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Erhart Jiří, Prof., Mgr., Ph.D.

vedoucí katedry


  • Katedra fyziky FP TUL, Studentská 2, 46117 Liberec
  • Kancelář: C3029, budova C


  • +420 485 35 3400
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Konzultační hodiny

    Čtvrtek 14.30 - 15.30

Erhart Jiří, Prof., Mgr., Ph.D.

Ostatní informace

  • 1983-1988 MSc. degree from the Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic in the field of theoretical physics

    1989-1991 research stays with the Technical University of Liberec and Institute of Physics, Academy of Sciences of the Czech Republic, Prague

    1991-1999 Ph.D. degree in the field of Solid State and Materials Research from the Institute of Physics, Academy of Sciences of the Czech Republic, Prague and Faculty of Mathematics and Physics, Charles University in Prague

    1998 - 1999 Research fellow and postdoc with prof. Wenwu Cao, Materials Research Laboratory, The Pennsylvania State University, University Park, U.S.A.

    2001 Associate Professor at the Department of Physics, Technical University of Liberec

    2003 (3 months) The Matsumae International Fellowship at Tokyo Institute of Technology, Tokyo, Japan

    2002, 2004 (2 x 1 month) research fellow at City University of Hong Kong, P.R.China

    2009 (1 month) research fellow at Harbin Institute of Technology, Harbin, P.R.China

    2012 Professor at the Department of Physics, Technical University of Liberec

    2015 (1 month) invited professor and Erasmus teacher at Institut National Polytechnique de Toulouse, Toulouse, France


  • Electromechanical properties of ceramics, crystals and composites. Domain engineering in ferroelectric crystals. Measurement and mathematical modeling of piezoelectric components (e.g. piezoelectric bimorphs, unimorphs, transformers, etc.). Theory of ferroelectric domains and domain walls. Physics experiments and demonstrations in Physics education.


  • Books and book chapters

    J.Tichý, J.Erhart, E.Kittinger, J.Přívratská: Fundamentals of Piezoelectric Sensorics, Mechanical, Dielectric, and Thermodynamical Properties of Piezoelectric Materials Springer Verlag 2010, ISBN 978-3-540-43966-0

    L.Pardo and J.Ricote (editors): Handbook on “Multifunctional Polycrystalline Ferroelectric Materials”, Springer Series in Materials Science, Vol. 140, Springer Verlag 2011, ISBN 978-90-481-2874-7 (Chapter: J.Erhart: Domain engineered piezoelectric resonators)

    J.Erhart, P.Půlpán, M.Pustka: Piezoelectric ceramic resonators, Springer International Publishing Switzerland 2017, ISBN 978-3-319-42480-4

    Research publications

    J.Erhart, V.Paidar: Statistics of Asymmetrical [001] Tilt Grain Boundaries, phys.stat.sol. (a) 129 (1992) 135-141

    J.Erhart, I.Trubelík: Computer Simulation of the 36.87o[001]{310} Symmetrical Tilt Grain Boundary Structure in B.C.C. Metals, phys.stat.sol. (b) 179 (1993) 329-336

    V.Paidar, J.Erhart: Geometry of Sigma 9 and Sigma 11 Asymmetrical Grain Boundaries, Interface Science 1 (1993) 115-124

    J.Erhart, V.Paidar: Characterisation of (340)/(010) Asymmetrical Grain Boundary, Mater. Sci. Forum 294-296 (1999) 381-384

    J.Erhart, W.Cao: Effective Material Properties in Twinned Ferroelectric Crystals, J. Appl. Phys. 86, 2 (1999) 1073-1081

    J.Erhart, W.Cao: Effective Symmetry and Physical Properties of Twinned Perovskite Ferroelectric Single Crystals, J. Mater. Research 16, 2 (2001) 570-578

    J.Erhart, W.Cao, J.Fousek: The Structure of S-walls in  Ferroelastics, Ferroelectrics 252 (2001) 137-144

    J.Erhart, L.Burianová: What is really measured on d33-meter? J.European Ceram.Society 21 (2001) 1413-1415

