research papers
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.
Keywords: quasicrystal approximants; rotation electron diffraction; strong-reflections approach; structure determination; decagonal.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S1600576716000042/jo5016sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S1600576716000042/jo5016Isup2.hkl | |
Portable Document Format (PDF) file https://doi.org/10.1107/S1600576716000042/jo5016sup3.pdf |
CCDC reference: 1445018
Computing details top
(I) top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
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* |