A new ternary compound with the BGa8Ir4 structure type in the Al–Au–Ir system

Kadok, J.; de Weerd, M.-C.; Boulet, P.; Fournée, V.; Ledieu, J.

doi:10.1107/S2052520618016712

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A new ternary compound with the BGa₈Ir₄ structure type in the Al–Au–Ir system

J. Kadok, M.-C. de Weerd, P. Boulet, V. Fournée and J. Ledieu

Following the recent determination of the Al₃AuIr structure, a new ternary phase has been identified in the Al–Au–Ir phase diagram. It has a chemical composition Al₉(Au;Ir)₄ with an apparently low gold content. Its crystal structure has been determined with single-crystal X-ray diffraction. The new compound crystallizes in the tetragonal crystal system and has been successfully solved in space group I4₁/acd (Pearson symbol tI104) with lattice parameters a = 8.6339 (2) and c = 21.8874 (7) Å. Atomic environments are described as well as similarities with the BGa₈Ir₄ compound.

Keywords: intermetallic; X-ray diffraction; crystal structure; entropy.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520618016712/dq5033sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S2052520618016712/dq5033Isup2.hkl Contains datablock I

CCDC reference: 1881225

Computing details top

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT; program(s) used to solve structure: SHELXL2014 (Sheldrick, 2014); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2014).

(I) top

Crystal data top

Al₇₂Au_2.50Ir_29.50	D_x = 8.249 Mg m⁻³
M_r = 8104.88	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I4₁/acd	Cell parameters from 9909 reflections
a = 8.6339 (2) Å	θ = 3.7–44.3°
c = 21.8874 (7) Å	µ = 66.45 mm⁻¹
V = 1631.58 (9) Å³	T = 296 K
Z = 1	Platelet, black
F(000) = 3405	0.05 × 0.05 × 0.01 mm

Data collection top

Bruker APEX-II QUAZAR CCD diffractometer	1177 reflections with I > 2σ(I)
Radiation source: micro sources	R_int = 0.064
ω scan	θ_max = 44.3°, θ_min = 3.8°
Absorption correction: multi-scan SADABS 2014/5	h = −16→16
T_min = 0.274, T_max = 0.749	k = −16→16
44132 measured reflections	l = −42→42
1629 independent reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0139P)² + 16.567P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.017	(Δ/σ)_max = 0.002
wR(F²) = 0.043	Δρ_max = 4.05 e Å⁻³
S = 1.13	Δρ_min = −1.85 e Å⁻³
1629 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
35 parameters	Extinction coefficient: 0.000130 (10)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ir1	0.0000	0.2500	0.01467 (2)	0.00316 (4)	0.923 (4)
Au1	0.0000	0.2500	0.01467 (2)	0.00316 (4)	0.0782 (4)
Ir2	0.19858 (2)	0.44858 (2)	0.1250	0.00368 (3)	0.922 (4)
Au2	0.19858 (2)	0.44858 (2)	0.1250	0.00368 (3)	0.0781 (3)
Al1	0.04687 (12)	0.03071 (12)	0.31109 (4)	0.0063 (2)
Al2	0.27779 (12)	0.19958 (12)	0.19068 (5)	0.0068 (2)
Al3	0.0000	0.2500	0.1250	0.0060 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ir1	0.00365 (14)	0.00361 (13)	0.00224 (5)	0.00039 (3)	0.000	0.000
Au1	0.00365 (14)	0.00361 (13)	0.00224 (5)	0.00039 (3)	0.000	0.000
Ir2	0.00358 (4)	0.00358 (4)	0.00390 (5)	0.00009 (3)	0.00000 (3)	0.00000 (3)
Au2	0.00358 (4)	0.00358 (4)	0.00390 (5)	0.00009 (3)	0.00000 (3)	0.00000 (3)
Al1	0.0084 (4)	0.0049 (4)	0.0057 (4)	0.0003 (3)	0.0004 (3)	0.0012 (3)
Al2	0.0049 (4)	0.0091 (4)	0.0064 (4)	0.0003 (3)	−0.0010 (3)	−0.0015 (3)
Al3	0.0080 (4)	0.0080 (4)	0.0020 (6)	−0.0043 (5)	0.000	0.000

