{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T05:32:45Z","timestamp":1778563965287,"version":"3.51.4"},"reference-count":96,"publisher":"IOP Publishing","issue":"45","license":[{"start":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T00:00:00Z","timestamp":1691625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T00:00:00Z","timestamp":1691625600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys.: Condens. Matter"],"published-print":{"date-parts":[[2023,11,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Upper limit of dislocation density without fracture is numerically calculated for slightly- ductile single-crystal ceramics for which the Griffith criterion for fracture and the Bailey\u2013Hirsch type relationship between applied stress and the dislocation density are nearly valid simultaneously in order to obtain useful information to improve functional, electrical, and mechanical properties of ceramics by the introduction of appropriate dislocations. Two models of fracture as a function of dislocation density are constructed; simple model and probability model. If the diameter of pre-existing microcracks is sufficiently small, the dislocation density could be as high as the crystallographic limit (<jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>\u223c<\/mml:mo>\n                        <mml:mrow>\n                           <mml:msup>\n                              <mml:mn>10<\/mml:mn>\n                              <mml:mrow>\n                                 <mml:mn>18<\/mml:mn>\n                              <\/mml:mrow>\n                           <\/mml:msup>\n                        <\/mml:mrow>\n                     <\/mml:math>\n                  \n                  <\/jats:inline-formula> m<jats:sup>\u22122<\/jats:sup>). Even if the typical diameter of pre-existing microcracks is not so small, there is some probability that the dislocation density could be as high as the crystallographic limit if the number of microcracks in the specimen is very small. Accordingly, the increase in ionic conductivity by several orders of magnitude without dendrite formation by introducing appropriate dislocations into single-crystal solid electrolytes with the dislocation density higher than about 10<jats:sup>17<\/jats:sup> m<jats:sup>\u22122<\/jats:sup> theoretically predicted by the authors may be practically possible.<\/jats:p>","DOI":"10.1088\/1361-648x\/aced31","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T18:31:10Z","timestamp":1691087470000},"page":"455701","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Theoretical upper limit of dislocation density in slightly-ductile single-crystal ceramics"],"prefix":"10.1088","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0654-6675","authenticated-orcid":true,"given":"Kyuichi","family":"Yasui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Koichi","family":"Hamamoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"key":"cmaced31bib1","author":"Cai","year":"2016","type":"book"},{"key":"cmaced31bib2","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1016\/j.pmatsci.2009.03.001","type":"journal-article","article-title":"Nanowire design by dislocation technology","volume":"54","author":"Ikuhara","year":"2009","journal-title":"Prog. Mater. Sci."},{"key":"cmaced31bib3","doi-asserted-by":"publisher","first-page":"1626","DOI":"10.2320\/matertrans.MF200928","type":"journal-article","article-title":"Oxide ceramics with high density dislocations and their properties","volume":"50","author":"Ikuhara","year":"2009","journal-title":"Mater. Trans."},{"key":"cmaced31bib4","doi-asserted-by":"publisher","first-page":"9355","DOI":"10.1021\/acsnano.0c04491","type":"journal-article","article-title":"Conceptual framework for dislocation-modified conductivity in oxide ceramics deconvoluting mesoscopic structure, core, and space charge exemplified for SrTiO3","volume":"15","author":"Porz","year":"2021","journal-title":"ACS Nano"},{"key":"cmaced31bib5","doi-asserted-by":"publisher","first-page":"9211","DOI":"10.1021\/acsnano.1c01557","type":"journal-article","article-title":"Dislocation-mediated conductivity in oxides: progress, challenges, and opportunities","volume":"15","author":"Armstrong","year":"2021","journal-title":"ACS