JOURNAL OF SCIENCE OF HNUE DOI. 10.13173/2354-1059 2017-0004 NaturalSci. 2017, Vol 62, No. 3, pp 27-36'
Tills paper is available online at http;//stdb.hnue.edu.vn
A N H H U O N G C U A N U T K H U Y E T DEN T I N H C H A T N H I E T D O N G C U A H O P K I M XEN KE A B C VCfl CAU T R U C L A P P H U O N G
T A M K H O I 6 A P S U A T K H O N G
Nguyen Quang Hoc', Le Hong Viet', Nguyin Ngoc Lan Anh' va Nguyin Thi Bich Nggc'
Khoa Vgt li. Trudng Dgi hoc Suphgm Hd Ngi 'Tncamg Si qudn Luc qudn 1. San Tdy. Hd Ndi
Tom tat. Trong bai bao chiing toi da rut ra bieu thiic giai tich ciia nong do niit khuyel can bang va cac dai lugng nhiet dong nhu khoang each lan can gan nhat trung binh, nang lupng lu do, cac he so nen dang nhiet va doan nhiet, cac mddun dan hoi dang nhiet va doan nhiel, he so dan nd nhiet, cac nhiet dung dang lich va dang ap, entropi ciia hgp kim xen ke tam nguyen cd khuyet lat vdi cau tnic lap phucmg tam khoi bang phu'otig phap niomcn thong ke, Cac bieu thuc thu dugc ciia cac dai lucmg nay phu ihuoc vao nhiet do, nong dp nguyen tu thay the, nong dp nguyen tiJr xen ke va nong dp niil khuyel can bing Cac kel qua li thuyet dugc ap dung cho hap kim xen ke FeCrSi trong khoang nhiet dp tir 600 den 1000 K, khoang nong do nguyen tii Ihay the tir 0 den 15% va khoang nong do nguyen lu xen ke tir 0 den 5%.
Tu- khoa: Hop kim xen ke tam nguyen va nhj nguyen, hgp kim Ihay the, phirong phap momen thdng ke, nguyen hi thay the, nguyen hi xen ke. niil khuyel can bang
1. Mtf dau
Cac tinh chit nhiet dgng va dan hoi cua hgp kim xen ke ed khuyet tat thu hiit su quan lain cua nhi6u nha nghien cuu li thuyet va thuc nghiem [1-9]. Mgt so cdng trinh tnrdc day da nghien eiiu tinh c h i t nhiet dgng ctia kim loai, hgp kim thay the nhj nguyen va hap kim xen ke nhj nguyen cd khuylt tat biing phuong phap mdmen thdng ke [7. 10] Trong bai bao nay, cung bang phuang phap mdmen thdng ke chung ldi nit ra bieu thue giai tich ciia ndng d o mit khuyet can bang va cac dai lugng nhiet d o n g ciia hgp kim xen ke tam nguyen ABC ed khuyet tat vdi cau tnic lap phuong lam khdi (LPTK) d ap s u i t khdng. Cac ket qua li ihuyel dugc ap dung tinh s6 cho hgp kim xen ke FeCrSi trong khoang nhiet dp tir 600 din 1000 K. khoang nong dp nguyen tu thay the tir 0 den 15% va khoang ndng do nguyen lu xen ke tir 0 den 5%.
2 . N d i d u n g n g h i e n c u u
2.1. C^c dai lu-ffng nhiet dong ciia hffp kim xen ke tam nguyen cd khuyet tat vdi cdu true lap phuonng tam khoi o^ ap suat khdng
Xet hgp kim xen ke A B C vdi cau triic lap p h u a n g t a m khoi, trong do nguyen t u chinh A d cac dinh. nguyen t u thay the B d tam khdi, nguyen lu xen ke C d cac tam mat, Gia sii cd N^
Ngay nhan bai: 11 /8/2016. Ngay nhan dang: 7/3/2017.