Geometric parameters (Å, º) top

Ir1—Al3	2.4148 (1)	Al1—Ir1^xi	2.6589 (10)
Ir1—Al2ⁱ	2.5481 (10)	Al1—Au1^xi	2.6589 (10)
Ir1—Al2ⁱⁱ	2.5481 (10)	Al1—Al1^xii	2.726 (2)
Ir1—Al1ⁱⁱⁱ	2.5491 (10)	Al1—Al2^xiii	2.7431 (15)
Ir1—Al1^iv	2.5491 (10)	Al1—Al2^ix	2.7778 (15)
Ir1—Al2ⁱⁱⁱ	2.6262 (10)	Al1—Al2^xii	2.8160 (14)
Ir1—Al2^iv	2.6262 (10)	Al2—Au1^xiv	2.5481 (10)
Ir1—Al1^v	2.6589 (10)	Al2—Ir1^xiv	2.5481 (10)
Ir1—Al1^vi	2.6589 (10)	Al2—Au2^xv	2.6086 (10)
Ir2—Al3	2.4247 (1)	Al2—Ir2^xv	2.6086 (10)
Ir2—Al2^vii	2.6086 (10)	Al2—Ir1ⁱⁱⁱ	2.6262 (10)
Ir2—Al2^viii	2.6086 (10)	Al2—Au1ⁱⁱⁱ	2.6262 (10)
Ir2—Al1^ix	2.6113 (11)	Al2—Al1^xvi	2.7431 (15)
Ir2—Al1ⁱⁱ	2.6113 (11)	Al2—Al1^ix	2.7778 (15)
Ir2—Al1^v	2.6364 (10)	Al2—Al2^ix	2.780 (2)
Ir2—Al1^x	2.6364 (10)	Al2—Al1^xii	2.8160 (14)
Ir2—Al2ⁱⁱⁱ	2.6751 (11)	Al3—Au1ⁱⁱⁱ	2.4148 (1)
Ir2—Al2	2.6751 (11)	Al3—Ir1ⁱⁱⁱ	2.4148 (1)
Al1—Au1ⁱⁱⁱ	2.5492 (10)	Al3—Au2^xvii	2.4247 (1)
Al1—Ir1ⁱⁱⁱ	2.5492 (10)	Al3—Ir2^xvii	2.4247 (1)
Al1—Au2^ix	2.6113 (11)	Al3—Al1^x	2.8274 (10)
Al1—Ir2^ix	2.6113 (11)	Al3—Al1^vi	2.8274 (10)
Al1—Au2^xi	2.6363 (10)	Al3—Al1^v	2.8274 (10)
Al1—Ir2^xi	2.6363 (10)	Al3—Al1^xii	2.8274 (10)

