Main Article Content


The application of Martin's ideas about ballistic elementary events (jumping inside  a crystal or atoms detachment from a crystal) to decomposition, to limited solubility, as well as to the  growth of strongly anisotropic structures in strongly nonequilibrium systems under the influence of  intense external factors is considered. The essence of these ideas is that external influences on the  system force atoms to make jumps and exchange places in the sites of the crystal lattice. The frequency  of  such  "ballistic"  jumps  (as  the  antithesis  to  "thermal"  jumps  that  are  associated  with  thermal  fluctuations at a given temperature) doesn`t depend on temperature, but depends on the intensity of  external action (say, the radiation flux density and energy of particles). These ideas had been first  introduced for irradiated systems, but later applied to ball milling, to severe plastic deformation, of  course,  taking  into  account  the  grinding  of  grains. In  this  paper, we  consider  the  application  of  Martin's ideas to two phenomena: 

(1) nucleation, growth and ripening of nanofibers and nanobands of metal oxides in aqueous  solutions under the action of intensive stirring, 

(2) formation- of solid solutions and intermediate phases of metals in the contact zone by pulsed  action. 

The time evolution of an ensemble of three-dimensional parallelepipeds is being considered in  the first part of the present article. For this purpose, we derived a system of differential equations for  the rate of change of each size, taking into account the balance of attachment and detachment fluxes.  Based on the solutions of these equations, the asymptotic values of the growth rates of average sizes  can be predicted. Graphs of dependences of average sizes on time for different intensities of mixing  for a symmetric case are presented.  

The  application  of  the  idea  of  ballistic  jumps  to  phase  formation  with  impulse  action  on  diffusion pairs is being briefly considered in the second part. The influence of external action on the  solubility of components for the simplest (mathematically) case is analyzed.

Article Details

Materials Physics
Author Biographies

А. М. Gusak

Doctor of physical and mathematical sciences, professor, Honored Worker of Science and Technology of Ukraine Leading Researcher, Laboratory of Mathematical Physics, Department of Physics of Educational-Scientific Institute of Informational and Eduational Technologies, The Bohdan Khmelnytsky National University of Cherkasy, Cherkasy, Ukraine

Ya. І. Huriev

Undergraduate student of physics, Department of Physics of Educational-Scientific
Institute of Informational and Eduational Technologies The Bohdan Khmelnytsky National University of Cherkasy, Cherkasy, Ukraine

D. S. Gertsricken

Senior researcher, G. V. Kurdyumov Institute for Metal Physics of the N.A.S. of Ukraine, Kyiv, Ukraine


Martin, G. (1984). Phase stability under irradiation: Ballistic effects. Physical Review B, 30(3), 1424.

Bellon, P., & Martin, G. (1988). Irradiation-induced formation of metastable phases: a master-equation approach. Physical Review B, 38(4), 2570.

Martin, G. (1998). Modelling materials driven far from equilibrium. Current Opinion in Solid State and Materials Science, 3(6), 552-557.

Enrique, R. A., & Bellon, P. (2004). Nonequilibrium fluctuations, effective temperature, and effective interactions driven by irradiation of alloys. Physical Review B, 70(22), 224106.

Vaks, V. G., & Kamyshenko, V. V. (1993). On the theory of open systems: statistical thermodynamics and decomposition type phase transitions for the model of an alloy under

irradiation. Physics Letters A, 177(3), 269-274.

Pochet, P., Tominez, E., Chaffron, L., & Martin, G. (1995). Order-disorder transformation in Fe-Al under ball milling. Physical Review B, 52(6), 4006.

Pochet, P., Bellon, P., Chaffron, L., & Martin, G. (1996). Phase transformations under ball milling: Theory versus experiment. In Materials Science Forum (Vol. 225, pp. 207-216). Trans Tech

Publications Ltd.

Mazilkin, A., Straumal, B., Kilmametov, A., Straumal, P., & Baretzky, B. (2019). Phase transformations induced by severe plastic deformation. Materials transactions, MF201938.

