Structure determination of a pseudo-decagonal quasicrystal approximant by the strong-reflections approach and rotation electron diffraction

The structure of a complicated pseudo-decagonal (PD) quasicrystal approximant in the Al–Co–Ni alloy system, denoted as PD1, was solved by the strong-reflections approach on three-dimensional rotation electron diffraction (RED) data, using the phases from the known PD2 structure. RED shows that the PD1 crystal is primitive and orthorhombic, with a = 37.3, b = 38.8, c = 8.2 Å. However, as with other approximants in the PD series, the superstructure reflections (corresponding to c = 8.2 Å) are much weaker than those of the main reflections (corresponding to c = 4.1 Å), so it was decided to solve the PD1 structure in the smaller primitive unit cell first, i.e. with unit-cell parameters a = 37.3, b = 38.8, c = 4.1 Å and space group Pnam. A density map of PD1 was calculated from only the 15 strongest unique reflections. It contained all 31 Co/Ni atoms and many weaker peaks corresponding to Al atoms. The structure obtained from the strong-reflections approach was confirmed by applying direct methods to the complete RED data set. Successive refinement using the RED data set resulted in 108 unique atoms (31 Co/Ni and 77 Al). This is one of the most complicated approximant structures ever solved by electron diffraction. As with other approximants in the PD series, PD1 is built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with results from high-resolution electron microscopy images. The simulated electron diffraction patterns for the structure model are in good agreement with the experimental electron diffraction patterns obtained by RED.

Computing details

(I)

Crystal data

Pnam	α = 90°
a = 37.70100 Å	β = 90°
b = 39.71000 Å	γ = 90°
c = 4.10300 Å	V = 6142.63 Å^3

