VNU J O U R N A L O F SCI ENC E Nat Sci t.xv n^2 - 1999 IN V E S T IG A T IO N OF T H E R M O D Y N A M IC PR O PER TIES OF B IN A R Y A - B ALLOYS B Y TH E M O M ENT M ETH O D Vu Van Hung, Hoang Vail Tich, Nguyen Van Quang F acu ky o f Physics, Teacher's Training College - VNU A b str a ct By the m om en t method the thermodynamic quantities of binary A - B a llo y s w ith f c c s t r u c t u r e are co n sidered T h e a n a ly tic e x p r e ssio n o f t h e r m o d y n a m i c quavfiUes for the binary A - B alloys as the isothermal compressibility X t ^ linear thermal expansion coefficient a, the specific heat at constant volum C y are obtained The obtained results are apphed to A l - based binary alloys { A lC u , A l N i) ^ C u - based binary alloys { C iiA l) and N i - based binary ( N i A l ) and compared with the exper imental data I INTRODUCTION It is known th a t if the free energy of a system is known, we can find the thermo dynamic properties So it is vory important to dpterrnine the free energy V' although it is not easy to find Ỉ/' For idial system one can determine the exact expression of But on general one can only find the expression for by an approximate theory At first, wo shall restrict ourselves to the simplest case of pairwise interactions To calculatp Ự’ of biliaiv A B alloys we shall use the quasi-chemical approximation for the multi - conipoiu'ut systeiiis [1, 3] We denoto th r potential of interaction of an atom of ( oinponeiit A with that of componoiit B ^ a n d the numbers of atoms in these cDinpoiHnit bv N a The Gibbs froo orungy of such sVvStem can be written [2] as G = Y ^ NAfiAA + Here N ab M ab - kB TlnW {{N A ] { N a b }), (1) A4 (or V’AS is denote by ;vi(oi then expressions of th e corresponding nearest neighbors distances at tem perature T are equal to (15) here oq is the distance a at tem perature o K and deteimiiiecl from experiment By the moment method, the displacement, of the particle of the metal A is considered and is equal to [4 7.02 VỐ = ^ ■A, 2q2 Ả-4 0-2 3f)3 + Ẳ-6 ^40 «3 + ■0-4 k.^ TCth.T (16) «1 = + 13 47 , 23 ,2 0-2 = — + i — xxcthx c i n x -+t — X cc m t h XX -f+ - X cTii cth X, X, 6 25 121 ,50 o 16 ^ \ — + ^^.Tcth.T + — x cWi X + — r cth T + ^.T^cth X , 3 / 43 93 Ì 169 x t n x H -X: ^ c t h ^ r + ^ T ^ c t h ^ T + ^ T ^ c t h ' ‘ T + i , T ^ c t h ^ x , 0.3 = - - T +T o *J z where the param eter k haa the form ( 1 ) V - (d ^ ^ A ,A o \ ,Jd^ipA.Ao\ and the teim s V( — and \( dfu ^t^íì^ỉ ) are deteimined as in [6] W ith /e q ’ \ ! eq ^ d u ị g / eq the aid of (13) and (17) the expression of the displacement of the particle yi (or ya) has a form analogous to (16), but the parameter k in this case has the form (12) or (14) and the param eter has thjP corresponding form IB A = Ạ l A + b ) lAB = 1A + 24 ^ỡV A 4(ĩ•l)^ V a duL )eq V a 4)e q + (18) d ^ < ^ A A {r\)^ V d vĩn d u l /egj We notice th a t the nearest neighbor distance a of the binary A B alloy is approxi mately equal to the distances ữA.QAB Oĩ a s A- Besides, from (10) we see th a t the Helmholtz I n v e s tig a tio n o f Therm odynam ic P ro p erties o f B in a r y A - B A lloys by 45 free ('Ii( i f>,v i,' is H fiuu tioii of the Ii(>an'st no ig hho i (listancp a T h u s , pxpancling this f u n c t i o n on tlic ncaiPst iK'iglihoi distance a in spcond order approximation, wo find the follov/ing ('XjJK'ssious = iỊ' b V' a b (o ) = ^'a a { a n d ai(‘ t ' \}ỉ T h ( ' spoc iíic h e a t at c o n s t a n t p i ( ‘s s i n th (‘ aíliahaĩic coinpiossihility ; n i ii u 'd f r o m fho k n o w n t l i o n i i o d v i i a i u i c I f ' l a t i o n s 9T\'a' c , - Cr ( 26) f ' r -f \7 A t l a s t t h ( ‘ i s o l l u n n i a l a n d a d i a b a t i c l)ulk inochili D ị a n d o f l ) i u a i \ ‘ A B a llo \' ar(' ('(Ịual t o Br= l/xr fi.S’ - l / v , , (27) III N U M E R I C A L R E S U L T S F O R A l C u A l X i C u A l A N D X i A l A L L O Y S T h ( ' i n t i ' i a c t i o n p o t ( ‘n i i a l l)(‘t\ve en t w o a t o m s o f a iiK'tal is list'd ill t h e f o iu i of tlic n — fif oiii' [7j f{r) = IỈ I) ilt ÌÌỈ ~ \ Ì' ^ / /■() Vrn (28) - iỉ{ — ) r fioiii tli(' ('xporinuMital ( l a t a a n d li.iii a r o (lotoniiiiK’s hv tli i‘ \vh