Nghiên cứu chuyển pha cấu trúc lập phương tâm khối - lập phương tâm mặt trong kim loại, hợp kim

1 Bộ giáo dục đào tạo Trường đại học sư phạm hà nội 0o0 - TRANG PH BèA Nguyễn văn tới nghiên cứu chuyển pha cấu trúc lập phương tâm khối lập phương tâm mặt kim loại, hợp kim Chuyên ngành: vật lý chất rắn Mã số: 60 44 07 luận văn thạc sĩ vật lí Người hướng dẫn khoa học: Ts Nguyễn Thế lâm Hà Nội, 2010 LI CM N Lun ny c thc hin v hon thnh ti Trng HSP H Ni di s hng dn ca Tin s Nguyn Th Lõm, quỏ trỡnh hng dn thy ó truyn cho tụi nhng kinh nghim quý bỏu hc v nghiờn cu khoa hc Thy luụn ng viờn v khớch l tụi lờn hc v vt qua nhng khú khn Tụi ó tng bc tin hnh v hon thnh lun vi ti nghiờn cu chuyn pha cu trỳc lp phng tõm lp phng tõm mt kim loi, hp kim Tụi xin by t lũng kớnh trng, bit n chõn thnh v sõu sc nht i vi thy Tụi xin trõn trng cm n Ban Giỏm hiu trng HSP H Ni 2, Khoa Vt Lý, Phũng sau i hc trng HSP H Ni ó to mi iu kin thun li cho tụi hon thnh chng trỡnh cao hc v lun tt nghip Tụi xin trõn trng cm n S GD - T Tuyờn Quang, Trng THPT Hm Yờn ó to mi iu kin tt nht tụi hon thnh lun Cui cựng tụi xin cm n gia ỡnh, cỏc ng ng nghip v bn bố ó to iu kin, ng viờn, úng gúp nhng ý kin quý bỏu tụi hon thnh lun ny H ni, thỏng 09 nm 2010 Tỏc gi Nguyn Vn Ti LI CAM OAN Tụi xin cam oan lun ny l kt qu nghiờn cu ca tụi, khụng chộp hoc trựng vi kt qu ca bt k tỏc gi no ó c cụng b Nu sai tụi xin hon ton chu trỏch nhim H ni, thỏng 09 nm 2010 Tỏc gi Nguyn Vn Ti MC LC TRANG PH BèA LI CM N LI CAM OAN MC LC DANH MC CC CH VIT TT M U Chng I: CC LOI CHUYN PHA 1.1 Khỏi nim v chuyn pha cu trỳc 1.2 Cỏc loi chuyn pha 1.2.1 Chuyn pha loi I v chuyn pha loi II 1.2.2 Chuyn pha t tớnh 11 1.2.3 Chuyn pha siờu dn 14 Chng II: MT S KT QU THC NGHIM V CHUYN PHA CU TRC 19 2.1 Chuyn pha cu trỳc Fe1 Se 19 2.2 Chuyn pha t tớnh v cu trỳc bc mt Fe1+ySexTe1-x 31 2.2.1 Gii thiu 31 2.2.2 Kt qu thớ nghim v tho lun 34 2.2.3 Kt lun 44 Chng III: CHUYN PHA CU TRC LP PHNG TM KHI LP PHNG TM MT 45 3.1 Mụ hỡnh lý thuyt chuyn pha cu trỳc lp phng tõm lp phng tõm mt 45 3.2 Chuyn pha cu trỳc theo nhit T 50 3.2.1 S ph thuc ca khe nng lng vo nhit i vi mng lp phng tõm v mng lp phng tõm mt 50 3.2.2 Chuyn pha cu trỳc theo nhit lp phng tõm - lp phng tõm mt 51 3.3 Chuyn pha cu trỳc theo cht n 52 3.3.1 S ph thuc ca khe nng lng vo nng cht i vi mng lp phng tõm mt v mng lp phng tõm 52 3.3.2 Chuyn pha cu trỳc theo nng cht, lp phng tõm lp phng tõm mt 53 3.3.3 S ph thuc ca th húa vo nng cht i vi mng lp phng tõm mt v lp phng tõm 54 TI LIU THAM KHO 57 PH LC 62 DANH MC CC CH VIT TT AF Trt t cng tuyn BCC Lp phng tõm CDW Súng mt in ED Nhiu x electron FCC Lp phng tõm mt SDW Súng mt spin SQUID Lng t siờu dn TEM Phng