SnX 2o (X=Mg,Zn,Cd) مساهمة في دراسة الخواص البنيوية، الالكتـرونية، الضـوئية، المـرونة و الترموديناميكية للمواد السبينالية

(1)

ﻲﻤﻠﻌﻟا ﺚﺤﺒﻟا و ﻲﻟﺎﻌﻟا ﻢﯿﻠﻌﺘﻟا ةرازو

ﻒﯿﻄﺳ سﺎﺒﻋ تﺎﺣﺮﻓ ﺔﻌﻣﺎﺟ

1 طأ

ــــــ

ﺣوﺮ

ــ

ﺔ

ﻜﺑ ﺖﻣﺪﻗ

ــ

ﻌﻟا ﺔﯿﻠ

ــ

مﻮﻠ

ﺴﻗ

ـ

ءﺎﯾﺰﯿﻔﻟا ﻢ

مﻮﻠﻌﻟا ﻲﻓ هارﻮﺘﻛد ةدﺎﮭﺷ ﻰﻠﻋ لﻮﺼﺤﻠﻟ

ﺺﺼﺨﺘﻟا

:

ءﺎﯾﺰﯿﻓ

ﻢﺴﺠﻟا

ﺐﻠﺼﻟا

فﺮط ﻦﻣ

ﻋ

ــ

ﻟﻼ

ــــ

ﺟ ﻲ

ــــ

ﻤ

ــــ

لﺎ

ﺿﻮــــﻤﻟا

ـ

عﻮ

ﺘﻜﻟﻻا ،ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا ﺔﺳارد ﻲﻓ ﺔﻤھﺎﺴﻣ

ـ

ﻀﻟا ،ﺔﯿﻧوﺮ

ـ

ﻤﻟا ،ﺔﯿﺋﻮ

ـ

ﺔﻧوﺮ

ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا و

(

)

2 4

SnX O

X = Mg, Zn, Cd

ﺖﺸﻗﻮﻧ

ﺎﯿﻨﻠﻋ

ﺑ

ﺦﯾرﺎﺘ

18 /

02 /

2017

ﺔﻧﻮﻜﻤﻟا ﺔﻨﺠﻠﻟا مﺎﻣأ

ﻦﻣ

:

ﺴﯿﺋر

ــ

ــﺎ

1 ﻒ

ـ

ﯿـــــﻄﺳ سﺎـــﺒﻋ تﺎـــﺣﺮﻓ

ﺔﻌﻣﺎﺠﺑ ذﺎـــــﺘﺳأ

شﻮ

ـــــــ

ـﻌ

ﻣ لﺎ

ــ

ﻤﺟ .د

ﻓﺮﺸﻣ

ـــ

ﺎ

ﺤﺘﻤﻣ

ــ

ﺎﻨ

ــﻄﺳ سﺎـــﺒﻋ تﺎـــﺣﺮﻓ ﺔﻌﻣﺎﺠﺑ ذﺎـــــﺘﺳأ

ــ

ﻒـﯿـ

1 ﺔــــﻠﯿــﺴﻣ فﺎـــــﯿﺿﻮﺑ ﺪـــﻤﺤﻣ ﺔﻌﻣﺎﺠﺑ ذﺎـــــﺘﺳأ

ودﺎﻤﺣﻮﺑ ﺪﯿﺠﻤﻟا ﺪﺒﻋ .د

نﻮـﻨــــﺤﺳ ﻞﯿـﺿﻮﻓ .د

ﺤﺘﻤﻣ

ــ

ﺎﻨ

ﺎﻨــﺤﺘﻤﻣ

ﺞـﯾﺮﯾﺮﻋﻮﺑ جﺮﺑ ﻲﻤﯿھاﺮﺑﻻا ﺮﯿﺸﺒﻟا ﺔﻌﻣﺎﺠﺑ ذﺎﺘﺳأ

ﯿﻄﺳ سﺎﺒﻋ تﺎﺣﺮﻓ ﺔﻌﻣﺎﺠﺑ أ ﺮﺿﺎﺤﻣ ذﺎﺘﺳأ

ـ

ﻒ

1 لﻮــﺤﻛ ﻢﯿﻠﺤﻟا ﺪــﺒﻋ .د

ﻲــــــــﺤﯿﺷ ﺐﯿـﻄﻟا .د

ﺤﺘﻤﻣ

ــ

ﺎﻨ

ﺔ

ــ

ـــ

ﻠﯿﺴﻣ

فﺎﯿﺿﻮﺑ ﺪﻤﺤﻣ ﺔﻌﻣﺎﺠﺑ

أ ﺮﺿﺎﺤﻣ

ذﺎﺘﺳأ

ﻲ

ــ

ﺠ

ـــــــ

ﻌﺑ ﺐﯿ

ــ

ﺠﻧ .د

(2)

تاﺮﻜﺸ�

.ﻪيﻓ ﰷرﺎﺒ�ﻣ ﺎﺒ�يﻃ اﲑ�ثﻛ اﺪ�ﲪ ﻩﺪ�ﲪٔأ � ﺪﶵا و ﺮﻜﺸﻟا نٕا

زﺎﳒٕا ﰲ ﺪﯿﻌﺑ ؤأ ﺐﯾﺮﻗ ﻦﻣ ﱒﺎﺳ ﻦﻣ ﰻ ﱃٕا ﻞﯾﺰﳉا ﺮﻜﺸﻟ� مﺪﻘﺗٔأ

ﻟا ﻩﺬﻫ

ا �ﺎﺳﺮ

ﺔﻌﺿاﻮﺘﳌ

ﺺﺧٔأ و ،

ذﺎﺘ�ﺳ� ﺮ��

ودﲈﺣﻮﺑ ﺪﯿ�ا ﺪﺒﻋ

،

ﻒﯿﻄﺳ سﺎﺒﻋ تﺎ�ﺮﻓ ﺔﻌﻣﺎﲜ ﺚﺣ� و ذﺎﺘ�ﺳٔأ

1 ﻪﻌبتﺗ و ﻪﻓاﴍٕا ﲆ�

ﺮﳣ�ﺴﳌا

و ،�ﺎﺳﺮﻟا ﻩﺬﻫ ﱘﺪﻘﺗ ﻞيبﺳ ﰲ ﺔﳰﻘﻟا ﻪﲘﺎﺼﻧ و ﺎﻨﻟ

�ﺬﻛ

ﻪبﺣ و ةﺬﻔﻟا ﻪﺗدارٕا و ،ﺎﻨﻟ ﺔﻘﻠﻄﳌا ﻪﺘﻧﻮﻌﻣ

و ﲅﻌﻟا ﺮ�اﺰﺟ ءﺎﻨﺒﻟ ﺔﻨﯿتﻣ ﺪ�اﻮﻗ ءﺎﺳرٕا ﻞ�ٔأ ﻦﻣ ﺮﳣ�ﺴﳌا ﻩدﺎ� و ﻩﱪﺻو ،ﻂﻘﻓ ﻞﻤﻌﻟا و ﻞﻤﻌﻠل ضﺎيﻔﻟا

.ﺔﻓﺮﻌﳌا

ﰐاﺮﻜﺸتﺑ ﻪ�ﻮﺗٔأ ﲈﻛ

ﱃٕا

ذﺎﺘ�ﺳ�

شﻮﻌﻣ لﲈﺟ

،

ذﺎﺘ�ﺳٔأ

ﺚﺣ� و

ﺎﲜ

ﺔﻌﻣ

سﺎﺒﻋ تﺎ�ﺮﻓ

ﻒﯿﻄﺳ

1 ﺔﺸﻗﺎﻨﳌا ﺔﻨﳉ ﺔﺳﺎﺋﺮ� �ﻀﻔﺗ ﲆ�

.

ﱃٕا ﺮﻜﺸﻟ� ﻪ�ﻮﺗٔأ ﲈﻛ

ﺗﺎﺳ�

ﺬ

ﱒ و ﲔﻨﺤﺘﻤﳌا ﺔﻨﳉ ءﺎﻀﻋٔأ ة

:

ذﺎﺘ�ﺳ�

نﻮﻨﲮ ﻞﯿﺿﻮﻓ

،

ذﺎﺘ�ﺳٔأ

و

ﺚﺣ�

ﺔﻌﻣﺎﲜ

فﺎﯿﺿﻮﺑ ﺪﶊ

�ﯿ�ﺴﻣ

و ،

ذﺎﺘ�ﺳ�

لﻮﺤك ﲓﻠﳊا ﺪﺒﻋ

،

ﲑﺸبﻟا ﺔﻌﻣﺎﲜ ﺚﺣ� و ذﺎﺘ�ﺳٔأ

ﱕﺮ�ﺮﻋﻮﺑ جﺮ� ﻲﳰﻫاﺮ��

و

ﺘ�ﺳ�

ذﺎ

ﻲﺤﯿ�ﺷ ﺐﯿﻄﻟا

،

ذﺎﺘ�ﺳٔأ

ٔأ ﴐﺎﳏ

سﺎﺒﻋ تﺎ�ﺮﻓ ﺔﻌﻣﺎﲜ ﺚﺣ� و

ﻒﯿﻄﺳ

1 ذﺎﺘ�ﺳٔ�ا و ،

ﻲﺠﻌﺑ ﺐﯿﳒ

،

ذﺎﺘ�ﺳٔأ

ٔأ ﴐﺎﳏ

فﺎﯿﺿﻮﺑ ﺪﶊ ﺔﻌﻣﺎﲜ ﺚﺣ� و

�ﯿ�ﺴﻣ

.

رارز سرﺎﻓ ذﺎﺘ�ﺳ� �ٔأ و ﻲﻘيﻓر ﻲﻔﻜ� ﻻ �ذ نٔأ ﲏيﻘﯾ و ﺮﻜﺷٔأ و

ﻗ

ﺔﯾﺎﲜ ﺔﻌﻣﺎﲜ ﺔ

ءﺎﻘﻓر ﰻ و ،

ﻢﳯﻣ ﺮ�ذٔأ ةﲑﺴﳌا و بر�ا

ذﺎﺘ�ﺳٔ�ا

ﲑنﻣ

سﺎﻓر

ﻒﯿﻄﺳ ﺔﻌﻣﺎﲜ

1 و

ذﺎﺘ�ﺳٔ�ا

يداﺪ� ﺔﻔﯿﻠ�

ﻒﯿﻄﺳ ﺔﻌﻣﺎﲜ

1 ذﺎﺘ�ﺳ� و

.ﱁٕا...يوﺎﲜ ﻖﳊا ﺪﺒﻋ

ﺎﺘ�ﺳ� ﻢﳯﻣ ﺮ�ذٔأ ماﺮﻜﻟا ﰐﺬﺗﺎﺳٔأ ﰻ ﱃٕا ﺮﻜﺸﻟ� ﻪ�ﻮﺗٔأ نٔأ ﲏﺗﻮﻔﯾ ﻻ ﲈﻛ

ةذ

ﻲﻔﯾﴍ ﺔ�ﯿﻟوز

،

ةذﺎﺘ�ﺳٔأ

و

ﺔﻌﻣﺎﲜ ﺔثﺣ�

�ﯿ�ﺴﻣ فﺎﯿﺿﻮﺑ ﺪﶊ

ﻲﺠﻌﺑ ذﺎﺘ�ﺳ� و نﻮﻨﲮ ﻞﯿﺿﻮﻓ ذﺎﺘ�ﺳ� و ﺎﻨﻟ ﺔﻘﻠﻄﳌا ﺎﳤنﻮﻌﻣ ﲆ�

و ﺰ�اﺮﺣ دﺎنﻣ ذﺎﺘ�ﺳ� و ﺐﯿﳒ

و لﺪﻨﺻﻮﺑ ﺪﯿ�ا ﺪﺒﻋ ذﺎﺘ�ﺳٔ�ا

ﰊﺎﺒﺿ داﺮﻣ ذﺎﺘ�ﺳ� و ﺰ�ﺰﻌﺑ ﲓﻜﺣ ذﺎﺘ�ﺳ�

.ﱄ ﺎﻫﻮﻣﺪﻗ ﱵﻟا تاﺪ�ﺎﺴﳌا ﲆ� ﱒﺮﻜﺷٔأ تﺎﺷﻮﻬﻠﺑ ﲔﺴﺣ ذﺎﺘ�ﺳ�و

I

(3)

ءاﺪﻫٕﻻا

ﷲ ﻢﺴ�

ﻟا �و ﺪﶵا � ﻢﻬﻠلا ،

ﲈﻛ ﺮﻜﺸ

ﻚﻧﺎﻄﻠﺳ ﲓﻈﻋو ﻚ�و لﻼﳉ ﻲﻐبنﯾ

و ،

ﲑ� ﲆ� مﻼﺴﻟاو ةﻼﺼﻟا

ﶊ ﷲ دﺎﺒﻋ

ﺪﻌﺑ ﺎﻣٔأ ﲔﳌﺎﻌﻠل ﺔﲪر ثﻮﻌﺒﳌا ﺪ

:

ﻟا اﺬﻫ يﺪﻫٔأ

يﺪ� ةﺮﲦ ﻮﻫ ي�ا ﻊﺿاﻮﺘﳌا ﻞﻤﻌ

ﺎﻌﺴ� ﲏﺘﻠﲪ ﱵﻟا ﱃٕا

،

و ﻲـﺑرد ﲑﻨﯾ ﺎﺳاﱪﻧ ﱄ ﺖﻧﲀﻓ ﲇ�ٔ� تﺮﻬﺳ و

ءﺎﻄﻌﻟا ﺰﻣرو نﺎﻨﳊا ﻊﺒنﻣ

،

و

نﻣ

ﻊﺒ

ٔأ �ﻮﻤﻃ

ﷲ ﺎﻬﻈﻔﺣ ﺔبيﺒﳊا ﱊ

.

