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نظم ساختار نواري در سطح نانولايه هاي GdPtBi ،YPtBi و فاز نارسانای توپولوژيGdxY1-xPtBiبه ازاء x=0,0.25,0.5,0.75,1

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نظم ساختار نواري در سطح نانولايه هاي GdPtBi ،YPtBi و فاز نارسانای توپولوژيGdxY1-xPtBiبه ازاء x=0,0.25,0.5,0.75,1

چکیده

در این پایان نامه به مطالعه خواص ساختاری و الکترونی انبوهه YPtBi و GdPtBi از خانواده نیم هویسلر پرداخته شده است. نانولایه ترکیبات نیم هویسلر در مبدل­های الکتریکی و سلول­های خورشیدی مورد استفاده قرار می­گیرند. محاسبات در چارچوب نظریه تابعی چگالی و با روش امواج تخت بهبود یافته بعلاوه اوبیتال­های موضعی (APW+lo) و با استفاده از تقریب شیب تعمیم یافته (GGA96)، تقریب چگالی موضعی (LDA)، تقریب Engel-Vosko و پتانسیل تبادلی تصحیح شده بک-جانسون (mBJ) با کد محاسباتی وین انجام شده است.

خواص ساختاری آلیاژهای GdxY1-xPtBi به ازاء x=0,0.25,0.5,0.75,1و نانولایه­های YPtBi وGdPtBi در جهت بلورشناسی (001) مطالعه شده است. سپس وجود فاز توپولوژی را در این آلیاژها و نانولایه­ها مورد بررسی قرار داده­ایم. پارامترهای ساختاری مانند ثابت­های شبکه، مدول حجمی و مشتق مدول حجمی نسبت به فشار با استفاده از تقریب PBEsol در حضور برهمکنش اسپین-مدار و محاسبات فرومغناطیسی در توافق بهتری با نتایج تجربی موجود می­باشد. همچنین چگالی حالت­های الکترونی آلیاژها و نانولایه­ها را بررسی کرده­ایم. چگالی حالت­های الکترونی آلیاژ GdxY1-xPtBi را با استفاده از تقریب­های GGA، LDA، EV-GGAو پتانسیل تبادلی mBJ محاسبه کرده­ایم، که نتایج حاصل از چگالی حالت­های الکترونی نشان می­دهند،این آلیاژ به ازاءx=0 و x=0.25 به ترتیب شبه رسانای غیرمغناطیسی ورسانای فرومغناطیسی هستند،همچنین برای سایر مقادیر x آلیاژها شبه رسانای فرومغناطیسی هستند. نتایج ساختار نواری نشان می­دهند برای تمام مقادیر x آلیاژ GdxY1-xPtBi دارای فاز توپولوژی است (به معنای دیگر Γ6 وΓ8 جابه­جا شده است و وارونی نوار انرژی اتفاق افتاده است).

بعلاوه چگالی حالت­های الکترونی و ساختار نواری نانولایه­های YPtBi و GdPtBi با استفاده از تقریب­های GGA96، LDAو EV-GGA محاسبه شده است، که نتایج نشان می­دهند نانولایه­های YPtBi و GdPtBi، به ترتیب، دارای فاز غیرمغناطیسی و فرومغناطیسی هستند. همچنین این نانولایه­ها دارای نظم نواری معمولی هستند.

کلمات کلیدی: نظریه تابعی چگالی، فاز توپولوژی، خواص ساختاری، خواص الکترونی، ساختار نواری، چگالی حالت­های الکترونی، وارونی نوار.

فهرست مطالب

عنوان صفحه

فصل اول

نظریه تابعی چگالی

1-1 دستگاهبسذرهاي 0

1-2 تقريببورن-اپنهايمر 3

1-3 نظريهتابعيموج 4

1-3-1 روشهارتري 4

1-3-2 روشهارتري-فوک 8

1-4 نظريهتابعيچگالي 9

1-4-1 قضايايهوهنبرگ-کوهن 11

1-5 دستهمعادلاتتکذرهايکان-شم 15

1-6 انرژيتبادليهمبستگي 18

1-6-1تقريبچگاليموضعي 19

1-6-2تقريبشيبتعميميافته 19

1-6-3پتانسيلتبادلي-همبستگيبک-جانسوناصلاحشده (mBJ) 20

1-7روشهايحلمعادلههايکان-شم 21

1-7-1روشامواجتختبهبوديافته (APW) 22

1-7-2روشامواجتختبهبوديافتهخطي (LAPW) 24

عنوان                                                                                                              صفحه

