Pd_2.28(1)Zn_10.37(1)Al_0.35(1), a ternary γ-brass-type structure

Palladium zinc aluminium (2.28/10.37/0.35), Pd_2.28(1)Zn_10.37(1)Al_0.35(1), represents the upper limit of Al substitution into the parent cubic γ-brass Pd_2+xZn_11−x. The structure can be described in terms of a 26-atom cluster consisting of an inner tetra­hedron (IT), an outer tetra­hedron (OT), an octa­hedron (OH) and a cubocta­hedron (CO), with the substituted Al atoms partially occupying the IT (.3m) and CO (..m) sites.

Key indicators

• Single-crystal X-ray study
• T = 293 K
• Mean [sigma]() = 0.000 Å
• Disorder in main residue
• R factor = 0.027
• wR factor = 0.068
• Data-to-parameter ratio = 15.4

checkCIF/PLATON results

No syntax errors found



Alert level C
PLAT972_ALERT_2_C Large Calcd. Non-Metal Negative Residual Density      -1.87 eA-3
PLAT972_ALERT_2_C Large Calcd. Non-Metal Negative Residual Density      -1.80 eA-3
PLAT041_ALERT_1_C Calc. and Reported SumFormula    Strings  Differ          ?
PLAT045_ALERT_1_C Calculated and Reported Z Differ by ............       0.25 Ratio
PLAT068_ALERT_1_C Reported F000 Differs from Calcd (or Missing)...          ?
PLAT077_ALERT_4_C Unitcell contains non-integer number of atoms ..          ?

Alert level G
CELLZ01_ALERT_1_G Difference between formula and atom_site contents detected.
CELLZ01_ALERT_1_G ALERT: check formula stoichiometry or atom site occupancies.
           From the CIF: _cell_formula_units_Z    4
           From the CIF: _chemical_formula_sum  Al0.35 Pd2.28 Zn10.37
           TEST: Compare cell contents of formula and atom_site data

           atom    Z*formula  cif sites diff
           Al         1.40      1.42   -0.02
           Pd         9.12      9.08    0.04
           Zn        41.48     41.50   -0.02
REFLT03_ALERT_4_G Please check that the estimate of the number of Friedel pairs is
            correct. If it is not, please give the correct count in the
            _publ_section_exptl_refinement section of the submitted CIF.
           From the CIF: _diffrn_reflns_theta_max           34.80
           From the CIF: _reflns_number_total                339
           Count of symmetry unique reflns          193
           Completeness (_total/calc)            175.65%
           TEST3: Check Friedels for noncentro structure
           Estimate of Friedel pairs measured       146
           Fraction of Friedel pairs measured     0.756
           Are heavy atom types Z>Si present        yes
PLAT083_ALERT_2_G SHELXL Second Parameter in WGHT Unusually Large.      32.97
PLAT301_ALERT_3_G Note: Main Residue  Disorder ...................      57.00 Perc.
PLAT199_ALERT_1_G Check the Reported _cell_measurement_temperature        293 K
PLAT200_ALERT_1_G Check the Reported   _diffrn_ambient_temperature        293 K
PLAT811_ALERT_5_G No ADDSYM Analysis: Too Many Excluded Atoms ....          !

   0 ALERT level A = In general: serious problem
   0 ALERT level B = Potentially serious problem
   6 ALERT level C = Check and explain
   8 ALERT level G = General alerts; check

   7 ALERT type 1 CIF construction/syntax error, inconsistent or missing data
   3 ALERT type 2 Indicator that the structure model may be wrong or deficient
   1 ALERT type 3 Indicator that the structure quality may be low
   2 ALERT type 4 Improvement, methodology, query or suggestion
   1 ALERT type 5 Informative message, check


checkCIF publication errors

Alert level A
PUBL022_ALERT_1_A There is a mismatched ~ on line 134
              type phases, we attempted replacing Zn by Al in the parent Pd~2 +
              If you require a ~ then it should be escaped
              with a \, i.e. \~
              Otherwise there must be a matching closing ~, e.g. C~2~H~4~
PUBL022_ALERT_1_A There is a mismatched ~ on line 135
              ~<i>~x~</i>Zn~11 - ~<i>~x~</i> phase (Gourdon & Miller, 2006). Initially
              If you require a ~ then it should be escaped
              with a \, i.e. \~
              Otherwise there must be a matching closing ~, e.g. C~2~H~4~
PUBL022_ALERT_1_A There is a mismatched ~ on line 147
              Pd atoms on the OH sites is observed in binary Pd~2 + ~<i>~x~</i>Zn~11 -
              If you require a ~ then it should be escaped
              with a \, i.e. \~
              Otherwise there must be a matching closing ~, e.g. C~2~H~4~
PUBL022_ALERT_1_A There is a mismatched ~ on line 148
              ~<i>~x~</i> (Gourdon & Miller, 2006; Edstr\"om & Westman, 1969). An
              If you require a ~ then it should be escaped
              with a \, i.e. \~
              Otherwise there must be a matching closing ~, e.g. C~2~H~4~

   4 ALERT level A = Data missing that is essential or data in wrong format
   0 ALERT level G = General alerts. Data that may be required is missing

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S1. Comment

Various M₂Zn₁₁ phases [M = Rh (Gross et al., 2001), Pd (Gourdon & Miller, 2006), Ir (Arnberg & Westman, 1972), Pt (Harbrecht et al., 2002)] adopt the γ-brass type structure (Pearson code cI52). To study the influence of valence electron concentration (vec) on γ-brass type phases, we attempted replacing Zn by Al in the parent Pd_{2 + x}Zn_{11 - x} phase (Gourdon & Miller, 2006). Initially obtained as a side product, Pd_2.28 (1)Zn_10.37 (1)Al_0.35 (1) represents the upper limit of Al substitution in the Pd_{2 + x}Zn_{11 - x} phase. Further substitution of Al leads to 2×2×2 superstructures of γ-brass with lattice parameters ranging from 18.0700 (3) to 18.1600 (2) Å (Pearson code cF400–cF416) (Thimmaiah & Miller, 2010).

In terms of the 26-atom clusters (in bcc arrangement) commonly used to describe the structure of γ-brass, the inner tetrahedron (IT) and cuboctahedron (CO) are occupied by mixtures of Zn and Al atoms, the outer tetrahedron (OT) is fully occupied by Pd atoms, and the octahedron (OH) is occupied by a mixture of Zn and Pd atoms (Fig. 1a). Similar mixing of Zn and Pd atoms on the OH sites is observed in binary Pd_{2 + x}Zn_{11 - x} (Gourdon & Miller, 2006; Edström & Westman, 1969). An alternative description involves four interpenetrating icosahedra, which are constructed around each OT atom and encapsulate a tetrahedron formed by IT atoms (Fig. 1 b). The IT and OT sites are each surrounded by 12 nearest neighbours [at distances of 2.666 (1)–2.789 (2) Å and 2.624 (1)–2.794 (1) Å, respectively] forming distorted icosahedra. On the other hand, the coordination numbers are 13 around the OH site [2.591 (2)–2.945 (1) Å] and 11 around the CO site [2.612 (1)–2.945 (1) Å].

Related literature

For related literature, see: Arnberg & Westman (1972); Edström & Westman (1969); Gross et al. (2001); Gourdon & Miller (2006); Harbrecht et al. (2002); Thimmaiah & Miller (2010). For standardization of crystal structures, see: Gelato & Parthé (1987).

S2. Experimental

The title compound was prepared from 0.5 - g mixtures of the elements (Pd foil, MPC, Ames Laboratory, 99.999%; Zn ingot, MPC, Ames Laboratory, 99.999%; Al tear drop, MPC, Ames Laboratory, 99.999%) loaded into cleaned Ta tubes, which were placed in evacuated (10^-5 torr) and sealed silica tubes. The tubes were heated at 30 °C h^-1 to 850 °C, kept there for 12 h, cooled to 550 °C over 12 h, equilibrated there for 3 d, and then cooled to room temperature by shutting off the furnace.

