THOMA, WEAVER, FRIEDMAN, INSLEY, HARRISAND YAKEL
1096
and on its fuision and re-solidification phase. An approximation may be found for a by graphically integrating the experimental curves of gas evolution velocity us. time, from the beginning of the experiment to the (extrapolated) virtual cessation of gas evolution a t solidification. The flirther c*nlculationsare derived from the integration of the equation dr/dt
kz(1
- 2) + ki(1
- X)
(3)
obtained by dividing both sides of eq. 2 by a; we have 2: =
y/a; kl = j,; k = j a
( 4)
Integrating eq. 3 between 0 and t gives
and 8 above. k(1
Vol. 65
Rearranging eq. 8 yields
+ h/k)
=
4(d~/dt)m(l
X,
= (1
- ki/k)/2
(6)
In order to get the time corresponding to the maximum velocity of oxygen evolution, t, eq. 6 is substituted into eq. 5 giving t,
=
[l,'(k
+ kl)]
X In ( k l k l ) = [k(l
+ k ~ / k ) ] -X~ In (klki)
(7)
the maximum velocity of oxygen evolution is obtained by sub,dituting eq. 6 into eq. 3 (dzldt), .= k [ ( k
+ ki)/2k]'
= k(l
+ ki/k)'/4
(8)
I t is useful to conserve the ratio k l / k in the eq. 7
(9)
+
+
k = 4(d~/dt),( 1
Calculation of the Velocity Constants k and k , of Eq. 3.--The conditions for the velocity of oxygen evolution becoming maximum lead to 4.
+ kl/k)-'
and the substitution of eq. 9 into eq. 5 gives finally 4t,(d~/dt), = (1 ki/k) In (k/ki) = LI ( 10) Thus from the experimentally found values of maximum reaction velocity (dz/dt)m, and from the corresponding times tm, we may calculate the ratio k l / k for the different temperatures by using a graph or a table of the function LI (eq. 10). Then we compute: (1) the branching chain velocity constant k; ( 2 ) the monomolecular constant kl. Ad. 1. : eq. 7 gives after rearrangement k = h(k/kd/[tm(l kl/k)l l/(t&II) (11) and with eq. 10
+ ki/k) -'
(12)
A graph of the function LII may be helpful in solving eq. 11 LII
= (1
+ ki/k)-'
X
In (k/ki)
(13)
Ad 2 . : kl is found from k l / k and from k. Values for analytical grade KC10, are contained in Table IV. VELOCITYCONSTANTSk
TABLE IV AND kl (Ea. 3)
FOR
ANALYTICAL
KClOi Temp., OC.
10' k
IO4 kl
560
4 14 466 7 41
570
580
590
600
610
5 75 8 2 6 44
5 96 9 6 9 20
10 2 137 21 85
13 5 166 59 8
15 4 203 102 3
PHASE EQUILIBRIA I N THE SYSTEM LiF-YF3 BYR. E. THOMA,'~C. F.l v E B V E R , " H . A. F R I E D M A N , I ~ H . INSLEY,'~ L. A. HARRIS'^ A N D H. A. YAKEL,J R . ' ~ Reactor Chemistry Division and Metallurgy Division Oak Ridge National Laboratory,' Post Ofice Box X, Oak Ridge, Tennessee Received September 19, 1960
The phase equilibrium diagram of the condensed system LiF-YF3 is presented. Data were obtained from thermal analysis of heating and cooling curves and by identifying the phases present in small samples which were quenched after equilibration a t high tempemtures. Within the system two invariant points occur, the eutectic a t 19 mole yo YF3 and 695", and the peritectic a t 49 inole yo YF3 and 819'. The single interm$diate compound, LiF.YF:
