Simulation of Monolithic Silicon LLL Scanning X-Ray   Interferometer

Bianc, Giuseppe Bertolotto; Mana, Giovanni; Zosi, G.

doi:10.1143/jjap.36.5356

Cited by 2 publications

References 10 publications

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Linear Elasticity and Anisotropy

Barbero

Delfino

Palmisano

et al. 2014

Undergraduate Lecture Notes in Physics

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Notwithstanding the rigorous mathematical definition of crystal lattice given in Sect. 2.1.1, we have to admit that the concept itself of atomic planes in our context is rather fuzzy as it depends on several factors of influence. We would like to understand the effect of gravity on our experimental setup and will focus on the deformation of the atomic planes of our interest (in particular the {220} Bragg planes 1 ). The aim is to check in which way it depends upon the orientation of the atomic planes with respect to the macroscopic surfaces of the X-ray interferometer as well as upon the position of the contact points on an auxiliary platform. 2 To make this point clearer, we show in Fig. 3.1, where the normal to the (220) Bragg planes 3 is directed along the x axis, two possible configurations: at first sight we cannot decide which of the two, ([110] 4 To take a well-motivated decision, we have to solve the set of equations (3.4.4) which, being silicon anisotropic from the elastic point of view, depend on three 5 elastic constants (c 11 , c 12 , c 44 ). Before proceeding to solve the mentioned system of partial differential equations, we anticipate that, owing to the shape of the X-ray interferometer, their solution can be found only by means of a finite element package. 6 We now have to examine carefully the role of these constants; in fact, they are usually specified in a basis with coordinate axes aligned along 1 The symbol {220} indicates the family of (220), (220), (220), . . . Bragg planes. 2 The way a simple bar, for example the X-shaped platinum-iridium bar kept at Sèvres, deforms under the action of gravity depends on the so called Airy points [Phe96]. 3 The quantity d 220 , first cited in Chap. 1, Eq. (1.0.2.), is equivalent to d 220 . 4 In fact, in both cases the (220) planes are orthogonal to the x-axis, but the force of gravity is along

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Linear Elasticity and Anisotropy

Barbero

Delfino

Palmisano

et al. 2014

Undergraduate Lecture Notes in Physics

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Simulation of the thermoelastic behavior of an LLL x-ray interferometer

Bergamin

Cavagnero

Mana

et al. 2000

Review of Scientific Instruments

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In order to achieve the strictest tolerances required in the manufacturing of an x-ray interferometer of the triple Laue type (LLL) to be used in the accurate determination of the silicon lattice parameter, a new shape of the analyzer crystal is considered. The simulation of its behavior proves that, if specified elastic and thermal load upper limits are satisfied, the lattice plane deformations are compatible with a measurement uncertainty of a few parts in 10(9). (C) 2000 American Institute of Physics. [S0034-6748(00)02004-9]

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Simulation of Monolithic Silicon LLL Scanning X-Ray Interferometer

Cited by 2 publications

References 10 publications

Linear Elasticity and Anisotropy

Linear Elasticity and Anisotropy

Simulation of the thermoelastic behavior of an LLL x-ray interferometer

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