phỏp kớnh hin vi in t truyn qua XSRD Phng phỏp bt nhiu x M U Lý chn ti - Mt s kim loi, hp kim cú chuyn pha cu trỳc, chớnh s chuyn pha cu trỳc dn n s thay i v cỏc tớnh cht vt lý - Ti li cú s chuyn pha cu trỳc v chuyn pha ph thuc vo cỏc iu kin no? L mt cõu hi cn cõu tr li rừ rng v y - Vi lý nờu trờn chỳng tụi chn ti nghiờn cu chuyn pha cu trỳc lp phng tõm lp phng tõm mt kim loi, hp kim a mt cỏch gii thớch v hin tng ny Mc ớch nghiờn cu - Gii thớch c chuyn pha cu trỳc lp phng tõm (BCC) - lp phng tõm mt (FCC) ph thuc nhit , cht - ti l c s lý thuyt lm c s cho thc nghim, cú th to mt s vt liu mi nh mong mun - Xõy dng mụ hỡnh lý thuyt gii thớch chuyn pha cu trỳc núi chung Nhim v nghiờn cu - Nghiờn cu cỏc tớnh cht v c im ca mng tinh th lp phng tõm v lp phng tõm mt - Nghiờn cu s chuyn pha cu trỳc lp phng tõm - lp phng tõm mt - Kho sỏt s ph thuc ca cỏc tớnh cht ny vo nhit v cht i tng v phm vi nghiờn cu - Tinh th lp phng tõm khi, lp phng tõm mt - Cỏc kim loi, hp kim cú chuyn pha cu trỳc Phng phỏp nghiờn cu - Phng phỏp vt lý lý thuyt - Phng phỏp tớnh s Nhng úng gúp mi v khoa hc, thc tin ca ti - Xõy dng mụ hỡnh lý thuyt gii thớch s chuyn pha cu trỳc gia lp phng tõm lp phng tõm mt kim loi v hp kim - T mụ hỡnh lý thuyt ny s nh hng cho thc nghim cú th ch to nhng vt liu cú nhit chuyn pha khỏc phc v cho vic phỏt trin vt liu mi Cu trỳc lun - Ngoi phn m u, kt lun, ph lc v ti liu tham kho, ni dung lun c trỡnh by chng Chng 1: Cỏc loi chuyn pha Chng 2: Mt s kt qu thc nghim v chuyn pha cu trỳc Chng 3: Chuyn pha cu trỳc lp phng tõm - lp phng tõm mt Chng I CC LOI CHUYN PHA 1.1 Khỏi nim v chuyn pha cu trỳc Chuyn pha cu trỳc l s thay i trng thỏi i xng ca h Trng thỏi i xng bao gm mt vi kh nng sau: - S sp xp ca cỏc nguyờn t hoc phõn t Vớ d, tan chy bng hoc nc trng thỏi lng tr thnh trng thỏi khớ (hi nc) l cỏc vớ d v thay i sp xp cỏc phõn t H O ; - S gim tớnh i xng Chỳng ta tho lun di õy hai vớ d - tớnh cht st t v tớnh st in; - S tn ti ng thi cỏc khụng gian cú nhng tớnh cht khỏc Vớ d, mt cht bỏn dn cú th pha to cỏc ht mang in linh ng hoc l cỏc electron hoc cỏc l trng cú th phn ng vi mt trng in v to mt dũng in Tuy nhiờn, ụi khi, thay cho vic to mt mt n cỏc ht mang in p (= s ht mang/th tớch), vt liu phõn tỏch pha thnh cỏc khụng gian cú mt ht mang cao hn v thp hn (thp hn cú th bng khụng) 1.2 Cỏc loi chuyn pha 1.2.1 Chuyn pha loi I v chuyn pha loi II - Chuyn pha loi I: Cỏc loi chuyn pha m ú nng lng ca h thay i khụng liờn tc c gi l chuyn pha loi I VD S tan chy bng hoc nc t trng thỏi lng chuyn sang trng thỏi hi u l chuyn pha loi I - Chuyn pha loi II: Cỏc loi chuuyn pha m ú nng lng ca h thay i liờn tc, nhng o hm ca nng lng so vi nhit thỡ thay i khụng liờn