Tac gia lien he: Nguyen Quang Hoc, e-mail: hocnq(2^hnue.edu.vn
Nguy£n Quang Hpc, Le Hong Viel. Nguyen Ngoc Lan Anh va Nguyen Thi Bich Ngoc N^ nguyen tii B va N,. nguyen tir C va sd nguyen tu long edng la N = N^ + N„ + N^.. Ndng do
N N N
cua cac nguyen ur c, = —^ « c, = — ^ « c,, = —^. Nang lugng tu do ciia hgp kim li tuong N N N
cd dang [ 10]
w'Be-y'a+^c,{y/,,-ip,,) + TSf'-TS;''''.
trong dd ^ ^^ la nang lugng tu do ciia 1 nguyen tu A trong kim loai sach, ip gg la nang lugng tu do cua 1 nguyen tu B trong kim loai sach, ip^^. Ia nang lugng tu do ciia 1 nguyen ta C, y/ la nang lugng tu do eua 1 nguyen Hi A d vi tri lam khoi (goi la A,), ip . , la nang luang lu do ciia 1 nguyen tu A a vi tri dinli (ggi la A2).
la entropi eiia hon hgp cac nguyen tu A va C va entropi ciia hon hgp A, B, C va k^ la hing si Boltzmann.
Khi hgp kim ABC cd n niil khuyel d vj tri ciia cac niit mang thi nang lugng tu do ciia h ^ kim ABC li tudng chuyen thanh nang lugng tu do ciia hgp kim ABC cd khuyet lat hay nang lugng ty do ciia hgp kim ABC thuc
'V°A,c + ngll.^SC)-TS;'"'-. s;"' =«r,ta- (W + n)!
trong do S, la entropi ctia hon hgp cac nguyen nr A, B, C va niit khuygt va g / (ABC) la sij thay doi the nhiet dong Gibbs khi hinh thanh I niit khuyet va duac xac dinji boi
g / W S C ) . ( l - c . - 7 c , )gl{A) + c,g! (C)*2c,gl {A,)^4e,gl (A,)*c,gl (B). C' Trong phep gin diing mgt qua ciu ph6i vi,
gv W = n,{<l'"i->l'„) + Ayyx./.r„=(B,-l)if^,x.,,.,,,.,i,c.B.
trong do (i/^J la nang lirgng tit do ciia I nguyen tu X tren qua ciu phoi vj thii nhit co tam la nil khuyet, n, la so nguyen tii tren qua ciu ph6i vi thii nhit, A (i/„ la sir thay doi nang lugng tir do cua nguyen tii X khi din khoi vi tri mit mang de tao thanh mit khuvft Do do,
28
Anh hutmg cua niil khuyet den tinh chat nhiel 3ang cua hop kim xen keabc voi eau tnic idp phuang..
gU'iSC) = (\-c,-lc,.)\^n,[if^»,-y/„) + A<f„) + c,.\n,(v''.i-v„) + liWrr~\ +
Vjr =(l-i".-''Cr)lf^+CrV/r + 2c, v/, +4c,\i/, +c,\f,-T(S'"' tS''^).
• c , n i { [ r t " - ( ( / , ] . ( 5 , - l ) l i ' , } + 2c,n|{[i//;,|'-i/;,].(S,^-l)(i/,J +
Tir di^u kien cue tieu cua nang lugng tu do iZiflt^ = 0 suy ra nAng do nut khuyet can bing I a". )„s
, { c,g',{B)\ ( c,g:.(C) n, =n, expl —^-^—^—- '"""I -——^^—- ,._ (I-C.-7C, )g,'(.<) + 2e,g,'(/l,)+4c,y,'(.<,)
(7)
26' 4
h —
k
Khoang lan can gan tnmg binh giiia 2 nguyen lii trong hgp kim co khuyet tat co the lay gan dung bang khoang lan can gan trung binh giira 2 nguyen tu trong hop kim ABC li tuong.
