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The method is shown can be applied for both a macro- and a nanocrystal with given number of atoms and with a certain surface shape. To realize this method, the parameters of the pair interatomic Mie–Lennard-Jones potential were determined by the self-consistent method on the base of the thermoelastic properties of a crystal. The method was tested on macrocrystals of 15 single-component substances for eight fcc crystals (Cu, Ag, Au, Al, Ni, Rh, Pd, and Pt) and for seven bcc crystals (Fe, V, Nb, Ta, Cr, Mo, and W). The calculations have been carried out at various temperatures and showed good agreement with the experimental data. Using fcc-Rh as an example, the change in the surface properties with a decrease in the nanocrystal size are studied along isotherms 10 K, 300 K, and 2000 K. It is shown that, at high pressures and low temperatures, there is a region, where function σ increases in the case of isomorphous–isothermic–isobaric decrease in the nanocrystal size. This region disappears as temperature increases",{"EN":186,"VI":187},"Temperature and Pressure Dependences of the Surface Energy for a Macro- and Nanocrystal","Sự phụ thuộc nhiệt độ và áp suất của năng lượng bề mặt ở tinh thể vĩ mô và tinh thể nano",{"VOID":189},"Q. Jiang, H. M. Lu, and M. Zhao, J. Phys.: Condens. Matter 16, 521 (2004). https:\u002F\u002Fdoi.org\u002F10.1088\u002F0953-8984\u002F16\u002F4\u002F001\nJ. Wang and S. Q. Wang, Surf. Sci. 630, 216 (2014). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.susc.2014.08.017\nF. Aqra and A. Ayyad, Appl. Surf. Sci. 257, 6372 (2011). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.apsusc.2011.01.123\nS. Schönecker, X. Li, B. Johansson, S. K. Kwon, and L. Vitos, Sci. Rep. 5, 14860 (2015). https:\u002F\u002Fdoi.org\u002F10.1038\u002Fsrep14860\nR. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson, and S. P. Ong, Sci. Data 3, 1 (2016). https:\u002F\u002Fdoi.org\u002F10.1038\u002Fsdata.2016.80\nS. De Waele, K. Lejaeghere, M. 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Kraminin, J. Phys. Chem. Solids 152, 109964 (2021). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jpcs.2021.109964",{"VOID":191},"10.1134\u002FS1063783421090250","PUBLICATION","VERIFIED","2025-01-24T12:54:16.039+00:00","Auto Verify",[197],"VI","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002FS1063783421090250",[200],{"id":201,"sortIndex":19,"researcher":18,"roles":202,"affiliations":204,"properties":213,"displayName":215,"givenName":18,"familyName":18},"b47a2b16-e26b-4b5a-aeb3-0603c2cb6a61",[203],"AUTHOR",[205],{"id":206,"sortIndex":19,"affiliation":207,"properties":18},"7fe8d793-8450-4bd0-9a71-aa211964f66c",{"id":206,"createTime":18,"updateTime":18,"relativeEntities":208,"slug":18,"properties":209,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":212,"statistic":18},[],{"title":210},{"VI":211},"Institute for Geothermal and Renewable Energy, Branch of the Joint Institute for High Temperatures, Russian Academy of Sciences, Makhachkala, Russia",[],{"title":214},{"VI":215},"M. N. Magomedov","ARTICLE",{"url":198,"publisher":218,"properties":263},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":219,"slug":10,"properties":220,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":223,"manageAffiliations":232,"indexDatabases":243,"url":18,"thumbnailPath":18,"statistic":258,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":221,"title":222},{"VOID":13},{"EN":15},[224,228],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":225,"label":226,"description":227,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":229,"label":230,"description":231,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},[233,238],{"id":35,"createTime":18,"updateTime":18,"relativeEntities":234,"slug":18,"properties":235,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":237,"statistic":18},[],{"title":236},{"EN":39},[],{"id":42,"createTime":18,"updateTime":18,"relativeEntities":239,"slug":18,"properties":240,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":242,"statistic":18},[],{"title":241},{"EN":46},[],[244,251],{"id":50,"indexDatabase":245,"url":61,"indexYears":62,"academicFieldIds":250,"indexDatabaseRanking":18},{"id":52,"createTime":18,"updateTime":18,"relativeEntities":246,"label":247,"description":248,"key":58,"publicationTags":249,"standard":18},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64,65],{"id":67,"indexDatabase":252,"url":80,"indexYears":18,"academicFieldIds":257,"indexDatabaseRanking":18},{"id":69,"createTime":18,"updateTime":18,"relativeEntities":253,"label":254,"description":255,"key":76,"publicationTags":256,"standard":18},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":19,"impactFactorByYear":259,"i10Index":93,"i10IndexLast5Year":94,"totalPublication":95,"totalPublicationByYear":260,"totalCitation":121,"totalCitationByYear":261,"totalCitationPerPublication":148,"totalCitationPerPublicationByYear":262,"hindexLast5Year":171,"hindex":171},{"2012":85,"2013":86,"2014":86,"2015":87,"2016":85,"2017":88,"2018":88,"2019":89,"2020":90,"2021":86,"2022":91,"2023":92},{"1997":97,"1998":98,"1999":99,"2000":100,"2001":101,"2002":102,"2003":103,"2004":104,"2005":99,"2006":103,"2007":105,"2008":106,"2009":107,"2010":108,"2011":97,"2012":103,"2013":109,"2014":110,"2015":111,"2016":112,"2017":113,"2018":114,"2019":115,"2020":116,"2021":117,"2022":118,"2023":119,"2024":120},{"1997":123,"1998":124,"1999":125,"2000":126,"2001":127,"2002":111,"2003":128,"2004":129,"2005":130,"2006":131,"2007":132,"2008":133,"2009":134,"2010":135,"2011":136,"2012":137,"2013":138,"2014":139,"2015":140,"2016":141,"2017":142,"2018":143,"2019":144,"2020":145,"2021":146,"2022":147},{"1997":150,"1998":151,"1999":152,"2000":153,"2001":154,"2002":155,"2003":156,"2004":157,"2005":158,"2006":155,"2007":159,"2008":160,"2009":161,"2010":162,"2011":163,"2012":164,"2013":165,"2014":166,"2015":167,"2016":168,"2017":155,"2018":165,"2019":169,"2020":170,"2021":90,"2022":92},{"pages":264,"volume":266},{"VOID":265},"1465-1479",{"VOID":267},"63","2021-12-21",2021,[60,78],false,{"id":273,"createTime":274,"updateTime":275,"relativeEntities":276,"slug":277,"properties":278,"entityType":192,"verifyStatus":193,"verifyTime":288,"verifyNote":195,"languages":18,"translateLanguages":289,"viewCount":19,"primaryUrl":290,"fullTextUrl":18,"authors":291,"publicationType":216,"publisherRelationship":344,"citationCount":18,"citationInfo":18,"publishDate":395,"publishYear":396,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":397,"openAccess":18,"references":18,"isForceReanalyzing":271},"700b56ae-fa52-4812-91c2-aa2c1eced646","2024-01-18T20:13:03.419+00:00","2026-09-05T14:22:44.156+00:00",[],"Phonon-spectrum-of-lead-oxychloride-Pb3O2Cl2-Ab-initio-calculation-and-experiment",{"abstract":279,"title":281,"references":284,"doi":286},{"EN":280},"IR and Raman spectra of Pb3O2Cl2 in the range of 50–600 cm–1 have been detected for the first time. Ab initio calculations of the crystal structure and the phonon spectrum of Pb3O2Cl2 in the framework of LCAO approach have been performed by the Hartree–Fock method and in the framework of the density functional theory with the use of hybrid functionals. The results of calculations have made it possible to interpret the experimental vibration spectra and reveal silent modes, which do not manifest themselves in these spectra but influence the optical properties of the crystal.",{"EN":282,"VI":283},"Phonon spectrum of lead oxychloride Pb3O2Cl2: Ab initio calculation and experiment","Phổ phonon của chì oxyclorua Pb3O2Cl2: Tính toán ab initio và thực nghiệm",{"VOID":285},"M. B. Sigman, Jr. and B. A. Korgel, J. Am. Chem. Soc. 127, 10089 (2005).\nO. I. Siidra, S. V. Krivovichev, T. Armbruster, and W. Depmeier, Z. Kristallogr. 223, 204 (2008).\nH. Podsiadlo, J. Therm. Anal. 37, 613 (1991).\nI. I. Leonidov, V. P. Petrov, V. A. Chernyshev, A. E. Nikiforov, E. G. Vovkotrub, A. P. Tyutyunnik, and V. G. Zubkov, J. Phys. Chem. C 118, 8090 (2014).\nR. Dovesi, V. R. Saunders, C. Roetti, R. Orlando, C. M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N. M. Harrison, I. J. Bush, Ph. D’Arco, and M. Llunell, CRYSTAL09 User’s Manual (University of Torino, Torino, Italy, 2010).\nB. Metz, H. Stoll, and M. Dolg, J. Chem. Phys. 113, 2563 (2000).\nG. Sophia, P. Baranek, C. Sarrazin, M. Rerat, and R. Dovesi, Phase Transitions 81, 1069 (2013).\nP. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 270 (1985).\nM. Prencipe, Laurea Thesis (Laurea University of Applied Sciences, Vantaa, Finland, 1990), p. 87.\nJ. Baima, A. Erba, M. Rérat, R. Orlando, and R. Dovesi, J. Phys. Chem. C 117, 12864 (2013).