S3. Refinement

Refinement of a starting model (Gourdon & Miller, 2006) led to a mixture of 0.09 (3) Pd and 0.91 (3) Zn in the OH sites. However, the IT and CO sites, initially assumed to be fully occupied by Zn atoms, exhibited elevated isotropic displacement parameters. Modeling these sites with a mixture of Zn and Al resulted in the refined composition Pd_2.28 (1)Zn_10.37 (1)Al_0.35 (1). Analysis of multiple crystals obtained from the same and other batches gave the same site occupancies. Within the limitation of the technique, semiquantitative energy-dispersive X-ray analysis corroborate this chemical composition. The structure was standardized by means of the program STRUCTURE TIDY (Gelato & Parthé, 1987). The highest peak and the deepest hole are located 1.26 Å and 1.18 Å, respectively, from Pd1.

Computing details

Data collection: X-AREA (Stoe & Cie, 2009); cell refinement: X-AREA (Stoe & Cie, 2009); data reduction: X-AREA (Stoe & Cie, 2009); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 2009); software used to prepare material for publication: SHELXTL (Sheldrick, 2008).

Figures

Fig. 1. Cubic γ-brass structure of Pd2.28 (1)Zn10.37 (1)Al0.35 (1) in terms of (a) 26-atom clusters in bcc arrangement, with different polyhedra emphasized, and (b) four interpenetrating Pd-centered icosahedra. The color scheme is shown and displacement ellipsoids are drawn at the 90% probability level.

palladium zinc aluminium (2.28/10.37/0.35)

Crystal data

Pd2.28Zn10.37Al0.35	Melting point: not measured K
Mr = 929.56	Mo Kα radiation, λ = 0.71073 Å
Cubic, I43m	Cell parameters from 2000 reflections
Hall symbol: I -4 2 3	θ = 3.2–34.8°
a = 9.1079 (11) Å	µ = 37.46 mm^−1
V = 755.54 (16) Å^3	T = 293 K
Z = 4	Rectangular, silver
F(000) = 1681	0.12 × 0.06 × 0.03 mm
Dx = 8.172 Mg m^−3

Data collection

Stoe/IPDS-II diffractometer	339 independent reflections
Radiation source: fine-focus sealed tube	337 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.069
φ and ω scans	θmax = 34.8°, θmin = 3.2°
Absorption correction: numerical (X-SHAPE and X-RED; Stoe & Cie, 2005)	h = −14→14
Tmin = 0.054, Tmax = 0.465	k = −14→13
11243 measured reflections	l = −14→14

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0249P)^2 + 32.9721P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.027	(Δ/σ)max < 0.001
wR(F^2) = 0.068	Δρmax = 1.05 e Å^−3
S = 1.02	Δρmin = −1.19 e Å^−3
339 reflections	Extinction correction: SHELXL97 (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
22 parameters	Extinction coefficient: 0.00118 (16)
0 restraints	Absolute structure: Flack (1983)
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.04 (4)

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pd1	0.32674 (6)	0.32674 (6)	0.32674 (6)	0.0101 (3)
Zn1	0.10828 (12)	0.10828 (12)	0.10828 (12)	0.0139 (5)	0.924 (17)
Al1	0.10828 (12)	0.10828 (12)	0.10828 (12)	0.0139 (5)	0.076 (17)
Zn2	0.35776 (15)	0.0000	0.0000	0.0135 (5)	0.91 (3)
Pd2	0.35776 (15)	0.0000	0.0000	0.0135 (5)	0.09 (3)
Zn3	0.31076 (9)	0.31076 (9)	0.03932 (12)	0.0162 (3)	0.966 (13)
Al3	0.31076 (9)	0.31076 (9)	0.03932 (12)	0.0162 (3)	0.034 (13)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pd1	0.0101 (3)	0.0101 (3)	0.0101 (3)	0.0007 (2)	0.0007 (2)	0.0007 (2)
Zn1	0.0139 (5)	0.0139 (5)	0.0139 (5)	0.0029 (4)	0.0029 (4)	0.0029 (4)
Al1	0.0139 (5)	0.0139 (5)	0.0139 (5)	0.0029 (4)	0.0029 (4)	0.0029 (4)
Zn2	0.0124 (7)	0.0140 (6)	0.0140 (6)	0.000	0.000	0.0034 (5)
Pd2	0.0124 (7)	0.0140 (6)	0.0140 (6)	0.000	0.000	0.0034 (5)
Zn3	0.0177 (4)	0.0177 (4)	0.0132 (5)	−0.0026 (3)	−0.0028 (2)	−0.0028 (2)
Al3	0.0177 (4)	0.0177 (4)	0.0132 (5)	−0.0026 (3)	−0.0028 (2)	−0.0028 (2)

