Phân cực hóa trị trong một số vật liệu

ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC T ự NHIÊN Đ Ể TÀI: PHÂN cực HOÁ TRỊ TRONG MỘT SỐ VẬT LIỆU • • • Mã số: QT-04-05 CHỦ TRÌ ĐỂ TÀI: TS Hồng Nam Nhật OẠi rtOC Quốc GIA nA NO ' rRUNG TÂM Th ô n g TiN í HU Vjt ITT Hà nội - 2005 ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC T ự NHIÊN Đ Ể TÀI: PHÂN cực HỐ TRỊ TRONG MỘT SỐ VẬT LIỆU • • • Mã số: QT-04-05 CHỦ TRÌ ĐỂ TÀI: TS Hồng Nam Nhật CÁC CÁN BỘ THAM GIA: ThS Phùng Quốc Thanh ThS Nguyễn Đức Thọ CN Lê Thị Anh Thư Hà nội - ‘2005 BÁO CÁO TÓM TẢT I)ồ tài: PHẢN c ự c HOÁ TRỊ TRONG MỘT SỐ VẬT LIỆU Mã số: QT-04-05 CHU TRÌ ĐỂ TÀI: TS Hồng N a m N h ậ t CÁC CAN B ộ THAM GIA: ThS P h ù n g Quốc T h a n h ThS Nguyễn Đức Thọ CN Lê Thị Anh T h M ục tiê u d ể tài Trong phạm vi đê tài TN-03-06, nghiệm thu n ă m 2004 ch úng dã tr in h 1>;)V nghiên cứu nhóm tác giả vấn dể p h â n cực hoá trị hợp ch ất perovskite Được hỗ trợ tiếp tục Đại học Quốc gia đê tài QT 04-05 cơng trì n h nghiên cứu sâu nh óm tác giả vể vấn để p hâ n cục tro ng nhóm vật liệu vối khả n n g ứng dụ n g cao M ục tiêu trực tiếp đề tài nghiên cứu m ột ph ơng p h p lý thuyết cho phép d ự đoán với độ tin cậy cao hệ sỏ p h â n cực vĩ mô vật liệu dựa nh p h ầ n cấu trúc tinh thê vật liệu Phương p h p tim thấy ph a i phư ơng p h p giải nhanh, hiệu quả, tỏi g iá n hoá qua trinh tinh toán p h ứ c tạp đưa lời giải p h ù hợp với thực nghiệm với ph ơn g p h p lượng tứ khác N hậ n thấ y việc tìm thấy phương p h p có tín h ứng dụn g cao nh đòi hoi r ấ t nhiều thời gian vật lực nên đề tài giới h n phạm vi cho phép tức bước đầu t h u ậ t toán kiếm chứng t h u ậ t tốn p h m vi nhóm vật liệu từ bán d ẫ n t h u thập, chế tạo lựa chọn k h ả nă ng cho phép đề tài Đề tài để cập tới nh ững vấn để cụ th ế sau: - thiêt lặp mối q u a n hệ trực tiếp cấu trúc vật liệu, bao gồm cấu trúc t inh thê cấu trúc biên, phân bố hạ t p h â n cực vĩ mỏ đo cua vật liộu; - xát' lập phương pháp tiện dụng hoà n toàn độc lập so với phường ph p iượng tử đê khảo sát dự đoán-sự phâ n cực vĩ mô dựa t iv n cấu trúc vi mô vật liệu Nội d u n g n g h i ê n c ứ u ■ th u th ậ p tài liệu vế họ GaAs, ỉnP, ZnO PZT chê tạo cần họ Ca, vYxMn()ị, C a I XP r xM n 3, Ca085P r 015R u xM n l xO :t, Ca, xN dk( M n F e ) „ BaTiOj, P b T i PZT composites, - xác định c ấ u trú c vật liệu phương ph p nh iễ u xạ tia X SEM kết họp VỚI p h â n tích Rietveld p p đo tí n h c h ấ t điện từ; - hoà n ch ỉn h p h ầ n mềm xác định hoá trị liên kết đối VỚI perovskite pha tạp PZT, GaAs ZnO, BaTiOị dựa t r ê n cấu trú c vật liệu: - bước đầu xây dự ng phẩn mểm xác định đặc tính íractal cấu trúc bif>n hạt: - r h i mối tương q u a n độ dẫ n vật liệu với cấu trú c biên hạt d ựa t r ê n mơ h ì n h th ẩ m th ấ u vối th a m số cấu trú c c biên hạt xác địn h thơng qua p h â n tích íractal cấu trúc biên; - ho àn tấ t mục tiêu đặt đề tài n h nêu phần trước Các k ế t q u ả đ t đ ợ c Đế tài kêt sau: • đ chi p h â n cực hoá trị tự p há t họ vật liệu bán d ẫ n loại pm u vs kite ph a tạ p đấ t hiếm, BaTiOị tr u y ề n thống PZT GaAs vv - cụ th ế o s t phâ n bơ hố trị liên kêt p h â n cực chi hão hồ khơng đồng trê n domain cation liên kêt; - c h ứ n g tỏ phụ thuộc tuyến tính cúa p h â n cực hố trị liên kêt vào t h n h p h ầ n kim loại thay th ế tính t ấ t yếu p h â n cực doma in liên kết; - chi p hụ thuộc tuyến tính p h â n cực hoá trị th n h phầ n kim loại thay thê (nếu có), đồng thời tính nguyên tắc tượng p h â n cực hoá trị dựa mối liên hệ bán kính ion hố trị hèn kết: - chi mối liên hệ đặc tính vặt lý vặt liệu, dặc biệt tính đẫn với cấu trúc íractal biên hạ t đa tinh th ế với dộ lớn cùa hạt k(‘! tm h : ■liưa mơ hình th ẩ m thấ u lý giải độ dẫ n vật liệu dựa cấu trúc bión hạt; • r u n g cố q u a n điếm lượng tử p hâ n cực vĩ mơ bàng cách tính độc lạp cua p h ả n cực hoá trị liên kết đôi với p h â n cực dipol cố diên (xuất phá t tu lệch m n g sở); - xây dự ng chê tính tốn hiệu dụ ng n h a n h gọn so với Munte-Carlo từ nguyên lý ban đầu điếu kiện đ m bảo độ tin cậy cao ( ’ac kèt nghiên cứu nhóm tác giá, đê cặp k hí a cạnh khác n h a u cua vấn đề này, công bô 02 báo 06 báo cáo tạp chi hội nghị vật lý năm 2004-2005 n h sau: V N Ư J o f Sci 2004, 02 báo A P P C '9 Hanoi, 2004, 02 báo cáo V G S7 Ha Lung 2004, 02 báo cáo IS A M A P 2005 Hanoi, 01 báo cáo Y V S M 2005, N Trang, 01 báo cáo Nội du ng nghiên cứu sử dụng 01 luận văn Cứ nhã n Lê thị A nh T h 01 luận án Thạc sỹ N g uyễn Đức Thọ T ìn h h ìn h s d ụ n g k in h phí Tơng k in h p h í cấp: 10.000.000 đ (mười triệu đồng) Cac hhoán chi T h a n h tốn dịch vụ cơng cộng: 400.000 đ (diện nước) Q u n lý phí: 400.000 d Hỗ u ợ đào tạo: 300.000 đ Chi cho hôi thảo: 1.210.000 đ T h u ê lao dộng tro ng nước: 4.000.