He so nen dang nhiet ciia hgp kim ABC thirc co dang [10]
I" aABc ]
^ ABC ^ - " " ^ ' ' ^ " • ' '
4a,, 3N[ da'„, j^
r , M I (s'"^, ] r / M l (a'-V, ) (8)
+ 2ri-n-i,+n («, -I Ic, — A\ +4\l-n,n,+n,.IS,-l]\c^—\ ^ \ +
+fl-«»,+/.,(fi,-l)lc, — f ^ l +[l-«A+'',(S.-0]^.-^|'^l +
3 ^ dr' Nguyen Quang Hpc, Le H6ng Viet, Nguyin Ngoc Lan Anh va Nguyin Till Bich Ngpc
I (a'V") 1 (d'V')') 1 fa'>F +nn, ( 1 - c , - 7 c , ) r - +2nn,c, ^ +4n,n,c
' ^ 'iNl dr;, )^ 3W|^ dr;, J^
1 fe'T;'"! 1 (d''*')!) 3N[ dr;, ]^ 2N{ dr; J,
1 f a ' l ' , ) 1 d'U„ haJd'k^. Lf,5tTl
3N{ dr)\ j ^ ^ e dr',. 4i,, j 3/;-^, 2k,.(dr„) I
1 ra'y'M 1 d'ul'l noi')' d'k'" i fdk';.
iN[ ai;; J ^ ~ 6 dl-,', 4k'" dr;) 2t'J'[fli;, He so dan no nhiet ciia hgp kim ABC thirc co dang [10]
+2h-n,,n^*n,.l^B^-l\]c^a^^+2n,ri,c,.a'))+4U-n,ni*nJB,,-i\]c,.a,,^
+ 4n,n,c,^.a'l) +[l-«,,«, +«4^B -IJJCJOB + n,,«|C^.ai" + +[l - n,.n^ + «„ (fi^ -1)] CfOfp * n„n,Ci.ai)'.
a
•^ r T[ 2 1+- dr„de en 2 r" '' '
. yyNhiet dung dang tich ciia hgp kim ABC thuc cd dang [10]
C«, = [l-n„«,.«,(B,-l)](l-c„-7c,.)c„,n,«,(l-c.-7c,)c;>
+2[\-n,n,*n,(s^ -^]]crC,^ +2n,n,c,c;'l +4[l-o,,«| +n, (B^_ -l)lct.C„
+ 4n.n,e,C',:)__t[\-n..n,A!2,{B,-l)]cgCyg,n„n,c,CS:iA
*[l-n„n,.n,(B^-\)]c,.Cy^,n,.n,c,.Ci)l..
'i +M\(2r +r<xyx<^thx^
s i n h ' x , + t j [ r ' ^ ' ' ' + 3 J sinh^x.
x^ 2x\ colh^ x^
sinh''xJ^. sinh^jt^
sinh^4' 4 ' « 2v"l
sinh"*
,„ .rSl^l^coflix^
'^"*^] sinh^x'Jl * 2 x ; » c o l h ' x ' J '
sinh"x'il'
(10)
Anh huang cua mil khuyet den tinh chdl nhi^l dqng ciia hop kim xen keabc voi cau tnic lap phuong...
trong dd C ^ y la nhiel dung dang tich ctia X tren qua cSu phdi vj thu nhit cd tam la mil khuyet.
Cac dai lugng nhiet ddng khac dugc suy ra tir cac mdi lien he nhiet ddng.
2.2. K e t q u a t i n h so doi v o i hgrp k i m F e C r S i Ddi vdi hgp kim FeCrSi, chiing toi sii dung thd cap n-m
(I I)
^^^d^kvl-lvl
trong dd cac thdng sd the dugc cho Irong Bang 1 [9]
Bdng 1. Cdc thong sd them ,n,Dj\^ ctia cdc vat lieu V|t lieu
Fe Cr Si
m 7,0 6,0 6,0
n 11,5 15,5 12,0
D[lO-"erg] i r.[lO-'»m]
6416,448 j 2,4775 6612,96 2,4950 45128.24 J 2,2950 Khi xet t u a n g tac giiia cac nguyen lu Fe va Si trong hgp kir.i xen ke FeSi, chiing tdi sii dung the (11) nliung tinh gan diing D -
^-^''^=^r(^]-"(^
(12)trong d o m va n" xac dinh bSng kinh nliiem. Do dd, cae thdng sd the n- m doi vdi hgp kim FeSi nhu trong Bang 2 [9].