\nS. Piskunov, E. Heifets, R. I. Eglitis, and G. Borstel, Comput. Mater. Sci. 29, 165 (2004).\nT. Bredow, K. Jug, and R. A. Evarestov, Phys. Status Solidi B 243, 10 (2006).\nH. Matsumoto, T. Miyake, and H. Iwahara, Mater. Res. 36, 1177 (2001).",{"VOID":287},"10.1134\u002FS1063783416020359","2024-12-29T14:21:36.235+00:00",[197],"https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002FS1063783416020359",[292,307,321],{"id":293,"sortIndex":19,"researcher":18,"roles":294,"affiliations":295,"properties":304,"displayName":306,"givenName":18,"familyName":18},"80ee649b-b9b6-4b5c-ae95-c5eb0b773d91",[203],[296],{"id":297,"sortIndex":19,"affiliation":298,"properties":18},"0af6366e-2000-45d6-b31e-aaec64290ab1",{"id":297,"createTime":18,"updateTime":18,"relativeEntities":299,"slug":18,"properties":300,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":303,"statistic":18},[],{"title":301},{"VI":302},"Ural Federal University, Yekaterinburg, Russia",[],{"title":305},{"VI":306},"D. O. Zakir’yanov",{"id":308,"sortIndex":309,"researcher":18,"roles":310,"affiliations":311,"properties":318,"displayName":320,"givenName":18,"familyName":18},"113dc3f8-d0fe-460e-992a-ba8aa3841b86",1,[203],[312],{"id":297,"sortIndex":19,"affiliation":313,"properties":18},{"id":297,"createTime":18,"updateTime":18,"relativeEntities":314,"slug":18,"properties":315,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":317,"statistic":18},[],{"title":316},{"VI":302},[],{"title":319},{"VI":320},"V. A. Chernyshev",{"id":322,"sortIndex":323,"researcher":18,"roles":324,"affiliations":325,"properties":341,"displayName":343,"givenName":18,"familyName":18},"b64e3a76-db62-4b70-869a-21ddf8ba51ba",2,[203],[326,332],{"id":297,"sortIndex":19,"affiliation":327,"properties":18},{"id":297,"createTime":18,"updateTime":18,"relativeEntities":328,"slug":18,"properties":329,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":331,"statistic":18},[],{"title":330},{"VI":302},[],{"id":333,"sortIndex":309,"affiliation":334,"properties":340},"0711937e-646e-4630-ab5c-638d80982f4a",{"id":333,"createTime":18,"updateTime":18,"relativeEntities":335,"slug":18,"properties":336,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":339,"statistic":18},[],{"title":337},{"VI":338},"Institute of High-Temperature Electrochemistry, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia",[],{},{"title":342},{"VI":343},"I. D. Zakir’yanova",{"url":290,"publisher":345,"properties":390},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":346,"slug":10,"properties":347,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":350,"manageAffiliations":359,"indexDatabases":370,"url":18,"thumbnailPath":18,"statistic":385,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"issn":348,"title":349},{"VOID":13},{"EN":15},[351,355],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":352,"label":353,"description":354,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":356,"label":357,"description":358,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},[360,365],{"id":35,"createTime":18,"updateTime":18,"relativeEntities":361,"slug":18,"properties":362,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":364,"statistic":18},[],{"title":363},{"EN":39},[],{"id":42,"createTime":18,"updateTime":18,"relativeEntities":366,"slug":18,"properties":367,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":369,"statistic":18},[],{"title":368},{"EN":46},[],[371,378],{"id":50,"indexDatabase":372,"url":61,"indexYears":62,"academicFieldIds":377,"indexDatabaseRanking":18},{"id":52,"createTime":18,"updateTime":18,"relativeEntities":373,"label":374,"description":375,"key":58,"publicationTags":376,"standard":18},[],{"EN":55,"VI":55},{"EN":55,"VI":57},[60],[64,65],{"id":67,"indexDatabase":379,"url":80,"indexYears":18,"academicFieldIds":384,"indexDatabaseRanking":18},{"id":69,"createTime":18,"updateTime":18,"relativeEntities":380,"label":381,"description":382,"key":76,"publicationTags":383,"standard":18},[],{"EN":72,"VI":72},{"EN":74,"VI":75},[78,79],[82],{"impactFactor":19,"impactFactorByYear":386,"i10Index":93,"i10IndexLast5Year":94,"totalPublication":95,"totalPublicationByYear":387,"totalCitation":121,"totalCitationByYear":388,"totalCitationPerPublication":148,"totalCitationPerPublicationByYear":389,"hindexLast5Year":171,"hindex":171},{"2012":85,"2013":86,"2014":86,"2015":87,"2016":85,"2017":88