for Ce 14 Zn 45 Ge 1 ) indicating poor metals.Analyzing the Ce-f states it turns out that the magnetic moments break down upon Ge substitution, which is responsible for the DOS reduction.The reduction is due to the destruction of the magnetic moment of Ce atoms in the 2c position, because these states are predominant at the Fermi energy for spin polarized Ce 14 Zn 46 .They carry the largest magnetic moment of all Ce atoms and are therefore the most localized f-states with the largest uprise of all f-DOSes and therefore the largest value at Fermi energy.For Ce 14 Zn 46 the local f-moments are 0.27, 0.21, and 0m B for the 4-fold coordinated atoms, and 0.74m B for the Ce atoms in the 2c position.The breakdown of the magnetic moment upon substitution indicates also a weaker localization and consequently the DOS at Fermi energy is lowered: this leads to the reduction of the total DOS and indicates the thermodynamic stabilization of Ce 14 Zn 45 Ge 1 .Summarizing, the more pronounced covalent bonding between Ce and Ge seems to be the main factor for the stabilization.By substituting 4 Ge atoms the stabilization with respect to the tie-line is considerably enhanced.

Partial isothermal section at 600 C for less than 33.3 at.% Ce
The partial isothermal section at 600 C in the Ce-poor part of the ternary system Ce-Zn-Si was established from EPMA and Table 4 DFT derived equilibrium heat of formation (DFT) for T ¼ 0 K (in kJ mol À1 ) for Ce x (Ge,Zn) 1Àx as a function of Ce concentration x, in comparison to the adjusted DFT values (DFT-adj, see text) and T ¼ 0 extrapolation of the thermodynamic modeling (model) of Wang et al. 36 For Ce the a-phase was taken as reference.Local magnetic moment per Ce-atom m loc (in m B ) and the equilibrium volume per atom V 0 (in Å3 ) are also given

