we havt^ found the following expressions * For the f.c.c lattice: 7a... Tims, if tli' potential binary alloys AB at various prossuie.. The calculation Cal and ‘xporiniontal Exp 9] valu
Trang 1-NU J O U R N A L O F S CI E N C E , N a t Sci., t.x v , n “ 2 - 1999
T H E M E L T IN G T E M P E R A T U R E FOR B IN A R Y
ALLO YS A B AT VAR IO U S P R E SSU R E S
P h a r n D i n h T a m 1
t
Military Thchỉiicỉìl Acỉìdeinỵ
A b s t r a c t 7/ i c rquahoTis f o r Tĩìe^líi.ĩìg f.empe.ralure o f the TTi.ctals and b in a ry a llo y s
Á B /n fh( J i c ariíỉ b r c s t r i i c l u T t s are o b t a i n e d by t he moTiieni Tiiefhod T h e v a l u e s
o f ÌỈÍC i n c U i ĩ i g t u i n p v r a i i r r e obt ũĩ Tì ed b y s o l v i n g t h e s e e q u a t i o n s a r e i n g o o d a g r e e m e n t
a tfii e r p c ì ỉ ì r i e ì ì l a ỉ d a t a
I INTRODUCTION IljcK' ai<' various iiuMliocls of investigation of the fusion for crystal such as Liiide- imiiii UK'iliud Siiuoii rqiiation [ 1 ] pseudo - poĩ('iitial luothod [ 2,3] Those m ethods I(4p to hncc('ssiiill\- iiivrsti«at(' tho fusion of some simple metals Tlie (Jevelopnient of the
‘I\'síalliu(> statf' and th(^ uioiiHuit nioỉhod has given tlio rquation for molting to m p rra tu rp )f th(’ lurtals and l)inai \' allo\'S AB witli a \'ÍT\’ small fonc(*ntration of atoms B at pressiiii' ) — I) and tli(' ('(juatioii toi rli(' uu'ltiu^ t<'nip(narui(‘ of tli(' iu(*tals at various pressures
tli(' ('CỊiiatioiis foi iiK'liinn r oi npo r at ur o o f t ho m r t a l s a n d a l l oy s A B w i t h f.r.c
u h I !)-( ( s t r u c l u K ' s a t \ - a i i i > u s PK' SSUK' S ' r i i ( ' c a k ' u l a t i o n K ' s n l t s a i ( ' i n ^ 0 0 ( 1 a g r o f ' u i o u t
ỈỈ Till-: K Q r A 'n O X S FOR MKLTLXC TKM PERA TU RE OF THE METALS
AND BINARY ALLOYS AB
Hsiii” tli(' Liudf'inaiiii assumption [ 1 the ('qiiiUion for iiK'ltiiio t(*inp('iaturo of the
« ‘ ì t Z p )
Athene ((r) - \ hv uK‘an sq u an ' (lisplacoiiKMit of atoms ill tho lattice vibration; a - Tho lattice
Trang 236 P h a m Dinh Tam
foi Hi
(2)
of atoms ill the lattico vibration of the effective system ( a đ )
Similar to [61 wo have
(ả-ÍỈ)
(3)
TT +
(4)
obtain tho following result
ự ) = C A { » l ) + C u { u ị )
H /
X
Wi )
0
h ĩ ■
((i)
of the two first aiul second coordination splieres we havt^ found the following expressions
* For the f.c.c lattice:
(7a)
Trang 3i ip^g\a) - + Ị - \p^g\a) - (p^A^a)
The M e l t i n g T e m p e r a t u r e f o r B i n a r y A llo ys A B
1 + -
o
( 3) / X ( 3 ) ,
‘f a (")
-1 2o2
(2)
2 f l 3 3
, ( 1 )
( 1 )
^For ^/i.e b.c.c lattice:
9a^
( 2 )
+
+
3o 4 3^
- ^ a \ " )
ip^s\n) - v^Í4^(a)
3o3
( 1 )
(7b)
(7c) 37
(7d)
(7e)
(8a)
(8b)
(8c)
(8d)
(8e)
- radii of the two first and second coordination spheres, they have been defined in [7 ]
Put ( 5 ) into ( 1 ) wo obtain the equation for melting tem perature in thệ binary alloys AB
C a Ì ĩ I^ a ) + C B { y ị )
-( ^ n l P A B Ị I 1 1 7 b V
Av?(-*)(a) -*ớ
1^' a
Trang 438 P h a m Dinh Tarn
In tli(* (equation ( 9) - const, is deti'nninoil 1)V th(' ('xị;)('iiiiK’ntal (lata for the molting
toinppiatuK' of tliO alloys at piossun' p = 0 { oi at Ị)I(\SS111(‘ p / 0 ) Tims, if tli(' potential
binary alloys AB at various prossuie Put ( 6 ) into ( 1) \V(‘ obtain tlio (equation for
{1 0)
( 8 b )( for t h e b c c l a tt i c e ); (ia - tht' l a t t i c e s p a c i u g s o f Iiu'tal a t h e y arc (k'tCMuiiH'd in [G : const is (letininiued by the expeiinunital d a ta tor t h r nioltiiig tonipi'iatiiK' of th(' iiiPtal
a at prcssiiK' p = 0.