Data collection

h = →	l = →
k = →

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

	x	y	z	Uiso*/Ueq
Co1	0.388239	0.172689	0.250000	0.025330*
Co2	0.388239	0.672689	0.250000	0.025330*
Co3	0.696479	0.077319	0.250000	0.025330*
Co4	0.696479	0.577319	0.250000	0.025330*
Co5	0.888300	0.017991	0.250000	0.025330*
Co6	0.888300	0.517991	0.250000	0.025330*
Co7	0.196807	0.232052	0.250000	0.025330*
Co8	0.196807	0.732052	0.250000	0.025330*
Co9	0.197720	0.112893	0.250000	0.025330*
Co10	0.079736	0.077127	0.250000	0.025330*
Co11	0.079736	0.577127	0.250000	0.025330*
Co12	0.579507	0.231426	0.250000	0.025330*
Co13	0.579507	0.731426	0.250000	0.025330*
Co14	0.505032	0.018360	0.250000	0.025330*
Co15	0.505032	0.518360	0.250000	0.025330*
Co16	0.888495	0.136960	0.250000	0.025330*
Co17	0.888495	0.636960	0.250000	0.025330*
Co18	0.004377	0.172823	0.250000	0.025330*
Co19	0.004377	0.672823	0.250000	0.025330*
Co20	0.506885	0.136536	0.250000	0.025330*
Co21	0.506885	0.636536	0.250000	0.025330*
Co22	0.578968	0.114133	0.250000	0.025330*
Co23	0.578968	0.614133	0.250000	0.025330*
Co24	0.270515	0.020163	0.250000	0.025330*
Co25	0.268815	0.132597	0.250000	0.025330*
Co26	0.310376	0.076846	0.250000	0.025330*
Co27	0.771216	0.173355	0.250000	0.025330*
Co28	0.771216	0.673355	0.250000	0.025330*
Co29	0.889161	0.207369	0.249999	0.025330*
Co30	0.889161	0.707369	0.249999	0.025330*
Co31	0.200307	0.043174	0.250000	0.025330*
Al1	0.197720	0.612893	0.250000	0.025330*
Al2	0.527235	0.077338	0.250000	0.025330*
Al3	0.527235	0.577338	0.250000	0.025330*
Al4	0.835581	0.172822	0.250000	0.025330*
Al5	0.835581	0.672822	0.250000	0.025330*
Al6	0.026865	0.232161	0.250000	0.025330*
Al7	0.026865	0.732161	0.250000	0.025330*
Al8	0.219493	0.172703	0.250000	0.025330*
Al9	0.219493	0.672703	0.250000	0.025330*
Al10	0.335559	0.018378	0.250000	0.025330*
Al11	0.335559	0.518378	0.250000	0.025330*
Al12	0.020798	0.045569	0.250000	0.025330*
Al13	0.020798	0.545569	0.250000	0.025330*
Al14	0.715982	0.137802	0.250000	0.025330*
Al15	0.715982	0.637802	0.250000	0.025330*
Al16	0.025638	0.112435	0.249999	0.025330*
Al17	0.025638	0.612435	0.249999	0.025330*
Al18	0.718716	0.017904	0.250000	0.025330*
Al19	0.718716	0.517904	0.250000	0.025330*
Al20	0.270515	0.520163	0.250000	0.025330*
Al21	0.811284	0.230586	0.250000	0.025330*
Al22	0.811284	0.730586	0.250000	0.025330*
Al23	0.268815	0.632597	0.250000	0.025330*
Al24	0.913902	0.077019	0.250000	0.025330*
Al25	0.913902	0.577019	0.250000	0.025330*
Al26	0.310376	0.576846	0.250000	0.025330*
Al27	0.335359	0.136406	0.250000	0.025330*
Al28	0.335359	0.636406	0.250000	0.025330*
Al29	0.144513	0.076645	0.250000	0.025330*
Al30	0.144513	0.576645	0.250000	0.025330*
Al31	0.413070	0.231245	0.250000	0.025330*
Al32	0.413070	0.731245	0.250000	0.025330*
Al33	0.814049	0.115371	0.250000	0.025330*
Al34	0.814049	0.615371	0.250000	0.025330*
Al35	0.408740	0.113124	0.250000	0.025330*
Al36	0.408740	0.613124	0.250000	0.025330*
Al37	0.200307	0.543174	0.250000	0.025330*
Al38	0.577905	0.040700	0.250000	0.025330*
Al39	0.577905	0.540700	0.250000	0.025330*
Al40	0.645103	0.229784	0.250000	0.025330*
Al41	0.645103	0.729784	0.250000	0.025330*
Al42	0.333865	0.207236	0.250000	0.025330*
Al43	0.333865	0.707236	0.250000	0.025330*
Al44	0.646832	0.117926	0.250000	0.025330*
Al45	0.646832	0.617926	0.250000	0.025330*
Al46	0.708093	0.203321	0.250000	0.025330*
Al47	0.708093	0.703321	0.250000	0.025330*
Al48	0.612293	0.173373	0.250000	0.025330*
Al49	0.612293	0.673373	0.250000	0.025330*
Al50	0.511547	0.207090	0.250000	0.025330*
Al51	0.511547	0.707090	0.250000	0.025330*
Al52	0.393619	0.048160	0.250000	0.025330*
Al53	0.393619	0.548160	0.250000	0.025330*
Al54	0.651927	0.030672	0.250000	0.025330*
Al55	0.651927	0.530672	0.250000	0.025330*
Al56	0.453552	0.175000	0.250000	0.025330*
Al57	0.453552	0.675000	0.250000	0.025330*
Al58	0.820934	0.040951	0.250000	0.025330*
Al59	0.820934	0.540951	0.250000	0.025330*
Al60	0.955334	0.025269	0.250000	0.025330*
Al61	0.955334	0.525269	0.250000	0.025330*
Al62	0.958503	0.124304	0.250000	0.025330*
Al63	0.958503	0.624304	0.250000	0.025330*
Al64	0.112720	0.020215	0.250000	0.025330*
Al65	0.112720	0.520215	0.250000	0.025330*
Al66	0.075904	0.197154	0.250000	0.025330*
Al67	0.075904	0.697154	0.250000	0.025330*
Al68	0.961812	0.226045	0.249999	0.025330*
Al69	0.961812	0.726045	0.249999	0.025330*
Al70	0.463635	0.075526	0.250000	0.025330*
Al71	0.463635	0.575526	0.250000	0.025330*
Al72	0.115090	0.132269	0.250000	0.025330*
Al73	0.115090	0.632269	0.250000	0.025330*
Al74	0.265807	0.215791	0.250000	0.025330*
Al75	0.265807	0.715791	0.250000	0.025330*
Al76	0.762391	0.067487	0.250000	0.025330*
Al77	0.762391	0.567487	0.250000	0.025330*
Al78	0.158330	0.176234	0.250000	0.025330*
Al79	0.158330	0.676234	0.250000	0.025330*
Al80	0.555929	0.172861	0.250000	0.025330*
Al81	0.555929	0.672861	0.250000	0.025330*
Al82	0.248802	0.077076	0.250000	0.025330*
Al83	0.125625	0.217798	0.250000	0.025330*
Al84	0.125625	0.717798	0.250000	0.025330*