Al3—Ir1—Al2ⁱ	129.46 (2)	Au2^ix—Al1—Al2^ix	59.43 (3)
Al3—Ir1—Al2ⁱⁱ	129.46 (2)	Ir2^ix—Al1—Al2^ix	59.43 (3)
Al2ⁱ—Ir1—Al2ⁱⁱ	101.08 (5)	Au2^xi—Al1—Al2^ix	132.14 (5)
Al3—Ir1—Al1ⁱⁱⁱ	130.58 (2)	Ir2^xi—Al1—Al2^ix	132.14 (5)
Al2ⁱ—Ir1—Al1ⁱⁱⁱ	65.12 (4)	Ir1^xi—Al1—Al2^ix	147.32 (4)
Al2ⁱⁱ—Ir1—Al1ⁱⁱⁱ	66.04 (4)	Au1^xi—Al1—Al2^ix	147.32 (4)
Al3—Ir1—Al1^iv	130.58 (2)	Al1^xii—Al1—Al2^ix	98.59 (5)
Al2ⁱ—Ir1—Al1^iv	66.04 (4)	Al2^xiii—Al1—Al2^ix	90.90 (4)
Al2ⁱⁱ—Ir1—Al1^iv	65.12 (4)	Au1ⁱⁱⁱ—Al1—Al2^xii	128.89 (5)
Al1ⁱⁱⁱ—Ir1—Al1^iv	98.84 (5)	Ir1ⁱⁱⁱ—Al1—Al2^xii	128.89 (5)
Al3—Ir1—Al2ⁱⁱⁱ	68.16 (2)	Au2^ix—Al1—Al2^xii	57.31 (3)
Al2ⁱ—Ir1—Al2ⁱⁱⁱ	153.61 (4)	Ir2^ix—Al1—Al2^xii	57.31 (3)
Al2ⁱⁱ—Ir1—Al2ⁱⁱⁱ	64.99 (4)	Au2^xi—Al1—Al2^xii	112.74 (4)
Al1ⁱⁱⁱ—Ir1—Al2ⁱⁱⁱ	88.51 (3)	Ir2^xi—Al1—Al2^xii	112.74 (4)
Al1^iv—Ir1—Al2ⁱⁱⁱ	120.67 (3)	Ir1^xi—Al1—Al2^xii	57.24 (3)
Al3—Ir1—Al2^iv	68.16 (2)	Au1^xi—Al1—Al2^xii	57.24 (3)
Al2ⁱ—Ir1—Al2^iv	64.99 (4)	Al1^xii—Al1—Al2^xii	81.32 (4)
Al2ⁱⁱ—Ir1—Al2^iv	153.61 (4)	Al2^xiii—Al1—Al2^xii	167.09 (5)
Al1ⁱⁱⁱ—Ir1—Al2^iv	120.67 (3)	Al2^ix—Al1—Al2^xii	101.88 (3)
Al1^iv—Ir1—Al2^iv	88.51 (3)	Au1^xiv—Al2—Ir1^xiv	0.000 (4)
Al2ⁱⁱⁱ—Ir1—Al2^iv	136.31 (4)	Au1^xiv—Al2—Au2^xv	115.68 (4)
Al3—Ir1—Al1^v	67.54 (2)	Ir1^xiv—Al2—Au2^xv	115.68 (4)
Al2ⁱ—Ir1—Al1^v	106.50 (4)	Au1^xiv—Al2—Ir2^xv	115.68 (4)
Al2ⁱⁱ—Ir1—Al1^v	101.64 (3)	Ir1^xiv—Al2—Ir2^xv	115.68 (4)
Al1ⁱⁱⁱ—Ir1—Al1^v	161.75 (2)	Au2^xv—Al2—Ir2^xv	0.000 (2)
Al1^iv—Ir1—Al1^v	63.09 (4)	Au1^xiv—Al2—Ir1ⁱⁱⁱ	115.01 (4)
Al2ⁱⁱⁱ—Ir1—Al1^v	98.51 (3)	Ir1^xiv—Al2—Ir1ⁱⁱⁱ	115.01 (4)
Al2^iv—Ir1—Al1^v	64.39 (3)	Au2^xv—Al2—Ir1ⁱⁱⁱ	114.47 (4)
Al3—Ir1—Al1^vi	67.54 (2)	Ir2^xv—Al2—Ir1ⁱⁱⁱ	114.47 (4)
Al2ⁱ—Ir1—Al1^vi	101.64 (3)	Au1^xiv—Al2—Au1ⁱⁱⁱ	115.01 (4)
Al2ⁱⁱ—Ir1—Al1^vi	106.50 (4)	Ir1^xiv—Al2—Au1ⁱⁱⁱ	115.01 (4)
Al1ⁱⁱⁱ—Ir1—Al1^vi	63.09 (4)	Au2^xv—Al2—Au1ⁱⁱⁱ	114.47 (4)