ﱃٕا

ﱵﳝﺰﻋ ماﻮﻗ ﻪﻣ�ﻫاو ﻪبﺣ نﰷ ﻦﻣ

ﱃٕا ،

ﷲ ﻪﻈﻔﺣ ﱄﺎﻐﻟا ﰊٔأ ﰐﺎيﺣ ءﺎﯿﺿ

.

�ﺎﺳﺮﻟا ﻩﺬﻫ زﺎﳒٕا �ﺻاﻮﻣ ﰲ ﲈﻋد ﱄ ﺖﻧﰷ ﱵﻟا ﺔﯿﻟﺎﻐﻟا ﱵﺟوز ﱃٕا

ةﺎﯿﳊا ﰲ ﰐﺮﻫز و يﺪﺒ� ة�ﻓ ﱃٕا و

ﻖﻟﺎﳋا ﺪﺒﻋ ﺐﯿﻬﺻ

و ...ﺪﲪٔأ و ﴬﳋ ﰐﻮﺧٕا ﰻ ﱃٕا و

ﺰﻌﻟا ﱵﺧ�أ

و ةﺰ�

ﺮ�� ﺺﺧٔأ

�ٔأ

نﰷ ي�ا ﺪﯿﻌﻟا

.ىﻮﺘ�ﺴﳌا اﺬﻫ ﱃٕا ﱄﻮﺻو و ﱵ�ﺳارد �ﺻاﻮﻣ ﰲ ﲈﻋد ﱄ

و

ﺖﯿ�ﺎتﻜﻟا ﱃٕا و اﲑﻐﺻ و اﲑﺒ� �ﺋﺎﻌﻟا ﺔﻓﰷ ﱃٕا

و ﻞﯿﻠﳉا ﺪﺒﻋ

�ﺷ

و ء�

ﲔﻘﯿﻟا رﻮﻧ

ﱘﺮﻣ و

ءﲈﺳٔأ و

.

:ﺚﺣﺎﺒﻟا

لﲈﺟ ﱄﻼ�

II

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ﺔﺳارد ﺖﻤﺗ صاﻮﺨﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا و ﺔﻧوﺮﻤﻟا ،ﺔﯿﺋﻮﻀﻟا ،ﺔﯿﻧوﺮﺘﻜﻟﻻا ،ﺔﯾﻮﯿﻨﺒﻟا 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O . لﺎﻤﻌﺘﺳﺎﺑ ﻞﻣﺎﻜﻟا نﻮﻤﻜﻟا ﻊﻣ ًﺎﯿﻄﺧ ةداﺰﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ﺔﻘﯾﺮط (FP-LAPW) لا ﺖﻠﻤﻌﺘﺳا .ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ رﺎطإ ﻲﻓ LDA و لا GGA ﺔﺠﻟﺎﻌﻤﻟ نﻮﻤﻛ لدﺎﺒﺘﻟا و ﻂﺑاﺮﺘﻟا (XC) بﺎﺴﺤﻟ ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا و ﺔﯿﻜﯿﻧﺎﻜﯿﻤﻟا و ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا ﺖﻠﻤﻌﺘﺳا . لا (GGA-EV) ﺔﻓﺎﺿا لا ﻰﻟإ LDA لاو GGA ﺔﺳارد ﻲﻓ صاﻮﺨﻟا ﺔﯿﺋﻮﻀﻟاو ﺔﯿﻧوﺮﺘﻜﻟﻹا . ﻢﯿﻗ ﻖﻓاﻮﺘﺗ ﺔﯿﻨﺒﻟا تﻼﻣﺎﻌﻣ ﺔﯾرﻮﻠﺒﻟا ﺔﯾرﺬﻟا تﺎﯿﺛاﺪﺣﻹا ،ﺔﯾرﻮﻠﺒﻟا ﺔﻜﺒﺸﻟا ﺖﺑﺎﺛ) طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻣو ( ﺔﺑﻮﺴﺤﻤﻟا ﺔﯿﺳﺎﺳﻻا ﺔﻟﺎﺤﻠﻟ ﻊﻣ ﺞﺋﺎﺘﻨﻟا ﺔﯿﺒﯾﺮﺠﺘﻟا ةﺮﻓﻮﺘﻤﻟا ﺔﯾﺮﻈﻨﻟاو . ﺔﺳورﺪﻤﻟا داﻮﻤﻟا نأ تﺎﺑﺎﺴﺤﻟا ﺞﺋﺎﺘﻧ ﺖﻨﯿﺑ ﻊﻧاﻮﻤﺑ ﻞﻗاﻮﻨﻟا فﺎﺼﻧأ ﺔﻠﺋﺎﻌﻟ ﻲﻤﺘﻨﺗ ةﺮﺷﺎﺒﻣ ﺔﯿﺳﺎﺳأ ﺔﻗﺎط -Γ -Γ . ﺎﻤﻛ تﺮﮭظأ ﺞﺋﺎﺘﻧ ﻂﺋاﺮﺷ ﺔﻗﺎﻄﻟا ﺔﯿﻧوﺮﺘﻜﻟﻻا ﻞﺼﺤﺘﻤﻟا ﺎﮭﯿﻠﻋ لﺎﻤﻌﺘﺳﺎﺑ لا GGA-EV ﻨﺴﺤﺗ ﺎ ﺮﺒﺘﻌﻣ ا ﺔﻧرﺎﻘﻣ تﺎﺒﯾﺮﻘﺘﻟﺎﺑ ىﺮﺧﻷا ﻲھو بﺮﻗأ ﻰﻟا ﺞﺋﺎﺘﻨﻟا ﻟا ﺔﯿﺒﯾﺮﺠﺘ . ﻊﻧاﻮﻣ ﻞﻛ ﺪﯾاﺰﺘﺗ .ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺪﯾاﺰﺘﺑ ﺔﺑﻮﺴﺤﻤﻟا ﺔﻗﺎﻄﻟا ﺔﯿﻧوﺮﺘﻜﻟﻹا تﻻﺎﺤﻟا ﺔﻓﺎﺜﻛ ﻞﯿﻠﺤﺗ ﻦﯿﺑ ﻊﻧاﻮﻣ ﻢﯿﻗ ﺺﻗﺎﻨﺗ نأ ﻦﻣ روﺮﻤﻟا ﺪﻨﻋ ﺔﻗﺎﻄﻟا 2 4 SnMg O ﻰﻟإ 2 4 SnZn O ﻢﺛ ﻰﻟإ 2 4 SnCd O ﻞﻋﺎﻔﺘﻟا ﻰﻟإ ﮫﻋﺎﺟرا ﻦﻜﻤﯾ -p d ﻲﻓ تﺎﺒﻛﺮﻤﻟا 2 4 SnZn O و 2 4 SnCd O . ﻦﻣ يﻮﻗﺎط لﺎﺠﻣ ﻲﻓ ﺔﯿﺋﻮﻀﻟا ﺖﺑاﻮﺜﻟا بﺎﺴﺣ ﻢﺗ 0 ﻰﻟإ 30 eV . ﺖﻨﯿﺑ ﯾاﺰﺗ تﺎﺑﺎﺴﺤﻟا ﺞﺋﺎﺘﻧ ﻦﻛﺎﺴﻟا لﺰﻌﻟا ﺖﺑﺎﺛ ﺪ 1(0) ε .ﺔﺳورﺪﻤﻟا تﺎﺒﻛﺮﻤﻠﻟ ﺔﻗﺎﻄﻟا ﻊﻧاﻮﻣ ﺺﻗﺎﻨﺗ ﻊﻣ ﻢﯿﻗ ﺺﻗﺎﻨﺘﺗ ﻦﻛﺎﺴﻟا رﺎﺴﻜﻧﻻا ﺔﻨﯾﺮﻗ (0) n ﺔﻨﻛﺎﺴﻟا ﺔﯿﺣﺎﻤﺴﻟا و 1(0) ε .ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺪﯾاﺰﺗ ﻊﻣ ﺪﯾﺪﺤﺗ ﻢﺗ ﺔﯿﺋﻮﻀﻟا فﺎﯿطﻻا ﻲﻓ ﺔﻤھﺎﺴﻤﻟا ﺔﯿﻧوﺮﺘﻜﻟﻻا تﻻﺎﺤﻟا ﻞﯿﻠﺤﺘﺑ ﻚﻟذو ﻰﻟإ ﺔﯿﺣﺎﻤﺴﻟا ﺔﻟاﺪﻟ ﻲﻠﯿﺨﺘﻟا ءﺰﺠﻟا ﻒﯿط ﻲﻧوﺮﺘﻜﻟا لﺎﻘﺘﻧا ﻞﻜﻟ ﺔﯾدﺮﻔﻟا تﺎﻤھﺎﺴﻤﻟا . ﻢﯿﻗ ﻖﻓاﻮﺘﺗ ﺎﮭﺑ ﺔﻄﺒﺗﺮﻤﻟا صاﻮﺨﻟا و ﺔﻧوﺮﻤﻟا تﻼﻣﺎﻌﻣ ﺖﺑاﻮﺛ) ﺔﻧوﺮﻤﻟا (C_{i j}) ، ﻎﻧﻮﯾ ﻞﻣﺎﻌﻣ ( )E ﺺﻘﻟا ﻞﻣﺎﻌﻣ ، ( )G نﻮﺳاﻮﺑ ﻞﻣﺎﻌﻣ ، ( )η يﺎﺒﯾد ةراﺮﺣ ﺔﺟرد و (θ_D) ( و ةرﻮﻠﺒﻟا يدﺎﺣﻷ تارﻮﻠﺒﻟا دﺪﻌﺘﻣ موﺪﻌﻤﻟا ﻂﻐﻀﻟا ﺖﺤﺗ ةﺮﻓﻮﺘﻤﻟا ﺔﯾﺮﻈﻨﻟا ﺞﺋﺎﺘﻨﻟا ﻊﻣ . ﺮﯿﻐﺘﺗ تﻼﻣﺎﻌﻣ ﺔﻧوﺮﻤﻟا (Ci j) ﻲﻄﺧ ﻞﻜﺸﺑ ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﻊﻣ P لﺎﺠﻣ ﻲﻓ ﻦﻣ 0 ﻰﻟإ 30 GPa . ﺔﺳارد ﺖﻤﺗ ﺔﻜﺒﺸﻟا ﺖﺑﺎﺛ) ﺔﻤﮭﻤﻟا ﺔﯿﺑﻮﻜﺳوﺮﻜﯾﺎﻤﻟا ﺔﯿﺋﺎﯾﺰﯿﻔﻟا تﻼﻣﺎﻌﻤﻟا ﻦﻣ ﺪﯾﺪﻌﻟا ﻰﻠﻋ ﻂﻐﻀﻟا و ةراﺮﺤﻟا ﺮﯿﺛﺄﺗ ﻞﻣﺎﻌﻣ ،ﺔﯾرﻮﻠﺒﻟا ﻂﻐﻀﻟا تﻮﺒﺜﺑ و ﻢﺠﺤﻟا تﻮﺒﺜﺑ ﺔﯾراﺮﺤﻟا ﺔﻌﺴﻟا ،يراﺮﺤﻟا دﺪﻤﺘﻟا ﻞﻣﺎﻌﻣ ،طﺎﻐﻀﻧﻻا و (يﺎﺒﯾد ةراﺮﺣ ﺔﺟرد ﮫﺒﺸﻟا جذﻮﻤﻨﻟا لﺎﻤﻌﺘﺳﺎﺑ ﻟا يﺎﺒﯾﺪﻟ ﻲﻧﻮﻣﺮﮭ . III

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The structural, electronic, optical, elastic and thermodynamic properties of three principal representatives of spinel oxides SnMg2O4, SnZn2O4 and SnCd2O4 have been

investigated using the Full Potential Linearized Augmented Plane Wave method (FP-LAPW) within density functional theory. The structural parameters, including the lattice constant (a), the free internal parameter (u) of the oxygen atom, the bulk modulus (B) and its pressure derivative (B') of the considered compounds, calculated using both the local density (LDA) and generalized gradient approximations (GGA) to the exchange-correlation potential, are consistent with the available literature data. The electronic properties, including the band structure, density of states and charge-carrier effective masses, of the studied materials are explored in detail using, in addition to the LDA and GGA-PBE, a new form of the GGA proposed by Engel-Vosko; named the GGA-EV, which is known by its improvement of the bands gaps. The results obtained for the band structure using GGA-EV show a significant improvement over other theoretical works and are closer to the experimental data. Optical functions, including the dielectric function ( )ε , the refractive index ( )n , the extinction coefficient ( )k , the reflectivity ( )R , the linear absorption spectrum ( )α and the electron energy-loss ( )L are calculated for the energy range 0-30 eV. The origins of the peaks and structures in the optical spectra are determined in terms of the calculated energy band structures. For a good description of the mechanical behavior of the studied compounds, we have first calculated theirs single-elastic constants (C_ij). The obtained numerical values of C_ij have been then used

to estimate the elastic anisotropy, verify the mechanical stability of the spinel structure, and also to calculate the sound waves velocities along the principles crystallographic directions. Based on the Voigt-Reuss-Hill method values, we have investigated the elastic properties of the polycrystalline phase of the considered compounds, including the bulk modulus B, shear

modulus G, Young modulus E and Poisson’s ratio η. The elastic properties have been

completed by calculating the isotropic acoustic wave velocities and Debye temperature.

