JOURNAL OF SCIENCE OF HNUE Natural Sci., 2014, Vol. 59, No. 4, pp. 3-8 This paper is available online at http://stdb.hnue.edu.vn
ANH HUONG CUA THONG SO TRAT TIT XA LEN SlT KHUECH TAN CUA HOP KIM THAY THE HAI THANH PHAN
Hoang Van Ti'ch
Khoci Vat It, TrKdng Dai hoc Supham fid Noi
Tom tat. Bai bao nghien ciiu anh hiJcfng ciia thong s6 trat tu xa len sU khuech tan cua hdp kim hai thanh phan khi sii dung phUdng phap thong ke mo men va h' thuyec tral tu. Nghien ciiu da nhan difdc bieu thiic giai tich xac dmh sU phu thuoc cua he .s6 khuech tan D, thCfa so c6 dang ham mu D,„ nang lUOng ki'ch boat E vao thong so trat tii xa. Cac ket qua da difcfc ap dung ti'nh so doi v6i mot .so hdp kim nhif AuCu.
AtiAl, FeTa, FcW, so sanh vdi thuc nghiem cho thay c6 sU phii hop tot.
Tif khda: Thong so trat tU xa, khuech tan, hdp kim hai thanh phan, phudng phap thong ke mo men, li ihuyet iral tu.
1. Md dau
StJ kliuech tan cua cac nguyen tijf trong tinh the diTdc If thuy6t va thuc nghiem xac nhan cong thiJc tfnh he s6 khugch tan tuan theo dinh luat Arrenhius [6]:
-A-iSf]
"'"••"•[-Hfj '"
trong do, D„: he so ti le va diTcfc gpi la thifa so c6 dang mu, E: nang lUdng kich boat tao nen bir6c nhay khuSch tan ciia mot nguyen tiJ, k-B- hang s6 Boltzman, T: nhiet do tuyet d6i. Trong cac tai lieu (1, 2-4], siifdung phirang phap thong ke mo men (PPTKMM), chiing toi da xac dinh dUdc he so khuech tan cua cac tinh the kim loai va hdp kim, kit qua nhan dUdc phu hdp vdi thirc nghiem cung nhir cac tac gia khac. Tuy nhien anh hudng cua cac thong s6 trat tit len sir khuech tan dac biet doi v6i hdp kim chifa dildc de cap din. Vi vay trong cong trinh nay chiing toi nghien ciJu anh hifdng ciia cac thong so trai tu len sir khuech tan cua cac nguyen tii" cua hdp kim thay the hai thanh phan co c2u trtic lap phUdng tarn dicn va lap phiTdng tarn khoi.
Ngay nhan bai' 25/12/2013. Ngay nhan diing; 10/3/2014.
Tat gia lien lac: Hoang Van Tich, dia chi e-mail: [email protected].
