JOURNAL OF SCIENCE OF HNUE DOI- 10.18173/2354-1059.2017-0003 Natural Sci 2017, Vol. 62, No. 3, pp. 17-26
This paper is available online at http://stdb.hnue.edu vn
N G H I E N C U t J L I T H U Y E T N O N G C H A Y C U A H O P K I M T H A Y T H E AB XEN K E N G U Y E N T U C VCfl C A U T R U C L A P P H U O N G T A M K H O I
N g u y e n ( ^ a n g H p c , D i n h CJuang V i n h , Le P h u a n g H o n g , P h a m Thi T h a n h L o a n , N g u y e n Q u y n h A n h va H o a n g T h i L i n h
Khoa Val li, Trudng Dgi hpc Supham Hd Not
Tom tat. Tir mo hlnh hpp kim thay the AB xen ke nguyen tu C va dieu kien ben vimg tuyet doi trang thai hgp kim. chdng toi rut ra bieu thiic giai tich cua nhiet do ben vung tuyet doi trang thai hgp kim va nhiet do nong chay cung vdi phucmg trinh dudng cong nong chay ciia hgp kim nay bang each ap dung phucmg phap thong ke momen. Ket qua thu duoc cho phep xac dinh nhiet do nong chay ciia hgp kim ABC 6 ca ap suat khong va duoi Eac dung cua ap suit Trong cac trudng hgp gidi han, ta thu duoc li thuyet nong chay cua kim loai, hop kim xen ke nhi nguyen va hgp kim thay the nhj nguyen.
Tir khda: Hgp kim xen ke. hgp kim thay the. nhiet do ben vung tuyel doi trang thai hgp kim
1. Mor dau
H o p kim ndi chung va hgp kim xen ke (HKXK) ndi rieng l i nhflng vat lieu phd bien irong khoa hpe v i cdng nghe vat lieu. Viec nghien cuu HKXK da v i dang thu hiit su quan t i m eda nhieu n h i nghien ciru.
Mdt trong cac tinh chit quan trpng ciia hgp kim la nhiet do ndng chiy (NDNC) cua nd d cac i p suit khac nhau [1, 2]. NDNC eua tinh the thuong dugc xac dinh tu phircmg trinh thyc nghiem Simon
P -P
-^"-^'(T.-Tj-l, (1) a
trong dd T„, la N D N C . P„ l i i p s u i t ndng chay, o v i c la nhiing hing sd, Pn va Ta la ap s u i t va nhiel do diem ba tren giin dd pha.
Thdng thudng, khi gia trj Po la nhd cd the bd qua thi cd thi v i l l (1) dudi dang
— = ( 7 ; , - ? o ) ' - ' - (2) a
Tuy nhien, (2) khdng the md ta su ndng chay cua tinh the d i p suit cao. Kumari va cdng su [3]
dua ra mgt p h u a n g trinh hien tugng luin cd dang
Ngay nhEin bai: 19/2/2017. Ngay nhan dang; 20/3/2017, Tac gia lien he; Nguyin Quang Hoc. e-mail: [email protected]
Nguyin Quang Hoc, Dmh Quang Vinh. Le Phurnig Hong. Pham Thi Thanh Loan, Nguyen Quynh Anh va Hoang Thi Linh
WP,-P«)]
^A+B(P„-P,), (3)
trong dd T^ va To tuang ung la NDNC d cac ap suit P„, va Pn, AT^ = '^m~K ^^ •^' ^ '^ nhiing hing so. Phuang trinh (3) cho phep xac dinh NDNC ciia tinh the a vung ap suat cao.
v l mat li thuyet, de xac dinh NDNC cda tinh the can phai sii dyng dieu ld?n can bang ctia hai pha rin va Idng. Tuy nhien, theo each nay khdng tim dugc bieu thuc ludng minh cua NDNC. Mpt sd nha nghien ciiu cho rang nhi?t do T,. tuang ung vdi gioi han ben vitng tuy^t ddi cua trang thai tinh the g mgt ap suat nhat dinh khdng xa NDNC d ap suit do. Vi the, cac tic gii cua [4] da ddng nhat dudng cong ndng chay vdi dudng cong gidi ban ben viing tuyet ddi ciia Irang Ihii tinh thi Vdi y tudng do. phuang phap Irudng phonon tu hgp va phuang phap ham phan bd mgt h^t dugc cac nha nghien ciru sdr dung de nghien cdn NDNC. Tuy nhien, cac ket qua thu dugc cdn chua phu hgp vdi Uiuc nghiem. Ttrdd mpt sd nhi khoa hgc nit ra ket luan ring Ididng thi tim NDNC bing each diing gidi h^n ben vflng chi ddi vdi mot pha ran. Mpt sd nha nghien cuu khic sii dyng hieu ung tuang quan de tinh nhiet do gidi han ben vung tuyet ddi ciia trang thai tinh the. Kit qua thu dugc tir hieu chinh nay tuy ed tot han nhung cung chi gidi han trong viing ip suit thip.