Thermal and pressure effects on some macroscopic properties of SnMg2O4, SnZn2O4 and

SnCd2O4 are predicted using the quasi-harmonic Debye model in which the lattice vibrations

are taken into account. We have computed the variations of the lattice constant (a), bulk

modulus (B), volume expansion coefficient (α), heat capacities (CV and CP) and Debye

temperature (θD)versus pressure and temperature in the ranges of 0 –30 GPa and 0 –1600 K.

The results of the present study are compared with the available experimental and theoretical data in the scientific literature to test the reliability of our results.

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1) Theoretical prediction of the structural, electronic and optical properties of SnB2O4 (B = Mg, Zn, Cd).

D. Allali, A. Bouhemadou, S. Bin-Omran.

Computational Materials Science 51 (2011) 194–205.

2) Prediction study of the elastic and thermodynamic properties of the SnMg2O4, SnZn2O4 and SnCd2O4 spinel oxides.

D. Allali, A. Bouhemadou, F. Zerarga, M.A. Ghebouli, S. Bin-Omran.

Computational Materials Science 60 (2012) 217–223.

3) Electronic and optical properties of ZnSc2S4 and CdSc2S4 cubic spinels by

the modified Becke - Johnson density functional.

A. Bouhemadou, S. Al-Essa, D. Allali, M.A. Ghebouli, S. Bin-Omran. Solid State Sciences 20 (2013) 127–134.

4) Electronic and optical properties of the SiB2O4 (B=Mg, Zn, and Cd) spinel

oxides : An ab initio study with the Tran-Blaha-modified Becke - Johnson density functional.

D. Allali, A. Bouhemadou, E. Muhammad Abud Al Safi, S. Bin-Omran,

M. Chegaar, R. Khenata, A.H. Reshak. Physica B 443 (2014) 24-34.

5) Elastic and thermodynamic properties of the SiB2O4 (B = Mg, Zn and Cd)

cubicspinels: An ab initio FP-LAPW study.

A. Bouhemadou, D. Allali, S. Bin-Omran, E. Muhammad Abud Al Safi, R. Khenata, Y. Al-Douri.

Materials Science in Semiconductor Processing 38 (2015) 192-202.

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density functional.

A. Bouhemadou, S. Bin-Omran, D. Allali, S.M. Al-Otaibi, R. Khenata, Y. Al-Douri, M. Chegaar, A.H. Reshak.

Materials Research Bulletin 64 (2015) 337-346.

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DFT

:

ﺔﯿﻧوﺮﺘﻜﻟﻻا ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ

(Density Functional Theory)

LDA

: ﻊﺿﻮﻤﻟا ﺔﻓﺎﺜﻛ ﺐﯾﺮﻘﺗ

(

Local Density Approximation

)

LSDA

:

ﻲﻌﺿﻮﻤﻟا ﻦﯿﺒﺴﻟا ﺔﻓﺎﺜﻛ ﺐﯾﺮﻘﺗ

(

Local Spin Density Approximation

)

GGA

:

ﻢﻤﻌﻤﻟا جرﺪﺘﻟا ﺐﯾﺮﻘﺗ (Generalized Gradient Approximation)

APW : ﻻا جاﻮﻣ ﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا ةداﺰ

(Augmented Plane Wave)

LAPW : ﻻا ﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣ ةداﺰ ﺎﯿﻄﺧ

(

Linearised Augmented Plane Wave

)

− FP LAPW : ﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ةداﺰ ﻞﻣﺎﻜﻟا نﻮﻤﻜﻟا ﻊﻣ ًﺎﯿﻄﺧ

: Full potential Linearized Augmented plane Wave −

FP LAPW

: Perdew−Burke Ernzerhof−

PBE

: Self Consistent Field

SCF ZB : ناﻮﻠﯾﺮﺑ ﺔﻘﻄﻨﻣ (Brillouin Zone) EOS : ﺔﯿﺳﺎﺳﻻا ﺔﻟﺎﺤﻟا ﺔﻟدﺎﻌﻣ

(

Equation of state

)

0 B : طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻣ (Bulk modulus) 0 B′ : طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻤﻟ ﻰﻟوﻻا ﺔﻘﺘﺸﻤﻟا (pressure derivative) XC E : طﺎﺒﺗرﻻا و لدﺎﺒﺘﻟا ﺔﻗﺎط

(

Exchange Correlation energy−

)

F E : ﻲﻣرﺎﻓ ﺔﻗﺎط

(

Fermi energy

)

SG : ﺔﯿﺋﺎﻀﻔﻟا ةﺮﻣﺰﻟا (Space Group) G : ﺺﻘﻟا ﻞﻣﺎﻌﻣ

(

Shear modulus

)

E : ﻎﻧﻮﯾ ﻞﻣﺎﻌﻣ

(

Young Modulus

)

ν : نﻮﺳاﻮﺑ ﻞﻣﺎﻌﻣ (Poisson coefficient) ijkl C : ﺔﻧوﺮﻤﻟا ﺖﺑاﻮﺛ ﺪﺘﻤﻣ

(

Tensor of elastic constants

)

ijkl

S

:

ﺔﻋوﺎﻄﻤﻟا ﺔﻧوﺮﻤﻟا تﻼﻣﺎﻌﻣ

(Tensor of constants deformation)

A

:

ﺮﻨﯾز ﻦﯾﺎﺒﺗ ﻞﻣﺎﻌﻣ

(

Zener anisotropy factor

)

g E : ضﺮﻋ ﻂﯾﺮﺷ ﺔﻋﻮﻨﻤﻤﻟا ﺔﻗﺎﻄﻟا

(

Energy band gap

)

DOS : تﻻﺎﺤﻟا ﺔﻓﺎﺜﻛ

(

Density of states

)

/ TDOS PDOS : ﻟا تﻻﺎﺤﻟا ﺔﻓﺎﺜﻛ / ﺔﯿﻠﻜﻟا تﻻﺎﺤﻟا ﺔﻓﺎﺜﻛ ﺰﺠ ﺔﯿﺋ

(

Total Partial density of states/

)

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ﮭﻔﻟا

ـ

ــــــ

سﺮ

تاﺮﻜﺸﺗ ءاﺪھﻻا ﺺﺨﻠﻣ Abstract ﺔﯿﻤﻠﻌﻟا تارﻮﺸﻨﻤﻟا تﺎﺤﻠﻄﺼﻤﻟا لﺎﻜﺷﻻا ﺔﻤﺋﺎﻗ لواﺪﺠﻟا ﺔﻤﺋﺎﻗ ﺔﻣﺎﻋ ﺔﻣﺪﻘﻣ 1.1 ﺔﻣﺪﻘﻣ 2.1 ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا تﺎﺒﻛﺮﻣ 3.1 ﺔﯾﺪﯿﺴﻛوﻷا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا 4.1 ﻦﻣ فﺪﮭﻟا ﺔﻟﺎﺳﺮﻟا 5.1 ﺔﻟﺎﺳﺮﻟا ﺔﯿﻨﺑ ﻊـــــــــــــــﺟارﻣﻟا :لوﻻا مﺳﻘﻟا يرظﻧﻟا رﺎطﻻا :لوﻻا ﻞﺼﻔﻟا ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ 1.1 ﺔﻣﺪﻘﻣ 2.1 :لوﻷا ىﻮﺘﺴﻤﻟا نرﻮﺑ ﺐﯾﺮﻘﺗ -ا ﺮﻤﯾﺎﮭﻨﺑ 3.1 :ﻲﻧﺎﺜﻟا ىﻮﺘﺴﻤﻟا ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ 1.3.1 تﺎﯾﺮﻈﻧ غرﺎﺒﻨھﻮھ و ﻦـھﻮﻛ 2.3.1 تﻻدﺎﻌﻣ ﻦھﻮﻛ مﺎﺷ 4.1 :ﺚﻟﺎﺜﻟا ىﻮﺘﺴﻤﻟا ﻦھﻮﻛ تﻻدﺎﻌﻣ لﻮﻠﺣ مﺎﺷ 5.1 ﺔﯿﻟاد لدﺎﺒﺗ طﺎﺒﺗرا I II III IV V VII XII XVI 02 03 06 07 08 09 14 15 16 16 17 20 20 VIII

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1.5.1 ﻊﺿﻮﻤﻟا ﺔﻓﺎﺜﻛ ﺐﯾﺮﻘﺗ 2.5.1 مﻣﻌﻣﻟا جردﺗﻟا بﯾرﻘﺗ ﻊــﺟاﺮﻤﻟا :ﻲﻧﺎﺜﻟا ﻞﺼﻔﻟا ﺎﯿﻄﺧ ةﺪﯾاﺰﺘﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ﺔﻘﯾﺮط 1.2 ﺔﻣﺪﻘﻣ 2.2 ﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا ﺔﺟﻮﻤﻟا ﺔﻘﯾﺮط اﺰ ةد APW 3.2 ﺔﯾﻮﺘﺴﻤﻟا ﺔﺟﻮﻤﻟا ﺔﻘﯾﺮط ا ةداﺰﻤﻟ ﺎﯿﻄﺧ LAPW 4.2 ﺔﻘﯾﺮط ﺔﯾﻮﺘﺴﻤﻟا ﺔﺟﻮﻤﻟا ةداﺰﻤﻟا ﺎﯿﻄﺧ ﻊﻣ ﻤﻟا تاراﺪﻤﻟا ﺔﯿﻌﺿﻮ LAPW+LO 5.2 ﺔﻘﯾﺮط ﺔﯾﻮﺘﺴﻤﻟا ﺔﺟﻮﻤﻟا ةداﺰﻤﻟا ﺔﯿﻌﺿﻮﻤﻟا تاراﺪﻤﻟا ﻊﻣ APW+lo 6.2 ﺞﻣﺎﻧﺮﺑ WIEN2k 1.6.2 ﺔﯿﻨﺒﻟا ﻒﻠﻣ ﺮﯿﻀﺤﺗ 2.6.2 داﺪﻋﻹا ﺞﻣﺎﻧﺮﺑ 3.6.2 ةرود داﺪﻋإ SCF 7.2 بﺎﺴﺤﻟا ﻞﯿﺻﺎﻔﺗ 8.2 برﺎﻘﺘﻟا رﺎﺒﺘﺧا 1.8.2 طﺎﻘﻧ دﺪﻌﻟ رﺎﯿﺘﺧا ﻦﺴﺣا K 2.8.2 ﻞﻣﺎﻌﻤﻠﻟ رﺎﯿﺘﺧا ﻦﺴﺣأ min max MT R ×K ﻊــﺟاﺮﻤﻟا :ﻲﻧﺎﺜﻟا ﻢﺴﻘﻟا ﺔﺸﻗﺎﻨﻤﻟا و ﺞﺋﺎﺘﻨﻟا :ﺚﻟﺎﺜﻟا ﻞﺼﻔﻟا ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا 1.3 ﺔﯿﺳﺎﺳﻻا ﺔﻟﺎﺤﻠﻟ ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا 2.3 ﺔﺳارد و ﺔﯾرﻮﻠﺒﻟا ﺔﻜﺒﺸﻟا ﺖﺑﺎﺛ ﻰﻠﻋ ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺮﯿﺛﺄﺗ ﻲﻧﻮﯾﻻا ﻞﻣﺎﻌﻤﻟا ﻊـﺟاﺮﻤﻟا :ﻊﺑاﺮﻟا ﻞﺼﻔﻟا ﺔﯿﻧوﺮﺘﻜﻟﻻا صاﻮﺨﻟا 1.4 ﻂﺋاﺮﺷ ﺔﻗﺎﻄﻟا ﺔﯿﻧوﺮﺘﻜﻟﻻا 2.4 تﺎﺒﻛﺮﻤﻠﻟ ﺔﯿﺌﯾﺰﺠﻟا و ﺔﯿﻠﻜﻟا ﺔﯿﻧوﺮﺘﻜﻟﻹا تﻻﺎﺤﻟا ﺔﻓﺎﺜﻛ 20 21 22 24 24 26 27 27 28 28 28 29 30 32 32 33 34 37 43 45 47 53 IX

