# Selection of CVD Diamond Crystals for X-ray Monochromator Applications Using X-ray Diffraction Imaging

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## Abstract

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## 1. Introduction

## 2. Samples

## 3. Experiments

## 4. Analysis of Rocking Curve Topographs

## 5. Dilational and Rotational Components of the Lattice Distortion

## 6. Conclusions

- The standard deviation of the effective lattice misorientation across the nearly flat regions of interest is in the range 20–70 $\mathsf{\mu}$rad.
- The averaged rocking curve width for these regions is about 130–165 $\mathsf{\mu}$rad (r.m.s.), which was found to be close to $\mathrm{\Delta}{\theta}^{tot}$ = 134–181 $\mathsf{\mu}$rad (r.m.s.) widths of the total rocking curve (integrated across the region). The effective intrinsic bandwidth of the reflector (FWHM) can be estimated as $\mathrm{\Delta}E/E\simeq 2.355\phantom{\rule{3.33333pt}{0ex}}\mathrm{\Delta}{\theta}_{\sigma}^{tot}/tan{\theta}_{C}$.
- The effective lattice misorientation observed in the rocking curve topographs was dominated by the shear/rotational components of the lattice distortion, which exceed the dilation-compression component by about a factor of 2 (peak-to-valley variation) in the studied nearly flat region of interest for a representative crystal plate. The standard deviation for the dilation-compression component across the region was found to be 24 $\mathsf{\mu}$rad.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Representative White-Beam X-ray Topograph

**Figure A1.**A white-beam topograph obtained in transmission (Laue) geometry from 131 reflection of plate CVD-B. Individual dislocations are not easily discerned, which confirms high dislocaiton density material.

## Appendix B. Rocking Curve Topographs for CVD-I Using Rotating Anode X-ray Source

**Figure A2.**Rocking curve topographs for the (110)-edge oriented diamond crystal plate CVD-I showing maps of peak reflectivity (${I}_{R}^{peak}$, normalized by the maximum value), rocking curve peak position ($\delta {\theta}_{m}$), width ($\mathrm{\Delta}{\theta}_{\sigma}$), and the effective radius of curvature R calculated from spline-interpolated $\delta {\theta}_{m}$.

## Appendix C. Total Rocking Curves for the Regions of Interest

**Figure A3.**Total rocking curves for the regions of interest showing data points, fits to the Gaussian and Lorentzian shapes for plates: (

**a**) CVD-B, (

**b**) CVD-N, and (

**c**) CVD-I. The dashed horizontal line shows the level corresponding to 1/2 of the rocking curve peak intensity.

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**Figure 1.**Experimental configurations for rocking curve topography of (110)-edge oriented diamond plates (

**a**and

**c**) and (100)-edge oriented diamond plates (

**b**). DCM—double crystal Si 111 (symmetric) monochromator; AD—digital area detector; ${\mathbf{H}}_{\mathbf{Si}}$ and ${\mathbf{H}}_{\mathbf{C}}$ along with the Miller indices denote reciprocal vectors of the Si beam conditioner crystal and the diamond crystal respectively. For each configuration the angular deflections of the X-ray beams correspond to the Bragg angles at the chosen photon energies as summarized in Table 1. The incidence angles on the strongly asymmetric beam conditioner crystals are exaggerated (increased) for clarity. See text for more details.

**Figure 2.**Laue geometry for a collimated monochromatic incident beam: ${\varphi}_{0}$ and ${\varphi}_{h}$ are the incidence angles with respect to the crystal surface normal z, ${l}_{0}$ is the base of the Borrmann triangle, and ${t}_{0}$ is the thickness of the crystal plate.