Straumal, B. B., Mazilkin, A. A., Protasova, S. G., Kilmametov, A. R., Druzhinin, A. V., & Baretzky, B. (2020). Phase Transformations in Nd–Fe–B-Based Alloys under High Pressure Torsion

at Different Temperatures. JETP Letters, 112(1), 37-44.

Straumal, B. B., Kilmametov, A. R., Mazilkin, I. A., Korneva, A., Zieba, P., & Baretzky, B. (2019). Phase Transformations in Copper—Tin Solid Solutions at High-Pressure Torsion. JETP Letters, 110(9), 624-628.

Zhang, J., Tang, Y., Lee, K., & Ouyang, M. (2010). Tailoring light–matter–spin interactions in colloidal hetero-nanostructures. Nature, 466(7302), 91-95.

Tang, Y., Zhang, Y., Malyi, O. I., Bucher, N., Xia, H., Xi, S., ... & Srinivasan, M. (2018). Identifying the origin and contribution of surface storage in TiO2 (B) nanotube electrode by in situ dynamic valence state monitoring. Advanced Materials, 30(33), 1802200.

Zhang, Y., Tang, Y., Deng, J., Leow, W. R., Xia, H., Zhu, Z., ... & Malyi, O. I. (2019). Correlating the Peukert’s constant with phase composition of electrode materials in fast lithiation

processes. ACS Materials Letters, 1(5), 519-525.

Rui, X., Tang, Y., Malyi, O. I., Gusak, A., Zhang, Y., Niu, Z., ... & Yan, Q. (2016). Ambient dissolution–recrystallization towards large-scale preparation of V2O5 nanobelts for high-energy battery applications. Nano Energy, 22, 583-593.

Tang, Y., Zhang, Y., Deng, J., Qi, D., Leow, W. R., Wei, J., ... & Chen, X. (2014). Unravelling the correlation between the aspect ratio of nanotubular structures and their electrochemical performance to achieve high‐rate and long‐life lithium‐ion batteries. Angewandte Chemie, 126(49), 13706-13710.

Gusak, A., Huriev, Y., Malyi, O. I., & Tang, Y. (2020). Elementary models of the “flux driven anti-ripening” during nanobelt growth. Physical Chemistry Chemical Physics, 22(17),


Gusak, A., Huriev, Y., & Schmelzer, J. W. (2020). Anisotropic Nucleation, Growth and Ripening under Stirring – A Phenomenological Model. Entropy, 22(11), 1254.

Gertzricken, D., Mazanko, V., & Falchenko, V. (1991). Pulse treatment and mass transfer in metals at low temperatures (Ympulsnaia obrabotka y massoperenos v metallakh pry nyzkykh temperaturakh. Kiev: Naukova dumka, 205, 3.

Mazanko, V., Gertzricken, D., Koval, Yu., Novomlynets, О., Mironov, D., Mironov, V., & Alekseeva, V. (2019). Features of phase formation during low-temperature martensitic transformations with explosive kinetics and impulsive deformations (Osobennosti fazoobrazovaniya pri nizkotemperaturnyih martensitnyih prevrascheniyah so vzryivnoy kinetikoy i impulsnyih deformatsiyah). 13th International Conference “Interaction of Radiation with Solids”, September 30 - October 3, 2019, Minsk, Belarus, з. 276-279.

Gertzricken, D. S., Kolenova- Zaporozhets, T. V., & Gusak, A. (2001). Possible mechanism of anomalous mass transfer under pulse loading. In Defect and Diffusion Forum (Vol. 194, pp. 1469-1476). Trans Tech Publications Ltd.

Gertzricken, D. S., Mazanko, V. F., Zaporozhets, T. V., & Gusak, A. (2005). Phase formation under pulse loading. In Defect and Diffusion Forum (Vol. 237, pp. 715-720). Trans Tech Publications Ltd.

Koval'chuk, A. O., Gertsriken, D. S., Gusak, A., & Mazanko, V. F. (2008). Models of mutual solubility increasing under the pulse loading. In Defect and Diffusion Forum (Vol. 277, pp. 69-74). Trans Tech Publications Ltd.