P. Wadley,
A. Crespi,
J. Gázquez,
M. A. Roldán,
P. García,
V. Novak,
R. Campion,
T. Jungwirth,
C. Rinaldi,
X. Martí,
V. Holy,
C. Frontera and
J. Rius Determining atomic positions in thin films by X-ray diffraction is, at present, a task reserved for synchrotron facilities. Here an experimental method is presented which enables the determination of the structure factor amplitudes of thin films using laboratory-based equipment (Cu Kα radiation). This method was tested using an epitaxial 130 nm film of CuMnAs grown on top of a GaAs substrate, which unlike the orthorhombic bulk phase forms a crystal structure with tetragonal symmetry. From the set of structure factor moduli obtained by applying this method, the solution and refinement of the crystal structure of the film has been possible. The results are supported by consistent high-resolution scanning transmission electron microscopy and stoichiometry analyses.
Supporting information
Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).
Crystal data top
As0.84Cu1.08Mn0.94 | γ = 90.00 (2)° |
Mr = 193.40 | V = 92.2 (4) Å3 |
2, P4/nmm | Z = 2 |
a = 3.82 (1) Å | F(000) = 174 |
b = 3.82 (1) Å | Dx = 6.967 Mg m−3 |
c = 6.318 (10) Å | µ = 85.38 mm−1 |
α = 90.00 (2)° | T = 293 K |
β = 90.00 (2)° | 2.00 × 2.00 × 2.00 mm |
Data collection top
Radiation source: fine-focus sealed tube | Rint = 0.000 |
Graphite monochromator | θmax = 49.4°, θmin = 7.0° |
34 measured reflections | h = 0→2 |
34 independent reflections | k = 0→3 |
10 reflections with I > 2σ(I) | l = 1→6 |
Refinement top
Refinement on F2 | 0 restraints |
Least-squares matrix: full | Primary atom site location: structure-invariant direct methods |
R[F2 > 2σ(F2)] = 0.046 | Secondary atom site location: difference Fourier map |
wR(F2) = 0.107 | w = 1/[σ2(Fo2) + (0.1P)2] where P = (Fo2 + 2Fc2)/3 |
S = 0.39 | (Δ/σ)max = 0.001 |
34 reflections | Δρmax = 0.83 e Å−3 |
3 parameters | Δρmin = −0.53 e Å−3 |
Special details top
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes)
are estimated using the full covariance matrix. The cell esds are taken
into account individually in the estimation of esds in distances, angles
and torsion angles; correlations between esds in cell parameters are only
used when they are defined by crystal symmetry. An approximate (isotropic)
treatment of cell esds is used for estimating esds 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 > 2sigma(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 (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Cu | 0.2500 | 0.7500 | 0.5000 | 0.045 (5) | |
