Аuthors
1*, 2**, 3, 3***, 3****1. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. National Research University of Electronic Technology, Bld. 1, Shokin Square, Zelenograd, Moscow, Russia, 124498
*e-mail: bardushkin@mail.ru
**e-mail: aakcht@gmail.com
***e-mail: 5ilova87@gmail.com
****e-mail: mfh.miet@gmail.com
Abstract
In this paper, mesoporous silicon-based structures with adsorbed water are considered in the temperature range 233–273 K. A mathematical model was developed for predicting the values of bulk density of the deformation energy caused by the difference in the thermal expansion coefficients of the heterogeneity elements in the materials studied, which occurs during the melting of water that froze in the mesopores. The model is based on the generalized singular approximation of random field theory and the concept of the stress concentration operator (fourth-rank tensor), which connects the average value of stresses throughout the material with its local values within a single inhomogeneity element. This approach takes into account the structure of the system based on the mesoporous silicon with sorbed water and the concentra-tion of inclusions and can be used to predict the melting temperature of ice confined inside the pores of a silicon matrix. Numerical calculations were performed using the developed model. The dependences of the bulk density of the deformation energy (local and average values) on the concentration of ice inclusions in the porous silicon matrix were studied. The calculation re-sults showed that the local elastic energy in the ice inclusions increases nonlinearly, while the orientation of the inclusions in the matrix does not affect the indicated energy characteristic sig-nificantly. An increase in the volumetric content of ice leads to a stabilization of the local elastic energy in the silicon matrix with a porosity of more than 40%. In this case, the average values of the bulk density of the deformation energy increase according to a law close to linear.
Keywords:
porous silicon, water, ice, matrix composite, thermoelastic properties, stress concentration tensor, bulk density of the deformation energy, modeling.References
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