Compound
x  X-ray powder diffraction of about 45 alloys (see Fig. 8).
Considering the high stability of the phase Ce(Si 1Àx Zn x ) 2 with the aThSi 2 type and the relatively slow reaction kinetic at 600 C (diffusion in cast alloys) the samples were prepared by powder metallurgical techniques i.e. via isothermal reaction synthesis starting from compacts of powder/lings in order to ensure establishment of true phase relations at this temperature.
In addition to the ternary compounds s 1 -Ce 7 Zn 21 (Zn 1Àx -Si x ) 2 , 0.45 # x # 0.99 and s 2 -Ce(Si 1Àx Zn x ) 2 , 0.36 # x # 0.73, both established previously in the 800 C isothermal section (for details see ref. 8), three new phases, which previously were not encountered at 800 C, 8 were found to exist at 600 C: s 5 -CeZn(Zn 1Àx Si x ) 2 , s 6 -CeZn 2 (Si 1Àx Zn x ) 2 , and s 7 -Ce 37 Zn 48 Si 15 .Moreover binary CeZn 11 enters the phase equilibria at 600 C. Similar to 800 C, solubility of Si is negligible for all binary compounds CeZn x with x > 2. Extended homogeneity regions were established for s 1 and s 2 , as well as for s 5 and s 6 (Table 1 for details see Table 5).The homogeneity range of s 1 -Ce 7 -Zn 21 (Zn 1Àx Si x ) 2 becomes slightly smaller at 600 C as compared to 800 C. The maximum concentration of Si in this phase practically remained the same, while the minimum amount of Si required to stabilize this phase slightly increased from x ¼ 0.28 (1.9 at.%Si Despite all these three-phase equilibrium triangles are narrow, we were able to prepare corresponding samples and to dene by EPMA the composition of the equilibrium phases involved.Ternary phases Ce(Si 1Àx Zn x ) 2 (a-ThSi 2 type), s 2 , and s 5 that coexist in three-phase equilibria with binary CeZn x (x $ 5) crystallized in ne microstructures, which made quantitative analyses by EPMA unreliable.The ne grains could not be agglomerated even with longer annealing time (more than two weeks).Therefore the ternary phases Ce(Si 1Àx Zn x ) 2 with a-ThSi 2 type, s 2 , and s 5 , and their composition were determined via   Rietveld renement in combination with the compositional dependence of lattice parameters presented in Fig. 9.
Microstructures of selected three-phase equilibria are given in Fig. 10.Alloys in equilibrium with Si, which were prepared from CeSi x master alloys containing CeSi 2 , did not reach complete equilibrium even aer re-powderization followed by hot pressing and/or long term annealing.Ce(Si 1Àx Zn x ) 2 , x # 0.25, with a-ThSi 2 type was always observed in those alloys.Moreover, long term annealing generally shied the overall alloy composition due to unavoidable evaporation of Zn, especially for alloys in the Zn-rich corner.However, equilibrated samples were easily obtained in case binary Ce-Si precursors with Ce content above 40 at.% were used.
Table 5 summarizes data on composition and lattice parameters of all phases coexisting in equilibrium at 600 C. The only uncertainty concerns the maximal solubility of Si in binary CeZn 2 .Our various attempts to prepare samples in the corresponding three-phase region s 7 + CeZn 2 + s 1 resulted in non-equilibrium alloys with about 5 at.%Si in the CeZn 2 -phase.It is noteworthy that the phase triangulation in and the high vapour pressure of Zn at elevated temperatures, it is difficult to obtain homogeneous cast alloys for the determination of the crystallization behaviour of alloys.On the other hand, the established isothermal section at 600 C shows that three-phase regions involved in equilibria with binary Ce-Zn compounds are very narrow and our attempts to equilibrate the samples at higher temperature resulted in a signicant change of the overall compositions.Filling the ampoules with argon slightly suppressed the Zn losses, but even in this case samples were heterogeneous, which at rst did not allow us to reliably determine the change in phase equilibria via annealing at different temperatures.This shi of the compositions during thermal treatment also hinders the interpretation of DTA.For instance, DTA measurements on single-phase s 5 and s 6 resulted in a sequence of several thermal effects that are difficult to reconcile with the phase triangulation.Investigation of the specimens aer DTA by SEM/EDX showed that samples became heterogeneous and contained regions with different phases (see Fig. 11).Reliable temperatures for isothermal reactions were only obtained for wide three-phase regions: CeSi 2 + s 5 + (Si), s 5 + s 6 + (Si), s 6 + CeZn 11 + (Si), CeZn 11 + (Zn) + (Si).The temperatures of invariant reactions that correspond to these elds were derived as follows: 727 C, 634 C, 561 C and 412 C, respectively.These four isothermal reaction temperatures were conrmed by DTA from the Zn-rich sample that contains s 6 , (Si), and CeZn 11 (close to the tie line (Si) + CeZn 11 ) (see Fig. 12).Aer three DTA runs the sample contains additionally s 5 , (Zn), and CeSi 2 , which suggests incongruent formation of both s 5 and s 6 .
All invariant reactions determined are summarized in the Scheil reaction scheme in Fig. 13 along with the partial isothermal sections (Fig. 14) at temperatures between the thermal effects established by DTA.Selected microstructures of alloys are presented in Fig. 15 and 16.Comparing the phase equilibria at 500 C (Fig. 14a) with those observed at 600 C  (Fig. 14b) we conclude on the existence of a transition type reaction U 1 (561 C aer DTA): L + s 6 5 CeZn 11 + (Si).
The characterization of sample Ce 5.9 Zn 59.8 Si 34.3 shows that s 6 coexists in equilibrium with (Si) and L(Zn) at 600 C (Fig. 15a), however aer annealing at 650 C s 6 was not observed in this sample, instead s 5 enters the equilibrium with L(Zn) and silicon (Fig. 14c and 15b).Such a change of phase equilibria requests another transition type reaction U 2 : L + s 5 5 s 6 + (Si) to occur between 600 and 650 C (634 aer DTA).
Although s 6 was observed in the sample Ce 7.6 Zn 78.4 Si 14 annealed at this temperature, s 6 does not participate in the equilibria at 710 C (Fig. 14d).It has to be noted that the microstructure of this sample contains four phases (s 6 , s 5 , CeZn 11 , and L(Zn), see Fig. 16b) and one of these phases has to be considered as non-equilibrium phase.Comparing this microstructure with the three-phase structure (s 5 , CeZn 11 and L(Zn)) obtained for this sample annealed at 750 C (Fig. 16c) we may safely conclude that s 6 is the non-equilibrium phase that forms during quenching from 710 C. On the other hand, the same sample annealed at 690 C showed only 3 phases (s 6 , CeZn 11 and L(Zn)).Based on these observations, the invariant reaction for the formation of s 6 is supposed to occur in the temperature range between 690 and 700 C (see Fig. 13).