Bdng 2. Cdc thdng so the n- m cda hap kim FeSi Hop kim
FeSi
m 2,0
n 5,5
£>[lO-"'erg] ^[lO-'°m]
17016,5698 ; 2,3845 Bang 3. Nong dp nut khuyet cdn bdng vd cdc dai luang nhiet dpng cua hop kim FeCrSi
li tudng (LT) vd cd khuyet tat (KT) & dp sudt khdng vdi ndng dp ccr= iO%
Dai lirong
olA -LT
OJAI-KT 0 0,01 0,03 0,05 0 0,01 0,03 0,05
600 2.4412 2.4543 2.4816 2.5097 2,4413 2.4547 2.4824 2.5108
700 2,4450 2.4581 2.4853 2,5134 2,4457 2,4590 2,4867 2,5150
800 2.4489 2.4619 2,4892 2.5172 2.4502 2,4635 2.4911 2,5193
900 2.4528 2.4659 2,4931 2,5211 2,4549 2,4682 2,4956 2,5238
1000 , 2.4569 2,4699 2,4972 2,5251 2,4599 2,4730 2,5004 2.5285
Nguyen Quang Hpc, Le H6ng Vict, Nguyin Ngpc Lan Anh va Nguyen Tlij Bich Ngoc
(10-')
(10"" Pa"')
,f,-KT (10"'^ Pa'')
d.-LT (IO-* K'')
a,-KT (10'' K'')
C,-LT (J/mol.K)
C,-KT (J/mol.K)
C,-KT (J/mol.K)
t.",-KT (J/mol.K)
32
0 0,01 0,03 0,05 0 0,01 0,03 0,05 0 0.01 0.03 0,05 0 0,01 0,03 0,05 0 0,01 0.03 0,05 0 0.01 0,03 0,05 0 0.01 0.03 0.05 0 0.01 0,03 0,05 0 0,01 0,03 0,05
0.0653 0.0242 . 0.0033 0.0004 3.7152 3,2172 2,578 2,1776 3,7292 3.2322 2.5925 2,2002 14.2289 12.0741 8,2315 5.1556 14,3089 12,1544 8,2792 5,1056 29,2017 29,0714 28,8110 28,2029 28,2017 28,0714 28.8110 28,2029 30,4849 29.7891 28,8552 28.7522 23.4808 29,7847 28.8505 28,7909
0,9308 0.3966 0,0720 0,0131 3,8939 3,3592 3,9007 2,2410 3.9079 3.3628 3.9204 2.2546 16.1194 12,8587 i ' A l 5,3334 16.1994 12,9201 8.35045 5,2834 30,1343 29,9988 29.7277 29.2746 30,1343 29.9988 29,7277 29,2746 31,9877 31,1301 30,0132 29,9539 31,9832 31,1271 30,0092 29,9976
5.1097 2.4247 0,5460 0,1229 4,0899 3,4865 2,7404 2,2998 4,1029 3.5033 2.7564 2.3116 16.6086 13,4568 8,8666 5,5022 16,6886 13,5455 8.89096 5.4522 31.1057 30.9585 30,6643 30,3382 32.1057 31.9585 31.6643 30,3382 33,908 33,5411 32,2076 31,1522 33,5868 33,5398 32,2046 31,2034
13,1514 6,8148 1,8299 0,4913 4,3 3,6492 2,8319 2,3563 4,3170 3,6552 2,8457 2,3713 17,7217 14,0835 9,1865 5.6688 17,8017 14,2051 9,1919 5.6188 32,1381 31.9745 31.6472 31.4311 33,1381 32,9745 32,6472 31,4311 36,3280 35,0521 33,4675 32,3856 36,3260 35,0481 33,4636 32,4487
16,9485 9,4906 2,9760 0,9331 4,5379 3,8042 2,9269 2,4111 4,5535 3,8202 2,9408 2,4341 18,6192 14,7509 9,5177 5,8375 18,6992 14.9025 9,51706 5.7875 33.2493 33,0649 32,6960 32,5812 34,2493 34,0649 33,7060 32,5821 38,2304 35,6886 34,8151 33,6857 38,2294 35,6866 34,8131 33,7624 ]
Anh hudng cua mit khuyet den tinh chdt nhiel dpng cua hop kim xen keahcvdi cdu tmc lgp phuang...
