Journal of Solid State Chemistry 201 (2013) 244–249

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Journal of Solid State Chemistry

0022-45

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Pd2Cd11�d (0.21rdr0.51)–a partly disordered g-brass type phaseand Pd0.238Cd0.762-a g-brass related incommensurate phase in thepalladium–cadmium system

Partha Pratim Jana n, Sven Lidin

CAS Chemical Centre, Lund University, Getingevagen 60, Box 124, Lund SE-22100, Sweden

a r t i c l e i n f o

Article history:

Received 6 December 2012

Received in revised form

18 January 2013

Accepted 29 January 2013Available online 12 February 2013

Keywords:

Intermetallic phases

Palladium

Cadmium

g-brass phase

Incommensurate phase

X-ray diffraction

96/$ - see front matter & 2013 Elsevier Inc. A

x.doi.org/10.1016/j.jssc.2013.01.044

esponding author. Fax: þ46 46 222 40 12.

ail addresses: Partha.Jana@polymat.lth.se,

a888@gmail.com (P. Pratim Jana), Sven.Lidin

a b s t r a c t

The Cd rich part of the Cd–Pd phase diagram was reassessed by means of synthesis and single crystal

and powder X-ray diffraction. The region contains two phases that have been reported to have

substantial compositional widths, Cd11Pd2 and Cd4Pd. The phase Cd11Pd2 that has previously been

reported to be a disordered g-brass crystallizing is space group P43m is here shown to crystallize in

I43m and the mechanism for compositional variation is explained. The phase Pd4Cd has previously been

shown to constitute a phase field or a phase bundle of modulated structures and here we determine the

structure of a compound Pd0.238Cd0.762 which crystallizes in the orthorhombic superspace group

Fmmm(a00)0s0 (F¼[(½, ½, 0, 0); (½, 0, ½, 0 ); (0, ½, ½, 0 )] with the fundamental cell dimensions

a¼4.687(2) A, b¼10.000(1) A, c¼14.140(2) A, q¼0.6432(6)a*.

& 2013 Elsevier Inc. All rights reserved.

1. Introduction

Hume-Rothery deduced that for some compounds (nowknown as Hume-Rothery compounds), formation occurs at aspecific valence electron concentration (vec) i.e. average numberof valence electrons/atom [1,2,3]. In 1936, Mott and Jones give thefirst interpretation of this phenomenon in terms of the interactionbetween the Fermi surface of radius kF and the Brillouin zonecharacterized by a reciprocal lattice vector based on the nearlyfree electron model [4,5]. A pseudogap occurs by the lowering ofthe kinetic energy of the valence electrons across the Fermi leveland this plays a key role in stabilizing Hume-Rothery phases[4,6,7,8]. Among them, the g-brass type phase had been implicitlyassumed to be stabilized at e/a¼21/13. Ekman studied the TM-Zn(TM¼Ni, Pd, Pt)—phases and proposed that they obey the Hume-Rothery electron concentration rule with e/a¼1.60, providedthat the valency of the TM and zinc is zero and two, respectively[9]. Electron microscopy studies on Cu–Zn, Ni–Zn and Pd–Znsystems revealed that a slight variation of vec results in a struc-tural modification of the g-brass type or g-brass relatedphases [10,11,12]. This finding suggests that g-brass region of

ll rights reserved.

@polymat.lth.se (S. Lidin).

TM–Zn/TM–Cd may be much more complex than previouslyassumed [13] and this motivated us to reexamine the g-brassregion of the Pd–Cd system of which g-brass type Pd2Cd11 [14,15]and a set of g-brass related orthorhombic phases were reported[16].