I I I T H E N U M E R I C A L C A L C U L A T I O N A N D D I S C U S S I O N
For Iiuinoiical calculation we chooso the interact ion potential between two atoms in metal in the form of the Lonnaid - Jones potential [8
v ? ( r ) =
D
Ĩ Ì — 111
whore D, To are deiennined by ('xperimont and //,?// ai(‘ (lotonniiiod by expíMÌPUce (Tal)l(’
I ) : r - radius of the coordination splioiP, defined ill [ 7
T a b le 1 Tho value of parainetois D, r(), li and ÌÌỈ of tli(' motals
M etals
P(Kbar) const
dp Vkbar/
T a b l e 2 The calculation (Cal) and (‘xporiniontal (Exp) 9] values of the melting tem perature of the metals
Trang 5The Me lti ng T e m p e m t u r e f o r B i n a r y A l l o y s A B , 39
d T m f K \
dp V kbary
T a b le 3 The molting tem perature of the alloys at various pressures
Tn,(K)
10 20 30 40 SO 60 70 p (Kbi
alloys ai various p r t s s u v t s
ig 1 T h t melting tempe.raiun of
Tfitiai ai various pressures.
(i hf dots correspond experimental
values f9j)
T1h‘ valiu‘8 of th(‘ nu'ltiiig tem perature for motals Al, Cu, Ag, P ĩ and for alloys
( ’uXi XiCii AuPt PdCiK PdA^y ai'(‘ given in Tables 2, 3 and are shown in the Figs 1,2.
p>a;.<«l I>n th<' i n i i i i i ‘i i < a l 1ul)lon i iiul th<- o l i t íiiiiiHỈ, w v l i a v t ’ t h e
(o u i u u ' n t s
- 'ĩli(' K'sults o f c a l c u l a t i o n o f t h e nii'lting t o n i p p i a t u n ' o f m o ta l y by t h e i n o i n o n t
- I li(' oỉ)taiỉi(Ml fusion cmvo of nii'tals and alloys has a form close to a straight lino
agKHYl with tlu' exppiinieiital data [9
A( ( oidiỉigly, the equations (9) and (10) allow to dotermine the melting tem p eratu re
ui \ hv l)iiiaiy alloys aiul niotals with f.c.c and b.c.c structurevs at various pressures.
REFEREN CES
Russian )
R Jones Phys Rev (A8)(1973) p.3215.
D Stroud, N w Ashcroft Phys Rev (B2)(1972) p.371.
\'u Van Hung, Nguyen Tang and Pham Dinh Tam Proc 2^^ ( I W O M S ' 95) Hanoi
Trang 65 1 Nguyon Tang, Pham Dinh Tam and Vu Van Hung Comm., in Phys 3(1997) p.47
7 - Pham Dinh Tain Corn, i.v Phys 2(1998) p 78.
T A P CHÍ K H O A ' H O C O HQ G H N , K H T N , t.x v , n ° 2 - 1999
NHIỆT ĐỘ NÓNG CHAY CỦA H Ợ P KIM THAY T H E AB Ở ÁP SƯẤT KHÁC NHA
Pham Đình Tám
Khoa L ý Hóa - K ỹ thuật Học viện K T Q S
trong các còng trình trước, chúng tôi thu được các phương trình mới xác định nhiệt đ(
nóng chảy của kim loại và hợp kim thay thế AB cấu trúc L P D T và L P K T ờ áp su ất khái
nhau Kết quả rinh số từ các phư ơng trình thu đ ư ạ c phù hợp tốt với các số liệu thự( nghiệm