Nano"},{"key":"cmaced31bib6","doi-asserted-by":"publisher","DOI":"10.1016\/j.nanoen.2021.105944","type":"journal-article","article-title":"Donor and acceptor-like self-doping by mechanically induced dislocations in bulk TiO2","volume":"85","author":"Muhammad","year":"2021","journal-title":"Nano Energy"},{"key":"cmaced31bib7","doi-asserted-by":"publisher","DOI":"10.1016\/j.mtnano.2021.100171","type":"journal-article","article-title":"Dislocation-mediated electronic conductivity in rutile","volume":"17","author":"Muhammad","year":"2022","journal-title":"Mater. Today Nano"},{"key":"cmaced31bib8","doi-asserted-by":"publisher","first-page":"1891","DOI":"10.1111\/jace.16881","type":"journal-article","article-title":"High temperature creep-mediated functionality in polycrystalline barium titanate","volume":"103","author":"Ren","year":"2020","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib9","doi-asserted-by":"publisher","first-page":"961","DOI":"10.1126\/science.abe3810","type":"journal-article","article-title":"Control of polarization in bulk ferroelectrics by mechanical dislocation imprint","volume":"372","author":"Hofling","year":"2021","journal-title":"Science"},{"key":"cmaced31bib10","doi-asserted-by":"publisher","DOI":"10.1063\/5.0010234","type":"journal-article","article-title":"Influence of dislocations on thermal conductivity of strontium titanate","volume":"117","author":"Johanning","year":"2020","journal-title":"Appl. Phys. Lett."},{"key":"cmaced31bib11","doi-asserted-by":"publisher","DOI":"10.1002\/adma.202203032","type":"journal-article","article-title":"Enhanced photoconductivity at dislocations in SrTiO3","volume":"34","author":"Kissel","year":"2022","journal-title":"Adv. Mater."},{"key":"cmaced31bib12","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1038\/nmat1614","type":"journal-article","article-title":"Switching the electrical resistance of individual dislocations in single-crystalline SrTiO3","volume":"5","author":"Szot","year":"2006","journal-title":"Nat. Mater."},{"key":"cmaced31bib13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.267601","type":"journal-article","article-title":"Atomic-scale measurement of flexoelectric polarization at SrTiO3 dislocations","volume":"120","author":"Gao","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"cmaced31bib14","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1038\/s41563-021-01102-3","type":"journal-article","article-title":"Enhanced superconductivity and ferroelectric quantum criticality in plastically deformed strontium titanate","volume":"21","author":"Hameed","year":"2022","journal-title":"Nat. Mater."},{"key":"cmaced31bib15","doi-asserted-by":"publisher","DOI":"10.1063\/1.4809945","type":"journal-article","article-title":"Effect of dislocation walls on the polarization switching of a ferroelectric single crystal","volume":"102","author":"Wu","year":"2013","journal-title":"Appl. Phys. Lett."},{"key":"cmaced31bib16","doi-asserted-by":"publisher","first-page":"1491","DOI":"10.1016\/j.ijsolstr.2008.11.021","type":"journal-article","article-title":"Computational modeling of domain wall interactions with dislocations in ferroelectric crystals","volume":"46","author":"Kontsos","year":"2009","journal-title":"Int. J. Solids Struct."},{"key":"cmaced31bib17","doi-asserted-by":"publisher","first-page":"4098","DOI":"10.1016\/j.jeurceramsoc.2021.02.023","type":"journal-article","article-title":"Large plastic deformability of bulk ferroelectric KNbO3 single crystals","volume":"41","author":"Hofling","year":"2021","journal-title":"J. Eur. Ceram. Soc."},{"key":"cmaced31bib18","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1039\/d0mh02033h","type":"journal-article","article-title":"Dislocation-toughened ceramics","volume":"8","author":"Porz","year":"2021","journal-title":"Mater. Horiz."},{"key":"cmaced31bib19","doi-asserted-by":"publisher","DOI":"10.1002\/admi.201901121","type":"journal-article","article-title":"Edge dislocations induce improved photocatalytic efficiency of colored TiO2","volume":"6","author":"Ren","year":"2019","journal-title":"Adv. Mater. Interfaces"},{"key":"cmaced31bib20","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1063\/1.1544440","type":"journal-article","article-title":"Dislocation-enhanced ionic conductivity of yttria-stabilized zirconia","volume":"82","author":"Otsuka","year":"2003","journal-title":"Appl. Phys. Lett."