GEOMETRIC CORRECTIONS FOR CALCULATING THE PAIR CORRELATION FUNCTION
https://doi.org/10.26583/vestnik.2025.3.9
EDN: VAOPKG
Abstract
The pair correlation function of inhomogeneities in samples is actively studied using small-angle scattering methods. Recently, it has become possible to determine this function from atom probe tomography (APT) data. This work examines the influence of the finite size and shape of a sample on the pair correlation function of inhomogeneities derived from APT data.
In a large cubic sample whose dimensions in all directions significantly exceed the characteristic correlation radius, the number of impurities near the sample boundaries can be considered much smaller than in the bulk. If this assumption is not fulfilled, a geometric factor arises, for which a general expression has been derived. The geometric meaning of this factor is the probability of a specific interpoint distance presence within the sample. For the case in which the sample is an elongated rectangular parallelepiped, an analytical expression for the geometric factor in terms of elementary functions is obtained.
The following model systems were considered: a completely uncorrelated distribution of centers, a simple cubic lattice, and a densely packed system of polydisperse hard spheres. These systems were chosen due to their differing degrees of spatial order. It is shown that accounting for the geometric factor yields the correct pair correlation function for the selected model systems of inhomogeneities.
Supporting agencies: The work was carried out within the framework of the state assignment of the National Research Center "Kurchatov Institute".
About the Authors
F. S. Dzheparov
National Research Center "Kurchatov Institute";
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
D. V. Lvov
National Research Center "Kurchatov Institute";
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
A. N. Tyulyusov
National Research Center "Kurchatov Institute";
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
J. Schmeissner
National Research Center "Kurchatov Institute";
National Research Nuclear University MEPhI
Russian Federation
Russian Federation
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Review
For citations:
Dzheparov F.S., Lvov D.V., Tyulyusov A.N., Schmeissner J. GEOMETRIC CORRECTIONS FOR CALCULATING THE PAIR CORRELATION FUNCTION. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(3):264-275. (In Russ.) https://doi.org/10.26583/vestnik.2025.3.9. EDN: VAOPKG
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