,"2018":88,"2019":89,"2020":90,"2021":86,"2022":91,"2023":92},{"1997":97,"1998":98,"1999":99,"2000":100,"2001":101,"2002":102,"2003":103,"2004":104,"2005":99,"2006":103,"2007":105,"2008":106,"2009":107,"2010":108,"2011":97,"2012":103,"2013":109,"2014":110,"2015":111,"2016":112,"2017":113,"2018":114,"2019":115,"2020":116,"2021":117,"2022":118,"2023":119,"2024":120},{"1997":123,"1998":124,"1999":125,"2000":126,"2001":127,"2002":111,"2003":128,"2004":129,"2005":130,"2006":131,"2007":132,"2008":133,"2009":134,"2010":135,"2011":136,"2012":137,"2013":138,"2014":139,"2015":140,"2016":141,"2017":142,"2018":143,"2019":144,"2020":145,"2021":146,"2022":147},{"1997":150,"1998":151,"1999":152,"2000":153,"2001":154,"2002":155,"2003":156,"2004":157,"2005":158,"2006":155,"2007":159,"2008":160,"2009":161,"2010":162,"2011":163,"2012":164,"2013":165,"2014":166,"2015":167,"2016":168,"2017":155,"2018":165,"2019":169,"2020":170,"2021":90,"2022":92},{"pages":391,"volume":393},{"VOID":392},"325-332",{"VOID":394},"58","2016-02-18",2016,[60,78],{"id":399,"createTime":400,"updateTime":401,"relativeEntities":402,"slug":403,"properties":404,"entityType":192,"verifyStatus":193,"verifyTime":414,"verifyNote":195,"languages":18,"translateLanguages":415,"viewCount":19,"primaryUrl":416,"fullTextUrl":18,"authors":417,"publicationType":216,"publisherRelationship":472,"citationCount":18,"citationInfo":18,"publishDate":523,"publishYear":524,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":525,"openAccess":18,"references":18,"isForceReanalyzing":271},"10028a3b-a324-43e8-9661-073ec79ea808","2024-01-13T00:23:33.262+00:00","2026-09-05T02:12:14.554+00:00",[],"Lattice-Structure-and-Dynamics-of-Two-Layer-Heterostructures-of-Barium-Strontium-Titanate-and-Layered-Bismuth-Titanate-of-Various-Thicknesses-on-a-Magnesium-Oxide-Substrate",{"abstract":405,"title":407,"references":410,"doi":412},{"EN":406},"The lattice structure and dynamics of single-crystal Bi4Ti3O12 with a thickness from 4 to 430 nm on a (001)MgO substrate with a previously deposited Ba0.4Sr0.6TiO3 sublayer (4 nm) have been studied. The two-layer structures were prepared by radio-frequency sputtering of ceramic targets of the corresponding compositions. The X-ray diffraction studies performed at room temperature have shown that, in this heterostructure, axis c of the Bi4Ti3O12 unit cell is perpendicular to the substrate, and direction [100] has an angle of ±45° to the [100]MgO direction. At the thicknesses of Bi4Ti3O12 to ~40 nm, the film unit cell is compressed in the direction of a normal to the substrate plane and extended in the conjugate plane, and the sign of the deformation is changed at large thicknesses. It is found that the phonon mode frequency in the Bi4Ti3O12 film shift and additional peaks appear in the Raman spectra, which demonstrates an increase in the degree of monoclinic distortion of the film crystal structure as compared to the crystal structure.",{"EN":408,"VI":409},"Lattice Structure and Dynamics of Two-Layer Heterostructures of Barium–Strontium Titanate and Layered Bismuth Titanate of Various Thicknesses on a Magnesium Oxide Substrate","Cấu trúc và động lực học mạng tinh thể của các dị cấu trúc hai lớp bari–stronti titanat và bismuth titanat phân lớp có các độ dày khác nhau trên đế magie oxit",{"VOID":411},"C. D. Theis, J. Yeh, D. G. Schlom, M. E. Hawley, G. W. Brown, J. C. Jiang, and X. Q. Pan, Appl. Phys. Lett. 72, 2817 (1998).\nG. W. Brown, M. E. Hawley, C. D. Theis, J. Yeh, and D. G. Schlom, Thin Solid Films 357, 13 (1999).\nW. Jo, H-J. Cho, T. W. Noh, B. I. Kim, D.-Y. Kim, Z. G. Khim, and S. Kwun, Appl. Phys. Lett. 63, 2198 (1993).\nK. Hwang and Y. Park, J. Mater. Res. 16, 2519 (2001).\nW. Jo, G-C. Yi, T. W. Noh, D-K. Ko, Y. S. Cho, and S.-I. Kwun, Appl. Phys. Lett. 61, 1526 (1992).\nB. H. Park, B. S. Kang, S. D. Bu, T. W. Noh, J. Lee, and W. Joe, Nature (London, U.K.) 401, 682 (1999).\nO. Khorkhordin, Chia-Pin Yeh, B. Kalkofen, and E. Burte, J. Cryst. Proc. Technol. 5, 49 (2015).\nD. H. Kuo and K. C. Chiang, Thin Solid Films 516, 5985 (2008).\nC. D. Theis, J. Yeh, D. G. Schlom, M. E. Hawley, G. W. Brown, J. C. Jiang, and X. Q. Pan, Appl. Phys. Lett. 72, 2817 (1998).\nC. M. Bedoya-Hincapie, E. R. Parra, J. J. Olaya-Florez, J. E. Alfonso, F. J. Flores-Ruiz, and F. J. Espinoza-Beltran, Ceram. Int. 40, 11831 (2014).