(300 đ Vật tư: 360.000 đ In ỉìn c h u y ê n môn: 160.000 d T h a n h tốn hợp đồng với bên ngồi: 3.170.000 đ ỉ)ã ỉ hông q u a c h ứ n g từ phòng tài vụ n gà y 09/11/2004 XA(' NH ẬN CỨA BCN KHOA C H Ủ TRÌ ĐỂ TÀI (Ký ghi rõ họ tên) (Ký ghi rỏ họ tên) XAC NH ẬN CỦA N HÀ TRƯỜN G HIỄU T R Ư Ỏ N Q GS.; jííạ iủ BRIEF REPORT BOND VALENCE POLARIZAT!ON IN SEVERAL MATERIALS C.KÌe: QT-04-05 Ma 111 responsible person: Dr Hoang N a m N h a t Inrurp orated members: MSc P h u n g Quoc T h a n h MSc Nguyen Duc Tho BSc Le thi Anh thu T h e p u r p o s e o f th e p ro ject ĩ 11 t ht‘ lormer project TN-03-06, successíulỉy ended in 2004 we ve discusscil our s tưdies on the problem of polarization in perovskites T h a n k to the ti m m g support from the Vietnam National Ưniversity, this project QT-0405 p r c s c n t s the more deeper and more complex stu dies of the au th o rs to the polan/.ation problem in the group of m at eria ls with high applicability The direct purpose o f this project is to s tu d y a new theoretical m ethod ivhich alloivs to predict, w ith high accuracy, the characteristics o f the valence po[arizntion in the m aterials, knouiing their several crystal structure aspects The neic m e th o d sh o u ld be efficient a n d quick, able to suppress the eom putơtional diỊỴiculty a n d provide the results comparable to o f the experim ents ur u f the uther quanturn m echanical methods Knmving t hat the achieving of such highly applicable method requires mon* t ime and s up po rt t h a n the project itseir can afford we restrict to the stuđy ol the m a t h e m a ti c a l algorithm a n d to the testin g of the se algorithms in th e grotip oi the semiconductive an d magnetic m a te ri a ls t h a t were eith er prcpatvtl ur collected hy ourselves from various sources Th e co nc re te suhjects oí’t.h(' |ii'())(‘ct are as follow: - lo est a bl is h the direct relationship between the s t r u c t u r e of m at eri al s (mcluđing crystal st ru c tu re a nd grain bou nd ary s tr uc tu re ) and their marroscopic m e asu rable polarization; - lo est a bl is h a simple but effective method totally in d e p en d e n t to the q u a n t u m -m e c h a n ic a l methods to study and predict th e macroscopic l>olanzation in ma teriaìs based on the ir st ru c tu re s T h e s u b j e c t o f th e p ro ject • to collect the h te tu re publication about the íamily GaAs ZnO PZT and m a n u f a c t u r e new if needed the íamily Ca,.xY ,M nO „ C a ,.J Jí \ M n Ca, s , R u vM n lxO t Ca,-xN dx(M n.Fe)Ot, BaTiOị, PbTiO, PZT composites - to d e t e r m i n e the crystal s tr uc tu re (based on X-Ray Diffraction Method a nd SEM with Rietveld technique incorporated); to m e a s u r e th e electric a n d m a g n e t i c p r o p e r t y of m a te r ia ls ; ■ tu complete the softwares for calculation of the bond valences in the dopeđ perovskites GaAs ZnO, BaTiO, ; - to est a bl is h the software base for the d e te r m in a ti o n of the ừacta! c c te ris tic s of the grain bo undary system: - ti) prove th e re lationship between the electric property of m a te ri a ls and the g r a m b ou nd a ry s tr uc tu re based on percolation theory modeỉ with h o u n d a r y char acteristics de termined as íractals; - to complete the purpose of project as settled in th e section above T h e o b t a in e d r e s u lt s The project achieved the following concrete results: - |)rơved t h a t th ere is a spontaneous polarization in the semiconductive a nd magn et ic m at eria ls of the families: doped perovskites traditional BaTiO, PZT GaAs, vv - Particularly we have inv e st ig at e d the d is tr ib utio n of boncl valence between the coordination m a in s and sh()W('(l thai tho re vvere the different a m o u n t of the s a t u r a t i o n va lrn c r in th SMallei near lOOOnm and each grain contained approximatedly 30-50 single crystal pieces, í arc;i of the gap spaces become practically stablized at the smallest unchanged minimuni: :!ie only remaining íầctor that drives conductivity vvas area of the cross-sections 10 Ruthemum dopped Ca , , N đ ,M n 0.2 >V UJ 0.1 ỉ • Rui” - nium doppeđ 2- Ca , / J , M n O j — r I E [eV] — J 1— 0.1 0.2 E [eV] FỈ-.4 ỉ ỉĩ^lìly imcar corrcspontlences betuccn B A and / versus activalion cnergy E (from left to right) The In MI I > rrelanon coefficicnts arc 0.4W o.