tc Nh rng, nhit dung cv hoc cp l o hm ca nng lng i vi nhit : CV (E / T ) V v C p (E / T ) P (1.1) Vỡ th chuyn pha loi hai ngha l nhit dung (hoc, nhit dung riờng = nhit dung/phõn t) l khụng liờn tc Khi cú s chuyn pha loi II lm thay i sp xp nguyờn t, cú th d dng thy s thay i bng nhiu x tia X, nhiu x ntron, hoc quột hin vi tia rũ Hỡnh 1.1 minh khỏi nim nh tớnh Chỳng ta hóy bt u vi mt phõn t cụ lp, mi hng khụng gian u tng ng vỡ th s i xng l khỏ cao Thc ra, s i xng cng tng ng i xng khụng gian ba chiu Gi s ta sp xp cỏc phõn t theo mt cỏch cú trt t, khụng gian ba chiu thỡ hai dng cú s sp xp i xng cao nht l dng hỡnh lp phng v hỡnh lc giỏc Chỳ ý, mc dự ta khụng th thay i cỏc bc nh gia mt hỡnh lc giỏc v mt hỡnh lp phng, nhng thay vo ú ta cú th thay i gia hỡnh lc giỏc v hỡnh lp phng liờn quan n chuyn ng phõn t xung quanh mt khong cỏch xỏc nh vi s suy gim nng lng nht nh Do ú, mt s chuyn pha gia cu trỳc lc giỏc v cu trỳc hỡnh lp phng l chuyn pha loi I Bõy gi xem xột hỡnh lp phng Nu ta to mt trc ln hn hoc nh hn mt chỳt so vi hai trc cũn li, thỡ hỡnh lp phng thnh mt hỡnh ch nht Hỡnh ch nht cú i xng khỏc v thp hn so vi hỡnh lp phng Bi vỡ s khỏc v cỏc trc l nh nu chỳng ta cú dng hỡnh ch nht vi nng lng cn thit to nờn s thay i tớnh i xng cú th tin n khụng iu ú ngha l, nng lng qua vựng biờn t i xng hỡnh lp phng thnh i xng hỡnh ch nht l liờn tc Do ú, mt s 10 chuyn pha t i xng hỡnh lp phng sang i xng hỡnh ch nht l mt s chuyn pha loi II Hỡnh sỏu cnh Hỡnh ch nht Hỡnh 1.1 Minh s thay i t i xng dng cu sang dng lp phng, lc giỏc v t dng lp phng sang i xng hỡnh ch nht S thay i tớnh i xng cng l mt hin tng chuyn pha Cú mt quan im khỏc v ý kin thay i s i xng ny Khi chỳng ta núi mt vt th cú i xng dng cu, chỳng ta mun núi rng tt c cỏc hng u tng ng, ngha l, hng ny hoc hng u nh Do vy, i xng dng cu, hai vt cú cỏc vộc t ch hng khỏc l tng ng iu ny ngha l bt k hng no cú vộc t ch ti u bng vi bt k hng khỏc, vỡ th bc ca cỏc vộc t cng khụng cú bc no c hỡnh 1.1 v quan sỏt c hai thay i t i xng dng cu sang dng lp phng v t dng lp phng sang i xng hỡnh ch nht Cú mt vi thay i m ta cú th thc hin i vi mt hỡnh lp phng trỡ trng thỏi hỡnh lp phng nh: 53 Kt qu t hỡnh 3.7 v hỡnh 3.8 cho thy nng cht n cng tng dn n khe nng lng cng gim, v nng lng t E ca h cng tng, n tng ti mt giỏ tr no ú thỡ = iu ny xy vi c mng lp phng tõm (BCC) v mng lp phng tõm mt (FCC), nhiờn nng cht n khe nng lng ca mi tinh th bng khụng l khỏc 3.3.2 Chuyn pha cu trỳc theo nng cht, lp phng tõm lp phng tõm mt 0.12 0.1 0.08 0.0772 BCC 0.06 FCC 0.04 0.02 0 0.193 0.5 1.5 2.5 3.5 Nng cht (n) Hỡnh 3.9 S ph thuc ca khe nng lng vo nng cht i vi mng lp phng tõm v mng lp phng tõm mt ( FCC 0.024 , BCC 0.0072 ) Kt qu