\nA. S. Anokhin, S. V. Biryukov, Yu. I. Golovko, and V. M. Mukhortov, Phys. Solid State 61, 139 (2019).\nQ. Zhou, B. J. Kennedy, and C. J. Howard, Chem. Mater. 15, 5025 (2003).\nX. Q. Pan, J. C. Jiang, C. D. Theis, and D. G. Schlom, Appl. Phys. Lett. 83, 2315 (2003).\nK. Liang, Y. Qi, and C. Lu, J. Raman Spectrosc. 40, 2088 (2009).\nP. R. Graves, G. Hua, S. Myhra, and J. G. Thompson, J. Solid State Chem. 114, 112 (1995).\nS. Kojima and S. Shimada, Phys. B (Amsterdam, Neth.) 219–220, 617 (1996).\nM. Osada, M. Tada, M. Kakihana, Y. Noguchi, and M. Miyayama, Mater. Sci. Eng. B Solid-State Mater. Adv. Technol. 120, 95 (2005).\nY. L. Du, M. S. Zhang, Q. Chen, and Z. Yin, Appl. Phys. A 76, 1099 (2003).\nA. V. Knyazev, M. Mączka, O. V. Krasheninnikova, M. Ptak, E. V. Syrov, and M. Trzebiatowska-Gussowska, Mater. Chem. Phys. 204, 8 (2018).\nM. K. Jeon, Y.-I. Kim, S.-H. Nahm, and S. I. Woo, J. Phys. D 39, 5080 (2006).",{"VOID":413},"10.1134\u002FS1063783419110039","2025-01-06T09:22:11.709+00:00",[197],"https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002FS1063783419110039",[418,433,446,459],{"id":419,"sortIndex":19,"researcher":18,"roles":420,"affiliations":421,"properties":430,"displayName":432,"givenName":18,"familyName":18},"08798c17-0b88-4545-9d9c-129330922146",[203],[422],{"id":423,"sortIndex":19,"affiliation":424,"properties":18},"14c21308-0e87-41aa-807d-4eab437d2d82",{"id":423,"createTime":18,"updateTime":18,"relativeEntities":425,"slug":18,"properties":426,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":429,"statistic":18},[],{"title":427},{"EN":428},"Federal Research Center Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, Russia",[],{"title":431},{"VI":432},"A. S. Anokhin",{"id":434,"sortIndex":309,"researcher":18,"roles":435,"affiliations":436,"properties":443,"displayName":445,"givenName":18,"familyName":18},"1c9eea07-1ca8-43a4-b0e9-6454e9aaa74f",[203],[437],{"id":423,"sortIndex":19,"affiliation":438,"properties":18},{"id":423,"createTime":18,"updateTime":18,"relativeEntities":439,"slug":18,"properties":440,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":442,"statistic":18},[],{"title":441},{"EN":428},[],{"title":444},{"VI":445},"Yu. I. 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I. Blokhintsev, Quantum Mechanics (Reidel, Dordrecht, The Netherlands, 1964; Nauka, Moscow, 1983).",{"doi":883},"10.1007\u002F978-94-010-9711-6",{"id":18,"text":885,"url":18,"identifiers":886},"V. I. Arnol’d, Supplementary Chapters of the Theory of Ordinary Differential Equations (Nauka, Moscow, 1978) [in Russian].",{},{"id":18,"text":888,"url":18,"identifiers":889},"P. Erdos and R. C. Herndon, Adv. Phys. 31, 65 (1982).",{"doi":890},"10.1080\u002F00018738200101358",{"id":18,"text":892,"url":18,"identifiers":893},"S. Raimes, Many-Electron Theory (Mir, Moscow, 1967; North-Holland, Amsterdam, 1972).",{},{"id":18,"text":895,"url":18,"identifiers":896},"D. S. Fisher and P. A. Lee, Phys. Rev. B: Condens. Matter 23, 6851 (1981).",{"doi":897},"10.1103\u002FPhysRevB.23.6851",{"id":18,"text":899,"url":18,"identifiers":900},"V. I. Klyatskin, Embedding Method in the Theory of Wave Propagation (Nauka, Moscow, 1986) [in Russian].",{},{"id":18,"text":902,"url":18,"identifiers":903},"V. A. Ambartsumyan, Dokl. Akad. Nauk SSSR 38, 76 (1943).",{},{"id":18,"text":905,"url":18,"identifiers":906},"G. I. Babkin and V. I. Klyatskin, Wave Motion 4, 327 (1982).",{"doi":907},"10.1016\u002F0165-2125(82)90002-6",{"id":18,"text":909,"url":18,"identifiers":910},"V. V. Babikov, Method of Phase Functions in Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].",{},{"id":18,"text":912,"url":18,"identifiers":913},"D. M. Sedrakyan and A. Zh. Khachatryan, Dokl. Nats. Akad. Nauk Arm. 98, 301 (1998).",{},{"id":18,"text":915,"url":18,"identifiers":916},"D. M. Sedrakian and A. Zh. Khachatrian, Phys. Lett. A 265, 294 (2000).",{"doi":917},"10.1016\u002FS0375-9601(99)00903-2",{"id":18,"text":919,"url":18,"identifiers":920},"M. V. Fedoryuk, Ordinary Differential Equations (Nauka, Moscow, 1985) [in