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3.4 و تﺎﻧوﺮﺘﻜﻟﻺﻟ ﺔﻟﺎﻌﻔﻟا ﺔﻠﺘﻜﻟا ﺔﺳارد بﻮﻘﺜﻟا 4.4 ﺔﻗﺎﻄﻟا ﻊﻧاﻮﻣ ﻰﻠﻋ ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺮﯿﺛﺄﺗ ﺔﺳارد ﻊـﺟاﺮﻤﻟا :ﺲﻣﺎﺨﻟا ﻞﺼﻔﻟا ﺔﯿﺋﻮﻀﻟا صاﻮﺨﻟا 1.5 ﺗ ﻒﯾرﺎﻌ 2.5 ﺞﺋﺎﺘﻨﻟا ﺔﺸﻗﺎﻨﻣ 1.2.5 ﺔﻟاد ﺔﯿﺣﺎﻤﺴﻟا 2.2.5 صﺎﺼﺘﻣﻻا ﻞﻣﺎﻌﻣ 3.2.5 ﻟا ﻞﻣﺎﻌﻣ و رﺎﺴﻜﻧﻻا ﺔﻨﯾﺮﻗ دﻮﻤﺨ 4.2.5 عﺎﯿﺿ ﺔﻟادو سﺎﻜﻌﻧﻻا ﻒﯿط ﺔﯿﻧوﺮﺘﻜﻟﻻا ﺔﻗﺎﻄﻟا 5.2.5 ﺔﺳارد ﻦﻛﺎﺴﻟا لﺰﻌﻟا ﺖﺑﺎﺛ ﻰﻠﻋ ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺮﯿﺛﺄﺗ ﻊﺟاﺮــــــﻤﻟا :سدﺎﺴﻟا ﻞﺼﻔﻟا ﺔﻧوﺮﻤﻟا صاﻮﺧ 1.6 ﺔﯿﻠﯿﻠﺤﺗ ﺔﺳارد 1.1.6 دﺎﮭﺟﻹا ﺪﺘﻤﻣ Tensor of stress 2.1.6 هﻮﺸﺘﻟا ﺪﺘﻤﻣ Tensor of deformation 2.6 مﺎﻌﻟا كﻮـــــھ نﻮﻧﺎــــــﻗ 3.6 ﺔﺒﻌﻜﻤﻟا ةرﻮﻠﺒﻟا ﺔﻧوﺮﻣ تﻼﻣﺎﻌﻣ 4.6 ﺔﺑﻼﺼﻟا و ﺔﻋوﺎﻄﻤﻟا ﺔﻧوﺮﻤﻟا تﻼﻣﺎﻌﻣ ﻦﯿﺑ ﺔﻗﻼﻌﻟا 5.6 بﺎﺴﺤﻟ ﺔﻠﻤﻌﺘﺴﻤﻟا ﺔﻘﯾﺮﻄﻟا ﺔﻧوﺮﻤﻟا ﺖﺑاﻮﺛ 6.6 ﺞﺋﺎﺘﻨﻟا ﺔﺸﻗﺎﻨﻣ 1.6.6 ﺎﮭﺑ ﺔﻘﻠﻌﺘﻤﻟا صاﻮﺨﻟا و ﺔﻧوﺮﻤﻟا ﺖﺑاﻮﺛ 2.6.6 يﺎﺒﯾد ةراﺮﺣ ﺔﺟرد 3.6.6 ﺔﻧﺮﻤﻟا جاﻮﻣﻷا ﺔﻋﺮﺳ 4.6.6 ﺔﻧوﺮﻤﻟا ﺖﺑاﻮﺛ ﻰﻠﻋ ﻲﻜﯿﺗﺎﺘﺳورﺪﯿﮭﻟا ﻂﻐﻀﻟا ﺮﯿﺛﺄﺗ طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻣ و ﻊﺟاﺮــﻤﻟا 58 59 62 64 66 66 81 82 83 85 87 89 89 91 94 97 98 98 99 101 104 105 107 109 X

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:ﻊﺑﺎﺴﻟا ﻞﺼﻔﻟا ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا صاﻮﺨﻟا

1.7 ﻟا يﺎﺒﯾﺪﻟ ﻲﻧﻮﻣﺮﮭﻟا ﮫﺒﺸﻟا جذﻮﻤﻨ The quasi-harmonic Debye model

2.7 ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا صاﻮﺨﻟا ﺔﺳارد 1.2.7 ﺔﯾرﻮﻠﺒﻟا ﺔﻜﺒﺸﻟا ﺖﺑﺎﺛ تاﺮﯿﻐﺗ a ﻂﻐﻀﻟا و ةراﺮﺤﻟا ﺔﺟرد ﺔﻟﻻﺪﺑ 2.2.7 طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻣ 3.2.7 يراﺮﺤﻟا دﺪﻤﺘﻟا ﻞﻣﺎﻌﻣ 4.2.7 ﻢﺠﺤﻟا تﻮﺒﺜﺑ ﺔﯾراﺮﺤﻟا ﺔﻌﺴﻟا تاﺮﯿﻐﺗ 5.2.7 ﻂﻐﻀﻟا تﻮﺒﺜﺑ ﺔﯾراﺮﺤﻟا ﺔﻌﺴﻟا تاﺮﯿﻐﺗ 6.2.7 يﺎﺒﯾد ةراﺮﺣ ﺔﺟرد تاﺮﯿﻐﺗ ﻊﺟاﺮـﻤﻟا ﺔﻣﺎﻋ ﺔﺻﻼﺧ ﺔﻣﺎﻋ ﺔﺻﻼﺧ 1 ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا . 2 ﺔﯿﻧوﺮﺘﻜﻟﻻا صاﻮﺨﻟا . 3 ﺔﯿﺋﻮﻀﻟا صاﻮﺨﻟا . 4 ﺔﻧوﺮﻤﻟا صاﻮﺧ . 4 ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا صاﻮﺨﻟا . 111 113 113 115 117 119 121 123 126 128 128 128 129 129 130 XI

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ﻗ

ـــــــ

ﺷﻻا ﺔﻤﺋﺎ

ـﻜ

ــــ

لﺎ

Figure 1.1: Flow chart for iterative solution of the Kohn-Sham equations. 19 Figure 2.1: Distribution of chemical unit cell spheres: muffin tin region (I) and interstitial

region (II). 25

Figure 2.2: The structure of the program WIEN2k. 30 Figure 2.3: Convergence of the total energy of SnMg2O4 function of the number of k-points k

in the irreductible Brillouin zone using LDA. 32

Figure 2.4: Convergence of the total energy of SnMg2O4 function of the number of cutoff

parameter R_MTmin×K_maxusing LDA. 33

Figure 3.1: A schematic representation of the cubic spinel structure of SnM2O4. Oxygen

atoms (red spheres) occupy the corners of the octahedral and tetrahedral; Sn and Mg are at the centres of the tetrahedral and octahedral, respectively. 38

Figure 3.2: Total energy Variation as a function of primitive cell volume obtained using : The LDA for SnMg2O4, SnZn2O4 and SnCd2O4. 40

Figure 3.3: lattice constant-pressure relation(a−p); the solid line is a quadratic least-squares

ﬁt: 2

0

( )

a P = +a αP+βP using the LDA for SnMg O , ₂ ₄ SnZn O and 2 4 SnCd O . 44 2 4

Figure 3.4: Internal parameter-pressure relation (u−p); the solid line is a quadratic least-squares ﬁt: u P

( )

= +u₀ qP rP+ 2) using the LDA for SnMg O , ₂ ₄ SnZn O and₂ ₄ SnCd O . 44 ₂ ₄

Figure 4.1: First Brillouin zone of the FCC lattice, the high symmetry points are indicated. 47 Figure 4.2: Electronic band structure of the cubic spinel SnMg2O4 along the high-symmetry

directions in the Brillouin zone, calculated using the LDA and GGA-EV. The Fermi level is

shifted to zero. 50

Figure 4.3: Electronic band structure of the cubic spinel SnZn2O4 along the high-symmetry

shifted to zero. 51

Figure 4.4: Electronic band structure of the cubic spinel SnCd2O4 along the high-symmetry

shifted to zero. 52

Figure 4.5: Site and angular momentum decomposed DOS for the cubic spinel SnMg2O4. The

Fermi level is set to zero. 55

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Figure 4.6: Site and angular momentum decomposed DOS for the cubic spinel SnZn2O4. The

Figure 4.7: Site and angular momentum decomposed DOS for the cubic spinel SnCd2O4. The

Figure 4.8: Pressure dependence of direct (Γ-Γ, L-L, X-X, K-K, W-W) and indirect

(K -Γ, L -Γ) energy band gaps for the cubic spinel SnMg2O4. The solid lines represent the

quadratic fit function. 60

(K -Γ, L -Γ) energy band gaps for the cubic spinel SnZn2O4. The solid lines represent the

(K -Γ, L -Γ) energy band gaps for the cubic spinel SnCd2O4. The solid lines represent the

Figure 5.1:Interactions of electromagnetic radiation with matter-absorption, reflection,

transmission. 64

Figure 5.2: Calculated imaginary part of the dielectric function for the spinel cubic SnMg O₂ ₄ , SnZn2O4 and SnCd2O4 at zero pressure and at 50 GPa. 68

Figure 5.3: Calculated real part of the dielectric function for the spinel cubic SnMg O , ₂ ₄ SnZn2O4 and SnCd2O4 at zero pressure and at 50 GPa. 69

Figure 5.4: The decomposition of the imaginary part of the dielectric function into

band-to-band contributions (top panel) and the transition energy band-to-band structure (down panel) for

2 4

SnMg O . 78

band-to-band contributions (top panel) and the transition energy band-to-band structure (down panel) for SnZn2O4. 79

band-to-band contributions (top panel) and the transition energy band-to-band structure (down panel) for SnCd2O4. 80

Figure 5.7: Absorption spectra of the spinel oxides SnMg O , SnZn₂ ₄ 2O4 and SnCd2O4 as

calculated using the EV-GGA functional. 81

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Figure 5.8: Refractive index n

( )

ω and extinction coefficient K

( )

ω spectra for the cubic spinel SnMg2O4, SnZn2O4 and SnCd2O4. 82

Figure 5.9: Optical reflectivity R

( )

ω and electron energy-loss function L

( )

ω spectra for the cubic spinel SnMg2O4. 83

( )

ω spectra for the cubic spinel SnZn2O4. 84

( )

ω spectra for the cubic spinel SnCd2O4. 84

Figure 5.12: Pressure dependence of the static dielectric constants (0)ε and static Refractive index constants n(0) for the cubic spinel SnMg2O4, SnZn2O4 and SnCd2O4. 86

Figure 6.1: Force exerted on the faces of a cube of an unit volume, in a body subject to

homogeneous constraints. 90

Figure 6.2: Stress compounds in the plane passing through the middle of the cube and

parallel to the C level (X2-X3). 91

Figure 6.3: Illustrates tow points of the body A and B, which occupy sites under

deformations. 92

Figure 6.4: The variation of total energy as a function of orthorhombic and monoclinic stress,

applied for SnMg2O4 using the LDA (a) and the GGA (b). 100

applied for SnZn2O4 using the LDA (a) and the GGA (b). 100

applied for SnCd2O4 using the LDA (a) and the GGA (b). 101

Figure 6.7: Single-crystal elastic constants and the bulk modulus (in GPa) as functions of

pressure for the SnMg2O4, SnZn2O4 and SnCd2O4 compounds. 108

Figure 7.1: Lattice constant versus temperature at different pressures (a). Lattice constant

versus pressure at different temperatures (b) for the SnMg2O4. 114

versus pressure at different temperatures (b) for the SnZn2O4. 114

versus pressure at different temperatures (b) for the SnCd2O4. 115

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Figure 7.4: The bulk modulus as function of temperature at different pressures (a). The bulk

modulus as function of pressure at T = 300 K (b) for the SnMg2O4. 116

modulus as function of pressure at T = 300 K (b) for the SnZn2O4. 116

modulus as function of pressure at T = 300 K (b) for the SnCd2O4. 117

Figure 7.7: Variation of the volume expansion coefficient with temperature (a) and with

pressure (b) for the SnMg2O4. 118

pressure (b) for the SnZn2O4. 118

pressure (b) for the SnCd2O4. 119

Figure 7.10: Heat capacity CV as function of temperature at pressure of 0, 10, 20 and 30 GPa

for the SnMg2O4. 120

for the SnZn2O4. 120

for the SnCd2O4. 121

Figure 7.13: Variation of the specific heat capacity CP with temperature at different pressure

for SnMg2O4. 122

for SnZn2O4. 122

for SnCd2O4. 123

Figure 7.16: Variation of the Debye temperature with temperature (a) and with pressure (b)

for the SnMg2O4. 124

for the SnZn2O4. 124

for the SnCd2O4. 125

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Table 3.1: Calculated lattice constant a0, internal structure parameters u, bulk modulus B0

and its pressure derivative B’ for the SnMg2O4, SnZn2O4 and SnCd2O4 compounds, compared

with experimental data and previous theoretical calculations. 41

Table 3.2: Calculated linear and quadratic pressure coefficients of the lattice constant a0

2 0

( ( )a P = +a αP+βP and internal parameter u u P

( )

= +u₀ qP rP+ 2) for SnMg O , ₂ ₄ 2 4

SnZn O and SnCd O₂ ₄. 43

Table 4.1: Some direct band gaps (Γ-Γ, L-L, X-X, K-K, W-W) (in eV), indirect band gaps

(K-Γ, L-Γ) (in eV) and UVBW is the upper valence band width in eV. 49

Table 4.2: Calculated effective masses of the electron (m ), the heavy hole (*_e m ) and the _hh∗

light hole (m ) (in units of free electron mass _lh∗ m ) for the SnMg₀ 2O4, SnZn2O4 and SnCd2O4

compounds, using GGA-EV method, compared with previous results. 59

Table 4.3: Calculated first- and second-order pressure derivatives for the SnMg2O4, SnZn2O4

and SnCd2O4 compounds, using the GGA-EV method.