Al1^iv—Ir1—Al1^vi	161.75 (2)	Ir2^xv—Al2—Au1ⁱⁱⁱ	114.47 (4)
Al2ⁱⁱⁱ—Ir1—Al1^vi	64.39 (3)	Ir1ⁱⁱⁱ—Al2—Au1ⁱⁱⁱ	0.000 (5)
Al2^iv—Ir1—Al1^vi	98.51 (3)	Au1^xiv—Al2—Ir2	113.37 (4)
Al1^v—Ir1—Al1^vi	135.07 (4)	Ir1^xiv—Al2—Ir2	113.37 (4)
Al3—Ir2—Al2^vii	130.00 (2)	Au2^xv—Al2—Ir2	113.04 (4)
Al3—Ir2—Al2^viii	130.00 (2)	Ir2^xv—Al2—Ir2	113.04 (4)
Al2^vii—Ir2—Al2^viii	100.01 (5)	Ir1ⁱⁱⁱ—Al2—Ir2	80.40 (3)
Al3—Ir2—Al1^ix	130.06 (2)	Au1ⁱⁱⁱ—Al2—Ir2	80.40 (3)
Al2^vii—Ir2—Al1^ix	65.29 (3)	Au1^xiv—Al2—Al1^xvi	57.46 (3)
Al2^viii—Ir2—Al1^ix	65.84 (3)	Ir1^xiv—Al2—Al1^xvi	57.46 (3)
Al3—Ir2—Al1ⁱⁱ	130.06 (2)	Au2^xv—Al2—Al1^xvi	58.96 (3)
Al2^vii—Ir2—Al1ⁱⁱ	65.84 (3)	Ir2^xv—Al2—Al1^xvi	58.96 (3)
Al2^viii—Ir2—Al1ⁱⁱ	65.29 (3)	Ir1ⁱⁱⁱ—Al2—Al1^xvi	150.09 (5)
Al1^ix—Ir2—Al1ⁱⁱ	99.88 (4)	Au1ⁱⁱⁱ—Al2—Al1^xvi	150.09 (5)
Al3—Ir2—Al1^v	67.78 (2)	Ir2—Al2—Al1^xvi	129.50 (5)
Al2^vii—Ir2—Al1^v	159.91 (3)	Au1^xiv—Al2—Al1^ix	57.00 (3)
Al2^viii—Ir2—Al1^v	63.06 (3)	Ir1^xiv—Al2—Al1^ix	57.00 (3)
Al1^ix—Ir2—Al1^v	96.48 (4)	Au2^xv—Al2—Al1^ix	130.25 (4)
Al1ⁱⁱ—Ir2—Al1^v	111.95 (3)	Ir2^xv—Al2—Al1^ix	130.25 (4)
Al3—Ir2—Al1^x	67.78 (2)	Ir1ⁱⁱⁱ—Al2—Al1^ix	111.34 (4)
Al2^vii—Ir2—Al1^x	63.06 (3)	Au1ⁱⁱⁱ—Al2—Al1^ix	111.34 (4)
Al2^viii—Ir2—Al1^x	159.91 (3)	Ir2—Al2—Al1^ix	57.19 (3)
Al1^ix—Ir2—Al1^x	111.95 (3)	Al1^xvi—Al2—Al1^ix	89.07 (4)
Al1ⁱⁱ—Ir2—Al1^x	96.48 (4)	Au1^xiv—Al2—Al2^ix	58.86 (4)
Al1^v—Ir2—Al1^x	135.56 (4)	Ir1^xiv—Al2—Al2^ix	58.86 (4)
Al3—Ir2—Al2ⁱⁱⁱ	67.20 (2)	Au2^xv—Al2—Al2^ix	142.03 (6)
Al2^vii—Ir2—Al2ⁱⁱⁱ	98.43 (4)	Ir2^xv—Al2—Al2^ix	142.03 (6)
Al2^viii—Ir2—Al2ⁱⁱⁱ	110.58 (3)	Ir1ⁱⁱⁱ—Al2—Al2^ix	56.15 (4)
Al1^ix—Ir2—Al2ⁱⁱⁱ	161.22 (3)	Au1ⁱⁱⁱ—Al2—Al2^ix	56.15 (4)
Al1ⁱⁱ—Ir2—Al2ⁱⁱⁱ	63.38 (3)	Ir2—Al2—Al2^ix	101.89 (5)
Al1^v—Ir2—Al2ⁱⁱⁱ	97.85 (3)	Al1^xvi—Al2—Al2^ix	109.01 (6)
Al1^x—Ir2—Al2ⁱⁱⁱ	64.56 (3)	Al1^ix—Al2—Al2^ix	81.06 (5)