**Figure 3.**Rocking curve topographs for the (100)-edge oriented diamond crystal plate (CVD-B): (

**a**) for the entire crystal showing maps of peak reflectivity (${I}_{R}^{peak}$, normalized by the maximum observed value), rocking curve peak position ($\delta {\theta}_{m}$), width ($\mathrm{\Delta}{\theta}_{\sigma}$), and the effective radius of curvature R calculated from spline-interpolated $\delta {\theta}_{m}$; (

**b**) for the region of interest where the radius of curvature is maximized ${R}_{0}\gtrsim $ 70 m (shown by the dashed rectangle in (

**a**)). The x and y coordinates in (

**b**) are shown with respect to the lower left corner of the rectangle. The limits of the colormaps for $\delta {\theta}_{m}$ and $\mathrm{\Delta}{\theta}_{\sigma}$ in (

**b**) are redefined to highlight variations in the mapped values.

**Figure 4.**Rocking curve topographs for the (110)-edge oriented diamond crystal plate (CVD-N): (

**a**) for the entire crystal showing maps of peak reflectivity (${I}_{R}^{peak}$, normalized by the maximum value), rocking curve peak position ($\delta {\theta}_{m}$), width ($\mathrm{\Delta}{\theta}_{\sigma}$), and the effective radius of curvature R calculated from spline-interpolated $\delta {\theta}_{m}$; (

**b**) for the region of interest where the radius of curvature is maximized ${R}_{0}\gtrsim $ 50 m (shown by the dashed rectangle in (

**a**)). The x and y coordinates in (

**b**) are shown with respect to the lower left corner of the rectangle. The limits of the colormaps for $\delta {\theta}_{m}$ and $\mathrm{\Delta}{\theta}_{\sigma}$ in (

**b**) are redefined to highlight variations in the mapped values.

**Figure 5.**Decoupled dilational and rotational contributions to the effective tilt $\delta {\theta}_{m}$ for plate CVD-N: (

**a**)for the entire crystal; (

**b**) for the region of interest where the radius of curvature is maximized ${R}_{0}\gtrsim $ 50 m.

**Table 1.**Parameters of the experimental configurations shown in Figure 1.

Configuration | (a) | (b) | (c) |
---|---|---|---|

E, [keV] | 8.2 | 9.83 | 8.05 |

${\theta}_{Si}$, [deg] | 37.38 | 43.38 | 23.66 |

${\eta}_{Si}$, [deg] | 36.2 | 41.4 | 22.2 |

${\theta}_{C}$, [deg] | 36.83 | 45.0 | 21.96 |

${\eta}_{C}$, [deg] | 90.0 | 90.0 | 54.7 |

**Table 2.**Statistical rocking curve characteristics for the regions of interest on selected sc-CVD diamond plates.

CVD Plate | CVD-B | CVD-N | CVD-I |
---|---|---|---|

$D\left(\delta {\theta}_{m}\right)$ [$\mathsf{\mu}$rad] | 20 | 58 | 73 |

$<\mathrm{\Delta}{\theta}_{\sigma}>$ [$\mathsf{\mu}$rad] | 132(17) | 164(39) | 155(53) |

$\mathrm{\Delta}{\theta}_{\sigma}^{tot}$ [$\mathsf{\mu}$rad] | 134 | 181 | 174 |

${R}_{0}$ [m] | ≳ 70 | ≳ 50 | ≳ 30 |

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**MDPI and ACS Style**

Stoupin, S.; Krawczyk, T.; Liu, Z.; Franck, C. Selection of CVD Diamond Crystals for X-ray Monochromator Applications Using X-ray Diffraction Imaging. *Crystals* **2019**, *9*, 396.
https://doi.org/10.3390/cryst9080396

**AMA Style**

Stoupin S, Krawczyk T, Liu Z, Franck C. Selection of CVD Diamond Crystals for X-ray Monochromator Applications Using X-ray Diffraction Imaging. *Crystals*. 2019; 9(8):396.
https://doi.org/10.3390/cryst9080396

**Chicago/Turabian Style**

Stoupin, Stanislav, Thomas Krawczyk, Zunping Liu, and Carl Franck. 2019. "Selection of CVD Diamond Crystals for X-ray Monochromator Applications Using X-ray Diffraction Imaging" *Crystals* 9, no. 8: 396.
https://doi.org/10.3390/cryst9080396