*)1) and ().l)l for the three cases consequentiy Fiiz.4 hovvs the interdependence between B, A and the activation energy E obtained for CaossPrc, ' ^i-xR j,0 3and Caj-xNdxMn0 ; tor comparison we also reprint the result from the ldimensioiKỉl analysis that has been reported in [1] for Cai_xNdxMn0 These strong linear correlations show the better fits from the 2-dimensional analysis (of areas B,A) than from the l-dimcnsional analysis (of lengths L, /) and signify that the physics of the grain contacts may be the 1!: i\ force for the final conductivity of material Reíerctioc* Minh, i lo a n g N a m Nhat, Phung Q uo c Thanh, Bach Thanh C o n g H o a n g Van Hai, Pr(H\ ọ f 9th A sia n - [lỊD a n i: I P a c ự ỉr !'ir sic s ( 'o n f , Hanoi, - th Oct 2004 To appcar [2] B.B M;ini!oỉbri>!, "The Fractaỉ G co m etry o f Nature”, W.H Freeman and Co Ncvv York, N Y 1983 [3] A Jou.íiìnc;iux ”W i n M P r o f : a visuaỉ Rictveld softw arc” ( P l) H ự u s le tĩe r 21 ( 1999) p 13 [4] s k [5] Phui; J AViiiì It 1997", Institute fur G e olo gie, Erlangen 1997 V Tluiiilì, Bach Thanh C o n g and Niĩuyen N g o e Dinh R roc o f V J S A S T Hanoi, 20 To appcar The Nintli Asia Paciílc Phvsics Coníerence (9,h APPC ) Structure and electric property of the compound Ca/ rN đ vM n 03 (x = 0, 0.1, 0.3, 0.5, 0.7, 9) (rcvisited by íractaỉ length-to-area technique) Dang Le Minh, Hoang Nam Nhat, Phung Quoc Thanh, Bach Thanh Cong Hoang Van Hai Facuỉty o f Physics Hanoi Univ ersity o f S c ie n c e s V N U - H N Perovskite type Cai.*NdxMnCMx 0:0 1:0.3;0 5;0.7;0.Ọ) were sintered hy a Standard ceramic technique The structure reíĩnement of Cai.xNdxMnO, was carrieđ out by Rietveld anaiysis of powder X-ray diíĩraction data The cell constants and ceỉl volume are increased vvith increasing Nd-substitution The V1n-0 distances and the Mn-O-Mn angỉes are also varied The đependences of resistivity on temperature vvere measured in the range 20K-600K For 0 5.467 7.667 227.4 1.924 169.0 ỉ 70.0 175.8 Grain Cryslal size[nm ] siz e[Ả ] Est 2480 342 002 03 0.71 (ỉ 14 1230 352 u.tw t.(»4 45 \ is thai the conduction might be explained according to the hoping-electron model b \ V Conclu \!uiion ;it low temperature showed the radical deveỉopment of resistivity above I07 Qcm 0.9 ỉ !ic application of the íractaỉ approach ỉed excitedly to the clear linear relationship mth-to-:ưea ratio and the activation ener^y; this proves that the grain and grain boundary ! infỉucnce on the conductivity of these materials The result offers a new look into the hanism of these perovskites, requiring the further investigation The ii for -v=0.7 a betvveen th have subsi : conduction Referencc> | l | D.L Min!í ị B.B M ì: Thanh IS.T Cong, H.N Nhai H.v Hai D.M Hong Proc o flh e VGS 2004 p 131-134 || "Tho IV;ictal Geometry o f Nature" W.H Preeman and Co Nevv York NY 1983 V* oí ihc VGS 7, 2004 p ì 46-149 pj H.N Kìvm |4 | A JotKiniK ”\V in M i'n ìf : a visual R ieiveld sortsvare" C P Ị) n e \\s!e tte r 21 (1 9 ) p 13 15 s Kruuss .ỉa Insiiiute tur G eologic r.rlangcn 1997 M Múi.ukỉa, J ot Solid Siatc Chem 63 19X6 p 290 |6| II Tu^ik: 17) ị Kob.1} |K| II Taguc |9 | II 'Li-uc i Tiiki/ T F.ndo I Sato and M Shimada i of Soỉid Slaltí Chem 92 1991 p 116 N*agai> i:ij M Shimadu J ot Solid State (.'hem 97 1992 p 476 ■si ca li 3-10* 2001 p 31 Tạp chi ĐHQG VNU Journal of Sciences Accepted In P re s s MODEL ( ONDl C T IV n Y FOR PEROVSKITES BASED ON T H E SC A L IN G PRO PERTY O F G RAIN BO U N D A R Y Phung Quoc Thanh Hoang Nam Nhat' and Bach Thanh Cong Paculty o f P hysics I niversity o f Natural S c i e n c e s - V N U HN 3 N g u y ên Trai Thanh Xuan Hanoi V I E T N A M ABSTRACT We present the pcrcoỉatio n-theory model t'or expỉanation o f c o ndu ctiv ity o f pcrovskitcs based on thc s c a h n g property o f grain boundary íormation Assumrng a tw o-lay er sim p le e t ĩe c t i v e m edium model c o m p o s e d o f th e u in Its e lf as a íirs t lay e r an d th e b o