Force-Electric Coupling of Nanoscale Ferroelectric Domains Based on Piezoelectric Force Microscopy (PFM)

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Material</td><td class="align_center">Elastic constant (GPa)</td><td class="align_center">Piezoelectric coefficient (C/m<sup>2</sup>)</td><td class="align_center">Dielectric constant (10<sup>-9</sup> F/m)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">PZT-4</td><td class="align_center">138.67</td><td class="align_center">12.8</td><td class="align_center">6.521</td></tr><tr><td class="align_left">PZT-5A</td><td class="align_center">124.00</td><td class="align_center">12.6</td><td class="align_center">8.127</td></tr><tr><td class="align_left">BaTiO<sub>3</sub></td><td class="align_center">150.14</td><td class="align_center">11.5</td><td class="align_center">9.842</td></tr><tr><td class="align_left">(Ba<sub>a</sub>Ca<sub>b</sub>)TiO<sub>3</sub></td><td class="align_center">158.33</td><td class="align_center">10.8</td><td class="align_center">8.786</td></tr><tr><td class="align_left">PZT (<span class="nowrap"><svg height="11.439pt" id="M75" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 75.0602 11.439" width="75.0602pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M561 176C543 127 527 95 506 73C478 43 441 36 316 36C247 36 185 38 153 42C290 245 427 439 566 636L559 650H160C130 650 119 652 107 675H83C81 630 76 555 71 492L100 491C112 535 123 560 135 578C152 605 168 614 276 614H449C310 411 169 213 29 15L37 0H554C565 41 583 134 590 170L561 176Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.022,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.892,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.253,0)"><path d="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.066,0)"><path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.224,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.487,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.728,0)"><path d="M249 635C141 635 70 555 70 471C70 401 114 353 179 316C143 294 106 267 90 252C68 231 45 202 45 157C45 50 130 -12 237 -12C322 -12 435 52 435 169C435 256 372 304 303 343C349 374 375 398 383 407C401 429 411 458 411 487C411 569 344 635 249 635ZM238 603C285 603 337 567 337 482C337 422 310 385 276 358C205 393 145 426 145 500C145 552 179 603 238 603ZM248 20C183 20 125 70 125 163C125 218 158 268 206 300C284 261 355 217 355 143C355 66 308 20 248 20Z"></path></g><g transform="matrix(.013,0,0,-0.013,56.968,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,62.329,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,68.569,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg>)</span></td><td class="align_center">124.74</td><td class="align_center">5.92</td><td class="align_center">4.812</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Properties of piezoelectric ceramics.</div>

Journal of Nanomaterials

tab2

Table 2

Table 2: Force-Electric Coupling of Nanoscale Ferroelectric Domains Based on Piezoelectric Force Microscopy (PFM) 