Calculation of the Phase State of the [N(CH3)4]2CUCL4 Crystals

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dc.citation.epage32
dc.citation.issue2
dc.citation.spage28
dc.contributor.affiliationIvan Franko National University of Lviv
dc.contributor.affiliationUkrainian Academy of Printing
dc.contributor.affiliationThe State Higher School of Technology and Economics in Jarosław
dc.contributor.authorСвелеба, Сергій
dc.contributor.authorКатеринчук, Іван
dc.contributor.authorКуньо, Іван
dc.contributor.authorКарпа, Іван
dc.contributor.authorСемотюк, Остап
dc.contributor.authorБригілевич, Володимир
dc.contributor.authorSveleba, Sergii
dc.contributor.authorKaterynchuk, Ivan
dc.contributor.authorKuno, Ivan
dc.contributor.authorKarpa, Ivan
dc.contributor.authorSemotiuk, Ostap
dc.contributor.authorBrygilevych, Volodymyr
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2021-03-29T10:32:00Z
dc.date.available2021-03-29T10:32:00Z
dc.date.created2020-02-24
dc.date.issued2020-02-24
dc.description.abstractРозрахунок просторових змін станів амплітуди й фази параметрів було виконано у середовищі Python з використанням бібліотек Skipy та JiTCODE. У криталах [N(CH3)4]2CuCl4 існує неспіврозмірна фаза I1 при малих значеннях величини дальньої взаємодії (T<0.6) та неспіврозмірна фаза I2 при T≥1.0. Це та ж сама неспіврозмірна фаза, хоча поведінка амплітудних та фазових функцій у ней відрізняється за різних умов, згаданих вище. При T = 0.6 ÷ 1.0, спостерігається співіснування цих двох фаз, що проявляється у відсутності аномальних змін q під час переходу від синусоїдного режиму модуляції неспіврозмірної фази до режиму солітона.
dc.description.abstractThe calculation of the spatial changes of the amplitude and phase of the order parameter was performed in the Python environment with the use of the Skipy and JiTCODE libraries. In [N(CH3)4]2CuCl4 crystals, there is an incommensurate phase I1 at the small values of the magnitude of long-range interaction (T<0.6) and an incommensurate phase I2 at T≥1.0. This is the same incommensurate phase, although the behavior of the amplitude and phase functions in it is different under the different conditions mentioned above. At T = 0.6 ÷ 1.0, the coexistence of these two phases is observed which is manifested in the absence of anomalous changes of q during the transition from the sinusoidal mode of IC modulation to the soliton regime.
dc.format.extent28-32
dc.format.pages5
dc.identifier.citationCalculation of the Phase State of the [N(CH3)4]2CUCL4 Crystals / Sergii Sveleba, Ivan Katerynchuk, Ivan Kuno, Ivan Karpa, Ostap Semotiuk, Volodymyr Brygilevych // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 2. — P. 28–32.
dc.identifier.citationenCalculation of the Phase State of the [N(CH3)4]2CUCL4 Crystals / Sergii Sveleba, Ivan Katerynchuk, Ivan Kuno, Ivan Karpa, Ostap Semotiuk, Volodymyr Brygilevych // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 2. — P. 28–32.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/56266
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofComputational Problems of Electrical Engineering, 2 (10), 2020
dc.relation.references[1] D. G. Sannikov and V. A.Golovko, “Unproven ferroelastic with a incommensurate phase in an external electric field”, Izv. USSR Academy of Sciences. Ser.phys, vol. 53, no. 7, pp. 1251–1253, 1989.
dc.relation.references[2] S. Sveleba, I.Katerynchuk, O.Semotyuk, and O. Fitsych, “Phase diagram of the crystal [N(CH3)4]2CuCl4 “, Visnyk of Lviv. Univ. The series is physical, vol. 34, pp. 30–37, 2001.
dc.relation.references[3] I. M. Kunyo, I. V. Karpa, S. A. Sveleba, I. M. Katerinchuk, Dimensional effects in dielectric crystals [N(CH3)4]2MeCl4 (Me = Cu, Zn, Mn, Co) with incommensurate phase: monograph, Lviv: Ivan Franko Lviv National University, p. 220, 2019.
dc.relation.references[4] A. Gerrit, “Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE”. Mathematical Software. Chaos. p. 28, 2018. 043116.