Russian].",{},{"id":922,"createTime":923,"updateTime":924,"relativeEntities":925,"slug":926,"properties":927,"entityType":192,"verifyStatus":193,"verifyTime":936,"verifyNote":195,"languages":18,"translateLanguages":18,"viewCount":309,"primaryUrl":937,"fullTextUrl":18,"authors":938,"publicationType":216,"publisherRelationship":1001,"citationCount":1052,"citationInfo":1053,"publishDate":1056,"publishYear":1054,"citationAnalyzeStatus":629,"lastCitationAnalyze":924,"indexDatabases":1057,"openAccess":18,"references":1058,"isForceReanalyzing":271},"4abf1602-9bfd-4249-8029-cb2fb1db0ec1","2024-02-19T16:58:59.573+00:00","2026-08-18T01:40:36.618+00:00",[],"Description-of-ferroelectric-phase-transitions-in-solid-solutions-of-relaxors-in-the-framework-of-the-random-field-theory",{"abstract":928,"title":930,"gsPaper":932,"doi":934},{"EN":929},"A model based on the random-field theory is proposed for calculating the properties of solid solutions of ferroelectric relaxors. The electric dipoles randomly distributed in the system are treated as sources of random fields. The random field distribution function is calculated taking into account the contribution of nonlinear and correlation effects and the differences in the dipole orientations for different solid solution components. The dependence of the phase transition temperature T\n\n                  c\n                 on the concentration of solid solution components is analyzed. Numerical calculations are performed for the lead scandoniobate and lead scandotantalate solid solutions (PbSc1\u002F2Nb1\u002F2O3)1−x\n(PbSc1\u002F2Ta1\u002F2O3)x with different degrees of ordering and the lead magnoniobate and lead titanate solid solution (PbMg1\u002F3Nb2\u002F3O3)1−x\n(PbTiO3)x. It is shown that the higher transition temperature for more disordered solid solutions of the composition (PbSc1\u002F2Nb1\u002F2O3)1−x\n(PbSc1\u002F2Ta1\u002F2O3)x in the range 0≤x\u003C0.5 is associated with the larger nonlinearity coefficient for PbSc1\u002F2Nb1\u002F2O3 as compared to that for PbSc1\u002F2Ta1\u002F2O3. The theory provides a means for calculating the region of the coexistence of the phases with different symmetry groups in the temperature-composition phase diagram of the (PbMg1\u002F3Nb2\u002F3O3)1−x\n(PbTiO3) solid solution. Numerical calculations with the use of the fitting parameters obtained from the known transition temperatures T\n\n                  c\n                 for the solid solution components adequately describe the experimental phase diagrams for the aforementioned solid solutions of ferroelectric relaxors.",{"EN":931},"Description of ferroelectric phase transitions in solid solutions of relaxors in the framework of the random-field theory",{"VOID":933},"[\"12669968360651487751\"]",{"VOID":935},"10.1134\u002F1.1386469","2024-04-29T17:51:49.248+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002F1.1386469",[939,956,969,986],{"id":940,"sortIndex":19,"researcher":18,"roles":941,"affiliations":942,"properties":951,"displayName":953,"givenName":18,"familyName":18},"646405e7-cd31-4ea9-a555-1a74f4b20a4f",[203],[943],{"id":944,"sortIndex":19,"affiliation":945,"properties":18},"f015111b-2e99-417f-9814-b79c17472b8f",{"id":944,"createTime":18,"updateTime":18,"relativeEntities":946,"slug":18,"properties":947,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":950,"statistic":18},[],{"title":948},{"VI":949},"Frantsevich Institute of Materials Science Problems, National Academy of Sciences of Ukraine, Kiev, Ukraine",[],{"title":952,"gsAuthor":954},{"VI":953},"M. 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E. Cross, Ferroelectrics 150, 305 (1994).",{},{"id":18,"text":1063,"url":18,"identifiers":1064},"M. D. Glinchuk and V. A. Stephanovich, J. Appl. Phys. 85(10), 1722 (1999).",{},{"id":18,"text":1066,"url":18,"identifiers":1067},"M. D. Glinchuk and V. A. Stephanovich, J. Phys.: Condens. Matter 10, 11081 (1998).",{},{"id":18,"text":1069,"url":18,"identifiers":1070},"M. D. Glinchuk, V. A. Stephanovich, and B. Hilczer, J. Appl. Phys. (in press).",{},{"id":18,"text":1072,"url":18,"identifiers":1073},"M. D. Glinchuk and R. Farhi, J. Phys.: Condens. Matter 8, 6985 (1996).",{},{"id":18,"text":1075,"url":18,"identifiers":1076},"E. V. Colla, N. K. Yushin, and D. Viehland, J. Appl. Phys. 83(15), 3298 (1998).",{},{"id":18,"text":1078,"url":18,"identifiers":1079},"S. E. Park and T. R. Shrout, J. Appl. Phys. 82(4), 1804 (1997).",{},{"id":18,"text":1081,"url":18,"identifiers":1082},"C. A. Randal, A. S. Bhalla, T. R. Shrout, and L. E. Cross, J. Mater. Res. 5, 829 (1990).",{},{"id":18,"text":1084,"url":18,"identifiers":1085},"N. K. Yushin, E. I. Smirnova, E. A. Tarakanov, and