{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T02:42:24Z","timestamp":1771555344117,"version":"3.50.1"},"reference-count":60,"publisher":"AIP Publishing","issue":"2","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2010,7,15]]},"abstract":"<jats:p>An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differs significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited and hence the choice of the optimal solution which maximizes the piezoelectricity is complicated. Thus, a stochastic global optimization combined with homogenization is employed for the identification of the optimal granular configuration of the FE ceramic microstructure with optimum piezoelectric properties. The macroscopic equilibrium piezoelectric properties of polycrystalline FE is calculated using mathematical homogenization at each iteration step. The configuration of grains characterized by its orientations at each iteration is generated using a randomly selected set of orientation distribution parameters. The optimization procedure applied to the single crystalline phase compares well with the experimental data. Apparent enhancement of piezoelectric coefficient d33 is observed in an optimally oriented BaTiO3 single crystal. Based on the good agreement of results with the published data in single crystals, we proceed to apply the methodology in polycrystals. A configuration of crystallites, simultaneously constraining the orientation distribution of the c-axis (polar axis) while incorporating ab-plane randomness, which would multiply the overall piezoelectricity in ceramic BaTiO3 is also identified. The orientation distribution of the c-axes is found to be a narrow Gaussian distribution centered around 45\u00b0. The piezoelectric coefficient in such a ceramic is found to be nearly three times as that of the single crystal. Our optimization model provide designs for materials with enhanced piezoelectric performance, which would stimulate further studies involving materials possessing higher spontaneous polarization.<\/jats:p>","DOI":"10.1063\/1.3462450","type":"journal-article","created":{"date-parts":[[2010,7,17]],"date-time":"2010-07-17T22:14:29Z","timestamp":1279404869000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Optimal configuration of microstructure in ferroelectric materials by stochastic optimization"],"prefix":"10.1063","volume":"108","author":[{"given":"K. P.","family":"Jayachandran","sequence":"first","affiliation":[{"name":"Technical University of Lisbon IDMEC, Instituto Superior T\u00e9cnico, , Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]},{"given":"J. M.","family":"Guedes","sequence":"additional","affiliation":[{"name":"Technical University of Lisbon IDMEC, Instituto Superior T\u00e9cnico, , Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]},{"given":"H. C.","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Technical University of Lisbon IDMEC, Instituto Superior T\u00e9cnico, , Av. Rovisco Pais, 1049-001 Lisbon, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2010,7,16]]},"reference":[{"key":"2023080301531224200_c1","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1126\/science.1129564","volume":"315","year":"2007","journal-title":"Science"},{"key":"2023080301531224200_c2","volume-title":"Ferroelectric devices","year":"2000"},{"key":"2023080301531224200_c3","doi-asserted-by":"publisher","first-page":"1804","DOI":"10.1063\/1.365983","volume":"82","year":"1997","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-76464-1","volume-title":"Energy Harvesting Technologies","author":"Priya","year":"2009"},{"key":"2023080301531224200_c5","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1038\/nature03028","volume":"432","year":"2004","journal-title":"Nature (London)"},{"key":"2023080301531224200_c6","doi-asserted-by":"publisher","first-page":"014109","DOI":"10.1063\/1.1957130","volume":"98","year":"2005","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c7","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1143\/JJAP.21.1298","volume":"21","year":"1982","journal-title":"Jpn. J. Appl. Phys., Part 1"},{"key":"2023080301531224200_c8","doi-asserted-by":"publisher","first-page":"1267","DOI":"10.1088\/0034-4885\/61\/9\/002","volume":"61","year":"1998","journal-title":"Rep. Prog. Phys."