dc.relation.references[5] S. Sveleba, I. Katerynchuk, I. Kunyo, and I. Karpa, “Properties of Anisotropic Interaction of the Incommensurate Superstructure as Described by Dziloshinsky’s Invariant”, in Proc. X th International Scientific and Practical Conference “Electronics and Information Technologies” (ELIT-2018 , pp. 159–162, Lviv–Karpaty village, Ukraine August 30- September 2, 2018.
dc.relation.references[6] S. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, and Ja. Shmygelsky, “Peculiarities of the behavior of Lyapunov’s exponents from the symmetry of the thermodynamic potential described by the Lifshitz invariant”, Electronics and information technology, vol. 12. pp. 82–91, 2019.
dc.relation.references[7] S. A. Ktitorov, F. А. Pogorelov, and E. V. Charnaya, “Inhomogeneous states in thin films of an improperly disproportionate ferroelectric with a Lifshitz invariant”, Solid State Physics, vol. 51, Part. 8, pp. 1480–1482, 2009.
dc.relation.references[8] S. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, Ja. Shmygelsky. and O. Semotyjuk, “Peculiarities of the behavior of Lyapunov’s exponents under the condition of the existence of spatial domains of correlated motion of tetrahedral groups Electronics and information technologies”, vol. 13, pp. 108–117, 2020.
dc.relation.references[9] H. Z. Cummins, “Experimental Studies of structurally incommensurate crystal phases”, Physics Reports, vol. 185, no. 5,6, pp. 211–409, 1990.
dc.relation.referencesen[1] D. G. Sannikov and V. A.Golovko, "Unproven ferroelastic with a incommensurate phase in an external electric field", Izv. USSR Academy of Sciences. Ser.phys, vol. 53, no. 7, pp. 1251–1253, 1989.
dc.relation.referencesen[2] S. Sveleba, I.Katerynchuk, O.Semotyuk, and O. Fitsych, "Phase diagram of the crystal [N(CH3)4]2CuCl4 ", Visnyk of Lviv. Univ. The series is physical, vol. 34, pp. 30–37, 2001.
dc.relation.referencesen[3] I. M. Kunyo, I. V. Karpa, S. A. Sveleba, I. M. Katerinchuk, Dimensional effects in dielectric crystals [N(CH3)4]2MeCl4 (Me = Cu, Zn, Mn, Co) with incommensurate phase: monograph, Lviv: Ivan Franko Lviv National University, p. 220, 2019.
dc.relation.referencesen[4] A. Gerrit, "Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE". Mathematical Software. Chaos. p. 28, 2018. 043116.
dc.relation.referencesen[5] S. Sveleba, I. Katerynchuk, I. Kunyo, and I. Karpa, "Properties of Anisotropic Interaction of the Incommensurate Superstructure as Described by Dziloshinsky’s Invariant", in Proc. X th International Scientific and Practical Conference "Electronics and Information Technologies" (ELIT-2018 , pp. 159–162, Lviv–Karpaty village, Ukraine August 30- September 2, 2018.
dc.relation.referencesen[6] S. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, and Ja. Shmygelsky, "Peculiarities of the behavior of Lyapunov’s exponents from the symmetry of the thermodynamic potential described by the Lifshitz invariant", Electronics and information technology, vol. 12. pp. 82–91, 2019.
dc.relation.referencesen[7] S. A. Ktitorov, F. A. Pogorelov, and E. V. Charnaya, "Inhomogeneous states in thin films of an improperly disproportionate ferroelectric with a Lifshitz invariant", Solid State Physics, vol. 51, Part. 8, pp. 1480–1482, 2009.
dc.relation.referencesen[8] S. Sveleba, I. Katerynchuk, I. Kunyo, I. Karpa, Ja. Shmygelsky. and O. Semotyjuk, "Peculiarities of the behavior of Lyapunov’s exponents under the condition of the existence of spatial domains of correlated motion of tetrahedral groups Electronics and information technologies", vol. 13, pp. 108–117, 2020.
dc.relation.referencesen[9] H. Z. Cummins, "Experimental Studies of structurally incommensurate crystal phases", Physics Reports, vol. 185, no. 5,6, pp. 211–409, 1990.
dc.rights.holder© Національний університет “Львівська політехніка”, 2020
dc.subjectLyapunov’s exponents
dc.subjectthe incommensurate superstructure
dc.subjectsurface energy
dc.subjectbackward differentiation formula (BDF) method
dc.subjectPython
dc.titleCalculation of the Phase State of the [N(CH3)4]2CUCL4 Crystals
dc.title.alternativeРозрахунок фазних станів кристалів [N(CH3)4]2CUCL4
dc.typeArticle

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