Thermodynamics of Liquid Ca-Zn Alloys
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Equation [5] may be solved for a expression:
caand is given by the
1/ff
=
a'l/Z
O"ion exp RT
[6]
_=_
1
Ca
-
a
O"e
1/ff
exp RT
where,
Thermodynamics of Liquid Ca-Zn Alloys
1/ =
JADRANKA DELCET AND JAMES J. EGAN The free energies of mixing of liquid Ca-Zn alloys at 800°C were determined from emf measurements on cells of the following type us ing CaF 2 as a solid electrolyte:
,
"
Ca-Bt alloys whose thermodynamics have been previously determined were used as reference electrodes. Since CaF 2 possesses some electronic as well as ionic conductivity, the usual equations for obtaining the free energy from the values of electromotive force are not applicable. The emf for Cell [1] is given instead by the following equation first derived by Wagner r' !tCa
J/-lea
[1]
t iond/LCa
where ui:« and /Lea are the chemical potential of Ca at the left and right-hand electrodes, respectively, and tion is the transference number of ions in CaF 2 which is a function of the chemical potential of ca. The transference number of ions may be expressed as:
t;
ron
-
RT ff
I
RT I
n
[7]
n O"ion + 2.1"' n a Ca •
Thus the activity of Ca in Ca-Zn alloys may be determined from Cell [1] if the ionic and electronic conductivity of CaF 2 as well as the activity of Ca in CaBi (xc a = 0.10) alloys are known. The ionic conductivity of CaF 2 has been previously determined by Ure 3 and the electronic conductivity has been measured by the authors. 2
[1]
Ca- Zn (01 CaF 2 (5)1 Ca- Bi (l) XCa = 0.10
1 E = 2.1"'
E
O"ion
=--,----O"ion + O"e
[2]
70
- - - - P. CHIOTTI AND R.J.HECHT T =800 °C
..
60
:; 50
.2...,
40
LU._
0
30 20 10 0
0.2
0.4
0.6
0.8
1.0
Zn X Co Ca Fig. I-Excess partial molar free energies of Ca and Zn at BOO°C.
where O"ion and O"e are the ionic and electronic conductivity in CaF 2 • Also, a
1/2
[3]
O"e = O"eaCa
where O"~ is the electronic conductivity in CaF z whose Ca activity is one. It follows that, E =RT 2.1"'
ca - - - -a- - dIn aCa Jal.,;a t: uion + ueaCa a
uion
[4]
lIZ
0.80
0.60 Ol
:::;: l:j
0040
or,
,
t'
Ca
t lOn
RT aCa RT ion E = 2ff ln ~ + F In -!,-.
[5]
JADRANKA DELCET, formerly a Junior Research Associate at Brookhaven National Laboratory, is now finishing her Ph.D. thesis at the University of Zagreb, and JAMES J. EGAN is a Chemist at Brookhaven National Laboratory, Upton, NY 11973. Manuscript submitted November 2, 1977. 728-VOLUME 9B, DECEMBER 1978
0.20
0.20
1.00 0.80 0.60 Ca Fig. 2-Activities of Ca and Zn as a function of composition at BOO°C.
ISSN 0360-2141178/121I-0728$00.75/0 © 1978 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
0.40
X
METALLURGICAL TRANSACTIONS B
Table I. Some Thermodynamic Properties of Ca·Zn Alloys at 800°C
XC.
E[v)
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90
0.480 0.585 0.672 0.736 0.764 0.786 0.803 0.816 0.824
'1
aC. 2.15 X 2.16 X 1.54 X 7.17 X 1.47 X 2.72 X 4.39 X 6.56 X 8.50 X
0.210 0.315 0.402 0.466 0.494 0.516 0.533 0.546 0.554
-dc!., J
-C&.,J
-cfn' J
_CE, cal
-c", cal
75,380 54,720 37,210 23,5
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