},{"key":"cmaced31bib21","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1038\/nmat920","type":"journal-article","article-title":"Conducting nanowires in insulating ceramics","volume":"2","author":"Nakamura","year":"2003","journal-title":"Nat. Mater."},{"key":"cmaced31bib22","doi-asserted-by":"publisher","first-page":"241","DOI":"10.3390\/cryst8060241","type":"journal-article","article-title":"Influence of dislocations in transition metal oxides on selected physical and chemical properties","volume":"8","author":"Szot","year":"2018","journal-title":"Crystals"},{"key":"cmaced31bib23","doi-asserted-by":"publisher","first-page":"2399","DOI":"10.1111\/jace.18277","type":"journal-article","article-title":"Mechanical tailoring of dislocation densities in SrTiO3 at room temperature","volume":"105","author":"Okafor","year":"2022","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib24","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/acc0e4","type":"journal-article","article-title":"Influence of dislocations on ionic conductivity and dendrite formation in solid electrolytes","volume":"98","author":"Yasui","year":"2023","journal-title":"Phys. Scr."},{"key":"cmaced31bib25","doi-asserted-by":"publisher","first-page":"L1","DOI":"10.1016\/0921-5107(92)90175-9","type":"journal-article","article-title":"Impurities dislocation diffusion in single-crystal MgO","volume":"13","author":"Sakaguchi","year":"1992","journal-title":"Mater. Sci. Eng. B"},{"key":"cmaced31bib26","doi-asserted-by":"publisher","first-page":"560","DOI":"10.1111\/j.1151-2916.2003.tb03341.x","type":"journal-article","article-title":"Determination of pipe diffusion coefficients in undoped and magnesia-doped sapphire (\u03b1-Al2O3): a study based on annihilation of dislocation dipoles","volume":"86","author":"Tang","year":"2003","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib27","doi-asserted-by":"publisher","first-page":"R1257","DOI":"10.1088\/0953-8984\/15\/30\/202","type":"journal-article","article-title":"Diffusion and ionic conduction in nanocrystalline ceramics","volume":"15","author":"Heitjans","year":"2003","journal-title":"J. Phys.: Condens. Matter"},{"key":"cmaced31bib28","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.ultramic.2013.06.009","type":"journal-article","article-title":"TEM study of \u3008110\u3009-type 35.26\u00b0 dislocations specially induced by polishing of SrTiO3 single crystals","volume":"134","author":"Jin","year":"2013","journal-title":"Ultramicroscopy"},{"key":"cmaced31bib29","doi-asserted-by":"publisher","DOI":"10.1063\/1.4937909","type":"journal-article","article-title":"High dislocation density of tin induced by electric current","volume":"5","author":"Liao","year":"2015","journal-title":"AIP Adv."},{"key":"cmaced31bib30","doi-asserted-by":"publisher","first-page":"3384","DOI":"10.1039\/c8ta11292d","type":"journal-article","article-title":"Enhanced thermoelectric performance of higher manganese silicides by shock-induced high-density dislocations","volume":"7","author":"Gao","year":"2019","journal-title":"J. Mater. Chem. A"},{"key":"cmaced31bib31","doi-asserted-by":"publisher","DOI":"10.1143\/APEX.5.022703","type":"journal-article","article-title":"Formation of high-density dislocations and hardening in femtosecond-laser-shocked silicon","volume":"5","author":"Tsujino","year":"2012","journal-title":"Appl. Phys. Express"},{"key":"cmaced31bib32","doi-asserted-by":"publisher","DOI":"10.1016\/j.apmt.2021.101279","type":"journal-article","article-title":"Octacalcium phosphate crystals including a higher density dislocation improve its materials osteogenecity","volume":"26","author":"Hamai","year":"2022","journal-title":"Appl. Mater. Today"},{"key":"cmaced31bib33","doi-asserted-by":"publisher","DOI":"10.1063\/1.2804570","type":"journal-article","article-title":"Ultrawide range dielectric spectroscopy of BaTiO3-based perovskite dielectrics","volume":"91","author":"Tsurumi","year":"2007","journal-title":"Appl. Phys. Lett."