Pd2Cd11 was initially reported to be a g-brass type phasewhich crystallizes in the body center cubic space group I43m withlattice parameter ag¼9.96 A [14]. A structural refinement waspublished by L. Arnberg who used a model in the space groupP43m (Table 1) [15]. In recent years Schmidt et al. [16] found thattransition metal palladium–cadmium systems do not accommo-date only the g-brass type phase but also a closely relatedorthorhombic phase bundle or phase field. They reported struc-tural models for two single crystal structures—Pd0.213Cd0.787 andPd0.235Cd0.765 modeled as modulated composites in superspacegroup Xmmm(00g)s00 with the cell dimensions a¼9.9013(28) A,b¼14.0033(20) A, c1¼2.8510(7) A, c2¼4.6329(9) A q¼(8/13)c*and a¼9.9251(5) A, b¼14.0212(7) A, c1¼2.8635(2) A,c2¼4.6293(3) A, q¼(13/21)c* corresponding to superstructuresin the conventional three dimensional space groups Ccme andF2mm.

Against this background we reinvestigated the g-brass region ofthe Pd–Cd binary system [17]. We present here structural modelsfor g-brass type Pd2Cd11�d (0.21rdr0.51) an interval thatincludes that reported by Arnberg [15]. We also report an orthor-hombic g-brass related incommensurately modulated structureexists at slightly higher palladium content than that of thepreviously reported compounds Pd0.213Cd0.787 and Pd0.235Cd0.765.

Fig. 1. (top) Experimental (a) and calculated (b) X-ray powder diffraction pattern

of g-brass type Pd2Cd10.79. Vertical bars indicate the corresponding Bragg posi-

tions. (bottom) X-ray powder diffraction patterns in the 2y range 101–371

observed for single phase samples Pd2Cd10.49, Pd2Cd10.72, Pd2Cd10.79.

Table 1Refined structural data for Pd2Cd10.75 by Arnberg.

Cluster Site x y z SOF B a (A2)

1 Cd11 4e IT 0.1048(9) x x 0.75 1.6(2)

Pd12 4e OT �0.1734(6) x x 1 0.8(1)

Cd13 6f OH 0 0 0.3493(9) 0.184(18) 1.5(1)

Cd14 12i CO 0.3038(4) x 0.0474(4) 1 1.1(5)

2 Cd21 4e IT 0.6073(6) x x 1 1.3(1)

Pd22 4e OT 0.3292(5) x x 1 0.4(1)

Cd23 6f OH ½ ½ 0.8556(7) 1 0.7(1)

Cd24 12i CO 0.8076(4) x 0.5448(5) 1 1.0(1)

a B¼thermal parameters.

P. Pratim Jana, S. Lidin / Journal of Solid State Chemistry 201 (2013) 244–249 245

2. Material and methods

2.1. Synthesis and morphological features

The samples were synthesized starting from the pure elements:palladium (Alfa AesarZ99.995%) cadmium (ABCR, 99.999%) on a300 mg scale. The metals were sealed in small, previously de-gassedfused silica ampoules (length: 3 cm, diameter: 0.8 cm) under areduced argon pressure of about 0.5 Pa. The molar fraction xPd ofthe mixtures was systematically varied between 0.11 and 0.25. Theampoules were heated up to 973 K at a rate of 134.6 K h�1, kept atthis temperature for 12 h, then cooled down to 923 K during 400 h(0.125 K h�1 ). Hereafter, the samples were cooled to room tem-perature during 12 h. Samples richer in cadmium contained excesscadmium in form of few tiny globules next to the binary phase.

2.2. XRD data collection and processing

Six distinct single crystals extracted from different loadedcompositions were studied by means of single crystal X-raydiffraction. Suitable crystals of compounds were picked from thecrushed sample, mounted on a glass fiber and diffraction inten-sities were measured with a four circle diffractometer (XCalibur)equipped with MoKa radiation (l¼0.71073 A) at room tempera-ture 293 K. Data reduction was performed with an oxford diffrac-tion Crysalis software. The structure solution and the refinement(Tables 2–4) were carried out using the JANA2006 program [18,19].

All the samples were examined by X-ray powder diffractionexperiments to check the purity of single-phased samples, todetermine the adjacent phases and to identify new phases. Thepowder diffraction data were collected by a STOE WinXPOWdiffractometer (CuKa¼1.5406 A, 40 kV, 40 mA, Mythen 1 K detec-tor). All the diffractograms were recorded between 51o2yo901at room temperature.