Hoaog Van Tich 2. Noi d u n g nghien cihi
2.1. Li thuyet khuech tan cua cac nguyen tuf cua hdp kim thay the hai thanh phan
Xet hop kim hai thanll phin AB c6 clu trie lap phiiang tam dien (LPTD) lioac lap phUdng tam khoi (LPTK) g6m Nj, nguyen tO: loai A va Ng nguyen tii loai B, trong do N = NA + NB^ S6 nguyen tii cua he. Goi CA= C = ^ la nong do nguyen tu: A trong hop kim, CB=^= 1 - C la nong do nguyen tul B trong hap kim. Trong [1] chiing toi nhan duoc cong thiJc xac dinh he so khuech tan ciia nguyen tuf A trong hdp kim hai thanh ph4n AcBi-c uhu sau:
D.=D„.e.p(-g,) (2)
'"'^P {4}'='=''{^}
D„A=nifA^a'tgCexp^-p^}expi,j^} (3) trong do rii: s6 nguyen tijf nam trong qua c§u phoi vi thii" nhSt, SA' uang Itrong tao nen
mot vacancy, /A: thtra s6 tUdng quan, WA'. tin s6 budc nhay ciia nguyen t^ A vao vi tri vacancy, ks: hang so Boltzmann, T: nhiet do tuyet d6i, 5/: entropy tao vacancy. Do dai bade nhay khuech tan mot each gin dung phu thuoc tuyen tinh n6ng do cac nguyen tif A,Bll,2]:
UAB ~ CMA + {1 - c){aB - a„.) (4)
Nang lUdng kich boat E^ ciia nguyen tii A trong hdp kim dUdc xac dinh bdi cong thiJc:
EA= C [-(rj,+rj2)v;''+nni.;^+n2'/'2"'+(B.4-l)*;'']
+(1 - C) [-K+n2)Vf+niV>,*''+n2'/'2'''+(Bs-l)'*f ] -{BA-l)r,^+TSi *^*
d day ni, ji,2 la so nguyen tu! A (hoac B) nam trong qua cSu ph6i vi thiJ nhat va thii hai c6 tam la vacancy; cac dai lUdng B^, Be dugc tinh nhiT cong tbiJc doi vdi cac tinh the kim loai; t/jg" (a = A, B) la nang luong tu do Helmholtz cua nguyen tii kim loai a dinh xii trong qua clu ph6i vi thiJ nhat (hoac thii hai) c6 tam vacancy [1,3, 4], xac dinh theo cong thiic;
"/-r = 3Af I ^ + e[x + ln(l - e"'l j (6) 2.2. Anh hudng cua thong s8 trat tU xa len sU khuech tan cua hdp kim
thay the hai thanh phan
* Khdi niem ve trat tu nguyen tic
Hien tUdng trat tU cua nguyen ti trong hdp kim da dUdc nghien cilu tii lau [5]. D6i vdi mot so hdp kim thay the, d nhiet do du thap, cac nguyen tii se sap xSp sao cbo chiing thuoc mot thanh phan ciia hdp kim chi chiem cac nut thuoc mot loai xac dinh trong mang
Anh hudng cua thong s6 trat tuxa len su khuech idn cua hap kim thay the hai thanh pitdn
tinh the. Hdp kim trong trang thai nhil vay dUdc gpi la trat tU hdan toan. De dac tnfng cho s\i sap xep cac nguyen tiJ tai niit mang ngiicii ta dua vao cac thong s6 trat tit nhu sau:
- Thong so trat til xa lien quan d8n so nguyen tii loai khac nhau tren mot loai nut nhat dinh cua toan mang tinh the.
- Thong s6 dp trat ta gSn lien quan dSn s6 nguyen tiJf ti^fng loai bao quanh mot nguyen lit da cho, no cho biet trat tiT dinh xiJ.
* Thong so trat tuxa
Ta khao sat mot hdp kim thay the hai thanh phSn AB c6 N nguyen tuf. 6 trang thai trat tu hoan toan cac niit mang hi chi6m bdi nguyen tuf A dUdc gpi la niit loai a, cac nut hi chi€m bdi nguyen tiJf B gpi la niit loai b. Ki hieu N' la niit kieu i{i = a, h); Ui = X'/X la cac he so xac dinh cSu trtic hpp kim; Na la s6 nguyen tut loai a{a = A, B); CQ = Nc/N la n6ng dp titdng d6i cua nguyen tuf loai a; N^ la s6 nguyen tuf loai cv chidm cac niit kieu i.
Khi do ta c6 cac he thtJc:
NA+NB = N (7).
CA+CB = 1 (9):
N^. + N'^^NA^CAN (11):
X'^ + N'^ = N" = i^^N (13):
X'' + N'' = X (8);
f" + f'' = l (10):
X^ + N'B^NB^CBX (12):
iV^ + N ^ = .V" = t-iN (14).