Bdng 4. Nong dp nut khuyet can bang vd cdc dai lucmg nhiet dpng ciia hgp kim I tu-dng vd cd khuyet tgt d dp suat khong vdi ndng dp Cs, = 5%
f>9i Ivong
0 A -LT
oJA|-KT
(10-')
(10'-Pa'')
r,-KT (10'" Pa')
Q,-LT ( 1 0 ' K ' )
o,-KT (10'K'')
C,-LT (J/mol.K)
0 0,05 0.07 0,1 0 0.05 0,07 0,1 0 0,05 0,07 0,1 0 0,05 0,07 0,1
0 0,05 0,07 0,1
0 0,05 0,07 0,1 0 0,05 0,07 0,1
0 0,05 0,07 0,1
600 2,5067 2,5082 2,5097 2,5097 2,5078 2,5193 2,5199 2,5108 0,0016 0.0008 0.0007 0,0004 2,0269 2,1868 2.183 2.1776 2,0499 2,2098 2.2060 2.2002 5,1576 5,1566 5,1562 5,1556 5,1076 5,1066 5,1062 5,1056 28,2059 28,2044 28,2038 28,2029
700 2.5104 2.5149 2.5134 2,5134 2,5120 2,5135 2,5141 2,5150 0,0370 0,0220 0,0178 0,0131 2,078 2,2417 2.2377 2.2641 2.1010 2,2647 2.2607 2.2546 5,3354 5,3344 5,334 5,3334 5,2854 5,2844 5,284 5,2834 29,2776 29,2761 29,2755 29,2746
800 2,5142 2,5187 2.5172 2.5172 2,5163 2,5178 2,5184 2,5193 0,2839 0,1868 0,1580 0,1229 2,1315 2,3221 2.3449 2.2998 2,1545 2,3221 2,3179 2.3116 5,5042 5,5032 5,5028 5,5022 5,4542 5,4532 5,4528 5,4522 30,3402 30,3392 30,3388 30,3382
900 2,5181 2,5226 2,5211 2,5211 2,5208 2,5223 2,5229 2,5238 0,9273 0,6750 0,5945 0,4913 2,1877 2,3593 2.3779 2.3563 2,2107 2,3823 2.3779 2.3713 5,6708 5,6698 5,6694 5,6688 5,6208 5,6198 5,6194 5,6188 31,4331 31,4321 31.4317 31.4311
1000 2.5221 2.5266 2.5251 2.5251 2.5255 2,5270 2,5276 2,5285 1,4161 1,1495 1,0575 0,9331 2,2468 2,4227 2.4181 2.4111 2.2698 2.4457 2.4411 2.4341 5.8395 5.8385 5.8381 5,8375 5,7895 5.7885 5.7881 5.7875 32,5837 32,5822 32,5818 32,5812
Nguyen Quang Hoc. Le H6ng Viet, Nguyen Ngpc Lan Anh va Nguyen Thj Bich Ngpc
C, -KT (J/mol.K)
t,'„-KT (J/mol.K)
C,-KT (J/mol.K)
0 0,05 0,07 0,1
0 0,05 0,07 0,1
0 0,05 0,07 0,1
28,2059 28,2044 28,2038 28,2029 28,7612 28,7587 28,7577 28,7522 28,7931 28,7920 28,7916 28,7909
29,2776 29,2761 29,2755 29,2746 29,9589 29,9564 29,9554 29,9539 29,9998 29,9986 29,9983 29,9976
30,3402 30,3392 30,3388 30.3382 31,1542 31,1532 31,1528 31,1522 31,2054 31,2044 31,204 31,2034
31,4331 31,4321 31,4317 31,4311 32,3876 32,3866 32,3862 32,3856 32,4507 32,4497 32,4492 32,4487