2.3. Energy dispersive X-ray analysis

The composition of selected specimens were examined in ascanning electron microscope (a JEOL 3000 with a secondaryelectron (SEI) detector) providing an energy dispersive X-rayspectrometer (EDS). EDS spectra were recorded from thosesamples which had been previously studied by single crystalX-ray diffraction experiments. No impurities of elements heavierthan carbon were detected to be present in the selectedspecimens.

3. Results

3.1. Phase analysis

The homogeneity range and constitution of the cubic g-brasstype phase in the Pd–Cd system was examined by means ofpreparative methods, X-ray diffraction and EDS analyses.

Chemical composition determined by EDS and X-ray singlecrystal refinement shows a homogeneity range over 0.160rxPdr0.156 i.e., from Pd2Cd10.49 to Pd2Cd10.79. The g-brass typePd2Cd11�d coexists with a g-brass related binary orthorhombicphase of approximate composition Pd Cd4 at the palladium richend. Experimental and calculated X-ray powder diffraction pat-terns of g-brass type Pd2Cd10.79 over 2y range 101–90o are shownin Fig. 1 together with those for Pd2Cd10.49, Pd2Cd10.72 andPd2Cd10.79 over a 2y range 101–37o. Progressive depletion of Cdis reflected in the modified intensities at the low angle diffractionintensities of the X-ray powder diffractograms of the g-brass typePd2Cd11�d (0.21rdr0.51).

3.2. Refinement for Pd2Cd11�d

The intensity of the g-brass type Pd2Cd11�d could be indexedon the basis of a �9.9 A I-centered cubic unit cell. The structurewas solved [18,19] in the space group I43m (217).The structuresolution yielded four atomic positions in the asymmetric unit.At this stage the structure refinement converged at R(F)E0.06.Atomic sites displaying large thermal displacement parameterswere checked for occupancy and positional disorder. The best fitto the data was achieved for a model where two of the originalfour positions where split. The occupation parameters of theseoccupationally disordered sites were refined independently.An isotopic extinction correction yielded R(F) values between0.018 and 0.038 at the final refinement.

3.3. Refinement for Pd0.238Cd0.762

Diffraction patterns of g-brass related Pd0.238Cd0.762 display strongmain reflections and additional satellite reflections typical for amodulated phase. The main reflections can be indexed in agreementwith the orthorhombic space group Fmmm with the basiccell dimension: a¼4.687(2) A, b¼10.000(1) A, c¼14.140(2) A. Theobserved satellite reflections show a superstructure along the [100]

Table 2

Crystallographic data for the single crystal structure refinements of Pd2Cd11�d (0.21rdr0.51).

C1 C2 C3 C4 C5

Crystallographic dataChemical formula Pd2Cd10.492 Pd2Cd10.502 Pd2Cd10.598 Pd2Cd10.725 Pd2Cd10.787

EDS formula Pd16.3(2)Cd83.7(2) Pd16.0(4)Cd84.0(2) Pd15.8(4)Cd84.2(2) Pd15.7(4)Cd84.3(2) Pd15.5(2)Cd84.5(3)

Pearson symbol �cI50 �cI50 �cI50 �cI51 �cI51

xPd 0.160 0.160 0.159 0.157 0.156

Crystal system cubic

Space group type; Z I-43m (No.217); 4

a (A) 10.0170(9) 9.9593(3) 9.9550(2) 9.9626(3) 9.9969(3)

V/106 (A3) 1005.11(16) 987.84(5) 986.56(3) 988.82(5) 999.07(5)

rcalcd (mg m�3) 9.1973 9.3656 9.4504 9.5247 9.4733

m (mm�1) 25.099 25.559 25.794 26.001 25.863

Crystal color Silvery with metallic luster

Data collection

Diffractometer Four circle diffractometer, Xcalibur,Eos

Radiation MoKaMonochromator Graphite

Distance crystal-IP (mm) 50 50 50 50 50

T (K) 293(2) 293(2) 293(2) 293(2) 293(2)