1-7-3روشامواجتختبهبوديافتهخطيبااوربيتالهايموضعي(LAPW+lo) 25

1-8برهمکنشاسپين-مدار 25

1-8-1معادلاتديراک 26

فصل دوم

معرفی فاز توپولوژی

2-1 تقارنبرگشتزمان 30

2-1-1 برگشتزماندرسيستمهايفاقداسپين 31

2-1-2 برگشتزمانبرايسيستمهايبااسپين 33

2-2 تبهگنيکرامرز 36

2-2-1 تبهگنيکرامرزوحالتهايبلاخ 38

2-3 نظريهنواري 40

2-3-1 تأثيربرهمکنشاسپينمداربرتقارنبلور 40

2-4 اثرکوانتومیاسپينهال 42

2-4-1 حالتمرزي 43

2-4-2 ترازهايانرژي 46

2-4-3 تاريخچهنارساناهايتوپولوژي 47

عنوان                                                                                                              صفحه

فصل سوم

بررسی تشکیل فاز توپولوژی در آلیاژ GdxY1-xPtBi به ازاء x=0, 0.25, 0.5, 0.75, 1

3-1 آلياژهاينيمهویسلر 53

3-2 ساختاربلوري 54

3-2-1 پيوندشيميايي 54

3-2-2 شکافنواري 55

3-3 کاربردآلياژهاينيمهویسلر 56

3-3-1 سلولهايخورشيدي 56

3-3-2 ترموالکتريک 56

3-3-3 نارساناهايتوپولوژي 57

3-4 جزئياتمحاسبات 57

3-5 شبيهسازيساختاربلوريترکيباتYPtBiوGdPtBi 58

3-6 خواصساختاريترکيباتYPtBiوGdPtBi 58

3-6-1 ثابتهايشبکهتعادلي 58

3-7 بررسيخواصالکترونيترکيبات YPtBiوGdPtBi 61

3-7-1 چگاليحالتهايالکتروني 61

3-7-2 ساختارنواريترکيباتYPtBiوGdPtBi 65

3-7-3 بررسينظمنواريانبوههترکيباتYPtBiوGdPtBi 67

عنوان                                                                                                              صفحه

3-8 بررسيتشکيلفازتوپولوژيدرآلياژGdxY1-xPtBiبهازاءx=0,0.25,0.5,0.75,1 70

3-8-1 چگاليحالتهايالکترونيآلياژهايGdxY1-xPtBiبهازاءx=0.25,0.5,0.75 70

3-8-2 ساختارنواري 80

فصل چهارم

بررسی خواص الکترونی نانولایه های YPtBi و GdPtBi

4-1 لايههاينازک 87

4-2 جزئياتساختنانولايههايYPtBiوGdPtBiدرراستاي (001) 88

4-3چگاليحالتهايالکترونينانولايههايYPtBiوGdPtBi 89

4-4 ساختارنوارينانولايههايYPtBiوGdPtBi 93

4-5 بررسينظمنوارينانولايههاي YPtBiوGdPtBi 94

4-6 مقايسهنتايجنانولايههايYPtBiوGdPtBiباحالتانبوهه 97

نتایجحاصلازاینپایاننامه 100

منابعومأخذ 101

فهرست شکل­ها

عنوان                                                                                                              صفحه

شکل 1‑1:نمايشيازتقسيمفضايدرونياختهبسيطبهناحيهدرونجايگاهي (І) وبينجايگاهي (П). 22

شکل2-1 : مسيرکلاسيککهذرهدرt=0متوقفميشودوحرکتشمعکوسميگردد. 30

شکل2‑2: نمايشنواررسانشوظرفيت. 40

شکل 2‑3: تأثيربرهمکنشاسپينمداردرترازPدرمرکزمنطقهبريلوئن. الف-نمايشيازترازهادرنقطهΓبدوناثراسپينمدار. ب- جداييترازهاي p3/2وp1/2درحضوربرهمکنشاسپينمدار. ج- نمايشيازشبکهبدونتقارنواروني. 41