( )

2 0 g g E P =E +αP+βP , Eg in eV ,

(

)

1 2 in 10 eV GPa α − −

, β_{in 10 eV GPa}−4

(

)

−2_{and is the upper valence band width in eV 60}

Table 5.1: Calculated static dielectric constant ε(0), static refractive index n(0), first energy

for which dispersion is null and pressure coefficient of refractive index n(0) of SnMg2O4,

SnZn2O4 and SnCd2O4. Energy values are in eV, ε1

( )

0 _{and n(0) are dimension less.} 67

Table 5.2: Peak positions of the ε ω together with the dominant interband transition ₂( ) contributions to every peak and their location in the Brillouin zone for SnMg O . 70 ₂ ₄

Table 5.3: Peak positions of the ε ω together with the dominant interband transition 2( )

contributions to every peak and their location in the Brillouin zone for SnZn2O4. 72

Table 5.4: Peak positions of the ε ω together with the dominant interband transition ₂( ) contributions to every peak and their location in the Brillouin zone for SnCd2O4. 75

Table 6.1: Elastic constants Cij (in GPa), shear modulus G (in GPa), Young’s modulus E (in

GPa), Poisson’s ratios ν , Lame’s coefficients λ and μ(=G) (in GPa) and B/G ratio for the SnMg2O4, SnZn2O4 and SnCd2O4 materials at the equilibrium volume. 102

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l t m θD 2 4

SnZn2O4 and SnCd2O4. 105

Table 6.3: Calculated sound velocities (in ms-1) at zero pressure along the [100], [110] and

[111] directions, calculated from the elastic constants, for SnMg2O4, SnZn2O4 and

SnCd2O4. 107

Table 6.4: Calculated linear pressure coefficients of the pressure derivatives of the elastic

constants for SnMg2O4, SnZn2O4 and SnCd2O4. 108

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ﻘﻣ

ـ

ﻣﺪ

ــــــ

ﻋ ﺔ

ــــ

ﺔﻣﺎ

General IntroductIon

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1.1 ﺔﻣﺪﻘﻣ و ﺔﻔﺜﻜﻤﻟا ةدﺎﻤﻟا ءﺎﯾﺰﯿﻓ ﺐﻌﻠﺗ و ﻲﻓ داﻮﻤﻟا ﻢﻠﻋ رود ﺮﺿﺎﺤﻟا ﺎﻨﺘﻗ ا و ﺎﻤﮭﻣ رﻮﻄﺘﻟا ﻲﻓ ﺎﯿﺳﺎﺳأ و ﺎﻌﺳاو ﻻﺎﺠﻣ نﻼﻜﺸﯾ ﺎﻤﮭﻓ اﺬﻟ ،ﻲﺟﻮﻟﻮﻨﻜﺘﻟا ﻦﯿﺜﺣﺎﺒﻟا ﻦﻣ ﺮﯿﺒﻛ دﺪﻋ ﻂﺸﻨﯾ ﺚﯿﺣ ادﺪﺠﺘﻣ و ﻦﯿﯿﺒﯾﺮﺠﺘﻟا ﺎﮭﺻاﻮﺧ ﺔﻤﺋﻼﻣ ﻦﻣ ﺪﻛﺄﺘﻟا ﻻوأ ﺐﺠﯾ ،ﻲﺟﻮﻟﻮﻨﻜﺗ ﻖﯿﺒﻄﺗ ﻲﻓ ﺎﮭﻟﺎﻤﻌﺘﺳﻻ ﺎﻣ ةدﺎﻣ رﺎﯿﺘﺧا ﻞﺒﻘﻓ .ﻦﯿﯾﺮﻈﻨﻟا تﺎﻘﯿﺒﻄﺘﻟا ﻊﻣ (ﺦﻟا...ﺔﯿﺋﻮﻀﻟاو ﺔﯿﻜﯿﻧﺎﻜﯿﻤﻟاو ﺔﯿﻧوﺮﺘﻜﻟﻻاو ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻟا) ﺔﯿﺋﺎﻤﯿﻜﻟاو ﺔﯿﺋﺎﯾﺰﯿﻔﻟا .ﺔﺑﻮﻏﺮﻤﻟا ﻂﺒﺗﺮﺗ و ﺔﯿﺋﺎﯾﺰﯿﻔﻟا صاﻮﺨﻟا ﻟا داﻮﻤﻠﻟ ﺔﯿﺋﺎﯿﻤﯿﻜﻟا و ،ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺎﮭﺘﯿﻨﺒﺑ ﺎﻘﯿﺛو ﺎطﺎﺒﺗرا ﺔﺒﻠﺼ ﻚﻟﺬﻟ نﺈﻓ ﻲھ ﺔﺒﻠﺼﻟا داﻮﻤﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﯿﻨﺒﻟا ﺪﯾﺪﺤﺗ ءﺎﯾﺰﯿﻔﻟ ﻲﺴﯿﺋر فﺪھ و .ﺔﺒﻠﺼﻟا داﻮﻤﻟا ءﺎﯿﻤﯿﻛ ﺔﻓﺮﻌﻣ نإ ﺔﯿﻨﺒﻟا و ﻢﮭﻔﻟ يروﺮﺿ داﻮﻤﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا و ﺎﮭﯿﻠﻋ ﻞﺼﺤﺘﻤﻟا ﺔﯿﺒﯾﺮﺠﺘﻟا ﺞﺋﺎﺘﻨﻟا ﺮﯿﺴﻔﺗ ﺎﮭﺻاﻮﺨﺑ ﺆﺒﻨﺘﻠﻟ و ﺔﯿﺋﺎﯾﺰﯿﻔﻟا ﻤﯿﻜﻟا و .ﺎﯿﺒﯾﺮﺠﺗ ﺎﮭﺼﯿﺼﺨﺗ ﺪﻌﺑ ﻢﺘﯾ ﻢﻟ ﻲﺘﻟا ﺔﯿﺋﺎﯿ لﻮﺼﺤﻟا ﻦﻜﻤﯾ ﺎﯾﺮﻈﻧ ﻰﻠﻋ ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﯿﻨﺒﻟا داﻮﻤﻠﻟ .ﻢﻜﻟا ﺎﻜﯿﻧﺎﻜﯿﻣ ﺔﯾﺮﻈﻧ ﺐﺴﺣ ﺮﻐﻨﯾدوﺮﺷ ﺔﻟدﺎﻌﻣ ﻞﺤﺑ ﺪﻘﻟ و نﻮﯿﺋﺎﯿﻤﯿﻜﻟا رﻮط نﻮﯾﺮﻈﻨﻟا نﻮﯿﺋﺎﯾﺰﯿﻔﻟا و قﺮﻄﻟا ﻦﻣ ﺪﯾﺪﻌﻟا و تارﺬﻠﻟ ﺮﻐﻨﯾدوﺮﺷ ﺔﻟدﺎﻌﻣ ﻞﺤﻟ جذﺎﻤﻨﻟا و تﺎﺌﯾﺰﺠﻟا داﻮﻤﻟا و ﻲﺘﻟا ﻲﻓ ﺎﮭﻔﯿﻨﺼﺗ ﻦﻜﻤﯾ و لوﻷا ﻒﻨﺼﻟا .ﻦﯿﻔﻨﺻ ﺔﯿﺒﯾﺮﺠﺗ ﮫﺒﺷ قﺮط ةﺎﻤﺴﻤﻟا قﺮﻄﻟا ﻞﻤﺸﯾ (semi empirical− ) و ﻚﻟذ ءاﻮﺘﺣﻻ ﺎﻣأ .ﺔﯿﺒﯾﺮﺠﺘﻟا تﺎﯿﻄﻌﻤﻟا ﺾﻌﺒﺑ ﺔﻧﺎﻌﺘﺳﻻﺎﺑ ﻻإ ﺎﮭﻤﯿﻗ ﺪﯾﺪﺤﺗ ﻦﻜﻤﯾ ﻻ ﻲﺘﻟا تﻼﻣﺎﻌﻤﻟا ﺾﻌﺑ ﻰﻠﻋ جذﺎﻤﻨﻟا هﺬھ ةﺎﻤﺴﻤﻟا قﺮﻄﻟا ﻞﻤﺸﯿﻓ ﻲﻧﺎﺜﻟا ﻒﻨﺼﻟا دﺎﺒﻤﻟا قﺮط ﻰﻟوﻷا ئ

(ab int io (first principles)method)−

ﻲﺘﻟاو ﺔﻓﺮﻌﻣ اﺪﻋ ﺎﻣ ةدﺎﻤﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﯿﻨﺒﻟا بﺎﺴﺤﻟ ﺔﯿﺒﯾﺮﺠﺘﻟا تﺎﯿﻄﻌﻤﻠﻟ ﺎﮭﺘﺟﺎﺣ مﺪﻋو ﺔﻗد ﺮﺜﻛأ ﺎﮭﻧﺄﺑ زﺎﺘﻤﺗ ﺔﺳورﺪﻤﻟا ةدﺎﻤﻠﻟ ﺔﻠﻜﺸﻤﻟا ﺮﺻﺎﻨﻌﻠﻟ ﺔﯿﺋﺎﯿﻤﯿﻜﻟا ﺔﻌﯿﺒﻄﻟا . ئدﺎﺒﻤﻟا ﻰﻠﻋ ﺔﯿﻨﺒﻤﻟا ﺔﯿﺑﺎﺴﺤﻟا قﺮﻄﻟا ﺖﺤﺒﺻأ ﺪﻘﻟ ا ﺎﻨﺘﻗو ﻲﻓ ﻞﻜﺸﺗ ﻰﻟوﻷا و ﺔﯿﺳﺎﺳأ ةادأ ﺮﺿﺎﺤﻟ و تارﺬﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﯿﻨﺒﻟا بﺎﺴﺤﻟ ﺔﻟﺎﻌﻓ و تﺎﺌﯾﺰﺠﻟا داﻮﻤﻟا و و ﺔﯾﻮﯿﻨﺒﻟا ﺎﮭﺻاﻮﺨﺑ ﺆﺒﻨﺘﻟا ﮫﻨﻣ و ﺔﯿﻧوﺮﺘﻜﻟﻹا و ﺔﯿﻜﯿﻧﺎﻜﯿﻤﻟا و ﺔﯿﺋﻮﻀﻟا قﺮﻄﻟا هﺬھ ﺖﺤﺒﺻأ ﺪﻘﻟ .ﺎھﺮﯿﻏ و ﺮﯿﺴﻔﺘﻟ ﺔﻠﻀﻔﻤﻟا ﺔﻠﯿﺳﻮﻟا ﺎﮭﻧأ ﻞﺑ ﺎﮭﯿﻠﻋ ﻞﺼﺤﺘﻤﻟا ﺔﯿﺒﯾﺮﺠﺘﻟا ﺞﺋﺎﺘﻨﻟا ﻢﮭﻓ ﻞﺤﺗ نا ﺖﻋﺎﻄﺘﺳا ﺔﺑﺮﺠﺘﻟا ﻞﺤﻣ .ﺔﯿﺒﯾﺮﺠﺘﻟا تﺎﺳﺎﯿﻘﻟا ءاﺮﺟإ ﺎﮭﯿﻓ ﻞﯿﺤﺘﺴﯾ وأ ﺐﻌﺼﯾ ﻲﺘﻟا نﺎﯿﺣﻷا ﻦﻣ ﺮﯿﺜﻛ ﻲﻓ و ﺎﮭﺘﯿﻟﺎﻌﻓ ﻰﻟوﻷا ئدﺎﺒﻤﻟا سﺎﺳأ ﻰﻠﻋ ﺔﯿﻨﺒﻤﻟا ﺔﺜﯾﺪﺤﻟا ﺔﯿﺑﺎﺴﺤﻟا قﺮﻄﻟا ﺪﻤﺘﺴﺗ و ﺔﯿﻠﻋﺎﻓ ﻦﻣ ﺎﮭﺘﻗد ﺔﻗد ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ ] 1 ، 2 [

(Density functional theory (DFT))

ﺰﻜﺗﺮﺗ . ﺔﯾﺮﻈﻧ ﻰﻠﻋ ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ و غرﺎﺒﻨھﻮھ ﻮﻛ ھ ﻦ

[1] (Hohenberg and Kohn)

. سﺎﺳأ و هﺬھ ﺎﻣ مﺎﻈﻨﻟ ﺔﯿﻠﻜﻟا ﺔﻗﺎﻄﻟا نأ ﻮھ ﺔﯾﺮﻈﻨﻟا و .ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﻓﺎﺜﻜﻠﻟ ﺔﯿﻟاد نﻮﻜﺗ و .ﺔﻓﺎﺜﻜﻟا ﺔﯿﻟاد ﺔﯾﺮﻈﻧ رﺎطإ ﻦﻤﺿ ﺔﯿﺑﺎﺴﺤﻟا قﺮﻄﻟا ﻦﻣ ﺪﯾﺪﻌﻟا ﺖﯿﻨُﺑ ﺪﻘﻟ بﺎﺴﺤﻟ ﺔﻗد ﺮﺜﻛﻷا قﺮﻄﻟا ﻦﯿﺑ ﻦﻣ و ﻲﻟﺎﺤﻟا ﺖﻗﻮﻟا ﻲﻓ ﺔﺒﻠﺼﻟا داﻮﻤﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا ﺔﯿﻨﺒﻟا ﺎﮭﺗرﺪﻗ ﺖﺘﺒﺛأ ﻲﺘﻟا 2

(21)

نﻮﻤﻜﻟا ﻊﻣ ًﺎﯿﻄﺧ ةداﺰﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ﺔﻘﯾﺮط ﺪﺠﻧ ﺔﯾرﻮﻠﺒﻟا داﻮﻤﻟا صاﻮﺧ ﻦﻣ ﺪﯾﺪﻌﻟﺎﺑ ﺆﺒﻨﺘﻟا ﻰﻠﻋ ﻞﻣﺎﻜﻟا

(Full potential Linearized Augmented plane Wave (FP−LAPW))