t hỡnh 3.9 cho thy nng cht n tng thỡ khe nng lng gim v nng lng t E ca h tng Tng t nh chuyn pha cu trỳc theo nhit ta cú th thy cỏc giai on sau: - Khi nng cht n nC luụn cho thy BCC FCC iu ny dn n E BCC E FCC Do ú h tn ti dng FCC 54 - Khi nng cht tng ti giỏ tr ti hn n nC thỡ BCC FCC iu ny dn n EBCC EFCC H trng thỏi cõn bng ng gia hai pha FCC v BCC - Khi tip tc tng nng cht n nC thỡ BCC FCC v EBCC EFCC Do ú h tn ti dng BCC - T nhng lp lun trờn ta cú th thy: n nC , n nC v n nC cho thy tng dn nng cht n cho ti ln hn nng ti hn nC thỡ cú s chuyn pha cu trỳc ca h t lp phng tõm mt (FCC) sang lp phng tõm (BCC), v nng cht xy chuyn pha cu trỳc l nC 3.3.3 S ph thuc ca th húa vo nng cht i vi mng lp phng tõm mt v lp phng tõm 0.12 0.1 0.08 0.06 0.04 0.02 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Nng cht (n) Hỡnh 3.10 S ph thuc ca th húa vo nng cht i vi mng lp phng tõm mt ( FCC 0.024 ) 55 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.5 1.5 2.5 3.5 Nng cht (n) Hỡnh 3.11 S ph thuc ca th húa vo nng cht i vi mng lp phng tõm ( BCC 0.0072 ) 0.12 0.1 0.08 BCC 0.06 FCC 0.04 0.02 0 0.5 1.5 2.5 3.5 Nng cht (n) Hỡnh 3.12 S ph thuc ca th húa vo nng cht i vi mng lp phng tõm mt v mng lp phng tõm ( FCC 0.024 , BCC 0.0072 ) Hỡnh 3.12 l tng hp ca cỏc hỡnh 3.10 v hỡnh 3.11 cho thy tng dn nng cht n thỡ th húa ca h gim, nhiờn s gim l khụng ging i vi lp phng tõm (BCC) v lp phng tõm mt (FCC) 56 KT LUN Qua lun Nghiờn cu chuyn pha cu trỳc lp phng tõm lp phng tõm mt kim loi, hp kim chỳng tụi ó t c mt s kt qu sau: - Xõy dng c mụ hỡnh lý thuyt gii thớch s chuyn pha cu trỳc gia lp phng tõm lp phng tõm mt mt s kim loi v hp kim - Kho sỏt c s ph thuc ca khe nng lng, th húa ca cỏc mng lp phng tõm mt, lp phng tõm theo nhit - Kho sỏt c s ph thuc ca cỏc khe nng lng, th húa ca cỏc mng lp phng tõm mt, lp phng tõm vo nng cht - Chng minh c s tn ti ca chuyn pha cu trỳc lp phng tõm lp phng tõm mt nhit thay i - Chng minh c s tn ti ca chuyn pha cu trỳc lp phng tõm lp phng tõm mt cht thay i 57 TI LIU THAM KHO [1] A I Goldman, D N Argyriou, B Ouladdiaf, T Chatterji, A Kreyssig, S Nandi, N Ni, S L Budko, P C Canfield, and R J McQueeney, Phys Rev B 78, 100506 (R) (2008) [2] A I Goldman, D N Argyriou, et al., Physical Review B 78, 100506 (2008) [3] A J Drew, C Niedermayer, et al, Nature Materials, doi:10.1038/nmat2396 (2009) [4] A Subedi, L Zhang, D J Singh, and M H Du, Phys Rev B78, 134514 (2008) [5] B H Toby, Journal of Applied Crystallography 34, 210 (2001) [6] C Cruz, Q Huang, et al., Nature, doi: 10.1038/ nature 07057 (2008) [7] C de la Cruz, Q Huang, J W Lynn, J Li, W Ratcliff, J L Zarestky, H A Mook, G F Chen, J L Luo, N L Wang, and Pengcheng Dai, Nature (London) 453, 899 (2008) [8] C Fang, B A Bernevig, and J Hu, arXiv:0811.1294 (unpublished) [9] C Fang, H Yao, W F Tsai, J P Hu, and S A Kivelson, Phys Rev B 77, 224509 (2008) [10] D Fruchart, P Convert, P Wolfers, R Madar, J P Senateur, and R Fruchart, Mater Res Bull 10, 169 (1975) [11] D R Parker, M J Pitcher, et al., Chemical Communications, 2189 (2009) [12] E F Westrum, C Chou, and F Grnvold, J Chem Phys 30, 761 (1959) [13] F C Hsu, J Y Luo, et al., Proceedings of the National Academy of Sciences 105, 14262 (2008) 58 [14] F Gronvold, H Haraldsen, and J Vihovde, Acta Chem Scand (19471973) 8, 1927 (1954) [15] F Ma, W Ji, J Hu, Z.-Y Lu, and T Xiang, arXiv:0809.4732 (unpublished) [16] F Ma, Z.-Y Lu, and T Xiang, Phys Rev B 78, 224517 (2008) [17] F.-C Hsu et al., Proc Natl Acad Sci U.S.A 105, 14262 (2008) [18] G F Chen, Z Li, D Wu, G Li, W Z Hu, J Dong, P Zheng, J L Luo, and N L Wang, Phys Rev Lett 100, 247002 (2008) [19] H H Wen, G Mu, L Fang, H Yang, and X Zhu, Europhys Lett 82, 17009 (2008) [20] H Luetkens, H H Klauss, et al., Nature Materials, doi:10.1038/nmat 2397 (2009) [21] H Okamoto, J Phase Equilib 12, 383 (1991) [22] I I Mazin, D J Singh, M D Johannes, and M H Du, Phys Rev Lett 101, 057003 (2008) [23] I Tsubokawa and S Chiba, J Phys Soc Jpn 14, 1120 (1945) [24] J A Schottenfeld, A J Benesi, et al., Journal of Solid State Chemistry 178, 2313 (2005) [25] J B Ward and V H McCann, J Phys C 12, 873 (1979) [26] J C Lashley et al., Cryogenics 43, 369 (2003) [27] J Cui, Q Huang, and B H Toby, Powder Diffr 21, 71 (2006) [28] J Dong et al., Europhys Lett 83, 27006 (2008) [29] J H Tapp, Z J Tang, et al., Physical Review B 78, 060505 (2008) [30] J N Millican, D Phelan, et al., Solid State Communications 149, 707 (2009) [31] J W Lynn and P Dai, arXiv:0902.0091 (2009) [32] J Zhao, Q Huang, C de la Cruz, J W Lynn, M D Lumsden, Z A 59 Ren, Jie Yang, Xiaolin Shen, Xiaoli Dong, Zhongxian Zhao, and Pengcheng Dai, Phys Rev B 78, 132504 (2008) [33] J Zhao, Q Huang, C de la Cruz, S Li, J W Lynn, Y Chen, M A Green, G F Chen, G Li, Z Li, J L Luo, N L Wang, and Pengcheng Dai, Nature Mater 7, 953 (2008) [34] J Zhao, Q Huang, et al., Nature Materials 7, 953 (2008) [35] J Zhao, W Ratcliff, J W Lynn, G F Chen, J L Luo, N L Wang, J Hu, and P Dai, Phys Rev B 78, 140504 (R) (2008) [36] K L Komarek and P Terzieff, Monatsh Chem 106, 145 (1975) [37] K Sasmal, B Lv, et al., Physical Review Letters 101, 107007 (2008) [38] K.-W Yeh, T - W Huang, Y.-L Huang, T.-K Chen, F.-C Hsu, P M Wu, Y.-C Lee, Y.-Y Chu, C.-L Chen, J.