شکل 2-4: الف- حالتکوانتومیهال،ب- حالتکوانتومیاسپينهال. 43

شکل 2-5: مسيرحرکتالکترونبهدورناخالصي. الف-ساعتگرد،ب-پادساعتگرد. 44

شکل2-6: بازتابنورازسطحيکشيشهباروکشضدانعکاس. 44

شکل2-7: نماييازحالتکوانتومياسپينهال. 46

شکل 2-8:.ترازهايانرژيالف-نارسانامعمولي،ب-حالتکوانتومیهال،ج-حالتکوانتومیاسپينهال 47

شکل2-9: الف- نوارانرژيانبوههHgTeوCdTe. ب- نوارانرژيچاهکوانتومي(Hg|Cd)Te . ج-نمودارانرژيبرحسبضخامتچاهکوانتومي(Hg|Cd)Te. (بهترتيبازچپبهراست) 49

شکل2-10:ساختارالکترونينواريHgTe (CdTe) ،الف(د)-بدوناثرنسبيتي،ب(ه)-بادرنظرگرفتنبرهمکنشاسپينمدار،ج(ي)-بادرنظرگرفتنروابطکاملانسبيتي. 50

شکل3-1:الف-ساختارسنگنمک،ب-ساختارشبکهزینک-بلند،ج-ساختارخانوادهنیمهویسلرباگروهتقارنفضاییf4-3m 54

عنوان                                  صفحه

شکل 3‑2:گافنواريبرحسبميانگينعدداتمي. 55

شکل3-3: .مقايسهنظمنواريترکيبنيمهویسلرLuPtBiباHgTe. 57

شکل3-4: الف-ساختارYPtBi،ب-ساختارGdPtBiکهتوسطنرمافزارxcrysdenرسمشدهاست      58

شکل3-5: نمودارتغييراتانرژيکلبرحجمترکيب YPtBi. 59

شکل3-6:نمودارتغييراتانرژيکلبرحجمترکيب GdPtBi 59

شکل3-7: نمودارچگاليحالتهايالکترونيترکيبYPtBi. 61

شکل 3-8 : نمودارچگاليحالتهايالکترونيترکيبGdPtBi. 62

شکل 3-9: نمودارچگاليحالتهايالکترونيجزئيالف-ترکيبYPtBi،ب-ترکيبGdPtBi. 63

شکل 3-10:چگاليحالتهايالکترونياوربيتالياتمYدرترکيبYPtBi. 64

شکل3-11:چگاليحالتهايالکترونياوربيتالياتمGdدرترکيب GdPtBi .الف-اوربيتالs،ب-اوربيتالp،ج-اوربيتالd،د-اوربيتالf. 65

شکل3-12:ساختارنواريانبوههترکيبYPtBi. 66

شکل3-13: ساختارنواريانبوههترکيب GdPtBi . الف-اسپينبالا،ب-اسپينپايين 67

شکل3-14: ساختارنواريجزئيانبوههترکيب YPtBi . الف-اوربيتالهايs،ب-اوربيتالهايp 68

شکل3-15: ساختارنواريجزئيانبوههترکيبGdPtBiبرايالکترونهايبااسپينبالا. الف-اوربيتالهايS،ب-اوربيتالهايp 69

شکل3-16: چگاليحالتهايالکترونيبرايGd0.25Y0.75PtBiبااستفادهازرهيافتLDA. الف- چگاليحالتهايالکترونيکل،ب-چگاليجزئي 72

عنوان   صفحه

شکل3‑17:چگاليحالتهايالکترونيآلياژGd0.5Y0.5PtBiبااستفادهازرهيافتLDA. الف-چگاليکل،ب-چگاليجزئي. 74

شکل3‑18: چگاليحالتهايالکترونيآلياژGd0.75Y0.25PtBiبااستفادهازرهيافتLDA. الف-چگاليحالتهايالکترونيکل،ب-چگاليحالتهايالکترونيجزئي. 76

شکل3-19: چگاليحالتهايالکترونيآلياژ GdxY1-xPtBiبرايالکترونهايبا اسپین بالا بارهيافتLDA 79

شکل3‑20: چگاليحالتهايالکترونيآلياژGdxY1-xPtBiبرايالکترونهايبااسپينپايينبارهيافتLDA 79