. 2.1 ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا تﺎﺒﻛﺮﻣ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا (spinels) ﺔﻓوﺮﻌﻣ ﺔﯾرﻮﻠﺑ ﺔﺒﻠﺻ داﻮﻣ ﻲھ ﻞﯾﻮط ﻦﻣز ﺬﻨﻣ و ندﺎﻌﻤﻟا ءﺎﻤﻠﻋ ىﺪﻟ و ﻲﺋﺎﯿﻤﯿﻛ .ﺔﺒﻠﺼﻟا ةدﺎﻤﻟا ﻲﺋﺎﯾﺰﯿﻓ تﺬﺧأ ﺪﻘﻟ ﺔﻠﺋﺎﻋ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺐﻛﺮﻤﻟا ﻢﺳا ﻦﻣ ﺎﮭﻤﺳا 2 4 MgAl O "لﺎﻨﯿﺒﺴﻟا" ﺔﻤﻠﻛ نإ .ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺔﻠﺋﺎﻋ ﻦﻤﺿ اﺪﯿﺟ فوﺮﻌﻤﻟا ﻲﺘﻟا "ﺎﻨﯿﺒﺳ" ﺔﯿﻨﯿﺗﻼﻟا ﺔﻤﻠﻜﻟا ﻦﻣ ﺔﻘﺘﺸﻣ و ﺔﻛﻮﺸﻟا ﻲﻨﻌﺗ ةرﻮﻠﺑ ءاﻮﺘﺣﻻ ﻚﻟذ 2 4 MgAl O نإ .ةدﺎﺣ فاﻮﺣ ﻰﻠﻋ ﻲھ ارﺎﺸﺘﻧا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺮﺜﻛأ ﯿﻟﺎﻨﯿﺒﺴﻟا ــ ﯿﺼﻟا تاذ تﺎ ــ ﺔﻐ ﺔــﯿﺋﺎﯿــﻤﯿﻜﻟا 2 4 II III A B X و 2 4 IV II A B X ، ﯿﺣ ـ ﺚ , , IV Si A = Ge Sn و , , III B =Al Ga In و , , II II B = A =Mg Zn Cd ﺎﻣأ X يﺬﻟا و ﺆﻓﺎﻜﺘﻟا ﻲﺋﺎﻨﺛ ﺐﻟﺎﺳ نﻮﯾﻷ ﺰﻣﺮﯾ ﻮﮭﻓ ﻦﻣ ﺪﺣاو وأ ﻦﯿﺠﺴﻛوأ ةدﺎﻋ نﻮﻜﯾ ﺐﻟﺎﺨﻤﻟا ) تﺎﻨﯿﺟﻮﻜﻟﺎﺸﻟا ( X O, (chalcogen; = S, Se , Te) ] 3 [ . غاﺮﺑ فﺮط ﻦﻣ ةﺮﻣ لوﻷ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺔﯿﻨﺑ ﺪﯾﺪﺤﺗ ﻢﺗ (Bragg) ﺔﻨﺳ ﻲﻓ 1915 ] 4 [ ىوﺎﻜﯿﺸﯿﻧ و (Nishikawa) ﺔﻨﺳ ﻲﻓ 1915 ] 5 [ ﻊــﺟاﺮﻤﻟا ﻲﻓ ﻞــﯿﺼﻔﺘﻟﺎﺑ ﺔﯿﻨﺒﻟا هﺬـھ ﻒﺻو دﺎﺠﯾإ ﻦﻜﻤﯾ و ؛ ] 6 -8 [ . نﻮﻜﺗ ﺔﺒﻌﻜﻤﻟا ﺔﯾدﺎﻌﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯿﺋﺎﯿﻤﯿﻜﻟا ﺔﻐﯿﺼﻟا تاذ 2 4 AB X ﺔﺌﺒﻌﺗ ﺔﺻاﺮﺘﻣ و ﺔﺒﻌﻜﻣ ﺔﯾرﻮﻠﺑ ﺔﯿﻨﺑ هﻮﺟﻮﻟا ةﺰﻛﺮﻤﻣ

(FCC: Face centered cubic)−

ﺔﯿﺋﺎﻀﻔﻟا ةﺮﻣﺰﻟا ، 3 Fd m ) ﻢﻗر 227 لواﺪﺠﻟا ﻲﻓ ﺔﯾرﻮﻠﺒﻟا ( ] 9 [ . ﻞﻜﺸﻟا ﻞﺜﻤﯾ . 1 ﺔﯾرﻮﻠﺒﻟا ﺔﯿﻨﺒﻟا ﺐﻛﺮﻤﻠﻟ ﺔﯿﻟوأ ﺔﯿﻠﺨﻟ 2 4 SnMg O داﻮﻤﻠﻟ ﺔﯾرﻮﻠﺒﻟا ﺔﯿﻨﺒﻠﻟ جذﻮﻤﻨﻛ ﺔﯾدﺎﻌﻟا ﺔﺒﻌﻜﻤﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯿﻟوﻷا ﺔﯿﻠﺨﻟا يﻮﺘﺤﺗ .ﺔﺒﻌﻜﻤﻟا ﺔﯾدﺎﻌﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا ﻰﻠﻋ 8 تﺎﺌﯾﺰﺟ 2 4 A B X

(

A8B16X32

)

؛ 32 نﻮﯿﻧأ X و 8 تﺎﻧﻮﯿﺗﺎﻛ A و 16 نﻮﯿﺗﺎﻛ B . ،ﺔﯿﻟﺎﺜﻤﻟا ﺔﺒﻌﻜﻤﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﻲﻓ ﻟا ﻞﻐﺸﺗ تﺎﻧﻮﯿﺗﺎﻜ A ﻦﻤﺛ (1 / 8) ـﻟا 64 ﻟا ﻦﯿﺣ ﻲﻓ ،حﻮﻄﺴﻟا ﺔﯿﻋﺎﺑر ةﻮﺠﻓ تﺎﻧﻮﯿﺗﺎﻜ B ﻒﺼﻧ ﻞﻐﺸﺗ (1 / 2) ـﻟا 32 ةﻮﺠﻓ ﺔﯿﻧﺎﻤﺛ كﺎﻨھ ﺪﺟﻮﺗ ؛حﻮﻄﺴﻟا 96 ﺔﺒﻌﻜﻤﻟا ﺔﯾدﺎﻌﻟا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﻲﻓ تﺎﻧﻮﯿﻧﻷا ﻦﯿﺑ ةﻮﺠﻓ ] 10 [ . ﺔﯿﻠﺨﻟا أﺪﺒﻤﻟ رﺎﺘﺨﻤﻟا ﻊﻗﻮﻤﻟﺎﺑ ﺔﺒﻌﻜﻤﻟا تﺎﯿﻟﺎﻨﯿﺒﺴﻠﻟ ﺔﯿﻟوﻷا ةرﻮﻠﺒﻟا ﻞﺧاد تارﺬﻟا تﺎﯿﺛاﺪﺣإ ﻖﻠﻌﺘﺗ كﺎﻨھ . و ﺔﯿﻟوﻷا ﺔﯿﻠﺨﻟا أﺪﺒﻣ رﺎﯿﺘﺧﻻ نﺎﺘﯿﻧﺎﻜﻣإ نﺎﺘﻄﻘﻧ ﺎﻤھ ﻲﻄﻘﻧ ﺮظﺎــﻨﺗ تاذ ﻰﻟوﻷا ،نﺎﺘﺌﻓﺎﻜﺘﻣ 43m و ﻲﻓ نﻮﻜﺗ نﻮﯿﺗﺎﻜﻟا ﻊﻗﻮﻣ A ﺔﯿﻧﺎﺜﻟا ﺎﻣأ ﻲﻄﻘﻧ ﺮظﺎــﻨﺗ تاذ 3m و حﻮﻄﺴﻟا ﺔﯿﻋﺎﺑر ةﻮﺠﻓ ﻊﻗﻮﻣ ﻲﻓ نﻮﻜﺗ ﺔﻟﺎﺣ ﻲﻓ . 3

(22)

تاذ ﺔﻄﻘﻨﻟا ﻲﻓ ﺔﯿﻟوﻷا ﺔﯿﻠﺨﻟا أﺪﺒﻣ رﺎﯿﺘﺧا ﻲﻄﻘﻨﻟا ﺮظﺎﻨﺘﻟا 3m ، ﻲﻠــﯾ ﺎﻤﻛ تارﺬﻟا تﺎﯿﺛاﺪﺣإ نﻮﻜﺗ : تﺎﻧﻮﯿﺗﺎﻜﻟا A فﻮﻜﯿﻓ ﻊﻗﻮﻣ ﻞﻐﺸﺗ (Wyckoff position)

(

1 / 8, 1 / 8, 1 / 8

)

8a نﻮﯿﺗﺎﻜﻟا و B ﻊﻗﻮﻤﻟا ﻞﻐﺸﯾ

(

1 / 2, 1 / 2, 1 / 2

)

16d تﺎﻧﻮﯿﻧﻷا و O ﻊﻗﻮﻤﻟا ﻲﻓ ﻊﻗﻮﻤﺘﺗ 32 ( , , )e u u u ، ﺚﯿﺣ u ﻰﻋﺪﯾ ﺔﯿﺛاﺪﺣﻹا نﻮﯾﻸﻟ ﺔﯿﻠﺧاﺪﻟا X و ﺎﮭﺘﻤﯿﻗ نﻮﻜﺗ ﺔﯿﻟﺎﺜﻤﻟا ﺔﯾوﺎﺴﻣ 25 . 0 = ideal u ] 10 [ . ﺔﻤﯿﻗ ﺪﯾاﺰﺘﺗ ﺎﻣﺪﻨﻋ u بﺮﺘﻘﯾ نﻮﯿﻧﻷا X ﻮﯿﺗﺎﻜﻟا ﻦﻣ ن A هﺎﺠﺗﻻا ﻲﻓ

[ ]

111 حﻮﻄﺴﻟا ﺔﯿﻋﺎﺑر ةﻮﺠﻓ ﻢﺠﺣ دﺎﯾدزا ﻰﻟإ يدﺆﯾ ﺎﻤﻣ A و حﻮﻄﺴﻟا ﺔﯿﻧﺎﻤﺛ ةﻮﺠﻓ ﻢﺠﺣ نﺎﺼﻘﻧ B . أﺪﺒﻤﻟا رﺎﯿﺘﺧا ﺔﻟﺎﺣ ﻲﻓ ﺎﻣأ 43m ﻲﻠﯾ ﺎﻤﻛ تﺎﯿﺛاﺪﺣﻹا نﻮﻜﺗ ، : (0, 0, 0) A ، (5 / 8, 5 / 8, 5 / 8) B و ( , , ) O u u u ، ـﻟ ﺔﯿﻟﺎﺜﻤﻟا ﺔﻤﯿﻘﻟا و u ﺔﯾوﺎﺴﻣ نﻮﻜﺗ 375 . 0 = ideal u . زﺎﺘﻤﺗ .ﺔﯿﺟﻮﻟﻮﻨﻜﺘﻟا تﺎﻘﯿﺒﻄﺘﻟا ﺾﻌﺒﻟ ﺔﻤﺋﻼﻤﻟا صاﻮﺨﻟا ﻦﻣ ﺪﯾﺪﻌﻟﺎﺑ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺔﻠﺋﺎﻋ ﺰﯿﻤﺘﺗ تﺎﺟرد ﻲﻓ ﺔﯿﺋﺎﯿﻤﯿﻛ ﺔﻣوﺎﻘﻣ ،ﺔﯿﻟﺎﻋ ﺔﺑﻼﺻ ،ﺔﯿﻟﺎﻋ ﺔﯿﺳﺎﻜﻌﻧا ،ﺔﯿﻟﺎﻋ رﺎﮭﺼﻧا ﺔﻄﻘﻨﻟ ﺎﮭﻛﻼﺘﻣﺎﺑ داﻮﻤﻟا هﺬھ و ﺔﯿﻟﺎﻋ ةراﺮﺣ ﺾﻔﺨﻨﻣ ﻲﺋﺎﺑﺮﮭﻛ ناﺪﻘﻓ ] 11 ، 12 [ . صاﻮﺨﻟا هﺬھ ﺢﺷﺮﺗ أ ةرﻮﻛﺬﻤﻟا ﺎﻔﻧ ةﺪﻌﻟ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا تﺎﻘﯿﺒﻄﺗ ﺔﯿﺟﻮﻟﻮﻨﻜﺗ ﺔﻠﻤﺘﺤﻣ و ءﺎﯾﺰﯿﻓﻮﯿﺠﻟا لﺎﺠﻣ ﻲﻓ و ﺔﯾﺪﯾﺪﺣوﺮﮭﻜﻟا و ﺔـﯿﺴﯿطﺎـﻨﻐﻤﻟا ﺔﯿﻠﻗﺎﻨﻟا ﺔﻘﺋﺎﻓ و ﺔﺌﯿﺒﻟاو ﺰﯿﻔﺤﺘﻟا و ﺔﯿﺒﯾﺮﺠﺘﻟا تﺎﺳارﺪﻟا ﻦﻣ ﺮﯿﺜﻜﻟا مﺎﻤﺘھا عﻮﺿﻮﻣ داﻮﻤﻟا هﺬھ ﻞﻌﺟ ﺎﻤﻣ ، ﺔﯾﺮﻈﻨﻟا ] 13 -17 [ . 4

(23)

Figure 1: A schematic representation of the cubic spinel structure of SnM2O4. The oxygen

atoms (red spheres) occupy the corners of the octahedral and tetrahedral; Sn and Mg are at the centres of the tetrahedral and octahedral, respectively.The origin of the unit-cell is chosen at

the B (i.e., Sn) position.