-Y Luo, D C Yan, and M K Wu, Europhys Lett 84, 37002 (2008) [39] L Zhang, D J Singh, and M H Du, arXiv:0810.3274, Phys Rev B (to be published) [40] M H Fang, H M Pham, B Qian, T J Liu, E K Vehstedt, Y Liu, L Spinu, and Z Q Mao, Phys Rev B 78, 224503 (2008) [41] M Rotter, M Tegel, and D Johrendt, Phys Rev Lett 101, 107006 (2008) [42] M Rotter, M Tegel, et al., Physical Review Letters 101, 107006 (2008) [43] P Terzieff, Physica B & C 103, 158 (1981) [44] Q Huang (private communication) [45] Q Huang, Y Qiu, W Bao, M A Green, J W Lynn, Y C Gasparovic, T Wu, G Wu, and X H Chen, Phys Rev Lett 101, 257003 (2008) [46] S A J Kimber, D N Argyriou, F Yokaichiya, K Habicht, S Gerischer, T Hansen, T Chatterji, R Klingeler, C Hess, G Behr, A 60 Kondrat, and B Buchner, Phys Rev B 78, 140503 (R) (2008) [47] S Atzeri and G Mula, Solid State Commun 13, 157 (1973) [48] S Margadonna, Y Takabayashi, et al., Chemical Communications, 5607 (2008) [49] S Margadonna, Y Takabayashi, M T McDonald, K Kasperkiewicz, Y Mizuguchi, Y Takano, A N Fitch, E Suard, and K Prassides, Chem Commun (Cambridge) (2008) 5607 [50] S Matsuishi, Y Inoue, et al., Journal of the American Chemical Society 130, 14428 (2008) [51] Shiliang Li, Clarina de la Cruz, Q Huang, Y Chen, J W Lynn, Jiangping Hu, Yi-Lin Huang, Fong-Chi Hsu, Kuo-Wei Yeh, Maw-Kuen Wu, and Pengcheng Dai First-order magnetic and structural phase transitions in Fe1+ySexTe1-x Physical Review B 79, 054503 (2009) [52] T M McQueen, Q Huang, et al., Physical Review B 79, 014522 (2009) [53] T M McQueen, Q Huang, V Ksenofontov, C Felser, Q Xu, H Zandbergen, Y S Hor, J Allred, A J Williams, D Qu, J Checkelsky, N P Ong, and R J Cava, arXiv:0811.1613, Phys Rev B (to be published) [54] T Park, E Park, et al., Journal of Physics- Condensed Matter 20 (2008) [55] T M McQueen1, A J Williams1, P W Stephens, J Tao, Y Zhu, V Ksenofontov, F Casper, C Felser, and R J Cava The Structural Phase Transition in Fe1+Se [56] V B Zabolotnyy, D S Inosov, et al., Nature 457, 569 (2009) [57] V Cvetkovic and Z Tesanovic, arXiv:0808.3742 (2008) 61 [58] W Bao et al., arXiv:0809.2058 (unpublished) [59] W Schuster, H Mikler, and K L Komarek, Monatsh Chem 110, 1153 (1979) [60] X H Chen, T Wu, G Wu, R H Liu, H Chen, and D F Fang, Nature (London) 453, 761 (2008) [61] Y Chen, J W Lynn, J Li, G Li, G F Chen, J L Luo, N L Wang, Pengcheng Dai, C dela Cruz, and H A Mook, Phys Rev B 78, 064515 (2008) [62] Y Kamihara, T Watanabe, et al., Journal of the American Chemical Society 130, 3296 (2008) [63] Y Kamihara, T Watanabe, M Hirano, and H Hosono, J Am Chem Soc 130, 3296 (2008) [64] Y Mizuguchi, F Tomioka, et al., Applied Physics Letters 93, 152505 (2008) [65] Y Mizuguchi, F Tomioka, S Tsuda, T Yamaguchi, and Y Takano, Appl Phys Lett 93, 152505 (2008) [66] Z.