32,5855 32,5836 32,5829 32,5821 33,6877 33,6867 33,6863 33,6857 33,7644 33,7634 33,763 33,7624 BSng phuong phap mdmen thdng ke va gia thiel ve md hinh khuyet tat diem tai niil eua h(rp kim FeCrSi, chiing tdi da thu dirge cac kel qua nhu trong Bang 3 va Bang 4 Tir do ta nhan thay rang ndng dp mil khuyet can bang n^ ciia hgp kim FeCrSi giam khi ndng do nguyen tii xen ke Cs, tang va tang khi nhi^t do T tang. O cang gSn nhiet do ndng chay ciia hgp kim thi nong do niit khuyet can bang HV cang Idn. Chinh vi nong dg niit khuyet can bang n^, rat be d nhiet do thap nen cac tinh chSl nhiet d^ng ciia hgp kim FeCrSi cd khuyel tat khdng bi anh hudng dang ke va tuong tu nhu trudng hgp hgp kim FeCrSi li tudng. Tiiy theo eac dai lugng nhiel dong khac nhau ma sy anh hudng ciia ndng dp mil khuyet can bang ciing khac nhau. Cu the la he sd nen dang rid^txt lang c5 0,2%; mddun dan hdi dang nhiet Bj giam ca 0,2%.; he sd dSn nd nhiet OT tang cd 1.%,;
nhi^t dung ding lich Cr tanged 1,3%; nhiet dung dang ap C/=giam caO,l%.; h? so nen doan nhi?t
;^-^lang cd 0,2%. Doi vdi hgp kim FeCrSi d ciing ndng dp nguyen tu xen ke, ndng do niit khuyet can bing Kv cua hgp kim FeCrSi giam khdng dang k£ khi ndng dp nguyen tu thay the Cc, tang va lang khi nhiet dp Ttang.
Bang 5 va Bang 6 la ket qua th\rc nghiem ciia hp sd dan nd nhiet va nhiet dung ding ap cua kim loai Fe [8] va ket qua tinh sd ctia hesd dan nd nhiet va nhiet dung ding ap ciia kim loai Fe If s^;;
tudng theo phuang phap mdmen thdng ke. Trong tnidng hgp nong do nguyen tu xen k6 va nfing dp nguyen tu thay th6 din tdi khdng, do anh huang ciia nong do nut khuySl can bing la thu dugc cac dai lugng nhipt ddng ciia kim loai sach Fe gan vdi ket qua thuc nghiem hgn so vdi trudng hap khdng tinh den anh hudng cua nong do niit khuyet (tinh the li ludng). Dd la eg sd dl chiing to cac kel qua tinh loan ddi vdi linh chit nhiet dpng ciia hgp kim FeCrSi cd khuySl tal la phii hgp.
Bdng S. Syphu thupc nhift dp cua Oj- (10"* K"') doi vdi Fe li tudng (LT) vd cd khuyet tat (KT) tinh todn theo phuffng phdp mdmen thdng ke (MM) vd theo thtfc nghiem (TN) [8J
T(K)
a,(MM)-LT -KT o,(TN)
100 5,69
5,6 200 10,9
10 300 12,74
11,7 500 14,62
14,3 700 16,12 16,17 16,3
1000 18,61 18,67 19,2
Anh hudng cua mil khuyel den tinh chdl nhiet dong cua hop kim xen keabc voj cdu Iriic Idp phvo-ng..