(24)

3.1 ﺔﯾﺪﯿﺴﻛوﻷا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﺔﯿﻓﺰﺨﻟا تﺎﺒﻛﺮﻤﻟا ﻦﻣ ةﺮﯿﺒﻛ ﺔﻋﻮﻤﺠﻣ ﺔﯾﺪﯿﺴﻛوﻷا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا ﻞﻜﺸﺗ ~) 120 ،(ﺐﻛﺮﻣ ﺪﻘﻟو ﺖﻧﺎﻛ عﻮﺿﻮﻣ ﺔﯾﺮﻈﻨﻟا لﺎﻤﻋﻷا ﻦﻣ ﺪﯾﺪﻌﻟا و و ﺔﯿﺒﯾﺮﺠﺘﻟا ﺬﻨﻣ ﺺﺧﻷﺎﺑ ﺐﻛﺮﻤﻟا ﺢﺒﺻأ نأ 2 4 MgAl O وذ ﺔﯿﺟﻮﻟﻮﻨﻜﺗ ﺔﯿﻤھأ ] 18 ، 19 [ . ﺪﻘﻟ ﺔﯾﻮـﯿﻨﺒﻟا صاﻮﺨﻟا ﺔﺳارد ﻰﻠﻋ ﺎﺳﺎﺳأ تﺎﺳارﺪﻟا هﺬھ تﺰﻛﺮﺗ ] 20 -22 [ ، ﺔـﯿﻧوﺮﺘﻜﻟﻹا ] 23 -25 [ ﺔﯿﻜﯿﻧﺎﻜﯿﻤﻟا ، ] 21 ، 22 ، 26 -29 [ و ] ﺔﯿﺋﻮﻀﻟا 30 -32 [ تﺎﺒﻛﺮﻤﻟا هﺬھ ﺖﺤﺷر ﻲﺘﻟا ، ﺔﯿﺋﻮﻀﻟا تﺎﯿﻧوﺮﺘﻜﻟﻻا ﻲﻓ ﺔﯿﺟﻮﻟﻮﻨﻜﺘﻟا تﺎﻘﯿﺒﻄﺘﻟا ﺾﻌﺒﻟ و ءﺎﯾﺰﯿﻓﻮﯿﺠﻟا و ﺔﯿﺴﯿطﺎﻨﻐﻤﻟا . هﺬھ ﺮﯿﻀﺤﺗ ﻢﺗ ﺪﻘﻟ ﻀﺤﺘﻟا قﺮط ﻦﻣ ﺪﯾﺪﻌﻟا لﺎﻤﻌﺘﺳﺎﺑ داﻮﻤﻟا ــ ﺮﯿ ﻣ ــ ﺒﺘﻟا ﺔﻘﯾﺮط ﻞﺜ ــ ﺤﻟا ﺮﺨ ــ ﺘﻟا ،يراﺮ ﺪﯿﺒﻠ ﺟرد ﻲﻓ ــ ﺤﻟا ﺔ ـ ةراﺮ ﺤﻣ ،ﺔﯿﻟﺎﻌﻟا ــ لﻮﻠ -مﻼھ (sol gel)− ، ﺤﺴﻟا ــ ﻖ (ball milling)− ﻨﻟاو ــ طﺎﻨﻐﻤﻟا ﺮﺜ ـــ ﻲﺴﯿ (rf magnetron sputtering) ] 33 ، 34 [ . تﺎﻧﻮﯿﺗﺎﻜﻟا نﻮﻜﺗ A و B ﻓ ﻲ ﺔﯿﺋﺎﯿﻤﯿﻜﻟا ﺔﻐﯿﺼﻟا تاذ ﺔﯾﺪـﯿﺴﻛوﻷا ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻟا 2 4 AB O ﺎﻣإ و ﺆﻓﺎﻜﺘﻟا ﺔﯿـﺋﺎﻨـﺛ ﺆــﻓﺎﻜﺘﻟا ﺔﯿﺛﻼﺛ (A= Cd Mg Mn Zn, , , ; B= Al Ga In, , ...) ﺆﻓﺎﻜــﺘﻟا ﺔﯿﺋﺎﻨــﺛ وأ و ﺆﻓﺎﻜﺘﻟا ﺔﯿﻋﺎﺑر (B= , , , ;Cd Mg Mn Zn A=Si Ge Sn, , ...) . نﻮﯿﺗﺎﻜﻟا طﺎﺤﯾ A تﺎﻧﻮﯿﻧأ ﺔﻌﺑرﺄﺑ ﻦﯿﺠﺴﻛوأ (O) ﺔﻠﻜﺸﻣ حﻮﻄﺴﻟا ﺔﯿﻋﺎﺑر 4 O A نﻮﯿﺗﺎﻜﻟا نﻮﻜﯾ ﻦﯿﺣ ﻲﻓ B ﻦﯿﺠﺴﻛوأ تﺎﻧﻮﯿﻧأ ﺔﺘﺴﺑ ﺎطﺎﺤﻣ (O) ﺔﻠﻜﺸﻣ حﻮﻄﺴﻟا ﺔﯿﻧﺎﻤﺛ 6 O B ] 35 ، 36 [ . ﺪﻘﻟ ﻓﺎﻔــﺷ ﺔﻠﻗﺎﻧ تاﺪﯿـﺴﻛوﻷ ﺪﯾاﺰﺘﻤﻟا ﺐﻠﻄﻟا ىدأ ــ ﺔ

(TCO :Transparent Conducting Oxides)

ةﺰﮭﺟﻷا لﺎﺠﻣ ﻲﻓ ﺔﯿﺟﻮﻟﻮﻨﻜﺘﻟا تﺎﻘﯿﺒﻄﺘﻟا ﻞﺟأ ﻦﻣ ﺾﻔﺨﻨﻣ ﻦﻤـﺛو ﺔـﯿﻟﺎﻋ ةءﺎﻔــﻛ تاذ ةﺪﯾﺪـﺟ ﺔﺤﻄﺴﻤﻟا تﺎﺷﺎﺸﻟا ﻞﺜﻣ ،ﺔﯿﺋﻮﺿوﺮـﺘﻜﻟﻻا

(flat panel displays- )

ﺔﯿﺴﻤﺸﻟا ﺎﯾﻼﺨﻟا و ] 37 ، 38 [ ، ﻰﻟإ داﻮﻤﻟا هﺬھ لﻮﺣ ﺔﻔﺜﻜﻣ ثﺎﺤﺑأ ] 39 [ ﺔﯿــﻟﺎﻨﯿﺒﺴﻟا تاﺪﯿـﺴﻛوﻷا تزﺮـﺑ ﺪـﻘﻟ . 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O ﻦﻣ ﻞﯿﻠﻗ دﺪﻋ عﻮﺿﻮﻣ ﺔﯿﻟﺎﻨﯿﺒﺴﻟا تاﺪﯿﺴﻛوﻷا هﺬھ ﺖﻧﺎﻛ ﺪﻘﻟ .ةﺪﻋاو ﺔﻓﺎﻔــﺷ ﺔﻠﻗﺎﻧ تاﺪﯿـﺴﻛوﺄﻛ ﺔﯿﺒﯾﺮﺠﺘﻟاو ﺔﯾﺮﻈﻨﻟا ثﺎﺤﺑﻷا ] 20 ، 39 -45 [ . ،ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯾرﻮﻠﺒﻟا ﺔﯿﻨﺒﻟا ﺔﺳارد ﺖﻤﺗ ﺪﻗ ،ﺎﯿﺒﯾﺮﺠﺗ ﻦﻣ هوﺪﻋﺎﺴﻣ و ﻞﯿھ فﺮط (Hill .)et al ] 17 [ طﻮﻐﺿ ﺖﺤﺗ ﺔﯾرﻮﻄﻟا تﻻﻮﺤﺘﻠﻟ ﺔﯿﺒﯾﺮﺠﺗ ﺔﺳارد ﺖﻤﺗ ﺎﻤﻛ . ﻲﻟﺎﻨﯿﺒﺴﻟا ﺐﻛﺮﻤﻠﻟ ﺔﯿﻨﯿﺴﻟا ﺔﻌﺷﻻا دﻮﯿﺣ لﺎﻤﻌﺘﺳﺎﺑ ﺔﯿﻟﺎﻋ ﺔﯿﻜﯿﺗﺎﺘﺳورﺪﯿھ 2 4 SnZn O ﻦﻣ و نﺎﺷ فﺮط هوﺪﻋﺎﺴﻣ (Shenet al.) ] 44 [ . ةﺪﻣﺎﻌﺘﻤﻟا ﺔﯿﻨﯿﻌﻤﻟا ﺔﯿﻨﺒﻟا وأ ﺔﺒـﻌﻜﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ ةدﺎﻋ داﻮﻤﻟا هﺬھ رﻮﻠﺒﺘﺗ 6

(25)

ﺔﻤﯿﻘﺘﺴﻤﻟا (Orthorhombic) ﺮﯿﻀﺤﺘﻟا فوﺮظ ﺐﺴﺣ ] 39 ، 33 ، 45 [ . عزﻮﺗ ﺔﺳارد ﺖﻤﺗ ﺪﻘﻓ ﺎﯾﺮﻈﻧ ﺎﻣأ داﻮـﻤﻟا هﺬھ ﻲﻓ تﺎﻧﻮﯿﺗﺎﻜﻟا ياو فﺮط ﻦﻣ ﻎﻧﺎھز و

(Wei and Zhang)

[39] . نأ ﺎﻨﯿﺑ ﺪﻘﻟ 2 4 SnZn O نﻮﻜﯾ نﻮﻜﯾ ﺎﻤﻨﯿﺑ ﺔﺒﻌﻜﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ اﺮﻘﺘﺴﻣ 2 4 SnCd O ﺔﻤﯿﻘﺘﺴﻤﻟا ةﺪﻣﺎﻌﺘﻤﻟا ﺔﯿﻨﯿﻌﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ اﺮﻘﺘﺴﻣ ] 39 [ . ﺪﻘﻟ ﺔﻘﯾﺮط لﺎﻤﻌﺘﺳﺎﺑ ﺔﯾﺮﻈﻧ ﺔﺳارد ﺖﻨﯿﺑ FP LAPW− ﻊﻣ لا ﺐﯾﺮﻘﺗ LDA ، ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا ، ﻦﯿﺒﻛﺮﻤﻠﻟ ﺔﯿﺋﻮﻀﻟا و 2 4 SnZn O و 2 4 SnCd O ﺎﮭﺑ مﺎﻗ ةﺮﺷﺎﺒﻤﻟا ﺔﺒﻌﻜﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ و ﻒﺠﯿﺳ ياو

(Segev and Wei)

] 20 [ ﺔﯾوﺎﺴﻣ و ةﺮﺷﺎﺒﻣ ﺔﻗﺎط ﻊﻧاﻮﻣ ﻦﯿﺒﻛﺮﻤﻟا ﻦﯾﺬﮭﻟ نأ ، 0.50 eV و 0.17 eV ، ﻰﻠﻋ .ﺐﯿﺗﺮﺘﻟا مﺎﻗ ﻗ ﺎﯿﺳاﺮ و هوﺪﻋﺎﺴﻣ (Graciaet al.) ] 45 [ زﺎﺠﻧﺈﺑ ﺔﺳارد ﻰﻟوﻷا ئدﺎﺒﻤﻟا لﺎﻤﻌﺘﺳﺎﺑ ﺔﯾﺮﻈﻧ ، ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻠﻟ ﺐﻛﺮﻤﻠﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹاو ﻲﻠﯿﻨﯿﺒﺴﻟا 2 4 Zn SnO ﻏ ﺔﺒﻌﻜﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ ـ ﺮﯿ ﻟا ﻤ ــ ةﺮﺷﺎﺒ ﺪــﻘﻟ و . لﺎﻤﻌﺘﺳﺎﺑ ﺔﯾﺮــﻈﻧ ﺔﺳارد ﻚﻟﺬــﻛ ﺖﻨﯿﺑ ط ـــ ﺟﻮﻤﻟا ﺔﻘﯾﺮ ـــ ﺘﺴﻤﻟا ﺔ ـــ ﻤﻜﻟا ﻊﻣ ﺔﯾﻮ ـــ بذﺎﻜﻟا نﻮ

(pseudopotential plane wave - (PP−PW))