},{"key":"cmaced31bib34","author":"Tagantsev","year":"2010","type":"book"},{"key":"cmaced31bib35","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1080\/21663831.2020.1862933","type":"journal-article","article-title":"Surface strengthening of single-crystal alumina by high-temperature laser shock peening","volume":"9","author":"Wang","year":"2021","journal-title":"Mater. Res. Lett."},{"key":"cmaced31bib36","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1063\/1.1719922","type":"journal-article","article-title":"Ultrasonic treatment of specimens in the electron microscope","volume":"37","author":"Langenecker","year":"1966","journal-title":"Rev. Sci. Instrum."},{"key":"cmaced31bib37","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1103\/PhysRevLett.14.221","type":"journal-article","article-title":"Dislocation structure in ultrasonically irradiated aluminum","volume":"14","author":"Westmacott","year":"1965","journal-title":"Phys. Rev. Lett."},{"key":"cmaced31bib38","doi-asserted-by":"publisher","DOI":"10.1063\/5.0063334","type":"journal-article","article-title":"Importance of dislocations in ultrasound-assisted sintering of silver nanoparticles","volume":"130","author":"Yasui","year":"2021","journal-title":"J. Appl. Phys."},{"key":"cmaced31bib39","author":"Anderson","year":"2017","edition":"4th edn","type":"book"},{"key":"cmaced31bib40","doi-asserted-by":"publisher","first-page":"2399","DOI":"10.1016\/S1359-6454(99)00409-7","type":"journal-article","article-title":"Damage evolution in dynamic deformation of silicon carbide","volume":"48","author":"Shih","year":"2000","journal-title":"Acta Mater."},{"key":"cmaced31bib41","doi-asserted-by":"publisher","first-page":"28419","DOI":"10.1016\/j.ceramint.2021.06.259","type":"journal-article","article-title":"Damage formation mechanisms of sintered silicon carbide during single-diamond grinding","volume":"47","author":"Dai","year":"2021","journal-title":"Ceram. Int."},{"key":"cmaced31bib42","doi-asserted-by":"publisher","first-page":"1612","DOI":"10.3390\/ma16041612","type":"journal-article","article-title":"Critical roles of impurities and imperfections in various phases of materials","volume":"16","author":"Yasui","year":"2023","journal-title":"Materials"},{"key":"cmaced31bib43","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1080\/14786436408211912","type":"journal-article","article-title":"Crack nucleation in MgO single crystal","volume":"9","author":"Argon","year":"1964","journal-title":"Phil. Mag."},{"key":"cmaced31bib44","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1080\/14786435908238267","type":"journal-article","article-title":"The relationship between plastic flow and the fracture mechanism in magnesium oxide single crystal","volume":"4","author":"Stokes","year":"1959","journal-title":"Phil. Mag."},{"key":"cmaced31bib45","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1080\/14786435808237008","type":"journal-article","article-title":"Crack formation in magnesium oxide single crystals","volume":"3","author":"Stokes","year":"1958","journal-title":"Phil. Mag."},{"key":"cmaced31bib46","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.matchar.2018.08.039","type":"journal-article","article-title":"Dislocation arrangements within slip bands during fatigue cracking","volume":"145","author":"Li","year":"2018","journal-title":"Mater. Charact."},{"key":"cmaced31bib47","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/0001-6160(86)90192-6","type":"journal-article","article-title":"Quantitative measurement of persistent slip band profiles and crack initiation","volume":"34","author":"Hunsche","year":"1986","journal-title":"Acta Metall."},{"key":"cmaced31bib48","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1080\/14786437308217440","type":"journal-article","article-title":"Low-amplitude fatigue of copper and copper-5 at. % aluminium single crystals","volume":"28","author":"Woods","year":"1973","journal-title":"Phil. Mag."},{"key":"cmaced31bib49","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/S0927-0256(97)00045-1","type":"journal-article","article-title":"Simulation of microfracture process of brittle polycrystals: microcracking and crack propagation","volume":"8","author":"Kim","year":"1997","journal-title":"Comput. Mater. Sci."