u n d a ry a s a se c o n d lay e r It vvas m o d e le d th a t th e net resistivity p o f ĩhe m cdium depend s on the average grain siz e L boundary th ickncss L* and boundary fractal d im e n sio n D T h e obtam ed íormula was tested sp e c ific a lly for the perovskite system ( a„ s^Pr0 i 5Mnj xRuxO i ( v = 0 , 0 , 0 and 0 ) w h o s e structures and eỉectric propertics vverc rcported carlier by thesc authors [ V N U J o f Sci., X X , N o AP, 0 p 130-132 ] The determ mation o f tractal dimcnsion vvas bascd on the S tandard length-area technique and w as carried out usin g SEM im agcs vvhich w c re photographed at threc m agm fica tion scales 2, and 10^m T his d im e n sio n sh o w c d g o o d c o r r e s p o n d c n c e to th e s m a ỉỉ p o la ro n h o p in g e n e r g y in h ig h tem p e r a tu r e r e g io n an d g a v e v e r y g o o d fits to cxpcrim ental data for T < \ P ACS + n Fractaỉs - 61 72 Mn Grams - i Ed Crỵstal structurc and d e ícc ts K Í 'V W O R D S : pcrovskitc structurc íractal lirain boundary, c o ndu ctỉv ity C orrcspondin g author: E-mail: n a m n h a ií/ hn.vnn.vn, Tel: + - - 0 - 6 Fax: + - - 8 9 IM RODUCTION I he application of the ừactal techniques to tudy thc conduction mechamsm m the perovskite Lipcrconductors [1-3] 1S not nevv but for the ìanganate perovskites there 1S a lack of studies ealing directly with the grain boundary onductivity VVe knovv of only one work from )obrescu et al reporting the íractaỉ dirnension etermmation for Lai.xSrxCoO* [4] Aithough many tudics shovved the essential etĩects ol grain oundary on the macroscopic resistivity of erovskite [5], up-to-date there 1S still absent the novvỉeđge about the bouiularỵ geometry For the erovskites, one may adopt thc tVactal modeỉ and the lethod of determination ot' dimension írom the tuđies tbr metal oxides such as for the ìron uarti/ites [6] Here the measurement of the voltage rop distribưtion across the square matrix settled by le VVerner arrays was pertbrmed The apparent ísistivity vvasexpecteđ to depend on the electrode eparation / according to: p X /° ( 1) vvith D is the critical exponent related to the ractal dimension of the mozaic boundary system nderỉying the measured matrix Ít is also knovvn lat near the tlưeshold concentration ,YC the effective e s i s t i v i t v o f t h e p c r c o l a t i o n S y s t e m b e h a v e s as: p X ( \ - x c)ơ (2) with D' is another criticaỉ exponent The above dations however, not ìnclude t he term íorthe :mperature depenđence The common approach for < Tt vvas to consiđer (see Rao and Raychauhudry [51): p pn + p ị T (3) vvith the exponent n =5 2.5 and the ratio p|/po * 0'6 For T>TC, the usual attitude was to suggest Ither the small polaron hoping or the bandgap onduction modcl Both reỉy on the exponential levelopment of p according to T: Small polaroa: p x TcxpílV/,/ktìT) Bandgap: p X cxọ(E,/ktìT) (4) (5) Where the \Vp stands for the polaron hoping nergy and E„ for the activation energy Some uthors reported tỉìc variable hoping model v\ith p X xp\(T'/T)14] to bc suitabỉe for the manganate •erovskites, but we tbund this relation to be tìtted vorse in the testeđ samples (see Section 3) BOUNDARY RESiSTIVỊTY FROM FRACTAL VlEWPOINT We now adopt the two-layer simple effective medium model for the resistivity as has been used in Gupta et al [7] Consider tvvo media, the grain itself with size L and resistivity p(, and the boundary with thickness L’ and resistivity pịi The net resistivity is: p - p(, + ( L V L )pn (6 ) Smce the grains consist of the disordered single crystal pieces Ít is evident to suggest that above Tc the mtra-grain resistivity p(, evolutes according to (4) or (5) This resistivity may be iníluenced by the intra-grain single crystal boundary but is not expected to depend on the ìnter-grairì boundary The boundary resistivity pu may be gi ven, according to (1) - (3) as: Pb = ( P o + P i F ) ( r-.x c ) D / ° = = (p„ + p i D (.r-.vc)° (kL)° =/p„+ / p , r (7) with / = (knL Xd i)(a-vc)i> For each percolation system, the constant factor / is determined by the system composition and geometry By íitting (7) to the experỉment data the exponent n and p„ pị may be íound The p„ refers t o t he t emperature-independent p art o f the boundary resistivity vvhereas the pi to the temperature-dependcnt part The problenì