Application of the metalhydrogen equilibration for determining thermodynamic properties in the ti-cu system
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TRANSACTIONS A
A d o e s . The partial m o l a r free energy of B , G B , in the alloy, which is equilibrated with BHx and hydrogen gas u n d e r constant p r e s s u r e and temperature, equals that of B in B H x . This equilibrated hydride contains an amount of A atoms, which is negligibly s m a l l bec a u s e of much lower stability of the A hydride than the B hydride. Accordingly, the B hydride may be considered " p u r e " . G B in pure B H x can separately be determined from a variation of the hydrogen concentration with the p r e s s u r e of hydrogen gas in equilibrium with pure B m e t a l . The Gibbs-Duhem relation in the B-.H system under constant temperature and pressure is X B d G B + X H d G H = 0, which can be r e a r r a n g e d to: X B d i n t/B + X H d , u r H 2 = 0
[1]
where Xi is the mole fraction of component i, aB is the activity of component B with pure B placed as the standard state, and PH2 is the pressure of hydrogen gas in equilibrium with the alloy. In derivation of Eq. [1], the equility, GH in alloy = GH2/2 in gas, by virtue of the second law of thermodynamics and the approximation of " i d e a l " He gas have been used. Equation [1] can be integrated t o 1/2
112
h l a B = -- f P u 2
XHdPH2
[2]
0
because by definition aB = 1 for PH2 = 0, or pure m e t a l B. The r a n g e of integration in Eq. [2] extends to the hydride r e g i o n in the B-H system. In Fig. 1 is shown the plotting of X . / ( 1 - XH ) P ~ vs P~/~ for the ease of the Ti-H system, which will l a t e r be used for graphical integration in Eq. [2]. F i g u r e 1 was obtained by replotting McQuillan's dataa on the Ti-H system. In this way the activity of metallic component B in the hydride B H x can be determined, and it is equated to t o the activity of B in the A - B alloy which is thermodynamically equilibrated with the hydride as well as hydrogen gas. In Fig. 2 thus calculated activities of T i in " T i l l 2 " with pure a - T i used as the standard s t a t e are plotted a g a i n s t the hydrogen gas pressure. The next procedure is t o calculate the activity of B in the A - B alloy with no hydrogen dissolved. This calculation can be made if v a l u e s of PH2 have been d e t e r m i n e d over the whole compositional r a n g e of hydrogen in the A - B - H solution. A l o n g lines of constant
ISSN 0360-2133/ 79/0511-0529500.75 / 0 © 1979 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 10A, MAY 1979-529
X A / X B , w h i c h is the most c o m m o n e x p e r i m e n t a l condition for hydrogen absorption, a Gibbs-Duhem integ r a t i o n y i e l d s the f o l l o w i n g e q u a t i o n f o r the a c t i v i t y c o e f f i c i e n t (TB) of B . l a
-0.4 - -
x\ x
\
In VB/ B :
+
In
0.7
+
I.j;~I{(OIn(XH/P~:'I
][
/xA/O-XH).aX
~'
[3]"
- x a ,xB
*Equation [3] has been yielded from Eq. [12] of Ref. 13,in which G/~= const. -R T1n (XH/P~,) for "ideal" H2 gas, and m = B, k =H, and C~ = XA/Xa. w h e r e the s u p e r s c r i p t " + " s t a n d s for the b i n a r y A - B e a l
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