    M.Abplanalp, D.Barošová, P.Bridenbaugh, J.Erhart, J.Fousek, P.Günter, J.Nosek, M.Šulc: Ferroelectric Domain Structures in PZN-8%PT Single Crystals Studied by Scanning Force Microscopy, Solid State Communications 119 (2001) 7-12

    J.Erhart, S.Panoš: Piezoelectric Composite „Shear-moonie“ Transducer, Ann. Chim.Sci. Mat. 26 (2001) 173-176

    M.Abplanalp, D.Barošová, P.Bridenbaugh, J.Erhart, J.Fousek, P.Günter, J.Nosek, M.Šulc: Domain structures in PZN-8%PT and PMN‑29%PT single crystals studied by scanning force microscopy, J.Appl.Phys. 91 (2002) 3797-3805

    J.Erhart, W.Cao: Permissible symmetries of multi-domain configurations in perovskite

    ferroelectric crystals, J.Appl.Phys. 94 (2003) 3436-3445

    J. Nosek, J. Erhart: Some experimental investigations of electromechanical properties of (Pb(Zn1/3Nb2/3)O3)0.92–(PbTiO3)0.08 relaxor single crystals, Microelectronic Engineering 66 (2003) 733–737

    J.Erhart: Theoretical calculation of the temperature dependence for the material coefficients of the domain-engineered ferroelectric crystals, Ferroelectrics 292 (2003) 71-81

    M.Šulc, J.Erhart, J.Nosek: Interferometric measurement of temperature dependence of piezoelectric coefficients for PZN-8%PT single crystals, Ferroelectrics 293 (2003) 283-290

    M. Marvan, J. Erhart, J. Fousek: Role of soft dielectric energy in poling crystals or ceramics and in domain average engineering, Applied Physics Letters 84 (2004) 768-770

    J.Erhart: Domain wall orientations in ferroelastics and ferroelectrics, Phase Transitions 77 (2004) 989-1074

    S.Wada, K.Yako, H.Kakemoto, J.Erhart, T.Tsurumi: Enhanced piezoelectric property of BaTiO3 single crystals with the different domain sizes, Key Engineering Materials 269 (2004) 19-22

    T.Malysh, J.Erhart: Electric Field Applicability Limits for PZT Ceramics, Ferroelectrics 319 (2005) 45-56

    S.Panoš, D. Panošová, J.Erhart, M.Šulc: Contribution to the Measurement of the Material Constants on Domain-Engineered Ferroelectric Crystals, Ferroelectrics 319 (2005) 135-144

    J.Erhart, S.Wada: Theoretical calculation of the resonant frequency temperature dependence for domain-engineered piezoelectric resonators, Materials Science and Engineering B 120 (2005) 175-180

    J. Erhart, L. Rusin, L.Seifert: Resonant frequency temperature coefficients for the piezoelectric resonators working in various vibration modes, Journal of Electroceramics 19 (2007) 403-406

    P.Půlpán, J.Erhart, O.Štípek: Modeling of piezoelectric transformers, Ferroelectrics 351 (2007) 204-215

    P.Půlpán, J.Erhart: Transformation ratio of “ring-dot” planar piezoelectric transformer, Sensors and Actuators A 140 (2007) 215-224

    P.Půlpán, L.Rusin, J.Erhart: Influence of poling conditions on material properties of lead zirconate-lead titanate ceramics, Japanese Journal of Applied Physics 47, 10 (2008) 7953-7958

    J.Erhart, M.Franclíková, L.Rusin: Piezoelectric resonators with engineered domain structures, Ferroelectrics 376, 1 (2008) 99-115

    S. A. M. Tofail, D.Haverty, F.Cox, J.Erhart, P.Hana, V.Ryzhenko: Direct and ultrasonic measurements of macroscopic piezoelectricity in sintered hydroxyapatite, J. Appl. Phys. 105, 6 (2009) 064103

    E. Simon, J. Hlinka, S. Kamba, I. Gregora, J. Erhart: Influence of poling on far-infrared response of lead zirconate titanate ceramics, J. Appl. Phys. 106, 7 (2009) 074104

