Lattice strain effects in the measurement of the Si lattice parameter by Laue-case double-crystal diffractometry

2004 ◽  
Vol 37 (5) ◽  
pp. 773-777 ◽  
Author(s):  
Giovanni Mana ◽  
Carlo Palmisano ◽  
Gianfranco Zosi
Keyword(s):  
Strain Gradient ◽  
Lattice Spacing ◽  
Lattice Strain ◽  
Numerical Solutions ◽  
Theoretical Framework ◽  
Lattice Parameter ◽  
X Rays ◽  
Double Crystal ◽  
Analytical And Numerical Solutions ◽  
Measured Lattice Spacing

The measurement of the (220) Bragg-plane spacing of Si by Laue-case double-crystal diffractometry with an uncertainty lower than 10−8requires a detailed theoretical framework that includes the study of lattice strain. In the present paper, the propagation of X-rays through a deformed crystal is re-examined and the influence of a constant strain gradient on the centre of the reflection domain is studied by means of Takagi's equations. Their analytical and numerical solutions indicate that the measured lattice spacing refers to the crystal entrance surface.

Effects of Thermal Treatment on the Structure of Eu:YAG Nanopowder

2007 ◽  
Vol 128 ◽  
pp. 107-114 ◽  
Author(s):  
Maria Luisa Saladino ◽  
Eugenio Caponetti ◽  
Stefano Enzo
Keyword(s):  
Thermal Treatment ◽  
Lattice Strain ◽  
Rietveld Method ◽  
Lattice Parameter ◽  
Spherical Particles ◽  
X Rays ◽  
Garnet Phase ◽  
The Matrix ◽  
Different Temperatures ◽  
Co Precipitation

Eu:YAG nanopowder precursors were obtained by co-precipitation of aluminium, yttrium and europium nitrates solution with ammonia. The hydroxides precursors were calcined at different temperatures from 900 to 1200°C as a function of holding time (1, 2 and 6 hours). The presence of Eu3+ ions in the matrix was confirmed by Energy Dispersive X-rays analysis. X-Ray Diffraction investigation by the Rietveld method shows that the sample treated at 900°C for 1 hour is essentially the garnet phase with the minor presence of hexagonal and monoclinic metastable phases. The Eu3+ ions are incorporated into the garnet phase, as is suggested by the lattice parameter value being larger than that in literature data (homogeneous strain). For the sample treated at 900°C for 1 hour, electron microscopy observations showed agglomerates of spherical particles of mean size about 50 nm. At higher temperature treatments and for longer holding times the minority hexagonal and monoclinic phases totally disappeared. However, the lattice parameters of the cubic garnet phase gradually decreased with temperature, suggesting an expulsion of Eu3+ ions from the solid solution. Simultaneous with this, it was noted that the lattice strain reached a maximum value, but to later decrease, due to the vacancies created by the Eu species initially migrating to the surface of the coherent domains of diffraction. The lattice strain definitely decreased upon more drastic thermal treatments. Meanwhile, FEG-SEM and TEM observations on the same samples confirmed the growth of the garnet particles as a function of the thermal treatment.

Spatial imaging of monochromatic hard x‐rays from an APS undulator by the Kohzu double‐crystal monochromator (abstract)

1996 ◽  
Vol 67 (9) ◽  
pp. 3348-3348
Author(s):  
D.M. Mills ◽  
W.K. Lee ◽  
M. Keeffe ◽  
D.R. Haeffner ◽  
P. Fernandez
Keyword(s):  
X Rays ◽  
Double Crystal ◽  
Double Crystal Monochromator

scholarly journals Grazing-incidence X-ray diffraction of single GaAs nanowires at locations defined by focused ion beams

2013 ◽  
Vol 46 (4) ◽  
pp. 887-892 ◽  
Author(s):  
Genziana Bussone ◽  
Rüdiger Schott ◽  
Andreas Biermanns ◽  
Anton Davydok ◽  
Dirk Reuter ◽  
...  
Keyword(s):  
Gaas Substrate ◽  
Lattice Spacing ◽  
Molecular Beam ◽  
Grazing Incidence ◽  
Lattice Parameter ◽  
Ion Beams ◽  
Focused Ion Beams ◽  
X Ray Diffraction ◽  
X Ray ◽  
Gaas Nanowires

Grazing-incidence X-ray diffraction measurements on single GaAs nanowires (NWs) grown on a (111)-oriented GaAs substrate by molecular beam epitaxy are reported. The positions of the NWs are intentionally determined by a direct implantation of Au with focused ion beams. This controlled arrangement in combination with a nanofocused X-ray beam allows the in-plane lattice parameter of single NWs to be probed, which is not possible for randomly grown NWs. Reciprocal space maps were collected at different heights along the NW to investigate the crystal structure. Simultaneously, substrate areas with different distances from the Au-implantation spots below the NWs were probed. Around the NWs, the data revealed a 0.4% decrease in the lattice spacing in the substrate compared with the expected unstrained value. This suggests the presence of a compressed region due to Au implantation.

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