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Thermochemical Properties
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Reprint from
"ATOMIC ENERGY REVIEW'
Special Issue No.6
"ZIRCONIUM: PHYSICOCHEMICAL PROPERTIES
OF ITS COMPOUNDS AND ALLOYS"
INTERNATIONAL ATOMIC ENERGY AGENCY
VIENNA, 1976
b
I. THERMOCHEMICAL P R O P E R T I E S
C. B. ALCOCK, K.T. JACOB, S. ZADOR
Department of Metallurgy and Materials Science,
University of Toronto,
Toronto, Canada
NOTATION
Symbol
a
Meaning
Common units
'
activity
molar heat capacity
c a l / K . rnol
AG
Gibbs energy of reaction per mole
cal/mol, kcal/mol
A Gx,
partial molar f r e e energy of solution
of one mole of X2
cal/mol, kcal/mol
AH
heat of reaction
cal/mol, kcalfmol
A Hf
heat of formation a t 298 K
cal/mol, kcal/mol
A&
partial molar heat of solution of
solute i
cal/mol, kcalfmol
In
1%
log
log10
molar heat of evaporation, fusion,
sublimation o r transformation
P
L e , f, I, t
mole fraction of element A
A
atm
R
pressure
gas constant
cal/K
rnol
S298
standard entropy a t 298 K
cal/K
rnol
AS
entropy of reaction
cal/K
. rnol
AZ,
partial molar entropy of solution
of solute i
cal/K
rnol
'Je, f, r. t
molar entropy of evaporation, fusion,
sublimation o r transformation
cal/K
. rnol
T
absolute temperature
<>
solid state
P
{
1
(
1
gaseous state
[
1
dissolved state
(subscript denoting solvent)
liquid state
' Some unia are given pcr gram-atom rather than pcr gram-mole.
8
1.
ALCOCK et el.
ZIRCONIUM
$ 9 8 ( ~ar), = 9.32
H2,(Zr, a )
=
+ 0.05
cal/K g- at. [ I ]
0
Comprehensive studies were made on zirconium metal by Lustman and
Kerze (21 and Miller [31; Hultgren et al. (41 published a reliable assessment of the thermodynamic information available up to 1966. A review of
the metallurgy of zirconium by Douglass 151 gives a compilation of recent
investigations. F o r the values recommended here, the assessments of both
Hultgren et al. and Douglass were considered, supplemented by some work
published since.
.
1.1. Heat capacity of solid zirconium
There a r e a few recent measurements of the heat capacity of solid
zirconium. Klein and Danielson (6 1 obtained their values by pulse-heating
techniques. Douglass and Victor (quoted by Douglass [5]) used a Bunsen
ice-calorimeter to measure the heat capacity. Vollmer et al. [7] derived
their heat capacity values by an adiabatic calorimeter technique. The
results of all the above investigators were expressed in equations of the
form of Cp = a + bT + c T 2 cal/K g-at., and the respective constants a r e
tabulated in Table I. The Table also contains the heat capacity values of
both solid and liquid zirconium assessed by Kelley [8].
By combining the heat capacity values computed by the above workers,
the following equations a r e obtained:
Cp(rn)(cal/K. g-at.) = 5.463 + 2.144 X
Cp(p) (cal/K g-at.) = 5.137 + 1.5705 X
T
- 0.166 X lo5 T - ~
(298 - 1136 K)
lom3T + 8.776
X 105 T - ~
(1136
- 2125 K)
1.2. Heat capacity and entropy of gaseous zirconium
Hultgren et al. [41 tabulated the heat capacity of gaseous zirconium.
Their data were fitted by least-squares calculations to give the following
equations:
Cp(Zr) ( c a l / ~ g-at.) = 5.496 + 0.730 X 10" T
+ 0.8708
X 10' T - ~
S;,,(Z~) ( c a l / ~g-at.) = 43.315 [4]
1.3.
Condensed phases of zirconium
*
,
The a (hexagonal)
p (b.c.c.) transformation of zirconium was found
by Douglass and Victor (in Ref.[5]) to take place a t 1137 K with a heat of
transformation of 913 cal/g-at. Klein and Danielson [6 1 found TaeB = 1138 K,
and Vollmer et al. [7] reported 1155 K a s the transition temperature.