ymin�ymax (deg.) 2.87–28.19 2.89–28.71 4.09–28.27 2.89–28.76 4.07–28.59

Dj (deg.) 0.5 0.5 0.5 0.5 0.5

2ymax (deg.) 52.64 52.64 52.64 57.4 52.64

Reflns measured 1383 1656 5402 11270 1155

Index range �7rhr12 �11rhr12 �13rhr12 �13rhr13 �13rhr5

�11rkr12 �13rkr12 �12rkr12 �13rkr13 �12rkr10

�11r lr12 �13r lr12 �12r lr12 �13rkr13 �12rkr7

Completeness of Data set 0.9922 0.9922 0.984 0.9937 0.9844

Absorption Correction Multi-scan

Unique reflns 247 256 256 268 249

Rint 0.0658 0.0223 0.0368 0.0324 0.0248

Structure solution/refinement JANA 2006 package program18,19

Structure solution Superflip19

No. reflns used 247 256 256 268 249

No. variables 23 23 23 23 23

Observed reflns (I43s(I)) 236 250 251 265 242

R(F243s(F2)) 0.0381 0.0186 0.0189 0.0229 0.0181

R(F) (all data) 0.0399 0.0193 0.0195 0.0231 0.0191

ka 0.0004 0.0004 0.0004 0.0016 0.0004

wR (F2)(all data) 0.0853 0.0473 0.0513 0.0688 0.0497

GOF (all) 1.99 1.49 1.91 1.64 1.65

Drmin/rmax (eA�3) �2.37/2.79 �1.29/1.43 �0.89/1.71 �1.14/2.54 �1.03/1.43

a Weighting scheme: w¼1/[s2(I)þk(I)2)].

Table 3Structural data for Pd2Cd10.492(C1), Pd2Cd10.502 (C2), Pd2Cd10.598(C3) , Pd2Cd10.725 (C4), Pd2Cd10.787(C5).

Cluster Atom Site x y z SOF Ueqa (A2)

C1 Z(1) Cd10 2a CC 0 0 0 0.30(2) 0.051(6)

C2 0.282(10) 0.040(2)

C3 0.211(11) 0.035(3)

C4 0.157(13) 0.035(4)

C5 0.105(10) 0.028(5)

C1 Cd11 8c IT 0.1074(2) x x 0.690(10) 0.0210(7)

C2 0.10668(10) 0.708(5) 0.0194(3)

C3 0.10634(9) 0.777(5) 0.0173(3)

C4 0.10623(8) 0.840(6) 0.0166(3)

C5 0.10601(8) 0.882(5) 0.0171(3)

C1 Pd12 8c OT 0.32739(13) x x 1 0.0114(3)

C2 0.32766(6) 0.01260(16)

C3 0.32788(6) 0.01207(16)

C4 0.32812(7) 0.01207(18)

C5 0.32819(6) 0.01270(17)

C1 Cd13� 12e OH� ½ ½ 0.199(3) 0.184(18) 0.019(5)

C2 0.1969(11) 0.201(8) 0.0201(19)

C3 0.1948(14) 0.155(9) 0.017(3)

C4 0.193(2) 0.125(10) 0.021(3)

C5 0.191(4) 0.088(12) 0.030(6)

C1 Cd13 12e OH ½ ½ 0.1441(6) 0.80(2) 0.0161(12)

C2 0.1433(3) 0.781(9) 0.0163(6)

C3 0.1428(2) 0.825(10) 0.0152(5)

C4 0.1425(2) 0.864(10) 0.0145(5)

C5 0.1424(3) 0.903(13) 0.0153(6)

C1 Cd14 24g CO 0.30577(12) x 0.04583(15) 1 0.0257(5)

P. Pratim Jana, S. Lidin / Journal of Solid State Chemistry 201 (2013) 244–249246

Table 3 (continued )

Cluster Atom Site x y z SOF Ueqa (A2)

C2 0.30581(6) 0.04606(7) 0.0239(2)

C3 0.30614(5) 0.04562(7) 0.0217(2)

C4 0.30638(6) 0.04532(8) 0.0209(2)

C5 0.30678(5) 0.04481(7) 0.0208(2)

a Ueq is defined as one-third of the trace of orthogonalized Uij tensor.