Geometric parameters (Å, º)

Pd1—Al3^i	2.6240 (11)	Zn1—Zn3	2.6826 (17)
Pd1—Zn3^i	2.6240 (11)	Zn2—Pd2^vi	2.591 (3)
Pd1—Al3^ii	2.6240 (11)	Zn2—Zn2^vi	2.591 (3)
Pd1—Al3^iii	2.6240 (11)	Zn2—Al3^vii	2.6115 (12)
Pd1—Zn3^ii	2.6240 (11)	Zn2—Zn3^vii	2.6115 (12)
Pd1—Zn3^iii	2.6240 (11)	Zn2—Al3^viii	2.6115 (12)
Pd1—Al3^iv	2.6259 (12)	Zn2—Zn3^viii	2.6115 (12)
Pd1—Zn3^iv	2.6259 (12)	Zn2—Zn1^ix	2.6662 (12)
Pd1—Al3^v	2.6259 (12)	Zn2—Al1^ix	2.6662 (12)
Pd1—Zn3^v	2.6259 (12)	Zn2—Pd1^x	2.7936 (9)
Pd1—Zn3	2.6259 (12)	Zn2—Pd1^xi	2.7936 (9)
Zn1—Zn2	2.6662 (12)	Zn3—Pd2^i	2.6115 (12)
Zn1—Pd2^v	2.6662 (12)	Zn3—Zn2^i	2.6115 (12)
Zn1—Pd2^iv	2.6662 (12)	Zn3—Pd1^x	2.6240 (11)
Zn1—Zn2^v	2.6662 (12)	Zn3—Al3^xii	2.7245 (6)
Zn1—Zn2^iv	2.6662 (12)	Zn3—Al3^vii	2.7245 (6)
Zn1—Al3^v	2.6826 (17)	Zn3—Zn3^xii	2.7245 (6)
Zn1—Al3^iv	2.6826 (17)	Zn3—Zn3^vii	2.7245 (6)
Zn1—Zn3^v	2.6826 (17)	Zn3—Al3^i	2.7245 (6)
Zn1—Zn3^iv	2.6826 (17)	Zn3—Al3^ii	2.7245 (6)
Al3^i—Pd1—Zn3^i	0.00 (6)	Al3^vii—Zn2—Zn3^vii	0.00 (5)
Al3^i—Pd1—Al3^ii	118.459 (14)	Pd2^vi—Zn2—Al3^viii	68.97 (4)
Zn3^i—Pd1—Al3^ii	118.459 (14)	Zn2^vi—Zn2—Al3^viii	68.97 (4)
Al3^i—Pd1—Al3^iii	118.459 (14)	Al3^vii—Zn2—Al3^viii	137.93 (7)
Zn3^i—Pd1—Al3^iii	118.459 (14)	Zn3^vii—Zn2—Al3^viii	137.93 (7)
Al3^ii—Pd1—Al3^iii	118.459 (14)	Pd2^vi—Zn2—Zn3^viii	68.97 (4)
Al3^i—Pd1—Zn3^ii	118.459 (14)	Zn2^vi—Zn2—Zn3^viii	68.97 (4)
Zn3^i—Pd1—Zn3^ii	118.459 (14)	Al3^vii—Zn2—Zn3^viii	137.93 (7)
Al3^ii—Pd1—Zn3^ii	0.00 (6)	Zn3^vii—Zn2—Zn3^viii	137.93 (7)
Al3^iii—Pd1—Zn3^ii	118.459 (14)	Al3^viii—Zn2—Zn3^viii	0.00 (3)
Al3^i—Pd1—Zn3^iii	118.459 (14)	Pd2^vi—Zn2—Zn1	148.46 (4)
Zn3^i—Pd1—Zn3^iii	118.459 (14)	Zn2^vi—Zn2—Zn1	148.46 (4)
Al3^ii—Pd1—Zn3^iii	118.459 (14)	Al3^vii—Zn2—Zn1	107.81 (3)
Al3^iii—Pd1—Zn3^iii	0.00 (6)	Zn3^vii—Zn2—Zn1	107.81 (3)