    S. A. M. Tofail, C. Baldisseri, D. P. Haverty, J. B. McMonagle, J.Erhart: Pyroelectric surface charge in hydroxyapatite ceramics, J. Appl. Phys. 106, 10(2009) 106104

    M.Pustka, J.Erhart, P.Mokrý: Vibration control using piezoelectric bimorphs connected to negative capacitance circuits, Advances in Applied Ceramics 109, 3 (2010) 180-183

    L.Kozielski, M.Adamczyk, J.Erhart, K.Rusek: PLZT-Based Light Controlled Piezoelectric Transformer, Ferroelectrics 417 (2011) 161-169

    J.Erhart, P.Půlpán, M.Adamczyk: Domain engineered piezoelectric ceramic transformers, Ferroelectrics 423 (2011) 25-33

    J.Erhart, W.Cao: Three Dimensional Domain Structures for Domain Engineered Rhombohedral Perovskite Ferroelectric Crystals, Ferroelectrics 426 (2012) 13-20

    P.Psota, V.Lédl, R.Doleček, J.Erhart, V.Kopecký: Measurement of piezoelectric transformer vibrations by digital holography, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 59, 9 (2012) , art. no. 6306016, 1962-1968

    L.Kozielski, M.Adamczyk, J.Erhart, M.Pawełczyk: Application testing of Sr doping effect of PZT ceramics on the piezoelectric transformer gain and efficiency proposed for MEMS actuators driving, Journal of Electroceramics 29, 2 (2012) 133-138

    L. Kozielski, J. Erhart, F. J. Clemens: Light-Intensity-Induced Characterization of Elastic Constants and d33 Piezoelectric Coefficient of PLZT Single Fiber Based Transducers, Sensors 13, 2 (2013)  2419-2429

    J.Erhart: Bulk piezoelectric ceramic transformers, Advances in Applied Ceramics 112, 2 (2013) 91-96

    J.Erhart, P.Půlpán, L.Rusin: Bar Piezoelectric Ceramic Transformers, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 60, 7 (2013) 1479-1486

    J.Erhart, P.Půlpán, R.Doleček, P.Psota, V.Lédl: Disc Piezoelectric Ceramic Transformers, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 60, 8 (2013) 1612-1618

    M. Šimko, J. Erhart, D. Lukáš: A mathematical model of external electrostatic field of a special collector for electrospinning of nanofibers, Journal of Electrostatics 72, 2 (2014) 161–165

    C. Nadal, F. Pigache, J. Erhart: Modeling of a Ring Rosen-Type Piezoelectric Transformer by Hamilton’s Principle, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 62, 4 (2015) 709-720

    T. Sebastian, L. Kozielski, J. Erhart: Co-sintered PZT ceramics for the piezoelectric transformers, Ceramics International 41, 8 (2015) 9321-9327

    J.Erhart: Parameters and design optimization of the ring piezoelectric ceramic transformer, Journal of Advanced Dielectrics 5, 2(2015) 1550022

    T.Sebastian, J.Erhart: Bar Piezoelectric Ceramic Transformers Working in Longitudinal Mode, Ferroelectrics 486, 1 (2015) 13-24

    P.Půlpán, J.Erhart: Experimental Verification of an Analytical Model for the Ring-shaped Piezoelectric Transformer, Journal of Electrical and Electronics Engineering 8, 2 (2015) 23-28

    J.Erhart: Transformation and Load Parameters of the Disk Piezoelectric Transformer, IEEE Transactions on Power Electronics 31, 3 (2016) 2437-2442

    B. Wodecka-Dus, L. Kozielski, J. Erhart, M. Pawełczyk, D. Radoszewska, M. Adamczyk, D. Bochenek: Investigation of La3+ doping effect on piezoelectric coefficients of BLT ceramics, Arch. Metall. Mater. 62, 2 (2017) 691-696

    P.Půlpán, J.Erhart: Width-Extensional Piezoelectric Ceramic Transformer, Journal of Electrical and Electronics Engineering 11, 2 (2018) 21-26

    Vijay Bijalwan, Pavel Tofel, Jiří Erhart, Karel Maca: The complex evaluation of functional properties of nearly dense BCZT ceramics and their dependence on the grain size, Ceramics International 45 (2019) 317–326


