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Coherent diffraction imaging of nanoscale strain evolution in a single crystal under high pressure.

Yang W, Huang X, Harder R, Clark JN, Robinson IK, Mao HK - Nat Commun (2013)

Bottom Line: Here we report the successful de-convolution of these effects with the recently developed mutual coherent function method to reveal the three-dimensional strain distribution inside a 400 nm gold single crystal during compression within a diamond-anvil cell.The three-dimensional morphology and evolution of the strain under pressures up to 6.4 GPa were obtained with better than 30 nm spatial resolution.In addition to providing a new approach for high-pressure nanotechnology and rheology studies, we draw fundamental conclusions about the origin of the anomalous compressibility of nanocrystals.

View Article: PubMed Central - PubMed

Affiliation: High Pressure Synergetic Consortium, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, USA. wyang@ciw.edu

ABSTRACT
The evolution of morphology and internal strain under high pressure fundamentally alters the physical property, structural stability, phase transition and deformation mechanism of materials. Until now, only averaged strain distributions have been studied. Bragg coherent X-ray diffraction imaging is highly sensitive to the internal strain distribution of individual crystals but requires coherent illumination, which can be compromised by the complex high-pressure sample environment. Here we report the successful de-convolution of these effects with the recently developed mutual coherent function method to reveal the three-dimensional strain distribution inside a 400 nm gold single crystal during compression within a diamond-anvil cell. The three-dimensional morphology and evolution of the strain under pressures up to 6.4 GPa were obtained with better than 30 nm spatial resolution. In addition to providing a new approach for high-pressure nanotechnology and rheology studies, we draw fundamental conclusions about the origin of the anomalous compressibility of nanocrystals.

No MeSH data available.


Related in: MedlinePlus

Impact of the mutual coherence function (MCF) on the reconstructed images at 0.8 GPa pressure.The reconstructed amplitude plots at top, bottom and side views with (left) and without (right) MCF correction (a), and the corresponding line profiles along x and y (lateral), and z (longitudinal) directions of the MCF (b). The characterization function is a three-dimensional description of the degree of coherence between any two points with a certain distance along x, y, and z directions from an array centre.
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f2: Impact of the mutual coherence function (MCF) on the reconstructed images at 0.8 GPa pressure.The reconstructed amplitude plots at top, bottom and side views with (left) and without (right) MCF correction (a), and the corresponding line profiles along x and y (lateral), and z (longitudinal) directions of the MCF (b). The characterization function is a three-dimensional description of the degree of coherence between any two points with a certain distance along x, y, and z directions from an array centre.

Mentions: To de-convolute the influence of beam disturbance by the DAC gasket and pressure medium, modelled as a modified MCF, we used the method developed for CXDI with partial coherence15. The MCF is convolved with the calculated Fourier modulus before applying the modulus constraint. The unknown MCF function is updated regularly using iterative Richardson-Lucy algorithm2223. The searching criterion is to minimize the difference between the measured data and the convolution of this characterization function with calculated Fourier modulus. The reconstructed images using data measured at the initial pressure 0.8 GPa with and without partial coherence correction are shown in Fig. 2a. We found that the coherence correction gives a smoother crystal boundary and significantly improves the algorithm’s convergence, as found previously by Clark et al.15 The corresponding MCF function for this data set is plotted in Fig. 2b. The extracted MCF is a 3D function that includes the transverse coherence properties in the XY-plane, perpendicular to the incident X-ray beam direction, and the temporal (or longitudinal) coherence properties related to the monochromaticity of the wavefield along its Z-direction. The effect of applying the MCF is to blur the coherent intensity from measured sample by convolving it with the Fourier transform of the MCF1415. The comparison of the original measured and de-convoluted diffraction intensity distribution at 0.8 GPa is shown in Supplementary Fig. S1. The MCF, along X, Y and Z directions, is plotted in Fig. 2b, from where one can see from the smooth decay of the MCF that any pair of points separated by some distance are partially coherent.