Zn3^ii—Pd1—Zn3^iii	118.459 (14)	Al3^viii—Zn2—Zn1	107.81 (3)
Al3^i—Pd1—Al3^iv	62.53 (3)	Zn3^viii—Zn2—Zn1	107.81 (3)
Zn3^i—Pd1—Al3^iv	62.53 (3)	Pd2^vi—Zn2—Zn1^ix	148.46 (4)
Al3^ii—Pd1—Al3^iv	133.05 (4)	Zn2^vi—Zn2—Zn1^ix	148.46 (4)
Al3^iii—Pd1—Al3^iv	62.53 (3)	Al3^vii—Zn2—Zn1^ix	107.81 (3)
Zn3^ii—Pd1—Al3^iv	133.05 (4)	Zn3^vii—Zn2—Zn1^ix	107.81 (3)
Zn3^iii—Pd1—Al3^iv	62.53 (3)	Al3^viii—Zn2—Zn1^ix	107.81 (3)
Al3^i—Pd1—Zn3^iv	62.53 (3)	Zn3^viii—Zn2—Zn1^ix	107.81 (3)
Zn3^i—Pd1—Zn3^iv	62.53 (3)	Zn1—Zn2—Zn1^ix	63.08 (9)
Al3^ii—Pd1—Zn3^iv	133.05 (4)	Pd2^vi—Zn2—Al1^ix	148.46 (4)
Al3^iii—Pd1—Zn3^iv	62.53 (3)	Zn2^vi—Zn2—Al1^ix	148.46 (4)
Zn3^ii—Pd1—Zn3^iv	133.05 (4)	Al3^vii—Zn2—Al1^ix	107.81 (3)
Zn3^iii—Pd1—Zn3^iv	62.53 (3)	Zn3^vii—Zn2—Al1^ix	107.81 (3)
Al3^iv—Pd1—Zn3^iv	0.00 (7)	Al3^viii—Zn2—Al1^ix	107.81 (3)
Al3^i—Pd1—Al3^v	133.05 (4)	Zn3^viii—Zn2—Al1^ix	107.81 (3)
Zn3^i—Pd1—Al3^v	133.05 (4)	Zn1—Zn2—Al1^ix	63.08 (9)
Al3^ii—Pd1—Al3^v	62.53 (3)	Zn1^ix—Zn2—Al1^ix	0.00 (6)
Al3^iii—Pd1—Al3^v	62.53 (3)	Pd2^vi—Zn2—Pd1^x	126.98 (3)
Zn3^ii—Pd1—Al3^v	62.53 (3)	Zn2^vi—Zn2—Pd1^x	126.98 (3)
Zn3^iii—Pd1—Al3^v	62.53 (3)	Al3^vii—Zn2—Pd1^x	58.01 (3)
Al3^iv—Pd1—Al3^v	83.48 (4)	Zn3^vii—Zn2—Pd1^x	58.01 (3)
Zn3^iv—Pd1—Al3^v	83.48 (4)	Al3^viii—Zn2—Pd1^x	164.05 (6)
Al3^i—Pd1—Zn3^v	133.05 (4)	Zn3^viii—Zn2—Pd1^x	164.05 (6)
Zn3^i—Pd1—Zn3^v	133.05 (4)	Zn1—Zn2—Pd1^x	59.16 (3)
Al3^ii—Pd1—Zn3^v	62.53 (3)	Zn1^ix—Zn2—Pd1^x	59.16 (3)
Al3^iii—Pd1—Zn3^v	62.53 (3)	Al1^ix—Zn2—Pd1^x	59.16 (3)
Zn3^ii—Pd1—Zn3^v	62.53 (3)	Pd2^vi—Zn2—Pd1^xi	126.98 (3)
Zn3^iii—Pd1—Zn3^v	62.53 (3)	Zn2^vi—Zn2—Pd1^xi	126.98 (3)
Al3^iv—Pd1—Zn3^v	83.48 (4)	Al3^vii—Zn2—Pd1^xi	164.05 (6)
Zn3^iv—Pd1—Zn3^v	83.48 (4)	Zn3^vii—Zn2—Pd1^xi	164.05 (6)
Al3^v—Pd1—Zn3^v	0.00 (7)	Al3^viii—Zn2—Pd1^xi	58.01 (3)