Three peritectic-type reactions may be responsible for the formation of this phase: (i) L + s 5 5 s 6 , (ii) L + s 5 + CeZn 11 5 s 6 and (iii) L + s 5 + (Si) 5 s 6 .The latter reaction requests the existence of a three-phase eld s 5 + s 6 + (Si) at a temperature just below this invariant reaction.However, this three-phase eld is not observed at 650 C (see Fig. 14c), and thus rules out reaction (iii).Rietveld analysis of a sample with composition of Ce 24.5 Zn 37.5 Si 38.0 annealed at 650 C showed three phases: L(Zn) + s 5 + s 6 .However due to porosity of the sample it was not possible to reliably analyze the microstructure.Due to a strong degeneracy of the three-phase eld L(Zn) + s 5 + s 6 (compositions of these phases lie almost on one line; (see Fig. 14c), the two remaining possible invariant reactions (i) and (ii) are almost identical from a thermodynamic point of view.
The existence of a maximum on the solidus in the two-phase eld s 5 + s 6 would infer a three-phase invariant peritectic L + s 5 5 s 6 , but due to the difficulties in the interpretation of DTA we cannot provide such evidence.Thus the type of this reaction remains uncertain and is therefore denoted as a degenerated peritectic: L + s 5 , CeZn 11 5 s 6 in the temperature range 690 # T # 700 C (P D1 : Fig. 13).The invariant reaction recorded by DTA at 727 C (Fig. 12) is dened as transition type reaction U 3 , L + CeSi 2 5 s 5 + (Si).Conrmation is available from a comparison of the isothermal sections and microstructures of the alloys annealed at 710 (the micrograph is not shown due to its similarity to 650 C) and 750 C (Fig. 14d and e and 15b and c).Similar to the narrow three-phase eld L(Zn) + s 5 + s 6 , Rietveld analysis of sample Ce 22.7 Zn 42.9 Si 34.4 annealed at 750 C revealed three phase constituents: L(Zn), s 5 , and CeSi 2 consistent with the three-phase eld L(Zn) + s 5 + CeSi 2 .
The previously reported isothermal section at 800 C (ref.The results on the phase equilibria are consistent (i) with the single crystal growth experiments, which reveal a large crystallization eld of the aThSi 2 -type phase Ce(Si 1Àx Zn x ) 2 extending far into the Zn-rich corner (up to 95 at.%Zn), and consequently (ii) with a rather steep liquidus surface in the Zn-rich region, which infers a high degeneracy in the isothermal reactions involving the Zn-rich liquid.
3.6.Physical properties of s 5 -CeZn(Zn 1Àx Si x ) 2 and s 6 -CeZn 2 (Zn 0.28 Si 0.72 ) 2 Ac magnetic susceptibility measurements on a polycrystalline sample of s 5 CeZn(Zn 0.32 Si 0.68 ) 2 revealed a d-shape magnetic anomaly near T C $ 5 K (see Fig. 18) which is indicative of a   ferromagnetic transition.Accordingly, we performed dc magnetisation and dc susceptibility measurements on a few freely rotating, ux-grown single crystals of s 5 (with a total mass of 0.8 mg).Field dependent isothermal (see Fig. 19) as well as temperature dependent magnetisation (Fig. 20) measurements conrm ferromagnetic ordering about 4.4 K with a saturation moment near 1m B at 1.9 K and 6 T. The slightly lower T C of the ux-grown single crystals as compared to the polycrystalline bulk samples relates to slightly different compositions of s 5 bulk samples as compared to ux grown s 5 crystals CeZn(Zn 0.29 Si 0.71 ) 2 .
The ferromagnetic phase transition at T C $ 4.4 K is corroborated by distinct anomalies of the specic heat and electrical resistivity in Fig. 21 and 22, respectively.
The analysis of the inverse dc magnetic susceptibility in terms of a modied Curie-Weiss t, c(T) ¼ c 0 + C/(T À Q p ), in Fig. 20 reveals an effective paramagnetic moment of Ce near 2.5m B which is close to the effective moment of free Ce 3+ (2.54m B ).The negative value of the paramagnetic Curie temperature of À10 K obtained from analysing the data of freely rotating crystals refers to Kondo correlations rather than to a specic type of magnetic coupling (whether antiferro-or ferromagnetic).The relevance of Kondo correlations for s 5 is further revealed by the temperature dependence of the electrical resistivity in Fig. 22, showing typical Kondo lattice features, and by the specic heat data in Fig. 21.The magnitude of the specic heat anomaly at T C of s 5 -CeZn(Zn 0.29 Si 0.71 ) 2 single crystals is signicantly reduced as compared to the value expected from a basic local moment mean-eld approach.We thus analyse the temperature dependence and magnitude of the magnetic specic heat contribution in terms of a simple model for a ferromagnetic Kondo lattice system based on the resonant level model by Schotte and Schotte. 39,40The details of this model calculations are explained e.g. in ref. 41.
The corresponding t to the experimental data, indicated as solid line in Fig. 21, yields a ferromagnetic exchange coupling J ¼ 14.6 K and a Kondo temperature T K ¼ 5 K, thus, suggesting a ferromagnetic Kondo lattice ground state of s 5 -CeZn(Zn 0.32 Si 0.68 ) 2 .The largest deviation between the applied model and the experimental data is observed right above the ferromagnetic phase transition and relates to short range order and phonon contributions which are not included in the model.Using the same values for J and T K and an effective Landé factor g ¼ 2 to adjust the model for the unknown 4f wave function of the crystal eld ground state doublet, we calculated the temperature and eld dependent magnetisation displayed as solid lines in Fig. 19.The approximate agreement with the experimental data further supports the validity of a ferromagnetic Kondo model.The magnetic ground state properties of polycrystalline bulk samples of s 6 CeZn 2 (Zn 0.28 Si 0.72 ) 2 were studied by means of specic heat as well as dc and ac magnetic susceptibility measurements at temperatures down to 3 K.Within the experimental temperature range the s 6 phase displays Curie-Weiss type paramagnetic behaviour as demonstrated by the dc magnetic susceptibility depicted in Fig. 23.A modied Curie-Weiss t of the inverse susceptibility in the temperature interval 80-300 K is indicated as solid line in Fig. 23 and yields a temperature independent Pauli component c 0 ¼ 1.0 Â 10 À4 emu mol À1 , a paramagnetic Curie-Weiss temperature Q p ¼ À0.5 K being indicative for weak antiferromagnetic or very weak Kondo correlations.Via the Curie constant of this t an effective paramagnetic moment m eff ¼ 2.34m B is calculated, which is markedly reduced as compared to the Ce 3+ free ion value (2.54m B ).The heat capacity data of s 6 CeZn 2 (Zn 0.28 Si 0.72 ) 2 in Fig. 21 display an upturn at lowest temperatures, which may either refer to short range correlations above a magnetic phase transition taking place below 3 K or refer to Kondo correlations with a rather small characteristic energy of the order of one Kelvin.
Consistent with the small Seebeck coefficient (see top le inset in Fig. 22) electrical resistivity of s 5 indicates metallic type behaviour ruling out any thermoelectrically interesting behaviour.