R. Sommer, Fiz. Tverd. Tela (St. Petersburg) 36(2), 1321 (1994) [Phys. Solid State 36, 721 (1994)].",{},{"id":18,"text":1087,"url":18,"identifiers":1088},"V. Eremkin, V. Smotrakov, E. Gagarina, and I. Raevski, J. Korean Phys. Soc. 32(6), S1597 (1998).",{},{"id":18,"text":1090,"url":18,"identifiers":1091},"N. Setter and L. E. Cross, J. Appl. Phys. 51(6), 4356 (1980).",{},{"id":18,"text":1093,"url":18,"identifiers":1094},"N. Setter and L. E. Cross, Ferroelectrics 37, 551 (1981).",{},{"id":18,"text":1096,"url":18,"identifiers":1097},"M. D. Glinchuk, V. A. Stephanovich, B. Hilczer, et al., J. Phys.: Condens. Matter 11, 6263 (1999).",{},{"id":18,"text":1099,"url":18,"identifiers":1100},"M. D. Glinchuk and V. A. Stephanovich, J. Phys.: Condens. Matter 6, 6317 (1994).",{},{"id":18,"text":1102,"url":18,"identifiers":1103},"M. D. Glinchuk, V. A. Stephanovich, and R. Farhi, J. Phys.: Condens. Matter 9, 10237 (1997).",{},{"id":18,"text":1105,"url":18,"identifiers":1106},"M. Sepliarsky, M. G. Stachiotti, and R. L. Migoni, Phys. Rev. B 52(4), 4044 (1995).",{},{"id":18,"text":1108,"url":18,"identifiers":1109},"O. I. Korshunov, P. A. Markovin, and R. V. Pisarev, Ferroelectr. Lett. Sect. 13, 137 (1992).",{},{"id":18,"text":1066,"url":18,"identifiers":18},{"id":1112,"createTime":1113,"updateTime":1114,"relativeEntities":1115,"slug":1116,"properties":1117,"entityType":192,"verifyStatus":193,"verifyTime":1126,"verifyNote":195,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1127,"fullTextUrl":18,"authors":1128,"publicationType":216,"publisherRelationship":1157,"citationCount":1208,"citationInfo":1209,"publishDate":1212,"publishYear":1210,"citationAnalyzeStatus":629,"lastCitationAnalyze":1213,"indexDatabases":1214,"openAccess":18,"references":1215,"isForceReanalyzing":271},"5cf342c1-5b0f-47e3-8074-7b17523ccd5d","2024-01-12T08:19:34.982+00:00","2026-08-17T06:21:11.345+00:00",[],"Temperature-dependence-of-the-establishment-time-of-the-vacancy-equilibrium-in-simple-crystals",{"abstract":1118,"title":1120,"gsPaper":1122,"doi":1124},{"EN":1119},"Establishment times of vacancy equilibrium t* in spherical samples of simple crystals of radius R due to thermal motion of atoms during the process maximally approached to the equilibrium upon lowering the temperature from the melting point to the current value T have been calculated. It has been found that (i) with a decrease in T, the equilibrium time t* exponentially increases, and (ii) with a decrease in the sample radius R, the time t* exponentially decreases. The general tendency toward increase in the time t* due to lowering the temperature overlaps the effect of decreasing sample size R; therefore, for any small samples, the temperature range T \u003C T*, for which the diffusion process is almost frozen, always exists.",{"EN":1121},"Temperature dependence of the establishment time of the vacancy equilibrium in simple crystals",{"VOID":1123},"[\"6301721593350130651\"]",{"VOID":1125},"10.1134\u002FS1063783414020292","2024-05-03T16:13:57.438+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002FS1063783414020292",[1129,1144],{"id":1130,"sortIndex":19,"researcher":18,"roles":1131,"affiliations":1132,"properties":1141,"displayName":1143,"givenName":18,"familyName":18},"4c62cecd-6bda-44f8-b842-df9623ac3437",[203],[1133],{"id":1134,"sortIndex":19,"affiliation":1135,"properties":18},"8a950937-56ca-4463-9c44-24487fbb3cd2",{"id":1134,"createTime":18,"updateTime":18,"relativeEntities":1136,"slug":18,"properties":1137,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1140,"statistic":18},[],{"title":1138},{"VI":1139},"Karpov Scientific and Research Institute of Physical Chemistry, Moscow, Russia",[],{"title":1142},{"VI":1143},"Yu. 