Table 4Crystallographic and technical data for the single crystal structure refinement for

Pd0.238Cd0.762 (C6).

Chemical formula Pd0.238Cd0.762

EDS formula Pd00.215(3)Cd0.785(2)

Molecular weight 959.22

xPd 0.238

Crystal system; orthorhombic

Space group type Fmmm(a00)0s0

a (A) 4.687 (2)

b (A) 10.000(1)

C A) 14.140(2)

V (A3) 662.7(2)

Modulation wave vector 0.6432(6)

rcalcd (mg m�3) 9.6109

m (mm�1) 26.006

Crystal color Silvery with metallic luster

Data collection

Diffractometer Four circle diffractometer,

XCalibur, Eos

Radiation, l(A) MoKa, 0.7107

Monochromator graphite

T (K) 293(2)

y (deg.) 2.88–28.73

2Y (deg.) 52.64

Reflns measured 8181

Independent reflections 1445

Observed reflection(I43s(I)) 1017

Index range �6rhr6

�12rkr13

�18r lr17

�3rmr3

Completeness of data 99.53

Data reduction/

Absorption correction multi-scan

Rint 0.0664

Structure solution, refinement JANA 2006 package program18

Structure solution Superflip19

Structure refinement

Refinement on (F2)

R [F242s(F2)], wR (F2), S 0.0574, 0.1456, 1.58

Rmain 0.0324

Rsatellite,

First order 0.0513

Second order 0.0875

Third order 0.1431

No. of reflections 1017

No. of parameters 74

ka 0.0025

Drmin/rmax (eA�3) �5.60/5.67

a Weighting scheme based on measured s.u.’s w¼1/[s2(I)þkI2).

Fig. 2. Representation of two symmetrically and topologically distinct clusters

(defect bcc-type Pd4Cd19 and g-brass type Pd4Cd22) in the crystal structures of

Pd2Cd11�d grouped about the high symmetry points of the I-centered cubic unit

cell. Spheres representing sites with Pd in red and Cd in light gray, respectively.

(For interpretation of the references to color in this figure legend, the reader is

referred to the web version of this article.)

P. Pratim Jana, S. Lidin / Journal of Solid State Chemistry 201 (2013) 244–249 247

direction. The satellite reflections could be indexed by one modula-tion vector along the an direction. The modulation vector wasdetermined to q¼0.6432an. Additional systematic absences for satel-lites indicate a super space translation of ½ associated with themirror plane perpendicular to [010]. Hence, the corresponding 3þ1dimensional superspace group is Fmmm(a00)0s0 in agreement withpreviously published super space models [16,20,21].

The structure solution yielded four atomic positions in theasymmetric unit. Modulations on all the four positionswere checked using Fourier maps. Pd1 (½, 0, 0), M1 at (½, �1/7,

�1/6) and Cd2 (0, 0, �1/8) were well modeled but the positionCd3 was problematic. The fit of the model to the data is highlyimproved by introducing a composite model. The first subsystemconsists of three atoms, Pd1 at (½, 0, 0); M1 at (½, �1/7, �1/6);Cd2 (0, 0, �1/8) and second subsystem consists of one Cd3 atomat (3/4, ¼, 0) atom. The two subsystem reflection sets are definedby the matrices W1 and W2.

W1¼

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

0BBB@

1CCCA and W2

¼

1 0 0 0

0 1 0 0

0 0 1 0

1 0 0 1

0BBB@

1CCCA

The mixed metal position M1 at (½, �1/7, �1/6) is occupa-tionally modulated. This modulation is best described usingsquare (crenel) wave where the occupation of the M1 site is analteration between a Pd1 and a Cd1 atom. All the atoms werefurther modeled with modulations of positional and thermaldisplacement parameters.