was noi however the determination oi n [) or D' but Iheir physicaỉ foundation The procedures that vverc involved to estimate D, e.g m [6], not strictỊy relate D to the boundary resistivity As the measured resistivity heavily depends on the method and the apparature settỉement, the obtained D onỉy reĩers to the applied apparent resistivity At this moment there is no vvay to prove that D really corresponds to the true boundary resistivity For the puipose o f the íìrst approximation, we must adopt the asumption that the D, estimated by the procedure describeđ below, closely coníomis to the D obtained by measuring the apparent resistivity p To estimate D vve used the elassical lcngtharea reỉation, e.g described in [8j For each SEM magnification (each yardstick) G the ratio /g=Ls/La f the ỉ inear extents Ls determineđ on the basis of the grain domain perimeter G-length (in unit of image size) and Lạ determined on thc basis of the grain domain area G-area (in unit ot’ image area) is a constant: /G= L s/ L a = (G-Length)1n / (G-area)12 (8) vvith D be interpreted as the íYaetal dimension I the urain bouiHỈary Rcasonabỉy for the two itìerent magnifications G‘ and G the ratio: vi D-I (9) /, /(, - (G7G) Eviđently, the log-log plot from the relations ỈM*)) reveals the fractal dimension D TEST SAMPLES: Ca080.98) compaređ to of the band gap model (R2>0.96) It is reaỉly difficult to distinguish between the two models in the limited temperature region For the whole temperature range, both models shovved the shaip declines from the linearity at the temperature near Ts, whereas the variabỉe hoping modeỉ showed reỉatively good tít (R >0.95) both abovc and belovv T\ (Fig.3) t 10-Ị.im sc ale for A 0 , the rest w as o n n tte d for ỉarity The detemiined average grain size was 3750, 030 2360 and 3300nm for X from 0.00 to 0.07 íquentially (which means approx 156, 42 93 and 26 single crystal picces within each grain) ■ ÍT/ \ • ', ^ - ệ ý '• í r -v»' :■■ p— > •Y ' ị \ -y ■ ■ ■ c\A - : ':í>; c • "• ■i M m Ị Ỉ M - y ; r ík i [b a FICÌ ỉ SE M im age o f suríace for the sam p le ĩ= 0.0 at the I0jim s c a lc (a) A sa m p lc sc gm en ta tion mto smalỉ squarcs tor calculation o f the fract d im c n sỉo n íb) PIG.3 The fIts for the small polaron hoping modcl for tw o c a se s v=0.03 and 0 (other tw o c a sc s arc omitted fo r cỉarity) shovv the sharp d c c h n c s from the linearity at thc tcmpcraturc ncar T v The lincar approximation in thc high tcmpcrature r e g i o n h a s R2> T h e inset shovvs thc fit duc to the variablc hopinii m odel A lthou g h thc lincarity vvas lcss ihis fits thc w h o lc temperature range vvcỉl 10 00/T 5 10 1&0 ^2b 400 30 c 200 xs O T > 10 0K 100 0• 0000 005 010 015 T(K] FỈG.4 The differcntial curve d///(p)/d( l T ) drawn PIG.2 The d c v c lo p m e n t o f resist 1vity from I0K to against l/T for v=() 03 revcals thc drop o f thc activation e n e rg y w h c n thc temperaturc dccrcascs 350K for r=0.03-0.0 The insct shovvs A -0 0 ie We have re-measured the electric resistance by This Standard m e ch am sm a w a y from the bandvvidth-controlỉcd four e le c tro d e s te c h n iq u e m the ĩmperature range from 10 to 350K for cach 5K argucs for thc ch an g e in conduction T A B L E 1- The íractal an a ỉy sis o f bou ndary characteristics for Cao 8hmated the írnctal dimensíon D neeđeđ in relation ') accordincĩ to the tbllovvmg procedure 00 03 05 0.07 < 40 200 100 300 400 TỊKỊ First, casurc the total area of each SEM photograph, then vidc this area into the smaller squares and use iem to tì 11 each grain area The number of squares ỉled into one grain is just the G-area and the ìmber of squares that cross-over t he grain or run ver the grain boundary is just the linear extend Gength The log-log plot from these two quantities ítermines D (Fig.5) o V f ài log ( G - L c n g th ) FÍG The iog(G-Area) vs log(G-Length) plot T region) The lcasi squarc ftgure mcrìt R 0.02 The tangent points shovved the estim atcd T s for each c a se to be Ỉ20K ( - 0 ) and i Ỉ0K (.