Conclusions
As the Ce-Zn-Si system is an important part of multinary Mgbased Mg-Zn-Mn-RE-(Si) high strength lightweight alloys for automotive applications, we have explored the constitution of the Ce-Zn-Si subsystem and particularly have determined in this work the phase equilibria for the isothermal section at 600 C in the region with <33.3 at.%Ce.Five ternary compounds (s 1 , s 2 , s 5 to s 7 ) exist at the investigated region at 600 C. Several four-phase reactions in the Zn rich corner were detected by DTA, including the peritectic decomposition temperatures of s    Ce 7 Zn 21 (Zn 1Àx Si x ) 2 .DFT calculations elucidated the extent and nature of the stabilizing effect of Ge in Ce 7 Zn 23Àx Ge x discussing the electronic structure in terms of the density of states (DOS) and determining enthalpies of formation Ce 7 Zn 23Àx Ge x (x ¼ 0, 0.5, 2) as well as for several neighbouring binary Ce-Zn phases.
Physical property measurements document that neither s 5 nor s 6 are near a metal to insulator transition and thus exhibit rather metallic than semiconducting (thermoelectric) behaviour.Magnetic measurements as well as specic heat and electrical resistivity data reveal interesting ferromagnetic Kondo lattice behavior for s 5 -CeZn(Zn 1Àx Si x ) 2 with a Curie temperature T C ¼ 4.4 K, whereas s 6 displays Curie-Weiss type paramagnetic behavior down to 3 K.The effective paramagnetic moments of Ce obtained from Curie-Weiss t of s 5 (2.50m B ) and s 6 (2.34m B ) suggest that the ground state of Ce-ions in these compounds is trivalent or close to 3+.

