Elastizit�tsmessungen mit R�ntgenstrahlen

Sachs, G.; Weerts, J.

doi:10.1007/bf01397347

Cited by 32 publications

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“…The important role of x-ray Bragg backscattering in precision measurements was recognized a while ago (e.g., Sachs and Weerts 19 ). The technique was improved in the early 70s when x-ray backsattering instruments for measuring relative changes of lattice parameters in crystals with an accuracy of 10 −6 were built.…”

Section: Measurement Principlementioning

confidence: 99%

Ultraprecise studies of the thermal expansion coefficient of diamond using backscattering x-ray diffraction

Stoupin

Shvyd’ko

2011

Phys. Rev. B

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The linear thermal expansion coefficient of diamond crystals of type IIa and type Ia was measured in the temperature range from 10 to 295 K. Neither negative thermal expansion nor any substantial difference in the thermal expansion coefficient in crystals of the different types were observed. An empirical expression was obtained that approximates the temperature dependence of the thermal expansion coefficient of diamond. The T 3 temperature dependence of a Debye solid holds below ≈ 100 K with an accuracy of ≈ 10 −8 K −1. A slight increase in the value of the lattice parameter was found for Ia type crystal which suggests lattice dilatation by nitrogen impurity. The measurements were performed using Bragg diffraction in backscattering from diamond crystals of highly monochromatic 23.7 keV x-rays with the recently demonstrated high relative accuracy of 1.2 × 10 −8 in the determination of the lattice parameter [S. Stoupin and Yu. Shvyd'ko PRL 104, 085901 (2010)].

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Section: Measurement Principlementioning

confidence: 99%

Ultraprecise studies of the thermal expansion coefficient of diamond using backscattering x-ray diffraction

Stoupin

Shvyd’ko

2011

Phys. Rev. B

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“…Performing the proper tensor rotation (strain is a symmetric second-rank tensor) yields (4) where S ij ε refers to the strain tensor components in the sample's reference frame. Performing the proper tensor rotation (strain is a symmetric second-rank tensor) yields (4) where S ij ε refers to the strain tensor components in the sample's reference frame.…”

Section: Figurementioning

confidence: 99%

X-ray scattering: a wonderful tool to probe lattice strains in materials with small dimensions

Thomas¹,

Loubens²,

Gergaud³

2004

MRS Proc.

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X-ray diffraction was recognized from the early days as highly sensitive to atomic displacements. Indeed structural crystallography has been very successful in locating with great precision the position of atoms within an individual unit cell. In disordered systems it is the average structure and fluctuations about it that may be determined. In the field of mechanics diffraction may thus be used to evaluate elastic displacement fields. In this short overview we give examples from recent work where x-ray diffraction has been used to investigate average strains in lines, films or multilayers. In small objects the proximity of surfaces or interfaces may create very inhomogeneous displacement fields. X-ray scattering is again one of the best methods to determine such distributions. The need to characterize displacement fields in nanostructures together with the advent of third generation synchrotron radiation sources has generated new and powerful methods (anomalous diffraction, coherent diffraction, microdiffraction, …). We review some of the recent and promising results in the field of strain measurements in small dimensions via X-ray diffraction. INTRODUCTIONSince the beginning of the nineties condensed matter physics has been increasingly concerned with properties of nm size objects. This trend is not simply a consequence of the steady miniaturization in electron devices [1]. It is also a result of fundamental discoveries, which show that new physical (magnetic, electronic, mechanical, …) properties appear at this scale. The search for specific size effects on physical properties should not shadow the influence of extremely high elastic strains inherent to these scales. Indeed it is now well established that materials in small dimensions [2] can sustain extremely high elastic strains. X-ray diffraction (XRD) has been recognized from the very early days [3,4] as a very sensitive tool to investigate lattice spacings and thus displacement fields. Homogeneous strains can be determined in a straightforward manner in ultrathin layers using synchrotron radiation. Strain fields are, however, Mater. Res. Soc. Symp. Proc. Vol. 840

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“…The beginning of X-ray stress measurement was comprised of the strain measurement in 1925 [1], stress measurement in 1930 [2] by X-ray diffraction method and the stress measurement by the linearity of the sin 2 ψ in 1934 [3]. The sin 2 ψ method was established by 1960 [4,5].…”

Section: Introductionmentioning

confidence: 99%

A Unified Representation for Fundamental Equations of Various X-Ray Stress Measurement Methods

Ejiri,

Ohba,

Sasaki

2023

KEM

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The X-ray stress measurements by the sin2ψ method, the cos α method and the XRD2 method are basically composed of the fundamental equations based on diffraction vectors and the calculation for determining X-ray stress. The fundamental equations are expressed differently, which are due to the fact that the measurement systems associated with the incident X-ray control device and the diffracted X-ray detector are different. Although the dependent variable that is the measured quantity is the same diffraction angle theta in the fundamental equations, the main independent variable is different like the tilt angle ψ in the sin2 ψ method and the central angle α, γ of the Debye-Scherrer ring in the cos α method, the XRD2 method, respectively. Therefore, the stress determination method has been devised based on each the fundamental equation. By clarifying the differences between each X-ray stress measurement method and making a relationship, a unified representation for the fundamental equations is formalized. Therefore, a comparison of each X-ray stress measurement method is expressed in the same Euler space, and a conversion method for each X-ray stress measurement method is presented.

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Elastizit�tsmessungen mit R�ntgenstrahlen

Cited by 32 publications

References 0 publications

Ultraprecise studies of the thermal expansion coefficient of diamond using backscattering x-ray diffraction

Ultraprecise studies of the thermal expansion coefficient of diamond using backscattering x-ray diffraction

X-ray scattering: a wonderful tool to probe lattice strains in materials with small dimensions

A Unified Representation for Fundamental Equations of Various X-Ray Stress Measurement Methods

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