Elastic Properties and the Band Gap of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.488899pt" id="M1" height="16.6806pt" version="1.1" viewBox="-0.0657574 -12.1917 68.4182 16.6806" width="68.4182pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g187-66" d="M687 0V35C623 43 611 56 577 144C512 316 450 490 386 665L335 652L130 138C97 54 84 43 18 35V0H242V35C169 44 166 58 181 106C193 146 206 182 217 213H409C424 173 439 130 449 100C465 56 460 44 401 35V0H687ZM390 266H234C260 337 285 410 313 483H316L390 266Z"/></g><g transform="matrix(.017,0,0,-0.017,12.115,0)"><path id="g187-109" d="M270 0V32C208 38 203 43 203 110V703C146 688 72 674 15 667V637C70 630 75 628 75 567V110C75 45 70 41 10 32V0H270Z"/></g><g transform="matrix(.017,0,0,-0.017,16.885,0)"><path id="g187-79" d="M724 650H480V616C554 612 574 595 579 552C582 523 587 476 587 387V211H584L201 650H16V616C59 612 81 604 100 580S120 538 120 472V264C120 176 114 131 110 98C106 55 83 39 27 35V0H272V35C198 38 181 57 176 101C173 131 168 176 168 264V488H171L587 -10H635V387C635 476 641 523 644 554C649 599 670 613 724 616V650Z"/></g><g transform="matrix(.012,0,0,-0.012,29.695,4.134)"><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(.017,0,0,-0.017,37.213,0)"><path id="g187-81" d="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z"/></g><g transform="matrix(.012,0,0,-0.012,47.531,4.134)"><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,-0.012,53.379,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.012,0,0,-0.012,60.72,4.134)"><use xlink:href="#g50-121"/></g></svg> Semiconductor Alloy: A Comparative Study of Various<i> Ab Initio</i> Approaches

<div>Composition dependence of the elastic constants in the wurtzite (WZ) structure. Each graph presents one constant calculated using all the methods. Filled points represent the supercell (SC) alloy simulation while empty points represent the alchemical mixing (AM). Squares: finite difference method, circles: clamped case of DFPT, and triangles: relaxed case of DFPT.</div>

Advances in Materials Science and Engineering

fig3

Figure 3

Figure 3: Elastic Properties and the Band Gap of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.488899pt" id="M1" height="16.6806pt" version="1.1" viewBox="-0.0657574 -12.1917 68.4182 16.6806" width="68.4182pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g187-66" d="M687 0V35C623 43 611 56 577 144C512 316 450 490 386 665L335 652L130 138C97 54 84 43 18 35V0H242V35C169 44 166 58 181 106C193 146 206 182 217 213H409C424 173 439 130 449 100C465 56 460 44 401 35V0H687ZM390 266H234C260 337 285 410 313 483H316L390 266Z"/></g><g transform="matrix(.017,0,0,-0.017,12.115,0)"><path id="g187-109" d="M270 0V32C208 38 203 43 203 110V703C146 688 72 674 15 667V637C70 630 75 628 75 567V110C75 45 70 41 10 32V0H270Z"/></g><g transform="matrix(.017,0,0,-0.017,16.885,0)"><path id="g187-79" d="M724 650H480V616C554 612 574 595 579 552C582 523 587 476 587 387V211H584L201 650H16V616C59 612 81 604 100 580S120 538 120 472V264C120 176 114 131 110 98C106 55 83 39 27 35V0H272V35C198 38 181 57 176 101C173 131 168 176 168 264V488H171L587 -10H635V387C635 476 641 523 644 554C649 599 670 613 724 616V650Z"/></g><g transform="matrix(.012,0,0,-0.012,29.695,4.134)"><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(.017,0,0,-0.017,37.213,0)"><path id="g187-81" d="M42 650V615C112 608 121 601 121 516V133C121 48 112 41 37 34V0H347V34C262 41 253 48 253 133V271L321 254C332 254 347 254 362 256C468 269 567 330 567 464C567 529 540 579 493 611C453 639 397 650 318 650H42ZM253 570C253 585 255 595 262 601C268 606 280 611 299 611C360 611 423 574 423 461C423 326 343 300 307 300C286 300 265 305 253 310V570Z"/></g><g transform="matrix(.012,0,0,-0.012,47.531,4.134)"><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,-0.012,53.379,4.134)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.012,0,0,-0.012,60.72,4.134)"><use xlink:href="#g50-121"/></g></svg> Semiconductor Alloy: A Comparative Study of Various<i> Ab Initio</i> Approaches 

Advances in Materials Science and Engineering

Elastic Properties and the Band Gap of Semiconductor Alloy: A Comparative Study of Various Ab Initio Approaches

Figure 3