},{"key":"cmaced31bib50","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1088\/0965-0393\/3\/5\/007","type":"journal-article","article-title":"Simulation of dynamic fracture of an impact-loaded brittle solid: microcracked and polycrystalline solids","volume":"3","author":"Smith","year":"1995","journal-title":"Modelling Simul. Mater. Sci. Eng."},{"key":"cmaced31bib51","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1098\/rsta.1986.0101","type":"journal-article","article-title":"Brittle failure in compression: splitting, faulting and brittle-ductile transition","volume":"319","author":"Horii","year":"1986","journal-title":"Phil. Trans. R. Soc. A"},{"key":"cmaced31bib52","author":"Pelleg","year":"2014","type":"book"},{"key":"cmaced31bib53","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1111\/j.1151-2916.1960.tb13674.x","type":"journal-article","article-title":"Mechanical properties of magnesia single crystals in compression","volume":"43","author":"Hulse","year":"1960","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib54","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1111\/j.1151-2916.2001.tb00805.x","type":"journal-article","article-title":"Surprising results of a study on the plasticity in strontium titanate","volume":"84","author":"Brunner","year":"2001","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib55","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1111\/j.1151-2916.1963.tb11738.x","type":"journal-article","article-title":"Effect of crystal orientation on plastic deformation of magnesium oxide","volume":"46","author":"Hulse","year":"1963","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib56","doi-asserted-by":"publisher","first-page":"C150","DOI":"10.1111\/j.1151-2916.1982.tb10523.x","type":"journal-article","article-title":"Temperature dependence of strength and fracture toughness of ZrO2 single crystals","volume":"65","author":"Ingel","year":"1982","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib57","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.jmps.2014.05.005","type":"journal-article","article-title":"Continuum framework for dislocation structure, energy and dynamics of dislocation arrays and low angle grain boundaries","volume":"69","author":"Zhu","year":"2014","journal-title":"J. Mech. Phys. Solids"},{"key":"cmaced31bib58","author":"Anderson","year":"2017","edition":"3rd edn","type":"book"},{"key":"cmaced31bib59","author":"Munz","year":"1999","type":"book"},{"key":"cmaced31bib60","doi-asserted-by":"publisher","author":"Freiman","year":"2012","DOI":"10.3390\/ma5050922","type":"book"},{"key":"cmaced31bib61","type":"book","article-title":"Mechanical Behavior of Materials","volume":"vol 2","author":"Francois","year":"1998"},{"key":"cmaced31bib62","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s00603-009-0053-1","type":"journal-article","article-title":"Practical estimates of tensile strength and Hoek-Brown strength parameter mi of brittle rocks","volume":"43","author":"Cai","year":"2010","journal-title":"Rock Mech. Rock Eng."},{"key":"cmaced31bib63","author":"Sheorey","year":"1997","type":"book"},{"key":"cmaced31bib64","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1016\/0001-6160(67)90371-9","type":"journal-article","article-title":"Components of the flow stress of iron","volume":"15","author":"Dingley","year":"1967","journal-title":"Acta Metall."},{"key":"cmaced31bib65","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1080\/01418618608245293","type":"journal-article","article-title":"Long-range internal stresses and asymmetric x-ray line-broadening in tensile-deformed [001]-oriented copper single crystals","volume":"53","author":"Mughrabi","year":"1986","journal-title":"Phil. Mag."},{"key":"cmaced31bib66","doi-asserted-by":"publisher","first-page":"1018","DOI":"10.1515\/ntrev-2021-0074","type":"journal-article","article-title":"Large strain hardening of magnesium containing in situ nanoparticles","volume":"10","author":"Feng","year":"2021","journal-title":"Nanotechnol. Rev."},{"key":"cmaced31bib67","doi-asserted-by":"publisher","first-page":"1367","DOI":"10.1016\/0001-6160(83)90007-X","type":"journal-article","article-title":"Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals","volume":"31","author":"Mughrabi","year":"1983","journal-title":"Acta Metall."