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.

Danut Dragoi

Acta Crystallographica Section A Foundations and Advances

Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials.

The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial.

The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.

Acta Crystallographica Section A: Foundations and Advances publishes articles that report advances in the theory and practice of all areas of crystallography in the broadest sense. This includes not only traditional crystallography but also nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies, and the structure of strain and defects in materials.

The journal consists of two parts: a rapid-publication Advances section and the traditional Foundations section. Articles in the Advances section are of particularly high value and impact, receiving expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details can be found in the November 2013 Editorial.

The central themes of the journal focus on both experimental and theoretical studies of the properties and arrangements of atoms, ions, and molecules in condensed matter, whether periodic, quasiperiodic, or amorphous, ideal or real, as well as the theoretical and experimental aspects of various methods used to determine these properties and arrangements.

《Acta Crystallographica Section A: Foundations and Advances》期刊发表关于晶体学各个领域理论和实践进展的文章，涵盖传统晶体学、纳米晶体、元晶体、非晶材料、准晶体、同步辐射和XFEL研究、相干散射、衍射成像、时间分辨研究以及材料中应变和缺陷的结构等广泛主题。

该期刊分为两个部分：快速出版的“进展”部分和传统的“基础”部分。“进展”部分的文章具有特别高的价值和影响力，接受快速处理，并可能通过附带的科学评论文章和新闻稿进行突出展示。更多细节请参见2013年11月的社论。

该期刊的核心主题包括：对凝聚态物质中原子、离子和分子的性质及排列进行实验和理论研究，涵盖周期性、准周期性或非晶态的理想或实际情况；以及各种方法的理论和实验方面，以确定这些性质和排列。

Acta Crystallographica Section A: Foundations and Advances

The fundamentals of crystal orientation

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 and demonstrates the potential for new applications in industry and research.

Category	Quartile
材料科学	4
材料科学, 晶体学	3
材料科学, 化学综合	4

The fundamentals of crystal orientation

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