4. Discussion

Pd2Cd11�d crystallizes in the acentric cubic space group I43m

(217) with approximately 50–51 atoms per unit cell over sixcrystallographic positions forming a partly disordered g-brasstype structure. In a traditional approach, the g-brass type can bedescribed in terms of clusters-first introduced by Bradleyand Jones [22,23–30]. Within the cluster the atomic shells aredistinguished by two capital letters. CC designates the center of acluster, IT those occupying the vertices of an inner tetrahedron,OT stands for outer tetrahedron, OH is an octahedral shell and COfor cuboctahedron. In standard notation, the correspondingatomic positions are numbered 10–14.

In the cluster description of Pd2Cd11�d (Fig. 2) the CC position(Cd10) and the IT position (Cd11) are partially occupied with asum close to unity. This indicates a simple exchange mechanismwhere either the cluster center is occupied or the surroundingtetrahedron. This is also consistent with the short distance

P. Pratim Jana, S. Lidin / Journal of Solid State Chemistry 201 (2013) 244–249248

between these two sites that does not allow simultaneousoccupation. The outer tetrahedron that forms the next shell ofthe cluster is in anti-position to the inner tetrahedron, and hencethe influence of occupancy in the IT position on the OT position isnegligible. As a consequence, the OT position (Pd12) is fullyoccupied and displays no unexpected features in the thermaldisplacement parameters. The next shell, the octahedron OH(Cd13) is however close to the IT position, and therefore thisposition splits into two: Cd13 and Cd130 where Cd 130 (Figs. 3 and4) forms a smaller octahedron surrounding a single centralposition CC and Cd13 forms a larger octahedron that surroundsan inner tetrahedron IT. The relative occupancies agree well withthis interpretation. The occupancies of Cd10 and Cd130 areroughly equal as are those of Cd11 and Cd13 and further, thesum of occupancies for Cd13 and Cd130 is close to unity. We mayassume that the local cluster is either a defect bcc-type clusterwith shell sequence CC, OT, OH0, CO or a g-type cluster (Fig. 2) (IT,OT, OH, CO).

For electron compounds it is assumed that the disorderedphenomena on various crystallographic sites keep valence elec-tron concentration (vec) nearly constant. According to our inves-tigation the fully ordered g-brass type Pd2Cd11 does not occur.The depletion of cadmium from the inner tetrahetral site resultsin a concomitant accumulation of cadmium at the cluster center

Fig. 3. Fourier map for Pd2Cd11�d about Cd10 (0 0 0).

Fig. 4. (i) Vacancy at Cd10 site (VCd10¼1�sofCd10) and Cd11site (VCd11¼1�sofCd11) an

g-brass type Pd2Cd11�d.

that reduces the vec value of the g-brass type Pd2Cd11�d

(0.21rdr0.51) toward 21/13. In contrast, for the g-brass typePd–Zn binary phase, vec is shifted towards the ideal value of 21/13 with the partial substitution of divalent Zn by zero valent Pdon octahedral site [31]. Furthermore, for the g-brass typePt2Zn11�d (0.2odo0.3) the vec value is reduced by the vacancyformation of Zn on the inner tetrahedral site [13].

The structure of Pd0.238Cd0.762 is described by four atomicpositions and their modulations [16]. Among them, only M1 siteat (½, �1/7, �1/6) shows occupational modulation. The orderingof the partial occupancy of Pd and Cd on M1 site was modeled bya crenel wave [32]. It is an outstanding question if the orthor-hombic structures constitute a bundle of distinct phases or acontinuous phase field. The compound reported here is distinctlyincommensurate, with a q-vector of 0.6432an. The approximationq¼16/25an can be ruled out within the error of the experimentand hence any rational superstructure must have an a-axisconsiderably longer than 117 A (25n4.7 A). At this size, thedistinction between incommensurate and commensuratebecomes blurred. In a commensurate structure, the modulationfunction is sampled in a discrete number of points, and henceshifting the origin of the modulation function leads to distinctstructures. For a very long period commensurate structure thesampling is so dense that it is indistinguishable from the con-tinuous sampling characteristic of a truly incommensurate phase.By treating the structure as commensurate (25 fold superstruc-ture) it could be shown that the structure of Pd0.238Cd0.762 isinsensitive to origin changes. This shows that it is incommensu-rate, or that the corresponding commensurate super cell is solarge that the distinction is meaningless. Hence, we assert that thestructure of Pd0.238Cd0.762 is indeed incommensurably modulated[33,34,35,36,37,38].