},{"key":"cmaced31bib68","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1080\/14786436008238300","type":"journal-article","article-title":"The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver","volume":"5","author":"Bailey","year":"1960","journal-title":"Phil. Mag."},{"key":"cmaced31bib69","first-page":"591","type":"book","article-title":"Statistical approach to brittle fracture","volume":"vol 2","author":"Freudenthal","year":"1968"},{"key":"cmaced31bib70","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/j.engfracmech.2014.12.015","type":"journal-article","article-title":"An engineering methodology for constraint corrections of elastic-plastic fracture toughness\u2014Part I: a review on probabilistic models and exploration of plastic strain effects","volume":"134","author":"Ruggieri","year":"2015","journal-title":"Eng. Fract. Mech."},{"key":"cmaced31bib71","doi-asserted-by":"publisher","first-page":"4755","DOI":"10.1016\/S1359-6454(02)00313-0","type":"journal-article","article-title":"Effect of carbide distribution on the fracture toughness in the transition temperature region of an SA 508 steel","volume":"50","author":"Lee","year":"2002","journal-title":"Acta Mater."},{"key":"cmaced31bib72","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/S1359-6462(03)00239-2","type":"journal-article","article-title":"Comment on \u2018Effect of carbide distribution on the fracture toughness in the transition temperature region of an SA 508 steel\u2019","volume":"49","author":"Tanguy","year":"2003","journal-title":"Scr. Mater."},{"key":"cmaced31bib73","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s10704-006-0035-1","type":"journal-article","article-title":"Development of the local approach to fracture over the past 25 years: theory and applications","volume":"138","author":"Pineau","year":"2006","journal-title":"Int. J. Fract."},{"key":"cmaced31bib74","doi-asserted-by":"publisher","first-page":"5531","DOI":"10.1016\/j.actamat.2009.07.048","type":"journal-article","article-title":"A molecular dynamics study of self-diffusion in the cores of screw and edge dislocations in aluminum","volume":"57","author":"Pun","year":"2009","journal-title":"Acta Mater."},{"key":"cmaced31bib75","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.202105647","type":"journal-article","article-title":"Faster diffusion of oxygen along dislocations in (La, Sr) MnO3+\u03b4 is a space-charge phenomenon","volume":"31","author":"Borgers","year":"2021","journal-title":"Adv. Funct. Mater."},{"key":"cmaced31bib76","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1080\/01418618508237640","type":"journal-article","article-title":"Atomistic model calculations of pipe-diffusion mechanisms in MgO","volume":"52","author":"Rabier","year":"1985","journal-title":"Phil. Mag."},{"key":"cmaced31bib77","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1016\/0001-6160(81)90042-0","type":"journal-article","article-title":"A computer simulation study of pipe diffusion in body centered cubic metals","volume":"29","author":"Miller","year":"1981","journal-title":"Acta Metall."},{"key":"cmaced31bib78","doi-asserted-by":"publisher","first-page":"2213","DOI":"10.1063\/1.1697112","type":"journal-article","article-title":"Diffusion along dislocations","volume":"43","author":"Luther","year":"1965","journal-title":"J. Chem. Phys."},{"key":"cmaced31bib79","doi-asserted-by":"publisher","first-page":"9965","DOI":"10.1038\/s41598-018-27851-x","type":"journal-article","article-title":"Lithium-ion conducting oxide single crystal as solid electrolyte for advanced lithium battery application","volume":"8","author":"Kataoka","year":"2018","journal-title":"Sci. Rep."},{"key":"cmaced31bib80","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/j.msea.2008.01.030","type":"journal-article","article-title":"The relationships between the shear modulus, the bulk modulus and Young\u2019s modulus for porous isotropic ceramic materials","volume":"490","author":"Phani","year":"2008","journal-title":"Mater. Sci. Eng. A"},{"key":"cmaced31bib81","author":"Chiang","year":"1997","type":"book"},{"key":"cmaced31bib82","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1021\/acs.chemmater.5b03854","type":"journal-article","article-title":"Elastic properties of the solid electrolyte Li7La3Zr2O12 (LLZO)","volume":"28","author":"Yu","year":"2016","journal-title":"Chem. Mater."