Simulation of contrasts in X‐ray plane wave topographs of quartz crystals with induced growth striations

Härtwig, J.; Jäckel, K.‐H.; Lerche, Veronika

doi:10.1002/crat.2170220715

Cited by 30 publications

(2 citation statements)

References 8 publications

(3 reference statements)

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“…BOND, ANDRUS; BONSE; PARPIA 1976) which were replaced step by step by partially quantitative (PARPIA 1978;PARPIA et al) and quantitative ones using the isotropic (e.g. INDENBOM, KROUPA;HARTWIG;HARTWIG et al 1987) and further on the anisotropic theory of elasticity (e.g. KROUPA; HARTWIG, LERCHE).…”

Section: Introductionmentioning

confidence: 99%

Study of the Deformation State of a Crystal Plate with Inclined Seed Boundaries

Lerche

Härtwig

1992

Cryst. Res. Technol.

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The deformation state of crystal plates with an one-dimensionally inhomogeneous concentration of point defects where the direction of inhomogeneity is arbitrarily inclined with respect to the surfaces of the plate was calculated according to the theory of elasticity for the general case of anisotropy. As an example synthetic quartz plates with seed boundaries were regarded. On the basis of the calculated strain field we simulated optical density distributions of X-ray plane wave topographs of such crystals for a quantitative analysis of recorded topographs. Topography proved to be an alternative method in comparison with the determination of absolute lattice parameters for obtaining results concerning the anisotropy of quasiplastic strain due to the incorporation of point defects. Differing results on the basis of calculations according to the isotropic approximation of Hooke's law showed the necessity of anisotropic modelling in the present case.

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Section: Introductionmentioning

confidence: 99%

Study of the Deformation State of a Crystal Plate with Inclined Seed Boundaries

Lerche

Härtwig

1992

Cryst. Res. Technol.

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“…The strain field of a crystal plate with an inhomogeneous distribution of impurity atoms is calculated in[20] for the isotropic case and in[21] for the anisotropic case. It was applied to the quantitative analysis of x-ray topographs of quartz in[21][22][23][24][25]. An application to diamond, based on a different approach, was published in[14,18].…”

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confidence: 99%

HPHT growth and x-ray characterization of high-quality type IIa diamond

Burns

Chumakov

Connell

et al. 2009

J. Phys.: Condens. Matter

106

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The trend in synchrotron radiation (x-rays) is towards higher brilliance. This may lead to a very high power density, of the order of hundreds of watts per square millimetre at the x-ray optical elements. These elements are, typically, windows, polarizers, filters and monochromators. The preferred material for Bragg diffracting optical elements at present is silicon, which can be grown to a very high crystal perfection and workable size as well as rather easily processed to the required surface quality. This allows x-ray optical elements to be built with a sufficient degree of lattice perfection and crystal processing that they may preserve transversal coherence in the x-ray beam. This is important for the new techniques which include phase-sensitive imaging experiments like holo-tomography, x-ray photon correlation spectroscopy, coherent diffraction imaging and nanofocusing. Diamond has a lower absorption coefficient than silicon, a better thermal conductivity and lower thermal expansion coefficient which would make it the preferred material if the crystal perfection (bulk and surface) could be improved. Synthetic HPHT-grown (high pressure, high temperature) type Ib material can readily be produced in the necessary sizes of 4-8 mm square and with a nitrogen content of typically a few hundred parts per million. This material has applications in the less demanding roles such as phase plates: however, in a coherence-preserving beamline, where all elements must be of the same high quality, its quality is far from sufficient. Advances in HPHT synthesis methods have allowed the growth of type IIa diamond crystals of the same size as type Ib, but with substantially lower nitrogen content. Characterization of this high purity type IIa material has been carried out with the result that the crystalline (bulk) perfection of some of the HPHT-grown materials is approaching the quality required for the more demanding applications such as imaging applications and imaging applications with coherence preservation. The targets for further development of the type IIa diamond are size, crystal perfection, as measured by the techniques of white beam and monochromatic x-ray diffraction imaging (historically called x-ray topography), and also surface quality. Diamond plates extracted from the cubic growth sector furthest from the seed of the new low strain material produces no measurable broadening of the x-ray rocking curve width. One measures essentially the crystal reflectivity as defined by the intrinsic reflectivity curve (Darwin curve) width of a perfect crystal. In these cases the more sensitive technique of plane wave topography has been used to establish a local upper limit of the strain at the level of an 'effective misorientation' of 10(-7) rad.

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Investigation of quartz crystals with non-homogeneous distributions of impurity atoms by X-ray methods

Härtwig¹,

Holý²,

Kittner³

et al. 1988

Phys. Stat. Sol. (a)

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Lang‐ and section topography in transmission, plane wave topography in reflection, and precision lattice parameter determination are applied to the study of step like impurity atom distributions in quartz. The possibilities to describe the deformation fields connected with these distributions by means of the theory of elasticity, including also ansiotropic effects, are discussed. The applicability and the limits of the used X‐ray methods for the measurement of these deformation fields are investigated theoretically and experimentally. All the methods used yield the same values of parameters (step hight and width) of the model of the deformation field within the ranges of their experimental accuracy. Using the anisotropical theory of elasticity the results of the lattice parameter determination can yield information about the anisotropy of the quasiplastic dilatation due to the defects.

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Simulation of contrasts in X‐ray plane wave topographs of quartz crystals with induced growth striations

Cited by 30 publications

References 8 publications

Study of the Deformation State of a Crystal Plate with Inclined Seed Boundaries

Study of the Deformation State of a Crystal Plate with Inclined Seed Boundaries

HPHT growth and x-ray characterization of high-quality type IIa diamond

Investigation of quartz crystals with non-homogeneous distributions of impurity atoms by X-ray methods

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