Al3^i—Pd1—Zn3	62.53 (3)	Zn3^viii—Zn2—Pd1^xi	58.01 (3)
Zn3^i—Pd1—Zn3	62.53 (3)	Zn1—Zn2—Pd1^xi	59.16 (3)
Al3^ii—Pd1—Zn3	62.53 (3)	Zn1^ix—Zn2—Pd1^xi	59.16 (3)
Al3^iii—Pd1—Zn3	133.05 (4)	Al1^ix—Zn2—Pd1^xi	59.16 (3)
Zn3^ii—Pd1—Zn3	62.53 (3)	Pd1^x—Zn2—Pd1^xi	106.04 (6)
Zn3^iii—Pd1—Zn3	133.05 (4)	Pd2^i—Zn3—Zn2^i	0.00 (5)
Al3^iv—Pd1—Zn3	83.48 (4)	Pd2^i—Zn3—Pd1^x	153.49 (6)
Zn3^iv—Pd1—Zn3	83.48 (4)	Zn2^i—Zn3—Pd1^x	153.49 (6)
Al3^v—Pd1—Zn3	83.48 (4)	Pd2^i—Zn3—Pd1	64.47 (4)
Zn3^v—Pd1—Zn3	83.48 (4)	Zn2^i—Zn3—Pd1	64.47 (4)
Zn2—Zn1—Pd2^v	119.582 (10)	Pd1^x—Zn3—Pd1	142.04 (5)
Zn2—Zn1—Pd2^iv	119.582 (10)	Pd2^i—Zn3—Zn1	145.42 (6)
Pd2^v—Zn1—Pd2^iv	119.582 (10)	Zn2^i—Zn3—Zn1	145.42 (6)
Zn2—Zn1—Zn2^v	119.582 (10)	Pd1^x—Zn3—Zn1	61.09 (5)
Pd2^v—Zn1—Zn2^v	0.0	Pd1—Zn3—Zn1	80.96 (5)
Pd2^iv—Zn1—Zn2^v	119.582 (10)	Pd2^i—Zn3—Al3^xii	102.22 (4)
Zn2—Zn1—Zn2^iv	119.582 (10)	Zn2^i—Zn3—Al3^xii	102.22 (4)
Pd2^v—Zn1—Zn2^iv	119.582 (10)	Pd1^x—Zn3—Al3^xii	58.77 (4)
Pd2^iv—Zn1—Zn2^iv	0.0	Pd1—Zn3—Al3^xii	139.15 (3)
Zn2^v—Zn1—Zn2^iv	119.582 (10)	Zn1—Zn3—Al3^xii	104.13 (5)
Zn2—Zn1—Al3^v	65.28 (2)	Pd2^i—Zn3—Al3^vii	102.22 (4)
Pd2^v—Zn1—Al3^v	65.28 (2)	Zn2^i—Zn3—Al3^vii	102.22 (4)
Pd2^iv—Zn1—Al3^v	135.08 (8)	Pd1^x—Zn3—Al3^vii	58.77 (4)
Zn2^v—Zn1—Al3^v	65.28 (2)	Pd1—Zn3—Al3^vii	139.15 (3)
Zn2^iv—Zn1—Al3^v	135.08 (8)	Zn1—Zn3—Al3^vii	104.13 (5)
Zn2—Zn1—Al3^iv	135.08 (8)	Al3^xii—Zn3—Al3^vii	79.83 (8)
Pd2^v—Zn1—Al3^iv	65.28 (2)	Pd2^i—Zn3—Zn3^xii	102.22 (4)
Pd2^iv—Zn1—Al3^iv	65.28 (2)	Zn2^i—Zn3—Zn3^xii	102.22 (4)
Zn2^v—Zn1—Al3^iv	65.28 (2)	Pd1^x—Zn3—Zn3^xii	58.77 (4)
Zn2^iv—Zn1—Al3^iv	65.28 (2)	Pd1—Zn3—Zn3^xii	139.15 (3)
Al3^v—Zn1—Al3^iv	81.33 (6)	Zn1—Zn3—Zn3^xii	104.13 (5)
Zn2—Zn1—Zn3^v	65.28 (2)	Al3^xii—Zn3—Zn3^xii	0.00 (6)
Pd2^v—Zn1—Zn3^v	65.28 (2)	Al3^vii—Zn3—Zn3^xii	79.83 (8)