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Lett. 49 (2023). https:\u002F\u002Fdoi.org\u002F10.1134\u002FS1063785023010042",{"doi":1482},"10.1134\u002FS1063785023010042",{"id":1484,"createTime":1485,"updateTime":1486,"relativeEntities":1487,"slug":1488,"properties":1489,"entityType":192,"verifyStatus":193,"verifyTime":1500,"verifyNote":195,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1501,"fullTextUrl":18,"authors":1502,"publicationType":216,"publisherRelationship":1572,"citationCount":1623,"citationInfo":1624,"publishDate":1627,"publishYear":1625,"citationAnalyzeStatus":629,"lastCitationAnalyze":1628,"indexDatabases":1629,"openAccess":18,"references":18,"isForceReanalyzing":271},"1a3a1342-4c31-4691-8142-e79e67f0140b","2024-01-25T04:02:36.770+00:00","2026-08-16T22:12:39.097+00:00",[],"Phase-states-and-dielectric-properties-of-sodium-potassium-niobate-solid-solutions",{"abstract":1490,"title":1492,"gsPaper":1494,"references":1496,"doi":1498},{"EN":1491},"The temperature dependence of dielectric constant ɛ for single crystals of Na1−x\nKxNbO3 (0.04≲x≲0.15) is studied for the first time. From the shape of the ɛ(T) anomalies corresponding to rotational phase transitions, the type of interaction between the order parameters and the polarization is determined. A phenomenological model is developed which adequately describes the experimentally observed sequence of high-temperature (T>300°C) phase transitions, the dielectric anomalies associated with these transitions, and the changes in the phase states under the action of external factors (pressure, electric field).",{"EN":1493},"Phase states and dielectric properties of sodium-potassium niobate solid solutions",{"VOID":1495},"[\"15716356277665150492\"]",{"VOID":1497},"H. Megaw, Ferroelectrics 7(1–2), 87 (1974).\nL. E. Cross and B. J. Nicholson, Philos. Mag. 46(376), 453 (1955).\nR. Ishida and G. Honjo, J. Phys. Jpn. 34(11), 1279 (1973).\nK. S. Aleksandrov, A. T. Anistratov, B. V. Beznosikov, and N. V. Fedoseeva, Phase Transitions in Crystals of ABX 3 Halogen Compounds (Nauka, Novosibirsk, 1981).\nG. A. Smolenskii, V. A. Bokov, V. A. Isupov, N. N. Krainik, R. E. Pasynkov, A. I. Sokolov, and N. K. Yushin, The Physics of Ferroelectric Phenomena (Nauka, Leningrad, 1985).\nO. V. Kovalev, Irreducible Representations of Space Groups (Akad. Nauk Ukr. SSR, Kiev, 1961).\nM. Ahtee and A. M. Glazer, Acta Crystallogr. A 32(3), 434 (1976).\nM. Ahtee and A. W. Hewat, Acta Crystallogr. A 34(2), 309 (1978).\nC. N. W. Darlington, Philos. Mag. 31(5), 1159 (1975).\nI. P. Raevskii, M. P. Ivliev, L. A. Reznichenko, et al., Zh. Tekh. Fiz. 72(6), 120 (2002) [Tech. Phys. 47, 772 (2002)].\nI. P. Raevskii, L. A. Reznichenko, M. P. Ivliev, et al., Kristallografiya 48(3), 531 (2003) [Crystallogr. Rep. 48, 486 (2003)].\nC. N. W. Darlington and K. S. Knigth, Acta Crystallogr. B 55(1), 24 (1999).\nV. V. Eremkin, V. G. Smotrakov, and E. G. Fesenko, Fiz. Tverd. Tela (Leningrad) 31(6), 156 (1989) [Sov. Phys. Solid State 31, 1002 (1989)].\nT. Hidaka, Phys. Rev. B 17(11), 4363 (1978).\nI. P. Raevskii, L. A. Reznichenko, and A. N. Kalitvanskii, Zh. Tekh. Fiz. 50(9), 1983 (1980) [Sov. Phys. Tech. Phys. 25, 1154 (1980)].",{"VOID":1499},"10.1134\u002F1.1620106","2024-06-26T19:20:48.750+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1134\u002F1.1620106",[1503,1518,1533,1546,1559],{"id":1504,"sortIndex":19,"researcher":18,"roles":1505,"affiliations":1506,"properties":1515,"displayName":1517,"givenName":18,"familyName":18},"2d620fa2-8f14-4176-a72b-eb11bad6976e",[203],[1507],{"id":1508,"sortIndex":19,"affiliation":1509,"properties":18},"08c61951-0671-4b04-80b5-3006ee063dd0",{"id":1508,"createTime":18,"updateTime":18,"relativeEntities":1510,"slug":18,"properties":1511,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1514,"statistic":18},[],{"title":1512},{"EN":1513},"Research Institute of Physics, Rostov State University, Rostov-on-Don, Russia",[],{"title":1516},{"VI":1517},"M. P. 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The islands are shown to form four statistical ensembles, with the distribution in each of them being thermodynamically optimized and coinciding with the canonic distribution of thermodynamic probability.",{"EN":1640},"Ensembles of aluminum islands on the surface of strained poly(ethylene terephthalate) films",{"VOID":1642},"[\"17335657282535820025\"]",{"VOID":1644},"H. G. Kilian, R. Metzler, and B. Zink, J. Chem. Phys. 107(20), 8697 (1997).\nH. G. Kilian, V. I. Vettegren, and V. N. Svetlov, Fiz. Tverd. Tela (St. Petersburg) 42(11), 2024 (2000) [Phys. Solid State 42, 2083 (2000)].\nH. G. Kilian, Rubber Chem. Technol. (2002) (in press).\nH. G. Kilian, M. Koepf, and V. I. Vettegren, Prog. Colloid Polym. Sci. (2002) (in press).\nH. G. Kilian, V. I. Vettegren, and V. N. Svetlov, Fiz. Tverd. Tela (St. Petersburg) 43(11), 2107 (2001) [Phys. Solid State 43, 2199 (2001)].\nB. L. Lavenda, Statistical Physics. 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