THE POSSIBILITIES OF USING X-RAY DIFFRACTION ANALYSIS TO DETERMINE THE SIZE OF STRUCTURAL ELEMENTS IN NANOCRYSTALLINE MATERIALS

 

Tatiana V. Kislova

Senior Lecturer, Department of Forensic Science and Physical Materials Science,

Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

 

Konstantin O. Smirnov

Senior Lecturer, Department of Forensic Science and Physical Materials Science,

Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

 

Dmitriy S. Chuikin

General Director of Trubexpert LLC
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Generala Shumilova St, 29, 400057 Volgograd, Russian Federation

 

Abstract. X-ray diffraction analysis (XRD) is a fundamental method for studying the atomic structure of materials by analyzing diffraction patterns produced through the interaction of X-rays with matter. One of the key parameters determined via XRD is the crystal lattice parameter. Accurate measurement of this parameter is essential for understanding material properties such as solid solution formation, residual stresses, and thermal expansion coefficients. This article examines two primary approaches for lattice parameter determination: the difference method and the least squares method. The latter is preferred due to its superior handling of measurement errors and provision of more accurate results. Furthermore, the authors compare the packing coefficients for Body-Centered Cubic (BCC) and Hexagonal Close-Packed (HCP) lattices, demonstrating the advantages of the HCP structure in terms of atomic packing density. The study presents experimental results for a BCC niobium alloy and an HCP titanium alloy, along with theoretical data for HCP zinc oxide nanoparticles. The calculated packing coefficients were approximately 0.68 (68%) for the BCC lattice and 0.74 (74%) for the HCP lattice, confirming the higher atomic packing efficiency in the HCP structure. The conclusions recommend the use of the least squares method for reliable lattice parameter determination in nanocrystalline materials.

 

Key words: X-ray diffraction analysis, crystal lattice parameter, least squares method, body-centered cubic lattice, hexagonal close-packed lattice.

 

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