Bing each su dyng phucmg phap thdng ke mdmen (PPTKMM) va phuang phap tinh so, NguySn Tang va Vu Vin Hung [4, 5] chi dung mot pha rin cua tmh the de xac dinh NDNC.
Truoc het, cac lac gia nay xac dinh nhi?t dp bin vflng luy^t ddi 7; tuang ung vdi cic ap suit khic nhau bing PPTKMM. Sau dd, do NDNC T„, khdng khac nhieu vdi 7; nen cd thi thyc hien mpt phep hi?u chinh dl tii T, suy ra 7„,. Kit qua thu dugc bing PPTKMM phu hgp vdi thuc nghi?m lit hgn so vdi cac phuang phap khic.
2. Noi dung nghien cuu
Trong md hinli HKXK AC vdi ciu true LPTK, cac nguyen tu A cd kich thudc ldn nim a cac dinh (nut m^g) va tam khdi, cdn cac nguyen tu- xen ke C cd kich thudc nhd han nim d cic lim m^- Trong [6], chung tdi da nil ra bilu thuc giai tich eua khoang lan can gin nhit, nang lugng lien ket va cac thdng so hgp kim ddi vdi cac nguyen tii C, A. A, (nguyen lir A d tam khdi). A;
(nguyen td- A d dinh).
Phuong irinh trying thai ciia HKXK AC vdi ciu true LPTK d nhiet dp T dugc vill dudi dang
P. = -r(i^^excth.J-^], (4) [6 dr, IkdrJ
Ci 0 K va ap su5t P, phirong trinh co d^ng
Pv = -r,\—2. + — « — (5
[dr,
Ak 3rJ ' Neu biet dang cua the tuong tac p.„ thi (4) cho phep xac djnh khoang lan c|n^\x\P'^)\X = C,A,A^,Aj) giua cac hat trong tinh thS cr ap suit P va nhiet dp OK. Sau idii biet ) i , ( P , 0 ) , CO thS xac dinh cac thong so i , ( P , 0 ) , I'I, (/',0),)'j,(P,0),)',(P,0) 6 ap suit Idiong va OK cho tirng trucmg hpp. Dp doi trung binh ciia nguyen tir 7 „ (P, T) a nhiet do r va 6 ap suit Pdupe xac dinh nhu trong [6], Tir do suy ra Idioang lan cfn gin nhit n,(P,T) iing voi tirng 18
Nghien cdu li ihuyel ndng chdy cua hgp kim thay the AB xen ke nguyen lir C vdi cdu true...
trudng hgp sau
rAP<T) = r,,(,P,0)+y^(F,T),r„{P,T) = r,,(P,0)+y,I^P,T),
r,^(P,T)~r,^{P.T),r,JP,T)=r^^(P,0) + y..P,T). (6) Khoang lan can g i n nhat trung binh giija cac nguyen tii A trong HIOCK AC dupe tinh g i n dung theo bieu thiic
r,,(P:T) = r,_,{P,0) + y(P,T),
fi.,(F,0) = ( l - c J / ; , ( P , 0 ) + Cc^'/P,0),r,'^(F,0) = V3r,c(P,0),
y{P.T) = (^-^c,)y,{P,T) + c,y,(P.T) + 2c,y^(P.T) + 4c,y,^{P.T). (7) Trong HKXK ABC vol cau true LPTK (HKXK AC voi cac nguyen tir A 6 cac dinh va tam khoi, eac nguyen tu xen ke C p eac tam mat va sau do nguyen tij B thay thS nguyen hi A p tam khoi). khoang lan can gan nhat trung binh giua cac nguyen tii 6 nhiet dp T va ap suit P dupe xac dinh boi
i i „ ( F , r , c , , c , ) = £• , u , -JSf + c.a,•Jt,B=c- S + c . S ,
XTAC 1 XTB
Xr,c(P.T.c,) =
V3 5 W l
(8)^WAC Br,, (0,T)
Aa,,{,P,T,c,)lN{da\, I
h(Ox
4*7
d'k,, 1_
dai 2ky I da^
a,=r,,(P.T).