\~0.05) Fig.6 shows the fit resuỉts for two cases ,r=0.03 and 0.05 (the inset) The dotted lines denote the fit accordmg to the smaỉl polaron model (4) whereas the lines are accorđing to (7) The least square íigure of merit R < 0.02 The temperature at which the lines are tangential to the dotted lines is 120K (.r*0.03) and 110K (.V— 0.05) This temperature drops to 100K for v=0.07 Compared t o F c curves [ 10], t hese t emperatures coưespond to the Néel temperature T\ of the charge-ordering antifeưomagnetic to paramagnetic phase transition Table lists the povver f actor n the c onstant p a nd p I t hat vvere determined from the fits The n grew hncarly with Wp better than D vvith Wp (Fig.7) Recall the approximation for the boundary TABLE T h e íitt in g r e s u ỉts for th c povvcr ía cto r ỈU the constants po and p, Sampỉe X n Po [x 10 5Qcm] P [ x ỉ 5] 0.00 0.59 6099.0 -321.0 0.03 0.47 45.4 -4 0.05 0.41 23.5 rri Table summarizes the measuremení details id resuỉts (D,/, L and ) For the calculation of/, le percolation tlireshold concentration xc was set to :ro since all samples are above threshold; the 3iicentration X was set equal to the Mn47Mnu □rtion estimateđ by the Rietveld refinement [9] lỉso see Rao and Raychauhudry in [5]) and D' was ỉsumed equal to D A ỉarger grain size L tends to F!G.6 The fit e x a m p l c s íor v - 0 and 0.05 (thc insct) a c co r đ m g to (4 ) (high T rcgion) and (7 ) (lov\ 0.07 0.35 8.65 -1.1 'sist!vity was 6x10 Qcm [5.7] (confirmed to the ery lovv bounđary conductivity oí 10 ' in unit of h) Our modeỉ estimated the pure boundary ‘ sistivity to be Po o f order ~50x 10 s Qcm (Table 2), hích suggests the conductivity oí' order 10 e /h ìnce the (e2/h) corresponds to the minimal Mott íHiduchvity, the value of 10 is a much better stimation for the boundary conductivity than the ne 10 ' reporteđ earỉier r ■3 - ì imagcs really belongs to the boundary system but Ít lacks to bind to the apparent reststivity by Its nature A11 his s ta g e , t heir n corporation I nto the relation (7) was purely amodel To coníirni this model, one need to arrange the Werner arrav m a t r i x o n t he s a m p l e s t hat 1S to b u i l đ least 40x40 electrođes onto a suríace area approx lcm We leave this experiment for the íuture consideration REFERENCES [1] Daolun Chen D c x i n g Pang, Zhongjin Van g Sa Kong Litian W ang Ke V a n g and Guivvcn Q iao ' T h e rclationship betvveen su percond uchvity and m ic ro stru ctu rc th r o u u h th c fractal d im c n s io n s in V- r ổ ị ■Q B a - C u - com poun ds" J Phys c Soỉiđ Siatc Phys 21 ( 8 ) L I - L [2] Phillips, J c , "Supcrconducting and Rclatcd Oxides: P h y sic s and Nanoeni»mcering 111" SPIE 0ì ■ - f 0p* 0 w p[eV ] Proc 3481 (Ed D Pavuna and ! B o / o v ic ) ( 1998) p 87 [3] J c Phillips, "Fractal Nature and Scalin g Exponcnts o f N o n -D r u d e Currents in Non-Fcrm i FỈG The relations betw c en D // and Wp show aỉmost Imearity b e tw c cn n and Wp w h ereas this linearity holds for D o n l y i f e x c ỉ u d in g the case Y=0.00 ONCLUSION TliiS vvork is the first of its kindto apply the ractal analysis to study the boundary conduction in erovskites The use of the íractal technique in erovskites foccs several limitations due to the small ize of the snmples that usuaỉỉy not alỉovv the ìanutaciure ot' the YVerner array electrode matnx v*c shovved Ihat by using the SEM images, the oundary íractal dimension and the related boundary eometric properties, such as the average size and uckness, miụht be vvell estimated and that the stimated values successfully described the ĩmperature bchaviours of the resistivity for the ĩsted samplcs Furthermore, the fractal dimension hovved very good correspondence to the small olaron hoping energy in the high temperature ĩgỉon They also developed ỉinearly vvith the critical xponents n in the lovv temperature region; this fact rgues for tiie fractal nature of n% but the ontìrmation nceds further investigation In contrast the tractal dimension determined on the basis of ie voltage diop distribution across the Werner array latrix the dimension measured using the SEM Liquids" a r X i v :c o n d -m a t /0 104095 [4] G Dobrescu D Berger F Papa N I lo ncscu M Rusu "Fractal a n a ly sis o f micrographs and adsorption isotherm s o f Lai xSrxCoO< s a m p lc s ”, Journal o f O ptoe lc ctr o n ic s and A dvanced Materials, V o ỉ.5 N o (2 0 ) [5] C N R a o and B Ravcau, "Colossal M agnctoresistancc Charge ordering and Rcỉaĩcd Propcrtics o f M a n u a n csc O xidcs", World Scicntiílc Publishin g C o., S in gapore 1998 [6] S S.K rylo v, V F Lubchich, "The Apparcni Rcsistivity S c