ﺔﻧوﺮﻤﻟا و ﺔﯿﺋﻮﻀﻟا ،ﺔﯿﻧوﺮﺘﻜﻟﻻا ،ﺔﯾﻮﯿﻨﺒﻟا صاﻮﺨﻠﻟ ، ﻲﻠﯿﻨﯿﺒﺴﻟا ﺐﻛﺮﻤﻠﻟ 2 4 SnMg O هوﺪﻋﺎﺴﻣ و سﺎﻓر ﺎﮭﺑ مﺎﻗ ﺔﯾدﺎﻌﻟا ﺔﺒﻌﻜﻤﻟا ﺔﯿﻨﺒﻟا ﻲﻓ (Reffas .)et al ] 46 [ . 4.1 ﺔﻟﺎﺳﺮﻟا ﻦﻣ فﺪﮭﻟا تﺎﺒﻛﺮﻤﻠﻟ ﺔﯿﺋﺎﯾﺰﯿﻔﻟا صاﻮﺨﻟا ﻦﻣ ادﺪﻋ كﺎﻨھ نأ ﻖﺒﺳ ﺎﻤﻣ ﺢﻀﺘﯾ 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O ، ﻞﺜﻣ ،ىﺮﺧأ ﺔﯿﺋﺎﯾﺰﯿﻓ صاﻮﺧ كﺎﻨھ نأ ﺎﻤﻛ بﻮﻠﻄﻤﻟا ﻞﯿﺼﻔﺘﻟﺎﺑ سرﺪﺗ ﻢﻟ ،ﺔﯿﻧوﺮﺘﻜﻟﻹا صاﻮﺨﻟا ﻞﺜﻣ ﻘﯿﺒﻄﺘﻟا ﻞﺟأ ﻦﻣ ﺎﮭﺘﻓﺮﻌﻣ ﺔﯿﻤھأ ﻢﻏر ﺎﻘﻠﻄﻣ سرﺪﺗ ﻢﻟ ،ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا و ﺔﻧوﺮﻤﻟاو ﺔﯿﺋﻮﻀﻟا صاﻮﺨﻟا تﺎ فﺪھ نﺈﻓ اﺬﮭﻟ .ﺔﯿﺟﻮﻟﻮﻨﻜﺘﻟا ﺎﮭﺼﯿﺼﺨﺗ و ةﺪﯾﺪﺟ داﻮﻣ ﺮﯿﻀﺤﺗ ﺮﺒﺨﻤﺑ ﺎھﺮﯿﻀﺤﺗ ﻢﺗ ﻲﺘﻟا ،هﺬھ ﺎﻨﺘﻟﺎﺳر

(Laboratory for Developing New Materials and their Characterization(L.D.N.M.C))

ﺔﻌﻣﺎﺠﺑ ﻒﯿﻄﺳ سﺎﺒﻋ تﺎﺣﺮﻓ 1 فاﺮﺷإ ﺖﺤﺗ ﻷا ذﺎﺘﺳ ﺪﯿﺠﻤﻟا ﺪﺒﻋ ودﺎﻤﺣﻮﺑ ﺔﺳارد ، ﺨﻟا اﻮ ﺔﯾﻮﯿﻨﺒﻟا ص و ﺔﯿﻧوﺮﺘﻜﻟﻹا و ﺔﯿﺋﻮﻀﻟا و ﺔﯿﻟﺎﻨﯿﺒﺴﻟا داﻮﻤﻠﻟ ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا و ﺔﻧوﺮﻤﻟا ﺔﯿﻟﺎﺘﻟا : 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O لﺎﻤﻌﺘﺳﺎﺑ ﻞﻣﺎﻜﻟا نﻮﻤﻜﻟا ﻊﻣ ًﺎﯿﻄﺧ ةداﺰﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ﺔﻘﯾﺮط (FP−LAPW) ﺪﻘﻟ . ﺖﻤﺗ ﺔﯾرﻮﻠﺒﻟا ﺔﯿﻨﺒﻟا صاﻮﺧ ﺔﺳارد ﻊﺿﻮﻤﻟا ﺔﻓﺎﺜﻛ ﺐﯾﺮﻘﺗ لﺎﻤﻌﺘﺳﺎﺑ (LDA) ] 47 [ جرﺪﺘﻟا ﺐﯾﺮﻘﺗ و ﻢﻤﻌﻤﻟا (GGA) ] 48 [ لدﺎﺒﺗ نﻮﻤﻛ ﻞﺟأ ﻦﻣ -.طﺎﺒﺗرا ﺨﻟا ﺎﻣأ اﻮ ﺔﯿﻧوﺮﺘﻜﻟﻻا ص ﺖﻤﺗ ﺪﻘﻓ رد ا ﺘﺳ ﺎﮭ ﻞﯿﺼﻔﺘﻟﺎﺑ لا ﻦﯿﻠﻤﻌﺘﺴﻣ LDA ] 47 [ لاو GGA ] 48 [ لاو GGA EV− فﺮط ﻦﻣ ﺔﺣﺮﺘﻘﻤﻟا Engel Vosko− ] 49 [ . 7

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ﺪﻘﻟ ﺔﯿﻧوﺮﺘﻜﻟﻹا تﻻﺎﻘﺘﻧﻻا ﻦﯿﯿﻌﺗ ﻊﻣ ﺔﯿﺋﻮﻀﻟا ﺖﺑاﻮﺜﻟا ﺖﺒﺴﺣ ﺪﻘﻟ ؛ﺔﻠﺼﻔﻣ ﺔﺳارد ﺔﯿﺋﻮﻀﻟا صاﻮﺨﻟا ﺎﻨﺳرد ﯿﺋﻮﻀﻟا فﺎﯿطﻷا ﻦﻋ ﺔﻟوﺆﺴﻤﻟا ﺔﻧوﺮﻤﻟا ﺖﺑاﻮﺛ بﺎﺴﺣ ﻢﺗ ﺪﻘﻟ .ﺔ رﻮﻄﻠﻟ ﺎﮭﺑ ﺔﻄﺒﺗﺮﻤﻟا صاﻮﺨﻟا و يدﺎﺣأ ﺒﻟا ــ و ةرﻮﻠ رﻮــﻄﻟا ﺘﻣ ــ تارﻮﻠﺒﻟا دﺪﻌ ﻞھﺎــﻣ ﺔﻘﯾﺮط لﺎﻤﻌﺘﺳﺎﺑ (Mehl 's Method ) ] 50 [ تﺎــﺒﯾﺮﻘﺗ و ﺖﯾﻮﻓ -سور ﻞﯿھ

(Voigt−Re uss−Hill)

] 51 -53 [ . ﺎﻨھ ةرﺎﺷﻹا رﺪﺠﺗ ﺔﻘﺑﺎﺴﻟا ﺔﯾﺮﻈﻨﻟا تﺎﺑﺎﺴﺤﻟا نأ ﻰﻟإ ] 20 ، 39 ، 45 ، 46 ، 54 [ ﻖﻠﻄﻣ ﺮﻔﺻ ةراﺮﺣ ﺔﺟرد ﺪﻨﻋ ﺔﺳورﺪﻤﻟا داﻮﻤﻠﻟ ﺔﯿﺋﺎﯾﺰﯿﻔﻟا صاﻮﺨﻟا ﻲﻄﻌﺗ (0K) ﻦﻣ ﺪﯾﺪﻌﻟا ﻰﻠﻋ ﻂﻐﻀﻟا و ةراﺮﺤﻟا ﺮﯿﺛﺄﺗ ﺔﺳارﺪﺑ ﺎﻨﻤﻗ اﺬﮭﻟ .رﺎﺒﺘﻋﻻا ﻦﯿﻌﺑ يراﺮﺣ ﺮﯿﺛﺄﺗ يأ ﺬﺧأ نوﺪﺑ يأ ﯿﺋﺎﯾﺰﯿﻔﻟا تﻼﻣﺎﻌﻤﻟا ﯿﺑﻮﻜﺳوﺮﻜﯾﺎﻤﻟا ﺔ ﺔ ،يراﺮﺤﻟا دﺪﻤﺘﻟا ﻞﻣﺎﻌﻣ ،طﺎﻐﻀﻧﻻا ﻞﻣﺎﻌﻣ ،ﺔﻜﺒﺸﻟا ﺖﺑﺎﺛ ﻞﺜﻣ ﺔﻤﮭﻤﻟا ﻲﻧﻮﻣﺮﮭﻟا ﮫﺒﺸﻟا جذﻮﻤﻨﻟا ماﺪﺨﺘﺳﺎﺑ يﺎﺒﯾد ةراﺮﺣ ﺔﺟرد و ﻢﺠﺤﻟا تﻮﺒﺜﺑ و ﻂﻐﻀﻟا تﻮﺒﺜﺑ ﺔﯾراﺮﺤﻟا ﺔﻌﺴﻟا يﺎﺒﯾﺪﻟ

(Quasi harmonic debye mod el)−

5.1 ﺔﻟﺎﺳﺮﻟا ﺔﯿﻨﺑ ﺔﻓﺎﺿإ ،ﺔﻟﺎﺳﺮﻟا هﺬھ يﻮﺘﺤﺗ ﻦﯿﻤﺴﻗ ﻰﻠﻋ ،ﺔﻤﺗﺎﺨﻟاو ﺔﻣﺎﻌﻟا ﺔﻣﺪﻘﻤﻟا ﻰﻠﻋ :  ﺔﯿﻟاد ﺔﯾﺮﻈﻧ ئدﺎﺒﻣ لوﻷا ﻞﺼﻔﻟا مﺪﻘﯾ .ﻦﯿﻠﺼﻓ ﻰﻟإ ﻢﺴﻘﻨﯾ و ،بﺎﺴﺤﻠﻟ يﺮﻈﻨﻟا رﺎطﻹا لوﻻا ﻢﺴﻘﻟا ضﺮﻌﯾ ﺔﻓﺎﺜﻜﻟا (DFT) و ﺎﮭﺗﺎﺒﯾﺮﻘﺗ ﻊﺿﻮﻤﻟا ﺔﻓﺎﺜﻛ ﺐﯾﺮﻘﺗ ؛ (LDA) ﻢﻤﻌﻤﻟا جرﺪﺘﻟا ﺐﯾﺮﻘﺗ و (GGA) و . ﻦﯿﺒﯾ ئدﺎﺒﻣ ﻲﻧﺎﺜﻟا ﻞﺼﻔﻟا ﻞﻣﺎﻜﻟا نﻮﻤﻜﻟا ﻊﻣ ًﺎﯿﻄﺧ ةداﺰﻤﻟا ﺔﯾﻮﺘﺴﻤﻟا جاﻮﻣﻷا ﺔﻘﯾﺮط (FP−LAPW) ﻲﺘﻟا ، ﻰﻠﻋ ﺰﻜﺗﺮﺗ DFT و ﺞﻣﺎﻧﺮﺑ ﻲﻓ ﺔﺠﻣﺪﻤﻟا WIEN2k ] 55 [ .  ﺔﯿﺑﺎﺴﺤﻟا ﺞﺋﺎﺘﻨﻟا ﻲﻧﺎﺜﻟا ﻢﺴﻘﻟا ضﺮﻌﯾ ﺎﮭﺘﺸﻗﺎﻨﻣ و ،(لوﻻا ﻢﺴﻘﻟا ﻲﻓ ةرﻮﻛﺬﻤﻟا ﺔﻘﯾﺮﻄﻟا لﺎﻤﻌﺘﺳﺎﺑ ﺔﺑﻮﺴﺤﻤﻟا) ،ﺔﯿﻤﻠﻋ ﺔﺸﻗﺎﻨﻣ و ﻊﻣ ﺎﮭﺘﻧرﺎﻘﻣ ﺳارﺪﻟا تﺎ ﺔﯿﺒﯾﺮﺠﺘﻟا و ﺔﯾﺮﻈﻨﻟا ﻰﻠﻋ يﻮﺘﺤﯾ ،ﺔﯿﻤﻠﻌﻟا تارﻮﺸﻨﻤﻟا ﻲﻓ ةﺮﻓﻮﺘﻤﻟا لﻮﺼﻓ ﺔﺴﻤﺧ 3 ، 4 ، 5 ، 6 و 7 . تﺎﺒﻛﺮﻤﻠﻟ ﺔﯾرﻮﻠﺒﻟا ﺔﯿﻨﺒﻟا صاﻮﺧ ﺚﻟﺎﺜﻟا ﻞﺼﻔﻟا ﻲﻓ سرﺪﻧ 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O هﺬﮭﻟ ﺔﯿﻧوﺮﺘﻜﻟﻻا صاﻮﺨﻠﻟ ﺔﯿﺑﺎﺴﺤﻟا ﺞﺋﺎﺘﻨﻟا ﮫﯿﻓ ﺶﻗﺎﻨﻧ ﻊﺑاﺮﻟا ﻞﺼﻔﻟا ﺎﻣأ . ﺔﯿﺋﻮﻀﻟا صاﻮﺨﻟا ﺲﻣﺎﺨﻟا ﻞﺼﻔﻟا ﻲﻓ سرﺪﻧ ﻚﻟﺬﻛ و .تﺎﺒﻛﺮﻤﻟا سدﺎﺴﻟا ﻞﺼﻔﻟا ﻲﻓ و .ﺔﻠﺼﻔﻣ ﺔﺳارد ﺔﯿﻜﯿﻣﺎﻨﯾدﻮﻣﺮﺘﻟا صاﻮﺨﻠﻟ ﺔﯿﺑﺎﺴﺤﻟا ﺞﺋﺎﺘﻨﻟا سرﺪﻧ ﺮﯿﺧﻻا ﻞﺼﻔﻟا ﻲﻓ و .ﺔﯿﻜﯿﻧﺎﻜﯿﻤﻟا صاﻮﺨﻟا سرﺪﻧ تﺎﺒﻛﺮﻤﻠﻟ 2 4 SnMg O ، 2 4 SnZn O و 2 4 SnCd O ﻢھأ ﺺﺨﻠﺗ ﻲﺘﻟا و ﺔﻣﺎﻋ ﺔﺻﻼﺨﺑ ﻢﺘﺨﻧ ﺔﯾﺎﮭﻨﻟا ﻲﻓ و . .ﺚﺤﺒﻟا اﺬھ ﻲﻓ ﺎﮭﯿﻠﻋ ﻞﺼﺤﺘﻤﻟا ﺞﺋﺎﺘﻨﻟا 8

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