Interpreting oscillatory Bragg peak positions

Dragoi, Danut; Watkins, Thomas R.; Kozaczek, K. J.

doi:10.1107/s0021889896000684

Cited by 2 publications

(14 citation statements)

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“…As a comment, the values of ( ) tend to be close to the horizontal line parallel to the flat surface and cutting plane of two Si wafers, which have different orientations, (111) and (004), as used by Dragoi (1992). As we can see, the angle ' tends to be close to 3.5 on (111) Si wafers and about 1 on (004) Si wafers.…”

Section: Testing Equations With Data From the Literaturementioning

confidence: 56%

“…1 and 2 are the unknowns in the system of equations (1) and (2) found earlier by Dragoi (1992). Beyond the derivation of equations (1) and (2), given in Dragoi (1992), we mention that for a parallel family of planes of an object we need two parameters to characterize the surface orientation. We found that the two parameters to characterize the surface orientation of single crystals are and , the two unknowns of equations (1) and (2).…”

Section: Figurementioning

confidence: 97%

“…This formally means that the 1 variable, the experimental variable, is measured on the same scale as the variable. In the general case 1 and 2 are the angles measured between the incident X-ray beam S 0 and the cutting plane () when the maximum of reflection is reached (Dragoi, 1992). This definition holds for both oriented and disoriented crystals.…”

Section: Figurementioning

confidence: 99%

“…We can test equations (12) and (15) with data from the literature. For example, using the data in Table 4 of Dragoi (1992) gives the values for and ' shown in the last two columns of Table 1.…”

Section: Testing Equations With Data From the Literaturementioning

confidence: 99%

“…The variables in Table 1 are: ( ) is the Bragg angle, 1 ( ) is the first reflection reading on the scale when the 2 rotation is decoupled from (the detector is fixed), 2 ( ) is the second reflection reading on the scale, similar to 1 ( ), when the wafer/sample is rotated counter-clockwise 90 in its own plane, " ( ) is the chosen precision of the final solutions of equations (1) and (2) using a numerical method described by Dragoi (1992), n is the number of iterations, ( ) and ( ) are the solutions of equations (1) and (2), ( ) and ' ( ) are the values obtained with equations (15) and (12), respectively.…”

Section: Testing Equations With Data From the Literaturementioning

confidence: 99%

See 4 more Smart Citations

The fundamentals of crystal orientation

Dragoi¹

2018

Acta Cryst Sect A

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The method described in this paper improves the old methods of crystal orientation, applies new parametric equations for crystallography, and increases the precision and accuracy of measurements. The method applies to inorganic and organic crystals. A breakthrough in crystal orientation happened about 25 years ago when two equations dependent on the Bragg angle and an arbitrary direction in the crystal were developed. Unfortunately, they were analytically insolvable and their unique solution was found numerically. Finding the numerical solution of crystal orientation is challenging from a mathematical point of view. In these conditions the numerical solution was found using the Newton method. The Newton method required a specific programming that limits the full benefit of the method in the laboratory. In recent years, a new numerical technique called GRG (generalized reduced gradient), which can be run on many inexpensive computers, was found to be a good fit for these equations. The solutions that can be found with the GRG method are now completed with additional parametric equations; they are easy to use with computers in many laboratories. In this way, parametrization of nonlinear equations for X-ray crystal orientation determines the positions of a reference surface of the single crystal relative to its crystallographic system and to a goniometer setting with two perpendicular axes of rotation. This approach was successfully validated and checked for different Si wafers with (111) and (004) orientation. The paper shows an innovative approach through the parametric equations in conjunction with exact solutions found with a GRG subroutine. The results of the method demonstrate the potential for new applications in industry and research.

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Section: Testing Equations With Data From the Literaturementioning

confidence: 56%

Section: Figurementioning

confidence: 97%

Section: Figurementioning

confidence: 99%

Section: Testing Equations With Data From the Literaturementioning

confidence: 99%

Section: Testing Equations With Data From the Literaturementioning

confidence: 99%

See 3 more Smart Citations

The fundamentals of crystal orientation

Dragoi¹

2018

Acta Cryst Sect A

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Modeling of energy-dispersive X-ray diffraction for high-symmetry crystal orientation

Dragoi¹,

Dragoi²

2019

Acta Cryst Sect A

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The methods for X‐ray crystal orientation are rapidly evolving towards versatility, fewer goniometry measurements, automation, high accuracy and precision. One method that attracts a lot of attention is energy‐dispersive X‐ray diffraction (EDXRD) which is based on detecting reflections from crystallographic planes in a crystal at fixed angles of a parallel polychromatic X‐ray incident beam. In theory, an EDXRD peak can move in a diffraction pattern as a function of a crystallographic plane d‐spacing and its orientation relative to a fixed direction in space can change also. This is equivalent to the possibility of measuring the orientation of single crystals. The article provides a modeling for the EDXRD method whose main feature is the nonmoving crystal in the sense of traditional goniometry where the angle measurements of diffracting planes are a must. The article defines the equation of orientation for the method and shows the derivation in great detail. It is shown that the exact solutions of the equations can be obtained using the generalized reduced gradient method, a mathematical subroutine that is implemented in Excel software. The significance and scientific impact of the work are discussed along with the validated tested results.

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Interpreting oscillatory Bragg peak positions

Cited by 2 publications

References 0 publications

The fundamentals of crystal orientation

The fundamentals of crystal orientation

Modeling of energy-dispersive X-ray diffraction for high-symmetry crystal orientation

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