شکل3‑21:ساختارنواريمربوطبهآلياژGd0.25Y0.75PtBi.الف-اوربيتالsالکترونهايبااسپينبالا،ب-اوربيتالpالکترونهايبااسپينبالا،ج- اوربيتالsالکترونهايبااسپينپايين،د- اوربيتالpالکترونهايبااسپينپايين. 81

شکل3‑22:ساختارنواريمربوطبهآلياژGd0. 5Y0. 5PtBi،الف-اوربيتالsالکترونهايبااسپينبالا،ب-اوربيتالpالکترونهايبااسپينبالا،ج- اوربيتالsالکترونهايبااسپينپايين،د- اوربيتالpالکترونهايبااسپينپايين. 82

شکل3‑23: ساختارنواريمربوطبهآلياژGd0.75Y0.25PtBi.الف-اوربيتالsالکترونهايبااسپينبالا،ب-اوربيتالpالکترونهايبااسپينبالا،ج- اوربيتالsالکترونهايبااسپينپايين،د- اوربيتالpالکترونهايبااسپينپايين. 83

شکل 4-1:ساختارلايهوزيرلايه 87

شکل4-2:ياختهيکهنانولايهالف-YPtBi،ب-GdPtBiکهبانرمافزارxcrysdenرسمشدهاست. 89

شکل4-3: چگاليحالتهايالکترونينانولايهYPtBiبااستفادهازرهيافتGGA96. 89

شکل4-4: چگاليحالتهايالکترونينانولايهGdPtBi 90

عنوان                                  صفحه

شکل4-5: چگاليحالتهايجزئياتمهايسطحنانولايهYPtBiبااستفادهازرهيافتGGA96.(اتمهايPtدرلايه6،اتمهايYوBiدرلايه 7 قرارگرفتهاست.) 91

شکل4-6:چگاليحالتهايالکترونيجزئياتمهايسطحنانولايهGdPtBiبااستفادهازرهيافتGGA9 92

شکل4-7: ساختارنوارينانولايهYPtBiبارهيافتEV-GGA 93

شکل4‑8 ساختارنوارينانولايهGdPtBiبارهيافتEV-GGAالف-الکترونهايبااسپينبالا،ب-الکترونهايبااسپينپايين. 94

شکل4-9:ساختارنواريجزئينانولايهYPtBiبااستفادهازرهيافتEV-GGA،الف-اوربيتالS،ب-اوربيتالp 95

شکل4-10:ساختارنوارينانولايهGdPtBiبااستفادهازرهيافتEV-GGA،الف(ج)-اوربيتالSالکترونهايبااسپينبالا(پايين)،ب(د)-اوربيتالpالکترونهايبااسپينبالا(پايين) 96

شکل4-11:چگاليحالتهاياتمهايسطحوانبوهه،الف-ترکيب،ب-اتمY،ج-اتمPt،د-اتمBi 97

شکل4-12: چگاليحالتسطحوانبوهه،الف-ترکيبب-اتمGd،ج-اتمPt،د-اتمBi 98

فهرست جدول­ها

عنوان                                                                                                             صفحه

جدول3-1: ثابتهايشبکهومدولحجميترکيبGdPtBi. 60

جدول3-2 : ثابتهايشبکهومدولحجميترکيبYPtBi. 60

جدول3-3: گشتاورمغناطيسي (µB) ترکيبGdPtBi. 64

جدول 3-4: قدرتوارونينوار(eV) برايترکيباتYPtBiوGdPtBi . 70

جدول‏3‑5: مقدارگشتاورمغناطيسيکلآلياژGdxY1-xPtBi. 77

جدول3-6. ضريبرسانندگيگرماییآلياژGdxY1-xPtBiبارهيافتهايمختلف. 78

جدول 3-7 قدرتوارونينوارآلياژGdxY1-xPtBiبااستفادهازرهيافتهايمختلف. 84

جدول4-1 :گشتاورمغناطيسي(Bµ) نانولايهGdPtBi 92

جدول4-2: ضريبرسانندگيگرمایینانولايههايYPtBiوGdPtBi 99

242 دیدگاه برای نظم ساختار نواري در سطح نانولايه هاي GdPtBi ،YPtBi و فاز نارسانای توپولوژيGdxY1-xPtBiبه ازاء x=0,0.25,0.5,0.75,1

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