Khoang lan can gan nhat tnmg binh giua cac nguyen tu trong HKXK ABC vdi cau trdc LPTK d 0 K va ap suat P d u g c xac dinh bai
a^ABciP^ T^<^B^Cc) = ^AC^nA
•^07 (9)
Cac dai lugng trong (9) gidng n h u trong (8) nhung dugc xac dinh d 0 K.
Nan'g lugng ty do ciia HKXK ABC vgi cau true LPTK vdi dieu kien c^ « Cg «c^ cd dang [7]
Nguyin Quang Hpc, Dinh Quang Vinh, Ld Phucmg H6ng, Phjin Thi Thanh Loan, Nguyin Qujnh Anh va Hoang Thi Lmh
VAC =(^-'I'^C)VA+ '^cl'i + 2c,.»'., + 4c^w., - T S ' ^ ,
(10)
y/„ = 3 W e [ j : , + U i ( I - e " ' ' ' ) ] , A ' , - x , cothj:,.
trong do VA'VB tuong ling la cac nang lupng tu do ciia cac nguyen tii A. B trong cac kim loai sach A,B; ij/^ la nang lupng tu do cua nguyen tii Ai, y/^_ la nang lupng tu do eua nguyen tii A2, y/^ la nang lupng tu dp cua nguyen tii C trong HKXK, s,''"^ la entropi ciu hinh ciia HKXK ABC va 5;"^ la enh:6pi ciu hinh cUa HKXK AC.
Ap suat tinh theo nang lupng tu do boi
I dy )r 3V I da )r Dodo,
py =-„ ji(l-7t l i i i i + i^. -Ei!- + ic ^ ^ + 1,. ^"", I
1 (dU„ dU,A , , , „ \ dk. I ok,.
6 l , a i ^ „ da„,^ } 2k, da„^. 2k,. da,„
+ 2cc0x^^ coth x^^ -Z7—-—'- + 4Cf fo^^ coth x^^
' 2 * , , a a . s c ' ''2k,^da,sc +c,i.,coth.. ' J*L_,^,oth. ' - ^
I 2*5 dajgc 2k^ da^g^ J Co cae gan dting
dU„^ dU,„ dU„, dU„ 5C/.^ dU„, SC/,„ dU,„ dU„, 3U,^
S'AI, Sa, da„, da, ' da„, da, ' da„, da, 'da,,, da, _dk^_^dkj__dk^^dk^ dk^^^dk^ dk,^ dk,, dk,. dk,.
B^ABc Sa, ' da„^ da, ' da,,,,, da,^ ' da„,^ ~ da,^ ' da,,,, ~ da^
D}t
(12)
Nghien cdu li thuyet nong chdy cUa hap kim thay the AB xen ke nguyen id C vdi cdu tnic...
a,„,. 1 dk, , , 1 dk,.
y'a = — ^ 1 ^(l-7(L-^, ) x ^ c o t h x ^ 4- ^c^,x^. colhj:^.+
'''" k^ da^
6 L ^ ^ ^"^A
1 Sk^ I dk^
-2c^.x^ cothj:^ + -4c^^x^ coth.ic^
k^ Ba^ ' ' k^ da^
1 dk^
-Xa coth.)c k, da, ' " k
1 ^^A ,. 1 1 j c . c o t h x .
d day, YQ ddng vai trd nhu thdng sd Griineisen cua HKXK ABC. Khi do,
P =
a \ dU dU S i / . . dUn.
6V.„^ da. da^ da. da.
\da, daj\ V„,
Tir diSu kien gioi han ben viing tuyet dpi 8 P ^ ( dP
= 0 hay
dy,,,-, yda,,.
(14)
(15)
(dU„ dV„'[
' I * « ^A J
- J 2 ^ ( | - 7 C , ) — + c^—!^+2C(. L + 4cj 3 da, dar da, da.
.S'U,„ d'U„ d'U,,,^ d'U,,,^ (d'U„, S'U„
da\ dai ^^li '^"1 V '^"B ^^'A
-9/^e*39aJ-^\ =0.
Tir (14) suy ra
Tir do,
"ABC
3 dU„,
• da.
da^ da,.. da^
SU.. dU,.
dUg 8a^
-W„^ + by'„i
(16)
(17)
NguySn Q..ns H * . Dmh Qu.ng Vmh, L i Ptemig Htag. Ph.m Th, Th.nl. L o . . . Ngoyii. Quynh Anh . . Hoing TW Linh
- - ^ - - - - ^ ( - ' - ) ^ - ' ' % ^ ^ ^ - ^
^''^.A . (d'-v,. iEM.
8a. da.
(18)
Nhiet dp bSn viing trang thai hpp kim dupe xac dinh boi
7-, = 3«:„ -ra 2PV,.,.+- ( 1 - 7 . , . ) ^ . da.
d'V,.