Gpi P^ la xac suSt tim thay nguyen tu" loai a tren niit loai i. Khi do thong so trat tU xa trong hdp kim doi dildc xac dinh b6i bieu tht5c:
T / = — . (15) Do vay ta nhan dildc:
P^ = C4 + t/,7? (16); P'A = CA-iy.T] (17):
P'^ = CB-JybV (18), P'^ = CB + u,r)- (19):
Khi hdp kim 6 trang thai trat tU cao nhSt 7/ = r]n,ax^ P^ — 1- Tft (1^) ta c6:
• ' 7 , . „ = - ' r ^ (20) Khi hdp kim d trang thai v6 trat tu P^ = P^ = CA- TO (15) ta dugc 17 = 0.
2.3. A n h h i t d n g c u a t h o n g s o trat tU xa d e n s u k h u e c h t a n c u a hdp k i m thay the h a i t h a n h p h a n
TO cong thiic (4) va (15) ta dUdc tim dude bieu ihiic xac dinh sU phu thuoc cua khoang each trung binh giira cac nguyen tii cQa hdp kim kim AB vao thong so trat tU xa:
AAB -= IP-J. - '/{I - 'y„)]-aA + [1-PA + VH - "•.)! (Ofl - aA) (21) Su phu thuoc ciia nang lUdng tii do ciia hdp kim xac dinh bang each ket hdp bieu thiic nang lirdng tii do trong [1] va cong thiic (15) d l dang nhan dUdc:
l/'.4fl = {[PH - (1 - lA)n - (n. + 1)(1 - (Pi ~ (1 - IAH I^A) + , „ , {[1 - (P5 - (1 - 7 . 4 ) . ; ] [-V.B + li-J + TiiV-r]} - T S c ' '
Hoang Van Tich
Tif cac cong thiic (5) va (15), nang lupng kfch boat E^ ctia nguyen tuf A trong hdp kim hai thanh phSn AB phii thuoc vao thong s6 trat txixarj dUdc xac dinh bdi cong thiic:
EA= [PA''~V (l-Va)]. \^-{ni+n2)i^l''+n^ri''+n2ilj2^HBA-l)tl'']
+ [1-PA''+V (1-^^«)] • -{ni+n2)4>f+n,i'f+n2r2''HBB-l)i'f] ^^^^
-{BA-l)ri''+TSl
Tuf cac cong thiic (6) va (15), s\S phtj thuoc cua thfita so c6 dang ham mu DOA vao thong so trat c6 dang:
D,.A = {[PA - va ~ ••'»)]} nif^iaAsf
+ [1~P'A+ r)(l - .;.)] " . / ~ { ' M B ) ^ exp | 0
> / ^ l
(24)Khi biet dildc D„A va E^, dl dang xac dinh dUdc he s6 khuech tan phu thuoc vao thong so trat tii xa rj theo cong thiic (1).
2.4. Ket qua tinh so va thao luan
Sii dung PPTKMM vdi dang the Lennard-jones va cac edng thiic tii (1), (15), (18) d6n (24) kSt hop sii dung phan mem Maple de xac dinh sii phu thuoc ciia cac dai lliOng dac trUng cho sii khuech tan vao thong so trat tii xa cua mot so hdp kim cau triic LPTD va LPTK d ap suat p = 0, cac ket qua nhan diidc da dUdc trinh bay chi tiSt trong [7]. Dudi day la ket quii thu dUdc:
Hitih 1. SUphu thuoc cm dp dai budc nhay Hinh 2. Suphu thuoc NLTD vao thong sd trat vao thong so trat titxa ciia FeTa (Fe 90%) tuxa cua AuAl (Au 90%, rpAB(,*10-^^erg))
Anh hudng cua thong so trat tU xa len sU khuech tan cua hdp kim thay the hai tlianh plidn
»
A
•-»
•
4
•
IDOOK tlODK 120QK 13O0K 140DK 1S00K ItOOK 170M(
1W0K
• ^ ^ ;
- • - 1 0 0 0 K ;
• 1I00K i ' 1200K ' T 130CIK tr )4O0K
• I 5 0 0 K ' teoOK
• 1700K
— • - I B O O K
Hinh 3. SUphu thuoc cua NLKH vao thong so trat tUxa cua AuCu (Au 70%, Kcal/mol)
Hinh 4. Suphu thuoc cua thiia so Do vao thong s6 trat tu xa cua Fe W (Fe 90%)
Tif ket qua tren cac Hinh 1, 2, 3, 4 ta nhan thSy rang cac dai lUdng dac trirng cho sir khuech tan phu thuoc vao thong so trat \.\i khac nhau. Chang ban dp dai h\i(ic nhay, nang lifdng tu do tang khi thong s6 trat ti( xa tang trong khi do nang lUdng kich hoat va thufa s6 CO dang ham mu lai giam khi thong so trat ti( xa tang. Dieu nay chiing to rang chiing ta khong the bo qua anh hudng cua cac thong so trat tit den qua trinh khulch tan. Di£u dac biet la klii bo qua anh hu6ng cua thong s6 trat tu xa nghia la he d trong trang thai v6 trat tU hoan toan, ket qua cua chiing toi nhan dUdc phu hdp vdi cac ket qua ciia cac tac gia irudc day da cong b6 (xem [7]).