3. 3 .
Phase stability of Ce 7 Zn 23Àx Ge x 3.3.1.DFT phase stabilities.The enthalpy of formation DH DFT at T ¼ 0 K was derived from the DFT total energies E tot DFT as obtained from VASP according to:

Fig. 4
Fig. 4 Crystal structure of Ce 7 Zn 21 (Zn 1Àx Ge x ) 2 , x ¼ 0.75 projected along the c-axis and the coordination polyhedra for the Ce atoms.Atoms are drawn with anisotropic displacement parameters from Xray single crystal refinement.Please note that (with respect to the previously incorrect standardization of Ce 7 Zn 21 (Zn 1Àx Si x ) 2 ) the origin of the unit cell is now shifted by (1/2 0 0).

Fig. 5
Fig. 5 Comparison between experimental and DFT derived adjusted calculated enthalpies of formation for Ce-Zn binaries and Ce 7 Zn 23Àx Ge x .
) at 800 C to x ¼ 0.45 (3.0 at.%Si) at 600 C. The homogeneity range of s 1 at 800 C, studied by combination of XRPD, XRSC, and EPMA contradicts the claim of Hoos et al. 10 regarding 3.5 at.%Si as minimum amount of Si in this phase.The three-phase regions involving binary Ce-Zn phases with more than 75 at.%Zn at 600 C resemble those observed at 800 C.

Fig. 7
Fig. 7 Differences of total and local density of states, Ce 7 Ge 0.5 Zn 22.5 minus Ce 7 Zn 23 .

Fig. 8
Fig. 8 Partial isothermal section at 600 C (<33.3 at% Ce).The circles represent nominal compositions of alloys.The pink three phase fields are taken from ref. 8.

Fig. 6
Fig. 6 Panel (a): total and local density of states (DOS) for non spinpolarized Ce 7 Ge 0.5 Zn 22.5 .Panel (b): local DOS per atom.For better visibility, the local DOS for Ge is multiplied by a factor of 10.
8) suggested that s 5 is unstable at this temperature and decomposes into Ce(Si 1Àx Zn x ) 2 with a-ThSi 2 type, L(Zn), and possibly CeZn 11 or b-Ce 2 Zn 17 .Indeed DTA runs of sample Ce 7.6 Zn 78.4 Si 14 up to 850 C gave two signals between 780-790 C. Surprisingly

Fig. 14
Fig. 14 Partial isothermal sections in the Zn-corner at various temperatures.
reaction involving s 2 is not compatible with the existence of the three-phase eld s 2 + CeSi 2 + b-Ce 2 Zn 17 .Careful heat treatment between 850-900 C followed by XRPD and EPM analysis showed that an alloy annealed at 860 C the same phase constituents as in 850 C, while at 870 C Ce(Si 1Àx Zn x ) 2 with a-ThSi 2 type is additionally present in this sample.This fact narrows down the decomposition temperature of s 5 to 865 AE 5 C, and conrms the participation of Ce(Si 1Àx Zn x ) 2 with a-ThSi 2 type in the peritectic formation of s 5 .Taking into consideration similar arguments, as discussed above for the formation of s 6 , a degenerated invariant reaction of peritectic type P D2 : L + CeSi 2 , b-Ce 2 Zn 17 5 s 5 is assigned.The equilibria observed at 900 C could be explained by a transition type reaction U 5 : L + s 2 5 CeSi 2 + b-Ce 2 Zn 17 that occurs at 890 AE 10 C. One of the afore-mentioned thermal effects observed between 780-790 C could be attributed to a transition type reaction U 4 : L + b-Ce 2 Zn 17 5 s 5 + CeZn 11 .The phase eld L(Zn) + s 5 + CeZn 11 was still observed up to 770 C, while at 790 C it changed to L(Zn) + s 5 + b-Ce 2 Zn 17 .Note that in some samples CeZn 11 and/or s 6 were observed as the fourth or h phase.Based on the amount and morphology, those phases were considered to be formed during the quenching process.The stability of s 5 at 800 C has been incorporated in the new isothermal section shown in Fig. 17.It supersedes the older version by Malik et al. 8 In addition to the three-phase eld L(Zn) + s 5 + b-Ce 2 Zn 17 , two narrow three-phase elds are required to complete the section: CeSi 2 + s 5 + b-Ce 2 Zn 17 and L(Zn) + s 5 + CeSi 2 .Note that the three-phase eld L(Zn) + CeSi 2 + (Si) is still stable up to 900 C. Such narrow phase elds are complicated to investigate, and without careful control of the overall sample composition it may earlier have led to a wrong conclusion regarding the stability of s 5 .