alin g and Kractal Siruciurc o f an Iron Porm ation” í /v e s t ia P hysics o f the Solid banh V o l.3 , No 12, pp 0 - 1 Transỉatcd from Fizika Zem li N o 12 2002 pp 14-21 [7] A Gupta, G Q G o n g , G ang Xiao, p R D u n c o m b e p Lccocur p Trouilỉoud.Y Y Wang V p Dravis and J z Sun, Phys Rcv B54, R ỉ 562 (1996) [8] B B Mandelbrot, "The Fractal G eo m etry o f Nature", W.H Frceman and Co., Nevv York, NV 1983 (Chapter IV, 12 L ength -A re a -V o lu m c Reỉations, p 1 -1 1 ) [9] p Q Thanh H.N Nhat and B T C on g, V N U J o f S c ie n c e T X X N o AP, 0 , p 130-132 [10] p Q Thanh B.T C o n g , N N Dinh Privatc c om m u nication ISAMAP 2005 Hanoi, DHKHTN GRAIN BO UN DA RY EFFECT OíN CONDUC TIVITY O F PEROVSKITES Cao.85H1*0 15ỈV1n Ị_xR u XƠ A N A L Y Z E D BY F R A C T A L T E C H N I Q U E Phung Ọuoc Thanh, Hoang Nam Nhat and Bach Thanh Cong Faculty o f Physics Um vcrsity o f Natural S c i e n c e s - V N U HN We are speciíìcally concemed with the boundary etĩects on the conductivity of the slightly doped ruthenium manganates of the composition CaoxsPĩo 15Mn xRuxO.1 (.v=0.00, 0.03, 0.05, 0.07), these compounds have been prepared by the Standard ceramic technique and their structures vvere investigated by mean of the X-Ray and SEM method; then the resistance dependence on temperature and írequency was measured Several results on this subject have appeared earlier in [1] and [5]; this paper extends those resuits by developing, and then applying, the more complex 2-dimensional analysis of grain contact surtầce We measured the resistance from 100 to 500K and draw the ln(p) against 1000/T whose linear segments vvere used to calculate the conduction band activation energy E The SEMs were re-drawn and used for calculation of the length and areas of the random walk cross sections Our model of the boundary effects comes as tollowed First, we distinguish tvvo kinds of boundaries: (1) the single crystal boundaries vvhich occur due to the disorder o fth e single crystal pieces vvithin one grain; and (2) the grain boundaries which vvere results oi' the physical ordering of the grains vvithin the bulk material These both kinds should contribute to the ti na 1conductivity Let us suppose that the conđuctivity of the single-crystals depends only on the orientation of the preferred axis, thus the whole Fig.l The caỉcuỉatcd avcragc coíulticiancc oí' Ihc conducíivity of one grain (of one single crystal gram according to I(Snunihcr oClhc SII1UỈCcryslaỉ domains) depenđs on the statistical ordering of the entities // lor a limit numher oí ihc physical single crystal pieees This domain conductivity might directions (N=3 and 5) For thc largcr II ihc conductancc approachs a limit vaỉuc inherit the conductance anisotropy from the single crystals but in case the domain diameter was large enough, i.e the number of the single crystals \vithin One domain was adequate to provide the Gaussian distribution to the axes orientation, the anisotro py shoulđ be well suppressed and the clomains conduct isotropically in ưll dircrỉĩons We hold this presumption on isotropy in the following sections A model calculation of the averages is íeatured in Fig 1; here we assumed the preferred axis conductiv!ty vvas constant ơp and the distribution of its orientation was Gaussian Now let L denotes the length of a random vvalk cross section through a unit surtầce area seen in S tM images As re-drawn in Fig.2, when this L reduced, the area of the grain crosssections increases (smaller grains are better bound), and the contact surface between the grains also incieases Smaller L also associates with the greater ma in size d, the greater space gaps and the smaller conduciive cross-section Below are the empiricul luidings for the relationship between L, area of the space gaps A and area of the conductive crosssection (ỉ’)• l-D Fig The grain boundary: drawing o f the aroas A A (1) o f space gaps ihc lcngths L o f randoni walk cross- By Iissumiim AB B~Ả I.