Change elastic felds of single crystals depending on the structure core breach
DOI:
https://doi.org/10.15587/1729-4061.2013.19183Keywords:
spent nuclear fuel storage facility, elastic waves, displacement fields, integral equations, Green’s functionAbstract
The paper is related to the issues of spent nuclear fuel (SNF) storage and radioactive waste (RW) disposal. One of the aspects of changing the structure of materials when exposed to the charged-particle beam was theoretically considered. This situation is realized in the walls of SNF storage facilities and rocks, surrounding the RW storage facilities. To solve the problem of describing the geometry of the breach core, distortions around it, integral equations of elastic waves were applied. The equations, similar to the proposed are widely used in the electrodynamics when solving the problems of electromagnetic wave propagation in waveguides and their scattering on inhomogeneities. The problem was solved by numerical methods. It was assumed that the defect had the ellipsoidal shape. The displacement fields around the core of breach cluster depending on the size of this core were found. The sizes of the core are used in the given form - the ratio of semi-axes. Single crystals of cubic structure were studied. Tungsten and gold were considered as real materials. The displacement fields on their own axes <010> and <001> were counted. The areas of breach core sizes, at which they are stable and steady, were defined. The side ratio, when the stress fields around the cluster of the breach core have such orientation, which leads to the compression and reduction of the central zone of the breach, was found. Further, this can cause the core collapse. Taking into account the needs of the waste storage, such breaches are preferable since they reduce the defect formation in the material, surrounding the source of ionizing radiation.
References
- Прохоренко, Е. М. Вывод интегральных уравнений, описывающих рассеяние упругих волн в анизотропной среде. [Текст] / Е. М. Прохоренко. // Восточно-европейский журнал передовых технологий. – 2012. – №2/10(56). – С. 52-55.
- Хижняк, Н. А. Интегральные уравнения макроскопической электродинамики. [Текст] / Н. А. Хижняк. – Київ: Наукова думка, 1986. – 280с.
- Mahan, D. Gerald. Many Particle Physics [Текст] / Gerald D. Mahan. – N.Y.: Plenum Publishers, 2000. – 784 p.
- Wu, S. Y. General Recursive Relation for the Calculation of the Local Green's Function. [Текст] / S. Y. Wu, J. A. Cocks, C. S. Jayanthi. // Physical Review B. – 1994. – №49. – Р.7957
- Тихонов, А. Н. Уравнения математической физики. [Текст] / А. Н. Тихонов, А. А. Самарский – М.: Наука, 1972. – 735с.
- Doniach, S. Green's Functions for Solid State Physicists. [Текст] / S. Doniach, E. H. Sondheimer. – N. Y: Imperial Colege Press, 2004. – 312 p.
- Phillips, P. Advanced Solid State Physics. [Текст] / P. Phillips. – Cambridge: University Press,2012. – 402 p.
- Чапля, Є. Я. Математичне моделювання дифузійних процесів у випадкових і регулярних структурах. [Текст] / Є. Я. Чапля, О. Ю. Чернуха. – Київ: Наукова думка, 2009. – 303с.
- Лифшиц, И. М. Построение тензора Грина для основного уравнения теории упругости в случае неограниченной упруго-анизотропной среды. [Текст] / И. М. Лифшиц, Л. Н. Розенцвейг. // ЖЭТФ. – 1947. – №17.– Т.9. – С. 783-791.
- Лифшиц, И. М. К теории упругих свойств поликристаллов. [Текст] / И. М. Лифшиц, Л. Н. Розенцвейг. // ЖЭТФ. – 1946. – №16.– Т.10. – С. 967-980.
- Муратов, Р. З. Потенциалы эллипсоида. [Текст] / Р. З. Муратов. – М.: Атомиздат, 1976. – 286с.
- Prokhorenko, E. M. (2012). Conclusion of integral equalizations, describing dispersion of resilient waves in an anisotropic environment. Eastern-Europeаn journal of Enterprise Technologies, 2/10(56), 52-55.
- Khizhnyak, N.A. (1986). Integral equations of macroscopic electrodynamics. Scientific thought, 280.
- Mahan, D.Gerald. (2000). Many Particle Physics. Plenum Publishers, 784.
- Wu, S.Y., Cocks, J.A., Jayanthi, C.S. (1994). General Recursive Relation for the Calculation of the Local Green's Function. Physical Review B., 49, 7957.
- Tikhonov, A. N., Samarskiy, A. A. (1972). Equalizations of mathematical physics, 735.
- Doniach, S., Sondheimer, E.H. (2004). Green's Functions for Solid State Physicists. Imperial Colege Press, 312.
- Phillips, P. (2012). Advanced Solid State Physics. Cambridge: University Press, 402.
- Chaplya, Ya. I., Chernukha, O. Yu. (2009). A mathematical design of diffusive processes is in casual and regular structures. Scientific thought, 303.
- Lifshits, I.M., Rozentsveyg, L.N. (1947). Construction of the Green's tensor for the basic equations of the theory of elasticity in the case of an unbounded elastically anisotropic media environment. JETF, №17, V.9, 783-791.
- Lifshits, I.M., Rozentsveyg, L.N. (1946). On the theory of elastic properties of polycrystal. JETF, №16, V.10, 967-980.
- Muratov, R.Z. (1976).Potentials of ellipsoid. Atomizdat, 286.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Евгений Михайлович Прохоренко
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.