},{"key":"2023080301531224200_c9","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1038\/35002022","volume":"403","year":"2000","journal-title":"Nature (London)"},{"key":"2023080301531224200_c10","doi-asserted-by":"publisher","first-page":"3891","DOI":"10.1103\/PhysRevLett.86.3891","volume":"86","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"2023080301531224200_c11","doi-asserted-by":"publisher","first-page":"014112","DOI":"10.1103\/PhysRevB.68.014112","volume":"68","year":"2003","journal-title":"Phys. Rev. B"},{"key":"2023080301531224200_c12","doi-asserted-by":"publisher","first-page":"064107","DOI":"10.1103\/PhysRevB.72.064107","volume":"72","year":"2005","journal-title":"Phys. Rev. B"},{"key":"2023080301531224200_c13","doi-asserted-by":"publisher","first-page":"174106","DOI":"10.1103\/PhysRevB.73.174106","volume":"73","year":"2006","journal-title":"Phys. Rev. B"},{"key":"2023080301531224200_c14","volume-title":"Principles and Applications of Ferroelectrics and Related Materials","year":"1977"},{"key":"2023080301531224200_c15","doi-asserted-by":"publisher","first-page":"1965","DOI":"10.1111\/j.1551-2916.2006.01049.x","volume":"89","year":"2006","journal-title":"J. Am. Ceram. Soc."},{"key":"2023080301531224200_c16","doi-asserted-by":"publisher","first-page":"S303","DOI":"10.1088\/0965-0393\/12\/4\/S02","volume":"12","year":"2004","journal-title":"Modell. Simul. Mater. Sci. Eng."},{"key":"2023080301531224200_c17","doi-asserted-by":"publisher","first-page":"3657","DOI":"10.1016\/j.actamat.2006.03.023","volume":"54","year":"2006","journal-title":"Acta Mater."},{"key":"2023080301531224200_c18","doi-asserted-by":"publisher","first-page":"2587","DOI":"10.1088\/0957-4484\/16\/11\/020","volume":"16","year":"2005","journal-title":"Nanotechnology"},{"key":"2023080301531224200_c19","doi-asserted-by":"publisher","first-page":"054110","DOI":"10.1063\/1.2645889","volume":"101","year":"2007","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c20","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1016\/S0022-5096(99)00042-3","volume":"48","year":"2000","journal-title":"J. Mech. Phys. Solids"},{"key":"2023080301531224200_c21","doi-asserted-by":"publisher","first-page":"2913","DOI":"10.1016\/S1359-6454(99)00153-6","volume":"47","year":"1999","journal-title":"Acta Mater."},{"key":"2023080301531224200_c22","doi-asserted-by":"publisher","first-page":"4245","DOI":"10.1063\/1.1787590","volume":"96","year":"2004","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c23","doi-asserted-by":"publisher","first-page":"4104","DOI":"10.1063\/1.1558229","volume":"93","year":"2003","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c24","doi-asserted-by":"publisher","first-page":"024115","DOI":"10.1063\/1.1988978","volume":"98","year":"2005","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c25","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s001610100052","volume":"13","year":"2001","journal-title":"Continuum Mech. Thermodyn."},{"key":"2023080301531224200_c26","doi-asserted-by":"publisher","first-page":"816","DOI":"10.1016\/j.commatsci.2008.05.027","volume":"45","year":"2009","journal-title":"Comput. Mater. Sci."},{"key":"2023080301531224200_c27","volume-title":"Fundamentals of Powder Diffraction and Structural Characterization of Materials","year":"2005"},{"key":"2023080301531224200_c28","doi-asserted-by":"publisher","first-page":"232901","DOI":"10.1063\/1.2940215","volume":"92","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"2023080301531224200_c29","doi-asserted-by":"publisher","first-page":"7039","DOI":"10.1143\/JJAP.46.7039","volume":"46","year":"2007","journal-title":"Jpn. J. Appl. Phys., Part 1"},{"key":"2023080301531224200_c30","doi-asserted-by":"publisher","first-page":"7044","DOI":"10.1143\/JJAP.46.7044","volume":"46","year":"2007","journal-title":"Jpn. J. Appl. Phys., Part 1"},{"key":"2023080301531224200_c31","volume-title":"Physical Properties of Crystals: Their Representation by Tensors and Matrices","year":"1985"},{"key":"2023080301531224200_c32","doi-asserted-by":"publisher","first-page":"5941","DOI":"10.1103\/PhysRevB.50.5941","volume":"50","year":"1994","journal-title":"Phys. Rev. B"},{"key":"2023080301531224200_c33","doi-asserted-by":"publisher","first-page":"5505","DOI":"10.1143\/JJAP.38.5505","volume":"38","year":"1999","journal-title":"Jpn. J. Appl. Phys., Part 1"},{"key":"2023080301531224200_c34","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1080\/10408430490490905","volume":"29","year":"2004","journal-title":"Crit. Rev. Solid State Mater. Sci."},{"key":"2023080301531224200_c35","doi-asserted-by":"publisher","first-page":"232905","DOI":"10.1063\/1.3271682","volume":"95","year":"2009","journal-title":"Appl. Phys. Lett."