Coherent diffraction imaging of nanoscale strain evolution in a single crystal under high pressure.

Yang W, Huang X, Harder R, Clark JN, Robinson IK, Mao HK - Nat Commun (2013)

Impact of the mutual coherence function (MCF) on the reconstructed images at 0.8 GPa pressure.The reconstructed amplitude plots at top, bottom and side views with (left) and without (right) MCF correction (a), and the corresponding line profiles along x and y (lateral), and z (longitudinal) directions of the MCF (b). The characterization function is a three-dimensional description of the degree of coherence between any two points with a certain distance along x, y, and z directions from an array centre.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3644065&req=5

f2: Impact of the mutual coherence function (MCF) on the reconstructed images at 0.8 GPa pressure.The reconstructed amplitude plots at top, bottom and side views with (left) and without (right) MCF correction (a), and the corresponding line profiles along x and y (lateral), and z (longitudinal) directions of the MCF (b). The characterization function is a three-dimensional description of the degree of coherence between any two points with a certain distance along x, y, and z directions from an array centre.
Mentions: To de-convolute the influence of beam disturbance by the DAC gasket and pressure medium, modelled as a modified MCF, we used the method developed for CXDI with partial coherence15. The MCF is convolved with the calculated Fourier modulus before applying the modulus constraint. The unknown MCF function is updated regularly using iterative Richardson-Lucy algorithm2223. The searching criterion is to minimize the difference between the measured data and the convolution of this characterization function with calculated Fourier modulus. The reconstructed images using data measured at the initial pressure 0.8 GPa with and without partial coherence correction are shown in Fig. 2a. We found that the coherence correction gives a smoother crystal boundary and significantly improves the algorithm’s convergence, as found previously by Clark et al.15 The corresponding MCF function for this data set is plotted in Fig. 2b. The extracted MCF is a 3D function that includes the transverse coherence properties in the XY-plane, perpendicular to the incident X-ray beam direction, and the temporal (or longitudinal) coherence properties related to the monochromaticity of the wavefield along its Z-direction. The effect of applying the MCF is to blur the coherent intensity from measured sample by convolving it with the Fourier transform of the MCF1415. The comparison of the original measured and de-convoluted diffraction intensity distribution at 0.8 GPa is shown in Supplementary Fig. S1. The MCF, along X, Y and Z directions, is plotted in Fig. 2b, from where one can see from the smooth decay of the MCF that any pair of points separated by some distance are partially coherent.

Bottom Line: Here we report the successful de-convolution of these effects with the recently developed mutual coherent function method to reveal the three-dimensional strain distribution inside a 400 nm gold single crystal during compression within a diamond-anvil cell.The three-dimensional morphology and evolution of the strain under pressures up to 6.4 GPa were obtained with better than 30 nm spatial resolution.In addition to providing a new approach for high-pressure nanotechnology and rheology studies, we draw fundamental conclusions about the origin of the anomalous compressibility of nanocrystals.

View Article: PubMed Central - PubMed

Affiliation: High Pressure Synergetic Consortium, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, Illinois 60439, USA. wyang@ciw.edu

ABSTRACT
The evolution of morphology and internal strain under high pressure fundamentally alters the physical property, structural stability, phase transition and deformation mechanism of materials. Until now, only averaged strain distributions have been studied. Bragg coherent X-ray diffraction imaging is highly sensitive to the internal strain distribution of individual crystals but requires coherent illumination, which can be compromised by the complex high-pressure sample environment. Here we report the successful de-convolution of these effects with the recently developed mutual coherent function method to reveal the three-dimensional strain distribution inside a 400 nm gold single crystal during compression within a diamond-anvil cell. The three-dimensional morphology and evolution of the strain under pressures up to 6.4 GPa were obtained with better than 30 nm spatial resolution. In addition to providing a new approach for high-pressure nanotechnology and rheology studies, we draw fundamental conclusions about the origin of the anomalous compressibility of nanocrystals.

No MeSH data available.


Related in: MedlinePlus