As | 0.7500 | 0.7500 | 0.2347 (13) | 0.016 (3) | 0.96 |
Mn | 0.7500 | 0.7500 | 0.830 (3) | 0.024 (5) | 0.86 |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Cu | 0.025 (6) | 0.025 (6) | 0.085 (11) | 0.000 | 0.000 | 0.000 |
As | 0.013 (4) | 0.013 (4) | 0.020 (5) | 0.000 | 0.000 | 0.000 |
Mn | 0.016 (6) | 0.016 (6) | 0.038 (12) | 0.000 | 0.000 | 0.000 |
Geometric parameters (Å, º) top
Cu—Asi | 2.541 (7) | As—Cuvii | 2.541 (7) |
Cu—Asii | 2.541 (7) | As—Cuiii | 2.541 (7) |
Cu—Asiii | 2.541 (7) | As—Mniii | 2.732 (8) |
Cu—As | 2.541 (7) | As—Mnviii | 2.732 (8) |
Cu—Cuiv | 2.701 (7) | As—Mnix | 2.732 (8) |
Cu—Cui | 2.701 (7) | As—Mni | 2.732 (8) |
Cu—Cuiii | 2.701 (7) | Mn—Asx | 2.56 (2) |
Cu—Cuv | 2.701 (7) | Mn—Asiii | 2.732 (8) |
Cu—Mn | 2.827 (15) | Mn—Asviii | 2.732 (8) |
Cu—Mniii | 2.827 (15) | Mn—Asi | 2.732 (8) |
Cu—Mnii | 2.827 (15) | Mn—Asix | 2.732 (8) |
Cu—Mni | 2.827 (15) | Mn—Cuiii | 2.827 (15) |
As—Mnvi | 2.56 (2) | Mn—Cuvii | 2.827 (15) |
As—Cui | 2.541 (7) | Mn—Cui | 2.827 (15) |
| | | |
Asi—Cu—Asii | 115.79 (18) | Mnvi—As—Cuiii | 131.27 (16) |
Asi—Cu—Asiii | 97.5 (3) | Cui—As—Cuiii | 97.5 (3) |
Asii—Cu—Asiii | 115.79 (18) | Cuvii—As—Cuiii | 64.21 (18) |
Asi—Cu—As | 115.79 (18) | Mnvi—As—Cu | 131.27 (16) |
Asii—Cu—As | 97.5 (3) | Cui—As—Cu | 64.21 (18) |
Asiii—Cu—As | 115.79 (18) | Cuvii—As—Cu | 97.5 (3) |
Asi—Cu—Cuiv | 122.10 (9) | Cuiii—As—Cu | 64.21 (18) |
Asii—Cu—Cuiv | 57.90 (9) | Mnvi—As—Mniii | 81.4 (4) |
Asiii—Cu—Cuiv | 57.90 (9) | Cui—As—Mniii | 128.6 (3) |
As—Cu—Cuiv | 122.10 (9) | Cuvii—As—Mniii | 128.6 (3) |
Asi—Cu—Cui | 57.90 (9) | Cuiii—As—Mniii | 64.7 (3) |
Asii—Cu—Cui | 122.10 (9) | Cu—As—Mniii | 64.7 (3) |
Asiii—Cu—Cui | 122.10 (9) | Mnvi—As—Mnviii | 81.4 (4) |
As—Cu—Cui | 57.90 (9) | Cui—As—Mnviii | 64.7 (3) |
Cuiv—Cu—Cui | 180.0 | Cuvii—As—Mnviii | 64.7 (3) |
Asi—Cu—Cuiii | 122.10 (9) | Cuiii—As—Mnviii | 128.6 (3) |
Asii—Cu—Cuiii | 122.10 (9) | Cu—As—Mnviii | 128.6 (3) |
Asiii—Cu—Cuiii | 57.90 (9) | Mniii—As—Mnviii | 162.8 (8) |
As—Cu—Cuiii | 57.90 (9) | Mnvi—As—Mnix | 81.4 (4) |
Cuiv—Cu—Cuiii | 90.0 | Cui—As—Mnix | 128.6 (3) |
Cui—Cu—Cuiii | 90.0 | Cuvii—As—Mnix | 64.7 (3) |
Asi—Cu—Cuv | 57.90 (9) | Cuiii—As—Mnix | 64.7 (3) |
Asii—Cu—Cuv | 57.90 (9) | Cu—As—Mnix | 128.6 (3) |
Asiii—Cu—Cuv | 122.10 (9) | Mniii—As—Mnix | 88.73 (11) |
As—Cu—Cuv | 122.10 (9) | Mnviii—As—Mnix | 88.73 (11) |
Cuiv—Cu—Cuv | 90.0 | Mnvi—As—Mni | 81.4 (4) |