Bdng 6. Suph^ thupc nhiet dp ciia Cp(J/mol,K) doi vdi Fe li tudng (LT) vd cd khuyit tat (KT) tinh todn theo phuffng phdp mdmen thong ke (MM) vd theo thuc nghiem (TN) /8J
Tm
C^(MM)-LT C,(MM)-KT C,(TN)
100 11,38
12,067 200 21,79
21,503 300 25,53
25,13 500 29,43
29,64 700 32,85 32,96
34,62
3. Ket luan
Bai bao xay dung li thuyet nhiet dpng cua hap kim xen ke ABC (hap kim ihay the AB xen ke nguyen tu C) cd mil khuyel vdi cau tnic LPTK,, Theo ket qua tinh sd ddi vdi hop kim xen ke FeCrSi cd khuyet tat, ndng dp niit khuyet can bang tang theo nhiet do, giam theo ndng do nguyen tu xen ke va nong dp nguyen tii thay the. Do anh hudng ciia ndng dp mil khuyet can bang, cac dai lugng nhiet ddng ciia hgp kim cd khuyet tat van giu nguyen tinh chat nhu ddi vdi tnrdng hgp li tudng. Tuy nhien, cac gia tri ciia chiing ed sy thay ddi nhat dinh so vdi trudng hgp li tudng. Cu the la cac gia tri eiia he sd dan nd nhiet, cac he so nen dang nhiet va doan nhiet, nhiel dung dang lich va entropi lang so vdi trudng hgp li tudng (tang khoang Itr 0,2% den 1,4% tuy theo timg dai lugng); cdn cac gia tri cua mddun dim hoi dang nhiel va nhiet dung dang ap giam it sd vdi trudng hgp li tudng dac biet la cac gi4tri ctia nhiet dung dang ap giam khdng dang ke so vdi trudng hgp li tudng (giam 0,1%). Khi ndng dp nguyen lu thay the Cr bang khdng, ta thu dugc linh chat nhi?l dpng ciia hgp kim xen ke FeSi cd khuy6t l|t. Khi ndng dp nguyen tu xen ke Si bing khdng, ta thu dugc linh chat nhiet dgng ciia hgp kim thay the FeCr cd khuyet III. Con khi nong do nguyen tu thay Ihl Cr va ndng do nguyen tu xen ke bang khdng, la thu dugc tinh chat nhiel ddng ciia kim loai Fe cd khuyet tat.
TAI LIEU THAM KHAO [1] K-E. Mironov, 1967. Interstitial alloy. Plenum Press, New York.
[2] A.A, Smirnov, 1979. Theory of interstitial alloys,'Nsiika, Moscow (in Russian).
[3] W.B. Pearson. 1958. A handbook of lattice spaeings of metals and alloys. Pergamon. New York.
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Nguyen Quang Hpc, Le H6ng Vift, Nguyen Ngpc Lan Anh va Nguyen Thi Bich Nggc [9] N.Q. Hoc, D.Q.Vinh, N.T.Hang, N.T, Nguyet, L.X. Phuong, N. N. Hoa, N.T.Phuc and
T.T.Hien, 2016. Thermodynamic properties of a ternary interstitial alloy with BCC structure: Dependence on temperature, concentration of substitution atoms and concentration of interstitial atoms. Journal of Science of HNUE, Math, and Phys. Sci..
Vol.61. No7, pp. 53-62.
ABSTRACT
Influence of concentration of equilibrium vacancies on thermodynamic property of ternary interstitial alloy with BCC structure at zero pressure
Nguyen Quang Hoc', Le Hong Viet^. Nguyen Ngoc Lan Anh' and Nguyen Thi Bich Ngoc' 'Faculty of Physics. Hanoi National University of Education
'Tran Quoc Tuan University, Son Tay. Hanoi The analytic expressions for the concentration of equilibnum vacancies and the tha-modynamic quantities such as the mean nearest neighbor distance, the free energy, the isothermal and adiabatic compressibility, the isothermal and adiabatic elastic moduli, the thermal expansion coefFieient, the heat capacities at constant volume and al constant pressure, the entropy of ternary interstitial alloy with BCC structure are derived by the statistical moment method. The obtained expressions of these quantities depend on temperature, concentration of substitution atoms, concentration of interstitial atotns and concentration of equilibrium vacancies. The theoretical results are applied lo interstitial alloy FeCrSi in the interval of temperature from 600 to lOOOK, the interval of substitution atom concentration from 0 to 15% and the interval of interstitial atom concentration from 0 to 5%.
Keywords: Ternary and binary interstitial alloy, substitution alloy, statistical moment method, substitution atom, interstitial atom, equilibrium vacancy.
