A Comparative Analysis of Asymmetric (BaTiO<sub>3</sub>) <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-6.17692pt" id="M1" height="10.6452pt" version="1.1" viewBox="-0.0657574 -4.46828 37.9487 10.6452" width="37.9487pt"><g transform="matrix(.012,0,0,-0.012,0,4.134)"><path id="g50-41" d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"/></g><g transform="matrix(.012,0,0,-0.012,4.301,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.012,0,0,-0.012,10.149,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.012,0,0,-0.012,17.49,4.134)"><path id="g50-121" d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"/></g><g transform="matrix(.012,0,0,-0.012,24.325,4.134)"><path id="g50-42" d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"/></g><g transform="matrix(.012,0,0,-0.012,28.624,4.134)"><path id="g50-140" d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"/></g></svg>/(BaZrO<sub>3</sub>)<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.34426pt" id="M2" height="8.36642pt" version="1.1" viewBox="-0.0657574 -4.02216 16.0773 8.36642" width="16.0773pt"><g transform="matrix(.012,0,0,-0.012,0,4.134)"><use xlink:href="#g50-121"/></g><g transform="matrix(.012,0,0,-0.012,6.835,4.134)"><use xlink:href="#g50-140"/></g></svg> Superlattices via X-Ray Diffraction and Raman Spectroscopy

<div>(a) <i>θ</i>−2<i>θ</i> XRD profiles of asymmetric (BaTiO<sub>3</sub>)<svg height="8.06455pt" id="M22" style="vertical-align:-4.67949pt" version="1.1" viewbox="-0.0498162 -3.38506 28.749 8.06455" width="28.749pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,0,3.132)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,3.258,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.689,3.132)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.25,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.428,3.132)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.685,3.132)"><path d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"></path></g></svg>/(BaZrO<sub>3</sub>)<svg height="6.3382pt" id="M23" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -3.04709 12.1798 6.3382" width="12.1798pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,0,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.178,3.132)"><path d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"></path></g></svg> superlattices at different thicknesses of BT and BZ constituents. (b) XRD profile calculated for (BaTiO<sub>3</sub>)<svg height="8.06455pt" id="M24" style="vertical-align:-4.67949pt" version="1.1" viewbox="-0.0498162 -3.38506 28.749 8.06455" width="28.749pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,0,3.132)"><path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,3.258,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.689,3.132)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.25,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.428,3.132)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.685,3.132)"><path d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"></path></g></svg>/(BaZrO<sub>3</sub>)<svg height="6.3382pt" id="M25" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -3.04709 12.1798 6.3382" width="12.1798pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0091,0,0,-0.0091,0,3.132)"><path d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.178,3.132)"><path d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"></path></g></svg> SL with <i>x</i> = 0.7 ((BT)<sub>0.3Λ</sub>/(BZ)<sub>0.7Λ</sub> (black) in comparison with a measured XRD spectrogram (red). The variance between experiment and theory can be due to imperfect layer/layer interfaces that are neglected in the simulation model.</div>

Advances in Materials Science and Engineering

fig1

Figure 1

Figure 1: A Comparative Analysis of Asymmetric (BaTiO<sub>3</sub>) <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-6.17692pt" id="M1" height="10.6452pt" version="1.1" viewBox="-0.0657574 -4.46828 37.9487 10.6452" width="37.9487pt"><g transform="matrix(.012,0,0,-0.012,0,4.134)"><path id="g50-41" d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z"/></g><g transform="matrix(.012,0,0,-0.012,4.301,4.134)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.012,0,0,-0.012,10.149,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.012,0,0,-0.012,17.49,4.134)"><path id="g50-121" d="M545 403C545 425 527 451 498 451C448 451 400 404 312 286L290 341C262 412 246 451 219 451C182 451 138 404 92 345L112 323C152 368 169 378 181 378C192 378 201 359 216 321L257 214C184 115 142 69 113 69C102 69 93 73 88 79S78 89 68 89C47 89 24 61 24 40C24 8 49 -12 75 -12C125 -12 175 31 271 175L312 64C330 15 357 -12 382 -12C421 -12 475 35 515 98L496 121C466 88 439 62 420 62C402 62 384 92 363 147L325 247C349 280 374 309 397 333C422 361 446 381 462 381C471 381 481 374 488 366C493 360 499 357 505 357C521 357 545 380 545 403Z"/></g><g transform="matrix(.012,0,0,-0.012,24.325,4.134)"><path id="g50-42" d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z"/></g><g transform="matrix(.012,0,0,-0.012,28.624,4.134)"><path id="g50-140" d="M680 0V33C616 41 601 50 570 134C503 312 441 487 376 665L340 655C272 481 206 313 137 141C101 50 87 43 22 33V0H247V33C173 42 163 51 185 116C222 228 282 380 333 528H336C384 391 444 222 490 93C505 51 495 42 430 33V0H680Z"/></g></svg>/(BaZrO<sub>3</sub>)<svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.34426pt" id="M2" height="8.36642pt" version="1.1" viewBox="-0.0657574 -4.02216 16.0773 8.36642" width="16.0773pt"><g transform="matrix(.012,0,0,-0.012,0,4.134)"><use xlink:href="#g50-121"/></g><g transform="matrix(.012,0,0,-0.012,6.835,4.134)"><use xlink:href="#g50-140"/></g></svg> Superlattices via X-Ray Diffraction and Raman Spectroscopy 

Advances in Materials Science and Engineering

A Comparative Analysis of Asymmetric (BaTiO3) /(BaZrO3) Superlattices via X-Ray Diffraction and Raman Spectroscopy

Figure 1

A Comparative Analysis of Asymmetric (BaTiO₃) /(BaZrO₃) Superlattices via X-Ray Diffraction and Raman Spectroscopy