},{"key":"cmaced31bib83","author":"Ibach","year":"2009","edition":"4th edn","type":"book"},{"key":"cmaced31bib84","author":"Lide","year":"1994","edition":"75th edn","type":"book"},{"key":"cmaced31bib85","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1016\/j.actamat.2007.10.023","type":"journal-article","article-title":"The thermodynamic stability of amorphous oxide overgrowths on metals","volume":"56","author":"Reichel","year":"2008","journal-title":"Acta Mater."},{"key":"cmaced31bib86","doi-asserted-by":"publisher","first-page":"3019","DOI":"10.1021\/acs.chemmater.8b00649","type":"journal-article","article-title":"Particle morphology and lithium segregation to surfaces of the Li7La3Zr2O12 solid electrolyte","volume":"30","author":"Canepa","year":"2018","journal-title":"Chem. Mater."},{"key":"cmaced31bib87","author":"Mencik","year":"1992","type":"book"},{"key":"cmaced31bib88","doi-asserted-by":"publisher","first-page":"1981","DOI":"10.1007\/BF00547937","type":"journal-article","article-title":"Deformation and fracture of yttria-stabilized zirconia single crystals","volume":"21","author":"Lankford","year":"1986","journal-title":"J. Mater. Sci."},{"key":"cmaced31bib89","doi-asserted-by":"publisher","first-page":"4144","DOI":"10.1007\/BF01106850","type":"journal-article","article-title":"Deformation mechanisms in yttria-stabilized zirconia","volume":"23","author":"Lankford","year":"1988","journal-title":"J. Mater. Sci."},{"key":"cmaced31bib90","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1361\/10599490522158","type":"journal-article","article-title":"Microstructural modeling approach applied to rock material","volume":"14","author":"Duarte","year":"2005","journal-title":"J. Mater. Eng. Perform."},{"key":"cmaced31bib91","doi-asserted-by":"publisher","first-page":"3228","DOI":"10.1007\/s10853-010-4330-x","type":"journal-article","article-title":"Statistical quantification of the microstructural homogeneity of size and orientation distributions","volume":"45","author":"Luo","year":"2010","journal-title":"J. Mater. Sci."},{"key":"cmaced31bib92","first-page":"546","type":"journal-article","article-title":"A statistical theory of fracture","volume":"171","author":"Fisher","year":"1947","journal-title":"Trans. Am. Inst. Min. Metall. Eng."},{"key":"cmaced31bib93","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1111\/jace.16034","type":"journal-article","article-title":"Statistical size scaling of ceramic strength","volume":"102","author":"Lei","year":"2019","journal-title":"J. Am. Ceram. Soc."},{"key":"cmaced31bib94","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11665-012-0214-3","type":"journal-article","article-title":"Numerical analysis of sample-size effect on strength of alumina","volume":"22","author":"Hoshide","year":"2013","journal-title":"J. Mater. Eng. Perform."},{"key":"cmaced31bib95","author":"Brocks","year":"2018","type":"book"},{"key":"cmaced31bib96","first-page":"566","type":"book","article-title":"Brittle fracture","volume":"vol 2","author":"Francois","year":"2001"}],"container-title":["Journal of Physics: Condensed Matter"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T11:17:58Z","timestamp":1757762278000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-648X\/aced31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,10]]},"references-count":96,"journal-issue":{"issue":"45","published-online":{"date-parts":[[2023,8,10]]},"published-print":{"date-parts":[[2023,11,13]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-648x\/aced31","relation":{},"ISSN":["0953-8984","1361-648X"],"issn-type":[{"value":"0953-8984","type":"print"},{"value":"1361-648X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,10]]},"assertion":[{"value":"Theoretical upper limit of dislocation density in slightly-ductile single-crystal ceramics","name":"article_title","label":"Article Title"},{"value":"Journal of Physics: Condensed Matter","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2023 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2023-04-26","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-08-03","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2023-08-10","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}