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Three dimensional reciprocal space measurement by x-ray diffraction using linear and area detectors: Applications to texture and defects determination in oriented thin films and nanoprecipitates
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10.1116/1.4789984
/content/avs/journal/jvsta/31/2/10.1116/1.4789984
http://aip.metastore.ingenta.com/content/avs/journal/jvsta/31/2/10.1116/1.4789984

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Schematic representation of the reciprocal image of a face-centered crystal (such as Ni) for (a) an epitaxial texture, (b) a fiber texture, and (c) a randomly oriented film.

Image of FIG. 2.
FIG. 2.

(Color online) (a) Schematic representation of a four circle diffractometer and definitions of the χ, ω, 2θ, and ϕ angles. The φ and ψ angles are defined in the sample reference frame in (b).

Image of FIG. 3.
FIG. 3.

(Color online) Reciprocal space representation of the diffraction process from a single crystal (or a single grain). For the most common configuration involving an incident beam (S0 ) at an angle θ from the sample surface and a diffracted beam (S1 ) at 2θ, a symmetrical θ − 2θ scan corresponds to measuring reciprocal space along a direction that intersects the origin of the reciprocal lattice.

Image of FIG. 4.
FIG. 4.

(Color online) (a) Schematic representation of a Ni single crystal pole figure at d = 2.03 Å. (b) Reciprocal space representation of the Ni reciprocal lattice and pole figure (red half sphere) in three dimensions.

Image of FIG. 5.
FIG. 5.

(Color online) Schematics of the setups required to acquire pole figures using (a) a point detector, (b) a linear detector, and (c) an area detector.

Image of FIG. 6.
FIG. 6.

(Color online) Scan strategies to acquire pole figures using an area detector by exploiting (a) ϕ scans and (b) ω scans.

Image of FIG. 7.
FIG. 7.

(Color online) (a) Pole figure at d = 2.45 Å extracted from a video of pole figures from a Si(001) wafer. The video is available online. 8 Each frame in the video corresponds to a pole figure for a different d-spacing value. (b) Calculated intensities resulting from thermal diffuse scattering of x-rays by Si(001) at d = 2.45 Å.

Image of FIG. 8.
FIG. 8.

(Color online) Pole figures for three different d-spacing values from an heterogeneous GaP:MnP sample containing MnP precipitates in a GaP(001) matrix prepared by metal-organic vapor phase epitaxy. The d-spacing values are selected to reveal the (a) MnP(200) (d = 2.63 Å), (b) MnP(211) (d = 1.92 Å), and (c) MnP(111) (d = 2.47 Å) planes.

Image of FIG. 9.
FIG. 9.

(Color online) Pole figures for four different d-spacing values (3.27, 2.71, 1.94, and 1.89 ± 0.02 Å) measured following the reaction of a 10-nm-thick fluorine-doped Ni film with Si(001) during a thermal ramp at 3 °C s−1 from room temperature up to 345 °C. These pole figures are extracted from a video of 300 consecutive pole figures available online. 8 Each frame in the video corresponds to a pole figure for a different d-spacing value.

Image of FIG. 10.
FIG. 10.

(Color online) (a) Pole figure at d = 1.92 Å measured following the reaction of a 30-nm-thick from a 30-nm-thick Ni film with Si(001) during a thermal ramp at 3 °C s−1 at a temperature of 390 °C. This pole figure is extracted from a video of 300 consecutive pole figures available online. 8 Each frame in the video corresponds to a pole figure for a different d-spacing value. (b) Reciprocal space representation of the diffracted signal from the sample in (a) summed over ϕ from 55° to 65°.

Image of FIG. 11.
FIG. 11.

(Color online) (a) Pole figure, for d = 3.21–3.28 Å, from a heterogeneous GaP:MnP sample containing MnP precipitates in a GaP(001) matrix prepared by metal-organic vapor phase epitaxy. The red and orange arrows represent cuts in the 3D reciprocal space. The square represents the direction of the two vectors required to define the cut. (b) The spherical representation of the pole figure in (a) along with the two cuts in the 3D reciprocal space. Videos of the pole figure as well as of the 3D representation of reciprocal space are available online. 8 Each frame in the video corresponds to a pole figure for a different d-spacing value. (c) Reciprocal space cut associated with the red arrow, starting at GaP ( ) toward the GaP ( ) plane. The black arrows correspond to the reciprocal space vectors for the GaP ( ) and GaP ( ) planes. (d) Reciprocal space cut associated to the orange arrow, starting at GaP ( ) toward the GaP (111) plane. Planes identified in red result from twinning on GaP ( ), while planes identified in green arise from twinning on GaP (111). The red arrows correspond to reciprocal space vectors for the twinned GaP ( ) planes.

Image of FIG. 12.
FIG. 12.

(Color online) Definition of (a) the ω, χ, and ϕ angles, and (b) the orientation of the beam path in the laboratory reference frame. 2θ0 corresponds to the motor angle of the 2θ arm rather than the angle between the direct beam and a specific pixel (2θpix).

Tables

Generic image for table
TABLE I.

Fiber texture components for the θ phase of the Ni-Si system (space group: P63/mmc, a = b = 3.8 Å, c = 4.9 Å, α = γ = 90°, β = 120°).

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/content/avs/journal/jvsta/31/2/10.1116/1.4789984
2013-02-13
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three dimensional reciprocal space measurement by x-ray diffraction using linear and area detectors: Applications to texture and defects determination in oriented thin films and nanoprecipitates
http://aip.metastore.ingenta.com/content/avs/journal/jvsta/31/2/10.1116/1.4789984
10.1116/1.4789984
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