The fact that the structure is incommensurate is a necessarycondition for a continuous phase field, but it is no guarantee.Since the modulation is composition driven, it is difficult to studycontinuous transformations, but the fact that compounds withvery similar compositions may be synthesized and that there is anobvious mechanism for continuously varying the compositionargue strongly in favor of such a view.

The modulated structure presented herein is closely related tothe g-brass type Pd2Cd11�d (Fig. 5). It can be described by chainsof vertex sharing chains of closo-11 deltahedra and icosohedra(Fig. 5) [16]. Moreover it can be viewed by the chain of two sets ofatoms having different translational periodicities. Hence, the twosubunits bearing the chain of two sets of atoms have differentinteratomic spacing along the [100] direction. The spacings maybe represented by dividing the length of the long axis intoan integer number of segments (L and S) [16]. Note that, in theg-brass type Pd2Cd11�d the S/L¼5/3¼1.667. In the two structuresPd0.213Cd0.787 and Pd0.235Cd0.765 reported by Schmidt et al., the

d (ii) sof at Cd13 site and at Cd130 site vs. mole fraction of palladium (xPd) in the

Fig. 5. (a) Representation of the chains of vertex sharing 11 atom deltahedra and

face sharing double icosahedra in the structure of g-brass type Pd2Cd11�d along

[110]. (b) Commensurate approximation of the structure—Pd0.238Cd0.762 are

shown. Cd atoms are shown in red color and Pd in dark blue, respectively. The

top most figure displays the chains of two sets of atoms with different transla-

tional periodicities. The middle one represents the chains of vertex sharing closo-

11 deltahedra and icosahedra. The bottom one shows the chain of two face sharing

icosohedra, three face sharing icosahedra and closo-11 deltahedra. (For inter-

pretation of the references to color in this figure legend, the reader is referred to

the web version of this article.)

P. Pratim Jana, S. Lidin / Journal of Solid State Chemistry 201 (2013) 244–249 249

ratios of S and L distances are 13/8¼1.625 and 21/13¼1.615,respectively. For those structures reported from single crystalsdata, the L and S values are between the neighboring members ofthe Fibonacci series and the S/L values are near to golden mean.But for the reported structure herein, the ratio of the S and L

distances is close to 41/25¼1.64. An S/L ratio based on powderdata of 18/11 (not Fibonacci sequence numbers) based on asynchrotron derived ratio of 1.637 is reported at Pd poor regionby Schmidt et al.

Pd0.238Cd0.762 is an illustration of the fourth generation possi-ble structure with S/L¼41/25 on the Farey tree (discussed for thePd–Zn phase) which can display the following (ySD-SD-LT-SD-LT-SD-LT-SDy) unit cell arrangements along the a-direction in thePd–Cd binary system [20,39].

Similar composite structures were reported in the Pd–Zn andNi–Zn systems [20,31,38,39,40,41,42]. The similarities are veryfar-reaching as the compounds crystallize in the same superspacegroup and are describable using the same composite model.Hence, the g-brass related phases NiZn3�d, NiZn3.30 and PdxZn1�x

(x¼0.14–0.24)[20,31,39,42] and Pd0.238Cd0.762 are in fact isostruc-tural in 3þ1 dimensions.

Database linking

Crystallographic data for compounds C1, C2, C3, C4, C5, C6 hasbeen deposited with Fachinformationszentrum Karlsruhe,76344 Eggenstein-Leopoldshafen, Germany, (fax: (49) 7247-808-

666; e-mail: crysdata@fiz-karlsruhe.de) under CSD 425440(C1),425441(C2), 425442 (C3), 425443(C4), 425444(C5) and 425445(C6).

Acknowledgments

The authors wish to thank VR, the Swedish National ScienceResearch Council for the financial support.

Appendix A. Supporting information

Supplementary data associated with this article can be foundin the online version at http://dx.doi.org/10.1016/j.jssc.2013.01.044.

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