Structure model for the τ(μ) phase in Al–Cr–Si alloys deduced from the λ phase by the strong-reflections approach

There are very obvious common features in the electron diffraction patterns of the λ and τ(μ) phases in the Al–Cr–Si system. The positions of the strong reflections and their intensity distributions are similar for the two structures. The relation of the reciprocal lattices of the λ and τ(μ) phases is studied. By applying the strong-reflections approach, the structure factors of τ(μ) are deduced from the corresponding structure factors of the known λ phase. Rules for selecting reflections for the strong-reflections approach are described. Similar to that of λ, the structure of τ(μ) contains six layers stacked along the c axis in each unit cell. There are 752 atoms in each unit cell, 53 of them are unique. The corresponding composition of the τ(μ) model is Al_{3.82 − x}CrSi_x. Simulated electron diffraction patterns from the structure model are in good agreement with the experimental ones. The arrangement of interpenetrated icosahedral clusters in the τ(μ) phase is discussed.

Computing details

Figures

(tau-mu)

Crystal data

Cr156Al596	Z = 24
Mr = 24192.35	Dx = 2.363 Mg m^−3
Hexagonal, P63/mmc	Electrons radiation, λ = 0.0370 Å
Hall symbol: -P_6c_2c	T = 293 K
a = 32.3000 Å	Needle, black
c = 12.4000 Å	0.001 × 0.0001 × 0.000005 mm
V = 11203.6 Å^3

Data collection

Philips CM12 TEM diffractometer	k = ?→?
Radiation source: LaB6	l = ?→?
h = ?→?

Refinement

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Cr1	0.4119	0.2060	0.0724	0.5*
Cr2	0.3052	0.4591	0.2500	0.5*
Cr3	0.1551	0.3102	0.2500	0.5*
Cr4	0.1551	0.0775	0.2500	0.5*
Cr5	0.4125	0.5875	0.0724	0.5*
Cr6	0.3052	0.2258	0.2500	0.5*
Cr7	0.5385	0.3102	0.2500	0.5*
Cr8	0.5391	0.4609	0.2500	0.5*
Cr9	0.1762	0.2047	0.0724	0.5*
Cr10	0.1551	0.2270	0.2500	0.5*
Cr11	0.3840	0.6160	0.2500	0.5*
Cr12	0.2345	0.2333	0.2500	0.5*
Cr13	0.3821	0.2320	0.2500	0.5*
Al14	0.6172	0.3828	0.2500	0.5*
Al15	0.1756	0.3511	0.0691	0.5*
Al16	0.4640	0.2320	0.2500	0.5*
Al17	0.2246	0.3015	0.1349	0.5*
Cr18	0.3846	0.3834	0.2500	0.5*
Al19	0.3908	0.3114	0.2500	0.5*
Al20	0.3040	0.6079	0.2500	0.5*
Al21	0.2357	0.3809	0.2500	0.5*
Al22	0.3896	0.4603	0.2500	0.5*
Al23	0.5099	0.2550	0.0625	0.5*
Al24	0.6079	0.3040	0.1349	0.5*
Al25	0.4119	0.4417	0.0691	0.5*
Al26	0.3846	0.5360	0.2500	0.5*
Al27	0.1272	0.2543	0.0625	0.5*
Al28	0.1476	0.1464	0.2500	0.5*
Al29	0.0000	0.0000	0.2500	0.5*
Al30	0.3623	0.2531	0.0592	0.5*
Al31	0.4591	0.2990	0.1349	0.5*
Al32	0.5571	0.3499	0.0691	0.5*
Al33	0.3164	0.5397	0.1349	0.5*
Al34	0.0788	0.1576	0.1349	0.5*
Al35	0.3151	0.3908	0.1349	0.5*
Al36	0.3176	0.1588	0.1349	0.5*
Al37	0.3635	0.6365	0.0559	0.5*
Al38	0.3623	0.4888	0.0625	0.5*
Al39	0.2655	0.4404	0.0724	0.5*
Al40	0.2370	0.4739	0.2500	0.5*
Al41	0.4597	0.5403	0.1316	0.5*
Al42	0.5261	0.3797	0.2500	0.5*
Al43	0.2754	0.2543	0.0559	0.5*
Al44	0.5602	0.4398	0.0757	0.5*
Al45	0.4628	0.4653	0.2500	0.5*
Al47	0.2258	0.1563	0.1349	0.5*
Al48	0.4603	0.3908	0.1349	0.5*
Al49	0.1266	0.1067	0.0592	0.5*
Al50	0.0323	0.0645	0.0658	0.5*
Al51	0.0707	0.0794	0.2500	0.5*	0.500
Al52	0.3022	0.3084	0.2500	0.5*
Al53	0.5109	0.4891	0.0690	0.5*
Al54	0.3600	0.3380	0.0590	0.5*