Fig. 18
Fig. 18 Temperature dependent in-phase and out-of-phase ac susceptibility components, c 0 and c 00 , measured on polycrystalline s 5 -CeZn(Zn 0.32 Si 0.68 ) 2 with a field amplitude of 325 A m À1 and frequency of 100 Hz.

Fig. 19
Fig. 19 Isothermal magnetisation measurements of single crystalline s 5 -CeZn(Zn 0.29 Si 0.71 ) 2 ; the inset shows the corresponding Arrott plot, M 2 vs. H/M.The solid lines display a model calculation in terms of the resonant level model by Schotte and Schotte.

Fig. 20
Fig. 20 Temperature dependent dc magnetic susceptibility, c(T) at left axis, and inverse magnetic susceptibility, 1/c(T) at right axis, of freely rotating s 5 -CeZn(Zn 0.29 Si 0.71 ) 2 single crystals measured at 3 T; the solid line displays a modified Curie-Weiss fit of the inverse susceptibility.
5 and s 6 at 865 AE 5 C and 695 AE 5 C, respectively.To provide details on the solidication of Ce-poor alloys, a Schultz-Scheil diagram was constructed from DTA measurements and partial isothermal sections determined at various temperatures.The crystal structures of s 5 (CeNiSi 2 -type, Cmcm, a ¼ 0.42079(1), b ¼ 1.76522(3), c ¼ 0.41619(1) nm), and s 6 (ThCr 2 Si 2 -type, I4/ mmm, a ¼ 0.41757(1), c ¼ 1.05073(2) nm) were solved from X-ray single crystal diffraction data.An interesting case was met in the stabilization by extremely small amounts of Ge (less than $2 atom percent of Ge) of the ternary phases {La,Ce} 7 Zn 21 -(Zn 1Àx Ge x ) 2 , both isotypic with the structure of

Fig. 21
Fig. 21 Temperature dependent specific heat of s 5 -CeZn(Zn 0.29 Si 0.71 ) 2 single crystals and polycrystalline s 6 -CeZn 2 (Zn 0.28 Si 0.72 ) 2 ; the solid and dotted lines refer to the analysis of s 5 data in terms of the resonant level model by Schotte and Schotte and a tentative phonon contribution represented by a Debye function, respectively.

Fig. 22
Fig. 22 Temperature dependent electrical resistivity of polycrystalline s 5 -CeZn(Zn 0.32 Si 0.68 ) 2 .Bottom right inset shows the kink at the ordering temperature; top left inset shows the Seebeck coefficient above room temperature.

Fig. 23
Fig. 23 Temperature dependent dc magnetic susceptibility, c(T) at left axis, and inverse magnetic susceptibility, 1/c(T) at right axis, of polycrystalline s 6 -CeZn 2 (Zn 0.28 Si 0.72 ) 2 measured at 3 T; the solid line displays a modified Curie-Weiss fit of the inverse susceptibility.

Table 5
Three phase equilibria and lattice parameters of alloys annealed at 600 C this part of the phase diagram at 600 C is different from that established at 800C (ref.8)and this is essentially due to the formation of s 7 .Thus, two three-phase regions: Ce(Zn 1Àx Si x ) 2 (CeCu 2 -type) + s 2 + s 1 and Ce(Zn 1Àx Si x ) 2 (CeCu 2type) + s 2 + s 4 , which were observed at 800 C are now changed into two three-phase regions: s 7 + s 2 + s 1 and s 7 + Ce(Zn 1Àx Si x ) 2 (CeCu 2 -type) + s 1 , possibly due to the peritectoid formation of s 7 (s 2 + s 4 + Ce(Zn 1Àx Si x ) 2 5 s 7 ), and a U-type reaction (s 2 + Ce(Zn 1Àx Si x ) 2 5 s 1 + s 7 ) in the temperature interval 600 C < T < 800 C. 3.5.Formation of s 5 and s 6 and partial Schulz-Scheil diagram Due to the high melting point of cerium silicides Ce(Si 1Àx Zn x ) 2