|} kL we obtained for B: (2 ) section s ( dotted I ines) along grain boundurics and the diam eters íi o f graire in the tw o differeni su ríaces sh o w s the interplay bctvveen Ihese quantities: a sm alỉer li reduces A bui increasc L S A MA P 2005 í ỉa noi, D I I K H T N T h e num eiical p ro cedu re for ( I ) and (2) may be s u m m a r i / c d as iollovvs: 1.5 Q 0.5 - - caỉculatc ilie length-to-area ratio I - L/a; this was reíl-nvđ to as the 1-dimensional analysis that has been usetl in [1 ]; - m e;isu re 1111 areas A o f the v is ib le space gcìps to r 0.0 10 L [a u l 20 Fig I hc cmpiricai dependenccs hetuccn thc each m;ĩ Ĩivíìcation; estimate B = a-A and determine D ra"dom walk ‘cngih L and Ihc coiKiuct.vc cross ’ r I „ J scction arca B and the nap spacc area A lor in equntinn (1) via the log ot the averages of L and A; Caoiprõ.sMnoBíRuooaCMD-i 37 t= 08) similarlỵ calculate k in (2) via the slops and the interseciioii ol’thvi line log(a - A ) versus logịL) ;v'!yinu these tb m u ila e for the case o f Ca 08sPr0, 5Mn097Ru 003O 3one íound D = Bv 37 and k = 0.0N The results are shown in Fig.3; this picture says that at lower L, B falling while A raising cause botli Nviđening of the isolating gaps and reducing of the conductive crosssections: li.is c u u se q u en tly low ers the conductivity o f material At hig h cr L (finer grains), B runs up aiiiiosl linearly with L vvhile A approaches a limit At larger L~20, i.e where the grain size vv:is s■ allci near lOOOnm and each grain contained approximateđly 30-50 single crystal pieces, ; area of the gap spaces become practically stablized at the smallest unchanged mininiu!" 'he only remaining íactor that drives conductivity vvas area of the cross-sections 10 0.6 20 - Ruthentum đoppeđ 2- C a, ,N , M n Ê 10 u 0.4 G 0.2 0.0 0.1 E[eV] 0.2 E [eV] Length-to-area Fi‘4.4 I t;:lily Ịincar corrcspondcnccs betwccn B A and / versus actívation cncrgy E (from lefl to nghi) The relation co e ffic ie n is are 9 w and 0.91 for the threc cases sequ en tỉy lii \ o Fiu.4 ho\vs the interdependence between B A and the activation energy E obtained for CaoesPrú: :,.,Rj,03and Cai-,NdxMnOj; for comparison we also reprint the result from the 10 , thc totaỉ overlap ìntegral (which is proporliona! to aMỊangleỊ^distance") varricd ơnly a 'le crystal size appeared in good correspondence to the content of substịtution Nđ It T a b le I StriK :! p u ru n tc íe rs a n d re sisỉiv iỉv fỏ r perov.skttư S Y S fem ( 'a i xN d xM n ( ) i n li Samplc (Pnm.i 1» 14 mmm for x=' ' (t [A ] b fà ] c V [AJ ỊA3] M n-0 Mn-O-Mn Grain Crystaỉ ["] sizc[nm] size[A] [AI Est rr spon Length-top poỉar p area coef [Ucm] 14 092 1.51 E [eV ) C 'aM n03 5.25‘í 5.264 7.458 206.5 ! 87(> lí)5 8080 334 007 Ca1 ,Nd0 Mn< 5.2‘>5 294 480 15«) 2480 342 002 03 71 s 0.2(1 14 C a, NdojM>i' 5.3 '2 5.334 7.547 214 I.8XX 1(>7.0 1230 352 ().(W 04 45 } n 0X C a,, sNdo.ỉM nỉ * 5.374 5.374 7.591 219,0 i 903 169.0 1Ỉ2Ơ 361 0 12 022 18 2 Ca,, »Ndo7Mn( c d,, Ndo qM 11' ) 5 4 5.42«» 7 667 2C>‘> 2 2 9 0 5280 7950 375 0 392 10 117 141 O.OK Hanoi, Ỉ ỉcínctm Ocíobưr -3 2004 V ' 9y*>±' ' >í%^»;«fc*i v 'V í'í »■u-v • rp’* / # w*4 fặ V'v^ **•>4.:/'*■í' SCaẵ -SNdSíMnO, Iv Ví •í>'v7 Ca „ -;nea ratio and the activation energy; this proves that the grain and grain boundary I inHuonce on the conductivity of these materials The result offers a new look into the !ìanisnì of these perovskites, requiring the further investigation Refercnc 111 D L M iu ỉ Thanh B.T Cong H.N Nhat H.V.Hai D.M Hong Proc o fth e VGS 2004 p 131-134 j ị B.B M;k- ’ •( " I hc I ! ;icta! Geometry o f Nature" w H Preeman and Co New York NY 1983 j;>j H.N Nlì;!! c o f tlic \'G s 7, 2004 p ì 46-149 14 A Jouaiinc ”\ViuMi*rof: a visuaỉ Rieiveỉd sot\v\aa*" C PD new sietỉer 21 (1999) p 13 15 s kr;ius> .1 It 1V97 ’, institulc fur Cìcotogic p.rỉangcn 1997 Ị6|H.Tagu^ M Shit;utJu, J ot Solid State C liem 6.' 19X6 p 290 17 T Kõbỉiv ’ 'í';iki/ ‘a ; i , T Rndo Sato and M Shimada J ot Solid Siatc Chem 92 1991 p Ị 16 |X| lỉ.Tngik! NagiU) vi M Shimada J ot Solid Staic Chem s>7 1992 p 476 si ca li 10, 2001 p ...ĐẠI HỌC QUỐC GIA HÀ NỘI TRƯỜNG ĐẠI HỌC KHOA HỌC T ự NHIÊN Đ Ể TÀI: PHÂN cực HOÁ TRỊ TRONG MỘT SỐ VẬT LIỆU • • • Mã số: QT-04-05 CHỦ TRÌ ĐỂ TÀI: TS Hồng Nam Nhật CÁC CÁN BỘ THAM GIA: ThS Phùng... HOÁ TRỊ TRONG MỘT SỐ VẬT LIỆU Mã số: QT-04-05 CHU TRÌ ĐỂ TÀI: TS Hồng N a m N h ậ t CÁC CAN B ộ THAM GIA: ThS P h ù n g Quốc T h a n h ThS Nguyễn Đức Thọ CN Lê Thị Anh T h M ục tiê u d ể tài Trong. .. hình cho r n g tượng phâ n cực mò hồn tồn độc lập khơng phụ thuộc vào p h â n cực ỏ m n g co so Phân cực vĩ mô kết tr ì n h p h ả n b ố điện tích vùng hố trị tồn khối vật liệu (bulk material) k hô