Surface curvatures and diffraction profiles of sagittally bent Laue crystals
The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect r...
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| Published in: | Journal of applied crystallography Vol. 44; no. 4; pp. 665 - 671 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
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5 Abbey Square, Chester, Cheshire CH1 2HU, England
International Union of Crystallography
01-08-2011
Blackwell Publishing Ltd |
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| Abstract | The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect ratios have been studied experimentally by optical metrology and X‐ray measurements. The results were confirmed with finite‐element analysis using large‐deformation theory. The nonlinear relationship between the curvatures necessitates an experimentally determined parameter in the theoretical modeling of the diffraction profiles. By taking into account the local stress and the aspect ratio of the sagittally bent Laue crystal, the modified analytical approach successfully predicts the rocking‐curve width and the integrated reflecting power. The effect of extreme sagittal bending on the rocking curve is also discussed. To retain high reflectivity, the bending curvature should not exceed its critical value for the specified crystal geometry. Furthermore, the uniformity of the bending curvatures across the crystal surface has been examined, which suggests that the minimum crystal dimension should be approximately twice the size of the beam footprint. |
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| AbstractList | The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect ratios have been studied experimentally by optical metrology and X-ray measurements. The results were confirmed with finite-element analysis using large-deformation theory. The nonlinear relationship between the curvatures necessitates an experimentally determined parameter in the theoretical modeling of the diffraction profiles. By taking into account the local stress and the aspect ratio of the sagittally bent Laue crystal, the modified analytical approach successfully predicts the rocking-curve width and the integrated reflecting power. The effect of extreme sagittal bending on the rocking curve is also discussed. To retain high reflectivity, the bending curvature should not exceed its critical value for the specified crystal geometry. Furthermore, the uniformity of the bending curvatures across the crystal surface has been examined, which suggests that the minimum crystal dimension should be approximately twice the size of the beam footprint. |
| Author | Takacs, Peter Z. Kaznatcheev, Konstantine Zhong, Zhong Dooryhee, Eric Ghose, Sanjit Shi, Xianbo Rehak, Margareta L. |
| Author_xml | – sequence: 1 givenname: Xianbo surname: Shi fullname: Shi, Xianbo – sequence: 2 givenname: Sanjit surname: Ghose fullname: Ghose, Sanjit – sequence: 3 givenname: Zhong surname: Zhong fullname: Zhong, Zhong – sequence: 4 givenname: Margareta L. surname: Rehak fullname: Rehak, Margareta L. – sequence: 5 givenname: Konstantine surname: Kaznatcheev fullname: Kaznatcheev, Konstantine – sequence: 6 givenname: Peter Z. surname: Takacs fullname: Takacs, Peter Z. – sequence: 7 givenname: Eric surname: Dooryhee fullname: Dooryhee, Eric |
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| Cites_doi | 10.1107/S0021889889010800 10.1016/0168-9002(91)90536-Y 10.1107/S0108767302011261 10.1107/S0021889801010627 10.1107/S0909049507066368 10.1107/S0909049506031438 10.1143/JPSJ.26.1239 10.1063/1.1145712 10.1002/pssa.2210440113 10.1063/1.1699774 10.1063/1.1141605 10.1107/S0108767302016835 10.1107/S0567739470001596 10.1107/S0021889870006076 10.1107/S090904950802801X 10.1107/S002188988301047X 10.1117/12.294490 10.1107/S0021889801006409 |
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| References | Schulze (hx5128_bb13) 1995; 66 Feng (hx5128_bb7) 2008; 15 hx5128_bb2 Kalman (hx5128_bb9) 1983; 16 Caciuffo (hx5128_bb4) 1990; 61 Authier (hx5128_bb3) 1970; 26 Sanchez del Rio (hx5128_bb12) 1997; 3151 Zhong (hx5128_bb21) 2003; 59 Takagi (hx5128_bb15) 1969; 26 Zhong (hx5128_bb19) 2001; 34 Krisch (hx5128_bb10) 1991; 305 Taupin (hx5128_bb16) 1964; 87 Zhong (hx5128_bb18) 2001; 34 Egert (hx5128_bb5) 1970; 3 Penning (hx5128_bb11) 1961; 16 Albertini (hx5128_bb1) 1977; 44 Sutter (hx5128_bb14) 2008; 15 Honkimäki (hx5128_bb8) 2006; 13 White (hx5128_bb17) 1950; 21 Zhong (hx5128_bb20) 2002; 58 Erola (hx5128_bb6) 1990; 23 |
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| Snippet | The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design... |
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| SubjectTerms | Aspect ratio Bending Crystallography Crystals Curvature Diffraction Laue crystals Mathematical analysis Mathematical models monochromator crystals Monochromators sagittal bending Surface chemistry surface curvatures |
| Title | Surface curvatures and diffraction profiles of sagittally bent Laue crystals |
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