S'"oc ^'"". A .. ^ + 2c,. —^ + 4c,, r -
• da,. fla- 8<i^
c-V„ g'^n
trong do tit ea eac thong s6 dgu dupe tinh 6 nhiet dp T,. Tai nhiet dp T^,
Dodo,
T ^ 1
, £0, 5 t . 01,. dk,, , w. « ( l - 7 c v ) - ^ — ^ + c > - ' ^ + 2 t v — L — ' - +
^ t . / . L k, Sa, k,. da,. k, da,
'"A, <'*,!, ["ffi, et, CO, dk,, \ \ k, da, \ k„ dag k, da, )j
6 [ doA da^ oa^^ ca\
; ^ l _ ( l _ 7 c ) ^ f ^ ! t f i L Y _ „ a ' t J t o A . , _ \a,„..(ak,^ ^ s%_
K i ^k,[da,) '" flu; J 4k, ' 21-,, [fla, J ' " da' ,TS.=2PV,.,+-
(19)
(20)
hoi, a 4k,
ZMQ.\ -Zi 2k, da.
dk, Ik. I da.
a-k^
'~Sa\
d'k, dai
4 i ,
"ABC
2k,^ I 3a.,.
2k. [da.
8 I'A. ^OIA-^AB t * *
(21)
Nghien ctru Ii Ihuyel nong chay cua hgp kim [hay Ihe AB xen ke nguyen tuCv&i cdu trUc...
+4^ <K,BcK I ^^'-1, ^^ "IBCI'BJSk,
4kl [da,
J ' 4k] [aa,) '
Trong trutmg hop P^O, TS,
• ^ , T S . - - ^ L - l c , ) ^ . c , ^ . 2 c / - ^ . 4 c / ^ . e . ' - ^ ^ - c . ? ^ ] - h ' 6 [ dai dai ^a\ da\ da', ' da', J - { 1 - 7 ' c )
4k, '\ 2k,. \aa^
d'k,. hai^a,.
ak,, 2*. 1 ^
<iwc(akA,)' a'k, 2k,\da,^] dai
•iAi^(dk,] 5-*, «o),<j.,, \a,,,(dk,) [ 2 * . [ f l o j dai) 'Ik, '[2*, l^flaj
ifc f. -, \ali>rkB„( ak,) a].,,k.„ f ak, \
' ^ ^' 4S:; l^aaj ^ 4it^ [daj
(22) 5a^ 4A_,
a'A.rk,JSk,
*''A, 13",., +4Cf-
4*-;
^Atnrka.
Ak] \dag] " 4<t^ ^aa^
Do dudng cong gidi ban ben vQng tuyet ddi ciia tr^ng thai tinh the d khong xa duang cong ndng chay ciia tinh the nen nhiet dp 7, thugng ldn va cd the coi Xy COtll .x:^ a: 1 a nhiet dp T.
Dodd,
^J'./fl,.
at/,,,, a^',,, ^^,,1 da da da
dU.„, BU,„
da da
(23)
trong dd cac d^i lugng d ve phai dugc xac dinh of nhifit dp Tj. Tir ddva (22) suy ra
(1-7, "'ABCI'BJSk,) ^^ al,ckBjSk,]- , , _ ° ^ , A . ( g ^ - <
I-2c,.
4k] [aa,j ^ 4k', {Ba^) ' ' 4*-; [au,
a]„rk,J SI'A. ] . _ a\,ck,, { dk, ) _ a]„.k,„ f ak.
'' 4k: aa 4kl 1 da, 4k: \ Ba
(24)
NguySn Quang Hoc. Ellnh Quang Vinh , Cc Phuong Hong. Pham Tin Thanh Loan. Nguyen Quynh Anh va Hoang Thi Lmh
d'U,., 1 (l-7c,) d'U„
dai -{l-7c,) ^A!c_(dkA' _ d%
2k,[da,j """da]
[sffi-f^Y - £ ^
•^'MM7[flj;;J "'•'^ dai dai
til^Aa,,
da. + 4c, dai dkf 2k, I da.
B'U.„
' dai d'k,. I Pi(o,a,.
a*, 2k, I da.
d'k, da'.
hoi,a,„
4k,
(iV^A S°A S°C S^A.
i ^I^A „ 1 M„ 1 dk^
+ • --4c, +—-—^Cj, -c
k. da, k„ c'a,, k. da.