Al3—Ir2—Al2	67.20 (2)	Au1^xiv—Al2—Al1^xii	131.49 (5)
Al2^vii—Ir2—Al2	110.58 (3)	Ir1^xiv—Al2—Al1^xii	131.49 (5)
Al2^viii—Ir2—Al2	98.43 (4)	Au2^xv—Al2—Al1^xii	57.40 (3)
Al1^ix—Ir2—Al2	63.38 (3)	Ir2^xv—Al2—Al1^xii	57.40 (3)
Al1ⁱⁱ—Ir2—Al2	161.22 (3)	Ir1ⁱⁱⁱ—Al2—Al1^xii	58.37 (3)
Al1^v—Ir2—Al2	64.56 (3)	Au1ⁱⁱⁱ—Al2—Al1^xii	58.37 (3)
Al1^x—Ir2—Al2	97.85 (3)	Ir2—Al2—Al1^xii	112.27 (4)
Al2ⁱⁱⁱ—Ir2—Al2	134.40 (4)	Al1^xvi—Al2—Al1^xii	102.95 (4)
Au1ⁱⁱⁱ—Al1—Ir1ⁱⁱⁱ	0.000 (4)	Al1^ix—Al2—Al1^xii	167.85 (5)
Au1ⁱⁱⁱ—Al1—Au2^ix	115.54 (4)	Al2^ix—Al2—Al1^xii	96.42 (5)
Ir1ⁱⁱⁱ—Al1—Au2^ix	115.54 (4)	Ir1—Al3—Au1ⁱⁱⁱ	180.0
Au1ⁱⁱⁱ—Al1—Ir2^ix	115.54 (4)	Ir1—Al3—Ir1ⁱⁱⁱ	180.0
Ir1ⁱⁱⁱ—Al1—Ir2^ix	115.54 (4)	Au1ⁱⁱⁱ—Al3—Ir1ⁱⁱⁱ	0.0
Au2^ix—Al1—Ir2^ix	0.000 (6)	Ir1—Al3—Ir2	90.0
Au1ⁱⁱⁱ—Al1—Au2^xi	114.67 (4)	Au1ⁱⁱⁱ—Al3—Ir2	90.0
Ir1ⁱⁱⁱ—Al1—Au2^xi	114.67 (4)	Ir1ⁱⁱⁱ—Al3—Ir2	90.0
Au2^ix—Al1—Au2^xi	114.25 (4)	Ir1—Al3—Au2^xvii	90.0
Ir2^ix—Al1—Au2^xi	114.25 (4)	Au1ⁱⁱⁱ—Al3—Au2^xvii	90.0
Au1ⁱⁱⁱ—Al1—Ir2^xi	114.67 (4)	Ir1ⁱⁱⁱ—Al3—Au2^xvii	90.0
Ir1ⁱⁱⁱ—Al1—Ir2^xi	114.67 (4)	Ir2—Al3—Au2^xvii	180.0
Au2^ix—Al1—Ir2^xi	114.25 (4)	Ir1—Al3—Ir2^xvii	90.0
Ir2^ix—Al1—Ir2^xi	114.25 (4)	Au1ⁱⁱⁱ—Al3—Ir2^xvii	90.0
Au2^xi—Al1—Ir2^xi	0.000 (1)	Ir1ⁱⁱⁱ—Al3—Ir2^xvii	90.0
Au1ⁱⁱⁱ—Al1—Ir1^xi	113.85 (4)	Ir2—Al3—Ir2^xvii	180.0
Ir1ⁱⁱⁱ—Al1—Ir1^xi	113.85 (4)	Au2^xvii—Al3—Ir2^xvii	0.000 (6)
Au2^ix—Al1—Ir1^xi	113.28 (4)	Ir1—Al3—Al1^x	119.65 (2)
Ir2^ix—Al1—Ir1^xi	113.28 (4)	Au1ⁱⁱⁱ—Al3—Al1^x	60.35 (2)
Au2^xi—Al1—Ir1^xi	80.52 (3)	Ir1ⁱⁱⁱ—Al3—Al1^x	60.35 (2)
Ir2^xi—Al1—Ir1^xi	80.52 (3)	Ir2—Al3—Al1^x	59.67 (2)
Au1ⁱⁱⁱ—Al1—Au1^xi	113.85 (4)	Au2^xvii—Al3—Al1^x	120.33 (2)
Ir1ⁱⁱⁱ—Al1—Au1^xi	113.85 (4)	Ir2^xvii—Al3—Al1^x	120.33 (2)
Au2^ix—Al1—Au1^xi	113.28 (4)	Ir1—Al3—Al1^vi	60.35 (2)
Ir2^ix—Al1—Au1^xi	113.28 (4)	Au1ⁱⁱⁱ—Al3—Al1^vi	119.65 (2)