Pd2^iv—Zn1—Zn3^v	135.08 (8)	Pd2^i—Zn3—Zn3^vii	102.22 (4)
Zn2^v—Zn1—Zn3^v	65.28 (2)	Zn2^i—Zn3—Zn3^vii	102.22 (4)
Zn2^iv—Zn1—Zn3^v	135.08 (8)	Pd1^x—Zn3—Zn3^vii	58.77 (4)
Al3^v—Zn1—Zn3^v	0.00 (6)	Pd1—Zn3—Zn3^vii	139.15 (3)
Al3^iv—Zn1—Zn3^v	81.33 (6)	Zn1—Zn3—Zn3^vii	104.13 (5)
Zn2—Zn1—Zn3^iv	135.08 (8)	Al3^xii—Zn3—Zn3^vii	79.83 (8)
Pd2^v—Zn1—Zn3^iv	65.28 (2)	Al3^vii—Zn3—Zn3^vii	0.00 (4)
Pd2^iv—Zn1—Zn3^iv	65.28 (2)	Zn3^xii—Zn3—Zn3^vii	79.83 (8)
Zn2^v—Zn1—Zn3^iv	65.28 (2)	Pd2^i—Zn3—Al3^i	65.41 (4)
Zn2^iv—Zn1—Zn3^iv	65.28 (2)	Zn2^i—Zn3—Al3^i	65.41 (4)
Al3^v—Zn1—Zn3^iv	81.33 (6)	Pd1^x—Zn3—Al3^i	122.72 (4)
Al3^iv—Zn1—Zn3^iv	0.00 (6)	Pd1—Zn3—Al3^i	58.70 (3)
Zn3^v—Zn1—Zn3^iv	81.33 (6)	Zn1—Zn3—Al3^i	97.39 (5)
Zn2—Zn1—Zn3	65.28 (2)	Al3^xii—Zn3—Al3^i	80.50 (3)
Pd2^v—Zn1—Zn3	135.08 (8)	Al3^vii—Zn3—Al3^i	153.76 (7)
Pd2^iv—Zn1—Zn3	65.28 (2)	Zn3^xii—Zn3—Al3^i	80.50 (3)
Zn2^v—Zn1—Zn3	135.08 (8)	Zn3^vii—Zn3—Al3^i	153.76 (7)
Zn2^iv—Zn1—Zn3	65.28 (2)	Pd2^i—Zn3—Al3^ii	65.41 (4)
Al3^v—Zn1—Zn3	81.33 (6)	Zn2^i—Zn3—Al3^ii	65.41 (4)
Al3^iv—Zn1—Zn3	81.33 (6)	Pd1^x—Zn3—Al3^ii	122.72 (4)
Zn3^v—Zn1—Zn3	81.33 (6)	Pd1—Zn3—Al3^ii	58.70 (3)
Zn3^iv—Zn1—Zn3	81.33 (6)	Zn1—Zn3—Al3^ii	97.39 (5)
Pd2^vi—Zn2—Zn2^vi	0.0	Al3^xii—Zn3—Al3^ii	153.76 (7)
Pd2^vi—Zn2—Al3^vii	68.97 (4)	Al3^vii—Zn3—Al3^ii	80.50 (3)
Zn2^vi—Zn2—Al3^vii	68.97 (4)	Zn3^xii—Zn3—Al3^ii	153.76 (7)
Pd2^vi—Zn2—Zn3^vii	68.97 (4)	Zn3^vii—Zn3—Al3^ii	80.50 (3)
Zn2^vi—Zn2—Zn3^vii	68.97 (4)	Al3^i—Zn3—Al3^ii	111.69 (7)

Symmetry codes: (i) −y+1/2, z+1/2, −x+1/2; (ii) z+1/2, −x+1/2, −y+1/2; (iii) −x+1/2, −y+1/2, z+1/2; (iv) z, x, y; (v) y, z, x; (vi) −x+1, −y, z; (vii) −z+1/2, −x+1/2, y−1/2; (viii) −z+1/2, x−1/2, −y+1/2; (ix) x, −y, −z; (x) −x+1/2, −y+1/2, z−1/2; (xi) −x+1/2, y−1/2, −z+1/2; (xii) −y+1/2, −z+1/2, x−1/2.