On the photoelastic constants and the Brewster law for stressed tetragonal crystals

Rinaldi, D.; Davı́, Fabrizio; Montalto, Luigi

doi:10.1002/mma.4804

Cited by 15 publications

(25 citation statements)

References 19 publications

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“…The same issue was addressed in[Rinaldi et al 2018]; however, the results obtained there were related to specific cases of stress without the formal and more general treatment we give here; further, the treatment of cubic crystal was missing.…”

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confidence: 88%

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2020

Math. Mech. Compl. Sys.

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confidence: 88%

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2020

Math. Mech. Compl. Sys.

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“…In previous papers dedicated to the same problem [8,9], we obtained linear relations for n k (T) by a linearization procedure which involved the eigenvalues B k of B(T):…”

Section: Linearized Relationsmentioning

confidence: 99%

“…The typical solution of this problem is to first find the eigencouples (B k , u k ) of K(T), then take the square root of the inverse of (1.2) and, finally, if we need linearized relations, linearize the result about the unstressed state T = 0, like we did for instance in [8,9]. Such an approach has many limitations, since the possibility to find an explicit expression for the eigencouples (B k , u k ) (here u k is the eigenvector associated with B k ) depends heavily on the crystal symmetry trough M and on the stress tensor T: indeed, in [8,9] we considered a special state of stress. Moreover, for optically uniaxial materials the linearization about the unstressed state may not be well defined since the derivative of n k with respect to T may blow up for T → 0.…”

Section: Introductionmentioning

confidence: 99%

Exact and linearized refractive index stress-dependence in anisotropic photoelastic crystals

Davı́

2020

Proc. R. Soc. A.

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For the permittivity tensor of photoelastic anisotropic crystals, we obtain the exact nonlinear dependence on the Cauchy stress tensor. We obtain the same result for its square root, whose principal components, the crystal principal refractive index, are the starting point for any photoelastic analysis of transparent crystals. From these exact results we then obtain, in a totally general manner, the linearized expressions to within higher-order terms in the stress tensor for both the permittivity tensor and its square root. We finish by showing some relevant examples of both nonlinear and linearized relations for optically isotropic, uniaxial and biaxial crystals.

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“…where ρ is the mean ray between the ordinary and the extraordinary one, λ is the wavelength of the impinging light, θ 1 , θ 2 are the angles formed by the ray and optic axes, respectively, and ∆ the phase difference between the ordinary and extraordinary rays. These patterns are due to the structure of the crystals and are based on the theory of the Bertin surfaces [22][23][24] (Equation (2)), which are the virtual iso-delay surfaces that the light generates when crossing the sample (Figure 1d,e). As a matter of fact, Bertin's surfaces are the bijective relation between the light direction angle with the optic axes and a point in space and can be expressed as [19,20]:…”

Section: Conoscopic Fringe Patterns and Their Interpretationmentioning

confidence: 99%

Quality Control and Structural Assessment of Anisotropic Scintillating Crystals

et al. 2019

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Nowadays, radiation detectors based on scintillating crystals are used in many different fields of science like medicine, aerospace, high-energy physics, and security. The scintillating crystals are the core elements of these devices; by converting high-energy radiation into visible photons, they produce optical signals that can be detected and analyzed. Structural and surface conditions, defects, and residual stress states play a crucial role in their operating performance in terms of light production, transport, and extraction. Industrial production of such crystalline materials is a complex process that requires sensing, in-line and off-line, for material characterization and process control to properly tune the production parameters. Indeed, the scintillators’ quality must be accurately assessed during their manufacture in order to prevent malfunction and failures at each level of the chain, optimizing the production and utilization costs. This paper presents an overview of the techniques used, at various stages, across the crystal production process, to assess the quality and structural condition of anisotropic scintillating crystals. Different inspection techniques (XRD, SEM, EDX, and TEM) and the non-invasive photoelasticity-based methods for residual stress detection, such as laser conoscopy and sphenoscopy, are presented. The use of XRD, SEM, EDX, and TEM analytical methods offers detailed structural and morphological information. Conoscopy and sphenoscopy offer the advantages of fast and non-invasive measurement suitable for the inspection of the whole crystal quality. These techniques, based on different measurement methods and models, provide different information that can be cross-correlated to obtain a complete characterization of the scintillating crystals. Inspection methods will be analyzed and compared to the present state of the art.

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On the photoelastic constants and the Brewster law for stressed tetragonal crystals

Cited by 15 publications

References 19 publications

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Exact and linearized refractive index stress-dependence in anisotropic photoelastic crystals

Quality Control and Structural Assessment of Anisotropic Scintillating Crystals

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