On the features of the first order phase transition in nanosized ferroelectrics

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Abstract

An estimate of the nucleus critical size and the phase transition temperature in nanosized ferroelectrics with a first order phase transition is given. The influence of the external electric field strength on the nucleus critical size and the phase transition temperature and the temperature 

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About the authors

V. N. Nechaev

Military Educational and Scientific Centre of the Air Force N.E. Zhukovsky and Y.A. Gagarin Air Force Academy (Voronezh) of the Ministry of Defense of the Russian Federation

Email: shandvit@rambler.ru
Russian Federation, Voronezh, 394064

A. V. Shuba

Military Educational and Scientific Centre of the Air Force N.E. Zhukovsky and Y.A. Gagarin Air Force Academy (Voronezh) of the Ministry of Defense of the Russian Federation

Author for correspondence.
Email: shandvit@rambler.ru
Russian Federation, Voronezh, 394064

References

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2. Fig. 1. Temperature dependence of the critical radius Rcr/a of the nucleus (line – piecewise parabolic approximation, points – numerical solution) (a) and dependence of the temperature Tp of the first-order phase transition in the smallest ferroelectric particle (Rp = Rcr) on the parameter at its boundary for Rp/a: 1 – 267; 2 – 233; 3 – 200; 4 – 167; 5 – 133 (b).

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3. Fig. 2. Temperature dependence of the critical radius Rcr/a of the nucleus at: 1 – 0; 2 – 1⋅10−5; 3 – 2∙10−5; 4 – 3∙10−5; 5 – 4∙10−5 (a) and dependence of the temperature Tp of the first-order phase transition on the external electric field strength at Rcr/a: 1 – 1000; 2 – 300; 3 – 250; 4 – 200; 5 – 185; 6 – 150; 7 – 130; 8 – 100 (b).

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4. Fig. 3. Dependences of the smallest critical size of the nucleus on the external electric field strength at αs / a: 1 – ∞; 2 – 1⋅104; 3 – 5∙103; 4 – 4∙103; 5 – 3∙103; 6 – 2∙103; 7 – 1⋅103 (a) and the threshold strength of the external electric field on the parameter at the particle boundary (b).

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5. Fig. 4. Dependences of the width ΔT of the temperature hysteresis on the external electric field strength for at Rcr/a: 1 – ∞; 2 – 667; 3 – 467; 4 – 333; 5 – 267; 6 – 200; 7 – 167 (a) and the critical field strength on the particle radius Rp/a for: 1 – ∞; 2 – 5∙103; 3 – 2∙103; 4 – 1⋅103; 5 – 500; 6 – 250; 7 – 100; 8 – 50; 9 – 10; 10 – 0 (b).

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