},{"key":"2023080301531224200_c36","volume-title":"Classical Mechanics","year":"1978"},{"key":"2023080301531224200_c37","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","year":"1983","journal-title":"Science"},{"key":"2023080301531224200_c38","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/0045-7825(90)90148-F","volume":"83","year":"1990","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2023080301531224200_c39","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/S0045-7825(98)00231-X","volume":"172","year":"1999","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2023080301531224200_c40","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0022-5096(01)00021-7","volume":"50","year":"2002","journal-title":"J. Mech. Phys. Solids"},{"key":"2023080301531224200_c41","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1115\/1.1600472","volume":"70","year":"2003","journal-title":"Trans. ASME, J. Appl. Mech."},{"key":"2023080301531224200_c42","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.cossms.2006.05.001","volume":"9","year":"2005","journal-title":"Curr. Opin. Solid State Mater. Sci."},{"key":"2023080301531224200_c43","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.cossms.2004.03.010","volume":"8","year":"2004","journal-title":"Curr. Opin. Solid State Mater. Sci."},{"key":"2023080301531224200_c44","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.1016\/S0020-7683(98)00051-1","volume":"36","year":"1999","journal-title":"Int. J. Solids Struct."},{"key":"2023080301531224200_c45","doi-asserted-by":"publisher","first-page":"1663","DOI":"10.1016\/S0022-5096(98)00122-7","volume":"47","year":"1999","journal-title":"J. Mech. Phys. Solids"},{"key":"2023080301531224200_c46","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1177\/1045389X08091118","volume":"20","year":"2009","journal-title":"J. Intell. Mater. Syst. Struct."},{"key":"2023080301531224200_c47","doi-asserted-by":"publisher","first-page":"1534","DOI":"10.1088\/0964-1726\/16\/5\/005","volume":"16","year":"2007","journal-title":"Smart Mater. Struct."},{"key":"2023080301531224200_c48","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","year":"1953","journal-title":"J. Chem. Phys."},{"key":"2023080301531224200_c49","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1086\/422356","volume":"154","year":"2004","journal-title":"Astrophys. J., Suppl. Ser."},{"key":"2023080301531224200_c50","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s10832-007-9001-1","volume":"19","year":"2007","journal-title":"J. Electroceram."},{"key":"2023080301531224200_c51","doi-asserted-by":"publisher","first-page":"202901","DOI":"10.1063\/1.2203750","volume":"88","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"2023080301531224200_c52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/10584589808238761","volume":"20","year":"1998","journal-title":"Integr. Ferroelectr."},{"key":"2023080301531224200_c53","doi-asserted-by":"publisher","first-page":"7405","DOI":"10.1143\/JJAP.45.7405","volume":"45","year":"2006","journal-title":"Jpn. J. Appl. Phys., Part 1"},{"key":"2023080301531224200_c54","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10853-005-5925-5","volume":"41","year":"2006","journal-title":"J. Mater. Sci."},{"key":"2023080301531224200_c55","doi-asserted-by":"publisher","first-page":"032904","DOI":"10.1063\/1.2166480","volume":"88","year":"2006","journal-title":"Appl. Phys. Lett."},{"key":"2023080301531224200_c56","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0167-577X(99)00056-7","volume":"40","year":"1999","journal-title":"Mater. Lett."},{"key":"2023080301531224200_c57","unstructured":"M.\u2008Budimir, Ph.D. thesis, EPFL, 2006."},{"key":"2023080301531224200_c58","doi-asserted-by":"publisher","first-page":"054112","DOI":"10.1063\/1.2653925","volume":"101","year":"2007","journal-title":"J. Appl. Phys."},{"key":"2023080301531224200_c59","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1121\/1.1908324","volume":"28","year":"1956","journal-title":"J. Acoust. Soc. Am."},{"key":"2023080301531224200_c60","doi-asserted-by":"publisher","first-page":"750","DOI":"10.1111\/j.1551-2916.2005.00109.x","volume":"88","year":"2005","journal-title":"J. Am. Ceram. Soc."}],"container-title":["Journal of Applied Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jap\/article-pdf\/doi\/10.1063\/1.3462450\/13368261\/024101_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jap\/article-pdf\/doi\/10.1063\/1.3462450\/13368261\/024101_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T01:53:46Z","timestamp":1691027626000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jap\/article\/108\/2\/024101\/946110\/Optimal-configuration-of-microstructure-in"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,15]]},"references-count":60,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,7,15]]}},"URL":"https:\/\/doi.org\/10.1063\/1.3462450","relation":{},"ISSN":["0021-8979","1089-7550"],"issn-type":[{"value":"0021-8979","type":"print"},{"value":"1089-7550","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2010,7,15]]},"published":{"date-parts":[[2010,7,15]]},"article-number":"024101"}}