Au2^xi—Al1—Au1^xi	80.52 (3)	Ir1ⁱⁱⁱ—Al3—Al1^vi	119.65 (2)
Ir2^xi—Al1—Au1^xi	80.52 (3)	Ir2—Al3—Al1^vi	120.33 (2)
Ir1^xi—Al1—Au1^xi	0.000 (5)	Au2^xvii—Al3—Al1^vi	59.67 (2)
Au1ⁱⁱⁱ—Al1—Al1^xii	60.42 (4)	Ir2^xvii—Al3—Al1^vi	59.67 (2)
Ir1ⁱⁱⁱ—Al1—Al1^xii	60.42 (4)	Al1^x—Al3—Al1^vi	89.97 (4)
Au2^ix—Al1—Al1^xii	122.60 (2)	Ir1—Al3—Al1^v	60.35 (2)
Ir2^ix—Al1—Al1^xii	122.60 (2)	Au1ⁱⁱⁱ—Al3—Al1^v	119.65 (2)
Au2^xi—Al1—Al1^xii	117.91 (3)	Ir1ⁱⁱⁱ—Al3—Al1^v	119.65 (2)
Ir2^xi—Al1—Al1^xii	117.91 (3)	Ir2—Al3—Al1^v	59.67 (2)
Ir1^xi—Al1—Al1^xii	56.49 (4)	Au2^xvii—Al3—Al1^v	120.33 (2)
Au1^xi—Al1—Al1^xii	56.49 (4)	Ir2^xvii—Al3—Al1^v	120.33 (2)
Au1ⁱⁱⁱ—Al1—Al2^xiii	57.42 (3)	Al1^x—Al3—Al1^v	119.35 (4)
Ir1ⁱⁱⁱ—Al1—Al2^xiii	57.42 (3)	Al1^vi—Al3—Al1^v	120.69 (4)
Au2^ix—Al1—Al2^xiii	133.16 (5)	Ir1—Al3—Al1^xii	119.65 (2)
Ir2^ix—Al1—Al2^xiii	133.16 (5)	Au1ⁱⁱⁱ—Al3—Al1^xii	60.35 (2)
Au2^xi—Al1—Al2^xiii	57.97 (3)	Ir1ⁱⁱⁱ—Al3—Al1^xii	60.35 (2)
Ir2^xi—Al1—Al2^xiii	57.97 (3)	Ir2—Al3—Al1^xii	120.33 (2)
Ir1^xi—Al1—Al2^xiii	110.50 (4)	Au2^xvii—Al3—Al1^xii	59.67 (2)
Au1^xi—Al1—Al2^xiii	110.50 (4)	Ir2^xvii—Al3—Al1^xii	59.67 (2)
Al1^xii—Al1—Al2^xiii	95.13 (4)	Al1^x—Al3—Al1^xii	120.69 (4)
Au1ⁱⁱⁱ—Al1—Al2^ix	56.96 (3)	Al1^vi—Al3—Al1^xii	119.35 (4)
Ir1ⁱⁱⁱ—Al1—Al2^ix	56.96 (3)	Al1^v—Al3—Al1^xii	89.97 (4)

Symmetry codes: (i) y−1/4, x−1/4, z−1/4; (ii) −y+1/4, −x+3/4, z−1/4; (iii) y−1/4, x+1/4, −z+1/4; (iv) −y+1/4, −x+1/4, −z+1/4; (v) y+1/4, −x+1/4, z−1/4; (vi) −y−1/4, x+1/4, z−1/4; (vii) −x+1/2, y+1/2, z; (viii) y+1/4, −x+3/4, −z+1/4; (ix) −x+1/2, −y+1/2, −z+1/2; (x) −x, y+1/2, −z+1/2; (xi) −y+1/4, x−1/4, z+1/4; (xii) x, −y, −z+1/2; (xiii) x−1/2, y, −z+1/2; (xiv) −y+3/4, −x+1/4, z+1/4; (xv) −y+3/4, x−1/4, −z+1/4; (xvi) x+1/2, y, −z+1/2; (xvii) −x, −y+1/2, z.

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