Cui—Cu—Cuv | 90.0 | Cui—As—Mni | 64.7 (3) |
Cuiii—Cu—Cuv | 180.0 | Cuvii—As—Mni | 128.6 (3) |
Asi—Cu—Mn | 60.9 (2) | Cuiii—As—Mni | 128.6 (3) |
Asii—Cu—Mn | 173.8 (3) | Cu—As—Mni | 64.7 (3) |
Asiii—Cu—Mn | 60.9 (2) | Mniii—As—Mni | 88.73 (11) |
As—Cu—Mn | 88.8 (4) | Mnviii—As—Mni | 88.73 (11) |
Cuiv—Cu—Mn | 118.54 (16) | Mnix—As—Mni | 162.8 (8) |
Cui—Cu—Mn | 61.46 (16) | Asx—Mn—Asiii | 98.6 (4) |
Cuiii—Cu—Mn | 61.46 (16) | Asx—Mn—Asviii | 98.6 (4) |
Cuv—Cu—Mn | 118.54 (16) | Asiii—Mn—Asviii | 162.8 (8) |
Asi—Cu—Mniii | 173.8 (3) | Asx—Mn—Asi | 98.6 (4) |
Asii—Cu—Mniii | 60.9 (2) | Asiii—Mn—Asi | 88.73 (11) |
Asiii—Cu—Mniii | 88.8 (4) | Asviii—Mn—Asi | 88.73 (11) |
As—Cu—Mniii | 60.9 (2) | Asx—Mn—Asix | 98.6 (4) |
Cuiv—Cu—Mniii | 61.46 (16) | Asiii—Mn—Asix | 88.73 (11) |
Cui—Cu—Mniii | 118.54 (16) | Asviii—Mn—Asix | 88.73 (11) |
Cuiii—Cu—Mniii | 61.46 (16) | Asi—Mn—Asix | 162.8 (8) |
Cuv—Cu—Mniii | 118.54 (16) | Asx—Mn—Cu | 137.5 (3) |
Mn—Cu—Mniii | 122.9 (3) | Asiii—Mn—Cu | 54.4 (2) |
Asi—Cu—Mnii | 60.9 (2) | Asviii—Mn—Cu | 111.3 (5) |
Asii—Cu—Mnii | 88.8 (4) | Asi—Mn—Cu | 54.4 (2) |
Asiii—Cu—Mnii | 60.9 (2) | Asix—Mn—Cu | 111.3 (5) |
As—Cu—Mnii | 173.8 (3) | Asx—Mn—Cuiii | 137.5 (3) |
Cuiv—Cu—Mnii | 61.46 (16) | Asiii—Mn—Cuiii | 54.4 (2) |
Cui—Cu—Mnii | 118.54 (16) | Asviii—Mn—Cuiii | 111.3 (5) |
Cuiii—Cu—Mnii | 118.54 (16) | Asi—Mn—Cuiii | 111.3 (5) |
Cuv—Cu—Mnii | 61.46 (16) | Asix—Mn—Cuiii | 54.4 (2) |
Mn—Cu—Mnii | 85.0 (6) | Cu—Mn—Cuiii | 57.1 (3) |
Mniii—Cu—Mnii | 122.9 (3) | Asx—Mn—Cuvii | 137.5 (3) |
Asi—Cu—Mni | 88.8 (4) | Asiii—Mn—Cuvii | 111.3 (5) |
Asii—Cu—Mni | 60.9 (2) | Asviii—Mn—Cuvii | 54.4 (2) |
Asiii—Cu—Mni | 173.8 (3) | Asi—Mn—Cuvii | 111.3 (5) |
As—Cu—Mni | 60.9 (2) | Asix—Mn—Cuvii | 54.4 (2) |
Cuiv—Cu—Mni | 118.54 (17) | Cu—Mn—Cuvii | 85.0 (6) |
Cui—Cu—Mni | 61.46 (16) | Cuiii—Mn—Cuvii | 57.1 (3) |
Cuiii—Cu—Mni | 118.54 (16) | Asx—Mn—Cui | 137.5 (3) |
Cuv—Cu—Mni | 61.46 (16) | Asiii—Mn—Cui | 111.3 (5) |
Mn—Cu—Mni | 122.9 (3) | Asviii—Mn—Cui | 54.4 (2) |
Mniii—Cu—Mni | 85.0 (6) | Asi—Mn—Cui | 54.4 (2) |
Mnii—Cu—Mni | 122.9 (3) | Asix—Mn—Cui | 111.3 (5) |
Mnvi—As—Cui | 131.27 (16) | Cu—Mn—Cui | 57.1 (3) |
Mnvi—As—Cuvii | 131.27 (16) | Cuiii—Mn—Cui | 85.0 (6) |
Cui—As—Cuvii | 64.21 (18) | Cuvii—Mn—Cui | 57.1 (3) |
Symmetry codes: (i) −x+1, −y+2, −z+1; (ii) x−1, y, z; (iii) −x+1, −y+1, −z+1; (iv) −x, −y+1, −z+1; (v) −x, −y+2, −z+1; (vi) x, y, z−1; (vii) x+1, y, z; (viii) −x+2, −y+2, −z+1; (ix) −x+2, −y+1, −z+1; (x) x, y, z+1. |