-A Ren et al., Europhys Lett 83, 17002 (2008) [67] Z A Ren, W Lu, et al., Chinese Physics Letters 25, 2215 (2008) [68] Z P Yin, S Lebốgue, M J Han, B P Neal, S Y Savrasov, and W E Pickett, Phys Rev Lett 101, 047001 (2008) 62 PH LC Chng trỡnh Matlab function y=f0(kx, ky, kz) global dt T=86e-1; es=2.*cos(kx/2).*cos(ky/2).*cos(kz/2); E=sqrt(es.^2+dt^2); y=tanh(E/T)./E; function y=ff0(X) global dt dt=X(1); lamda=0.035; y = lamda*8*triplequad('f0',0,pi,0,pi,0,pi)-1; %chuong trinh ve delta=f(muy) clf; X=0:0.01:0.15; %plot(X,ff0(X)); delta=fzero('ff0',0.1) function y=f0(kx, ky, kz) global dt T=48e-1; es=cos(ky/2).*cos(kz/2) cos(kx/2).*cos(ky/2); + cos(kz/2).*cos(kx/2) + 63 E=sqrt(es.^2+dt^2); y=tanh(E/T)./E; function y=ff0(X) global dt dt=X(1); lamda=0.02; y = lamda*8*triplequad('f0',0,pi,0,pi,0,pi)-1; %chuong trinh ve delta=f(muy) clf; X=0:0.01:0.15; %plot(X,ff0(X)); delta=fzero('ff0',0.1) function y=fn1(kx,ky,kz) global dt muy T es=cos(ky/2).*cos(kz/2) + cos(kz/2).*cos(kx/2) cos(kx/2).*cos(ky/2); E=sqrt(es.^2+dt^2); Teta=tanh((muy+E)/T)+tanh((muy-E)/T); y=Teta./2; function y=fn2(delta,muy1) global dt muy T for i=1:length(delta) dt=delta(i); + 64 for j=1:length(muy1) muy=muy1(j); y(i,j)=triplequad('fn1',0,pi,0,pi,0,pi)0.006; % n=0.33 la tap chat end end function y= ftoi1(kx,ky,kz) global muy dt T es=cos(ky/2).*cos(kz/2) + cos(kz/2).*cos(kx/2) cos(kx/2).*cos(ky/2); E=sqrt(es.^2+dt^2); Teta=tanh((muy+E)/T)-tanh((muy-E)/T); y=Teta./(2*E); function y=ftoi2(delta,muy1) global dt muy T for i=1:length(delta) dt=delta(i); for j=1:length(muy1) muy=muy1(j); y(i,j)=0.024*triplequad('ftoi1',0,pi,0,pi,0,pi)-1; end end %ve contour + 65 global T T=1e-6; clf; dt=1e-6:0.01:0.15; muy=1e-6:0.01:0.15; Z=ftoi2(dt,muy); N=fn2(dt,muy); contour(dt,muy,Z,[0 0]);hold on; contour(dt,muy,N,[0 0]);grid on; %mesh(X,Y,Z); function y=fn1(kx,ky,kz) global dt muy T es=2.*cos(kx/2).*cos(ky/2).*cos(kz/2); E=sqrt(es.^2+dt^2); Teta=tanh((muy+E)/T)+tanh((muy-E)/T); y=Teta./2; function y=fn2(delta,muy1) global dt muy T for i=1:length(delta) dt=delta(i); for j=1:length(muy1) muy=muy1(j); y(i,j)=triplequad('fn1',0,pi,0,pi,0,pi)-0.3; % n=0.3 la tap chat end 66 end function y= ftoi1(kx,ky,kz) global muy dt T es=2.*cos(kx/2).*cos(ky/2).*cos(kz/2); E=sqrt(es.^2+dt^2); Teta=tanh((muy+E)/T)-tanh((muy-E)/T); y=Teta./(2*E); function y=ftoi2(delta,muy1) global dt muy T for i=1:length(delta) dt=delta(i); for j=1:length(muy1) muy=muy1(j); y(i,j)=0.0072*triplequad('ftoi1',0,pi,0,pi,0,pi)-1; end end %ve contour global T T=1e-6; Clf dt=1e-6:0.01:0.15; muy=1e-6:0.01:0.15; Z=ftoi2(dt,muy); 67 N=fn2(dt,muy); contour(dt,muy,Z,[0 0]);hold on; contour(dt,muy,N,[0 0]);grid on; %mesh(X,Y,Z); -