3. Ket luan
Tir cac kSt qua tinh toan chung toi nhan ihSy rang cac dai iUdng dac trUng cho &\i khuech tan ciia hpp kim nhtf dp dai cac budc nhay khuech tan, nang lupng kich hoat, thCra so CO dang ham mu deu phii thuoc vao thong so trat tu xa. Cac ket qua thu dUdc cho th3y CO su phu hdp vdi thUc nghiem va vdi trUdng hdp hdp kim d trong trang thai v6 trat tU, chiing toi thu dUdc kit qua gidng nhu ket qua ciia cac tac gia da dUdc cong bo. Kcl qua thu dUdc CO the md rpng cho cac clu triic lap phUdng khac va luc giac xep chat cung nhu cac cSu true khong thuoc dang lap phUdng.
TAI LIEU THAM KHAO
[1] Tich H, v., 2000. Li thuyet khuech tan cua cac tinh the kim loai vd h(fp kim. Luan an Tien .si Vat li, TrUbng Dai hoc SU pham Ha Noi.
Hoang Van Tich
[2] Tam P. D., 1999. Nghien ciiu cac tinh chdt nhiet dgng cua hap kim thay the A-B co cau true LPTD va LPTK hang PPTKMM. Luan an TiSn sT Vat h', TrUdng Dai hpc Qu6c gia Ha Noi.
[3] Hung V. v., Tich H. V., Jindo K. M, 2000. J. Phys. Soc. Jpn., 67, 2691.
[4] Hung v. v., Tich H. V., 1997. Proc. 7th APPC Beijing, China, 461.
[5] Boksctein B. S, Boksctein S. Z., Zuhovicki A. A. 1974. Nhiet dgng hoc vd dong hpc cua su khuich tan trong chdt ran. "Metallurgi", Mat-cO-va (nguyen ban tieng Nga).
[6] Tang N., 1982. Cong thvCc chinh xac cho nhifng tuang quan ciia he thong can bang.
"Fizika", Vuzov, Vyp. 6, 38-41 (nguyen ban tieng Nga).
[7] Hang N. T. M., 2013. Anh hudng cua thong sd trat tu xa len su khuech tan cua cac nguyen tii cua hop kim thay thi hai thanh phan bang phUdng phap thong ke mo men.
Luan van Thac sT Vat li li thuyet, TrU6ng Dai hpc Su pham Ha Noi.
ABSTRACT
Influence of parameter ordrers for the self-diffusion of binary alloys The paper studies the influence of the parameters order on the self-diffusion of the binary alloys using the statistical moment method. The analytic expression for the diffusion coefficient D, the pre-exponential factor D„ and the energy of activatin E are obtained. The obtained results are applied to AuCu, FeW, FeTa, AuAl binary alloys and compared with experimental data.