    V.Lédl, P.Psota. R.Doleček, J.Erhart, V.Kopecký: A digital holographic method for the measurement of piezoelectric transformer vibrations, 2011 International Symposium on Applications of Ferroelectrics and 2011 International Symposium on Piezoresponse Force Microscopy and Nanoscale Phenomena in Polar Materials, ISAF/PFM 2011 , (2011) art. no. 6013998

    L.Kozielski, M.Adamczyk, J.Erhart: PLZT-based photovoltaic Piezoelectric Transformer with light feedback, IOP Conf. Series: Materials Science and Engineering 18 (2011) 092001

    J.Erhart, P.Půlpán, R.Doleček, P.Psota, V.Lédl: Disc piezoelectric ceramic transformers, Proceedings of 2012 21st IEEE Int. Symp. on Applications of Ferroelectrics held jointly with 11th IEEE European Conference on the Applications of Polar Dielectrics and IEEE PFM, ISAF/ECAPD/PFM 2012 , art. no. 6297859

    J.Erhart, T.Sebastian: Effective Electromechanical Coupling for the Partially Electroded Ceramic Resonators of Different Geometries, THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. FASCICLE IX. METALLURGY AND MATERIALS SCIENCE, Vol. XXXIII, No. 2 (2015) 7-16, ISSN 1453 – 083X

    Physics Education

    J.Erhart: O několika fyzikálních pokusech, Školská fyzika 1/1995-1996, 11-16 (in Czech)

    J.Erhart: Měření na ručkových elektrických přístrojích, Školská fyzika 2/2000, 12-16 (in Czech)

    P.Půlpán, J.Erhart: Parametry piezoelektrických bimorfů, Elektro 3 (2002) 4-7 (in Czech)

    J.Erhart: Piezoelektrické “chytré” materiály pro elektrotechniku, PZT keramika, Elektro 11 (2002) 4-7  (in Czech)

    P.Půlpán, J.Erhart: Parametry piezoelektrických unimorfů, Elektro 1 (2005) 4-6 (in Czech)

    P.Půlpán, J.Erhart: Piezoelektrické transformátory, Elektro 1/2006, 8-12 (in Czech)

    J.Erhart: Elektromechanické jevy, Třípól, 3/2009, str. 6-7 (elektronický časopis pro studenty,  vydavatel firma ČEZ, www.tretipol.cz) (in Czech)

    J.Erhart, L.Šimek: Měříme magnetickou polarizaci permanentních magnetů, Matematika, fyzika, informatika 19 (2010) 595-601 (in Czech)

    J.Erhart: Demonstrujeme piezoelektrický jev, Matematika, fyzika, informatika 20 (2010) 106-109 (in Czech)

    J.Erhart: Ultrazvukové rozprašování kapalin, Třípól, červen 2011, str. 12 (elektronický časopis pro studenty, vydavatel firma ČEZ, www.tretipol.cz) (in Czech)

    J.Erhart, P.Desenský: Demonstrujeme teplotní vodivost, Matematika – fyzika –informatika 22, 5 (2013) 281-287 (in Czech)

    J.Erhart, L.Rusin, P.Hána: Měříme součinitel tepelné vodivosti kovů, Matematika – fyzika –informatika 22, 4 (2013) 355-361 (in Czech)

    J.Erhart: Experiments to demonstrate piezoelectric and pyroelectric effects, Phys. Educ. 48, 4 (2013) 438-447.

    J. Erhart: Measurement of elastic modulus and ultrasonic wave velocity by piezoelectric resonator, Eur. J. Phys. 36, 1 (2015) 015017

    J. Erhart: Měříme rezistivity kovových drátů a závislost odporu vodiče na jeho délce a průřezu, Matematika - fyzika - informatika 24 (2015) 26-34 (in Czech)



Vedoucí katedry

Prof. Mgr. Jiří Erhart, Ph.D.
Tel: +420-48-535-3400


Ludmila Sazamová
Tel: +420-48-535-3419


Katedra fyziky na FP TUL, Studentská 2, 461 17 Liberec