5f^ns dU„^
, '^B
da„ da^
(24)
Dd la phuong trinh dutmg giai han ben viing tuyet ddi ctia irang thai hgp kim. Neu biet thg nang luang lae hoan toan cd the xac dinh dugc ve phai cua phuang trinh tren. Ap suat la mdt ham cua khoang each lan can gan nhai trung binh
P = P(''ABC) (25)
Nhiet dp gidi han ben viing tuyet doi T, (0) eiia trang thai hop kim 6 ap suit P ^ 0 la r,(0) =
ISj-a*..
( , . , o , ) ^ . c , ^ . 2 c , ' - ^ . 4 c , ' - ^ . c . ^ ^ c , ^
da^ dOf- Ba^ Ba^ da^ da. (26)
trong do cac thdng sd a^g(~.
day , JQ dugc xac djnh d nhiet dd 7^.(0) va Ag„Ia hiing so Boltzmann.
Nhiet do gidi han ben vflng tuyel ddi ciia trang thai hgp kim a ap suSt P la
7;^r,(0)+ "'<:' , p ^ | T,.
(27)0'3ay, V^sc^yG'^yl^^'^ duge xac dinh t^i T^. Cd di6 lam giin dung nhiel do ndng chay r „ vdi nhiel do r^nay.
Co die ap dung phuang phap lap gan diing d6 giai phuang Uinh tren. Trong phep lap gin dling lan thu nhat,
r.=r,(0).M5|^.
O day, T,(Q) la nhiet do gidi han bgn vtJng tuyel ddi ciia tr^ng thai tinh thi d dp sudt Z' = 0 va 7; i la nhiet do gidi han ben vung tuyel ddi ciia trang diai tinh tM a ap suat P trong phep lap gan diing
Nghien cdu Ii ihuyel nong chdy cua hpp ktm thay the AB xen ke nguyen lu C voi cdu true...
lan thu nhit eua (27). Thay nghiem T,, vao (27), ta se thu dugc gia trj gin diing tdt hon eua T, la T^2. trong phep lap gan dling lin thii hai
7-^ - , 7 . (0)1 yAB^T,,)? V,Bc(Z
? ' , | ) V S 7 - ) •"•
Tirang tu vdi each lam tren, ta se thu dugc cac gia tri gin diing tdt hem eua T la T^^, 7^4,•••
d ap suit P nhd cac phep lap gan diing lin thu ba, lin thu tu,... Cac phep gin dung (28) va (29) dugc ap dung d ap suat thip.
Trong Irudng hgp ap suit cao, cd the tinh nhiet do ndng chay ctia hap kim d ap suit P theo cong thuc
^"'^"^^^ G(0) T ' t30) {B. + BlP)""
trong dd r„,(P),7,(0) tuang ung la nliiel do nong chay a ap suit P va d ap suit khdng, G{P),G(0) luong ung la mddun trugt d ap suat P va a ap suat khdng. S,, !a mddun dan hdi ding nhiet d ap suit khdng, Sy = — ^ , B^. = Bj.{P) \z mddun dan hdi d^ng nhiet d ap suit P
3. Ket luan
Bang PPTKMM, chiing tdi nit ra cac bieu thiic giai tich ciia nhiel do gidi han bin vimg tuyet ddi trang thai hgp ldm va nhiel do ndng chay cimg vdi phuang trinh dudng cong ndng chay cua HKXK ABC vdi cau tnic LPTK phu thudc vao ap suat. Trong cae trudng hgp gidi han, ta thu dugc li thuyet ndng chay ciia kim loai, hap kim thay the AB va HKXK AC.
TAI U£U THAM KHAO
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Thermodynamic properties of binary interstitial alloys with a BCC structure: dependence 25
Nguyin Quang Hoc, Dinh QuanS Vmh. Le Phirimg I lonp. Pham Thi Thanh Luan, Nguygn Quynh Anh va Hoang Thi Linh
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ABSTRACT
Study on melting theorj' of substitution alloy AB with interstitial atom C and body-centered cubis structure
Nguyen Quang Hoc, Dinh Quang Vinh, Le Phuong Hong, Pham Thi Thanh Loan, Nguyen Quynh Anh and Hoang Thi Linh Faculty of Physics. Hanoi National University of Education From the model of substitution alloy AB with interstitial atom C and the condition of absolute stabilizing for alloy stale, we derive the analytic expressions for temperature of absolute stabilizing for alloy stale and the melting temperature together with the equation of melting curve of this alloy AB using the statistical moment method. The obtained results allows lo determine the melting temperature of alloy ABC at zero pressure and under pressure. In limit casrs, we obtain the melting theory of metal, binary interstitial alloy and binary substitution alloy.
Keytvords: Interstitial alloy, substitution alloy, temperature of absolute stabilizing for alloy state.