Hultgren et al. [41 selected T,B = 1136 5 K, and this value is recommended
930 20 cal/g-at. i s the suggested value for the heat of transhere. L&,~=
formation incorporating the value recommended by Hultgren et al.
*
4
*
PART I.
THERMOCHEMICAL PROPERTIES
TABLE I. TRANSFORMATION DATA AND CONSTANTS OF THE Cp
EQUATIONS
Cp ( c a l / ~g-at.)
.
= a + bT + CT-2
Present
[41
assessment
The melting point of zirconium was reported by Douglass [51 a s
21 18 f 25 K and 2128 f 15 K, depending on the nature and magnitude of the
impurities present. Elyutin e t al. 191 found the melting point to be 2125 K
and the heat of fusion Lf = 5000 f 300 cal/g-at. In a n assessment 01 e a r l i e r
data, Hultgren et al. recommended the value of the melting point a s
2125 f 5 K. Considering the stated experimental e r r o r s , a n e r r o r limit of
f 10 K would seem m o r e reasonable. Hultgren e t al. 141 in a l a t e r assessment suggest 4.05 kcal/g-at. for the heat of fusion of zirconium. Combining
this with the value found by Elyutin e t al., Lf= 4500 f 500 cal/g-at. is
suggested.
1.4. Vapour p r e s s u r e
Hultgren et a1.[4] in their assessment selected L, = 145 500 f 1000 cal/g-at.
a s the heat of sublimation of zirconium. They report 4 = 29.71 cal/Keg-at.,
at a boiling point of 4682 K. The boiling point of zirconium is given a s
4644.05 K by Schick 1101 in his assessment. The value selected h e r e is
derived from the vapour p r e s s u r e equation for liquid zirconium by Ackermann
and Rauh 11 11, Tb = 4577 f 100 K.
Trulson and Goldstein 1121 measured the vapour p r e s s u r e over solid
and liquid zirconium in a 300 deg range around the melting point, employing
10
ALCOCK et
al.
TABLE 11. HEAT OF SUBLIMATION OF ZIRCONIUM
Ref.
Temp. range
(K)
AH:, (kcal. g-at.)
2nd law
tzr}
[ 111
(21)
[ 131
{ 211
[ 141
(21)
[ 121
(211
[I21
1990 -2540
- 2054
2230 - 2800
1966 - 2112
2148 - 2274
1950
143.7
5
3rd
1.1
law
143.1
140.4 t 2.2
145.3
148.4 t 4.4
141.9
135.1 t 3.6
141.6
134.6
141.6
t
4.9
Knudsen cell and mass-spectrometric techniques. No equation was derived
to describe the vapour p r e s s u r e dependence on temperature. Values for
the heat of sublimation a r e given in Table 11.
Koch and Anable 1141 conducted vapour p r e s s u r e measurements over
liquid zirconium by the Langmuir free evaporation method and obtained the
following equation:
log p (atm) = -30 940
T' + 6.52
(2229-2795 K)
More recently, Ackermamand Rauh 1111 measured the vapour p r e s s u r e over
both the solid and the liquid metal by a combination of m a s s effusion and
m a s s spectrometric techniques when the sample was contained in a singlecrystal tungsten crucible. There is reasonable agreement between the
measurements of the two groups of workers. Preference is given h e r e to
the values obtained by Ackermam and Rauh, because of their very careful
experimental techniques. Thus we have the following equation for liquid
zirconium :
log pzr(atm) = (-29 940
* 240) T-'
+ (6.541
* 0.080)
(T > 2134 K)
The vapour p r e s s u r e over the solid metal was computed a s
log pzr (atm) = (-30 810
* 240) T-' + (6.950 * 0.080)
(T < 2134 K)
Ackermam and Rauh suggest constant heat and entropy values for
zirconium in their temperature measurement range:
Le = 137.0 f 1.1 cal/g-at.
a, = 29.93
* 0.11 cal/K. g-at.
PART I.
THERMOCHEMICAL PROPERTIES
The vapour p r e s s u r e values measured by Ackermann and Rauh 1111
for liquid and solid zirconium were combined with the heat capacity equations
of a, 8, liquid and gas and with the heats and entropies of transformation
and fusion recommended in the present assessment. Thus the roomtemperature heat of sublimation of zirconium was calculated a s
L,,
2g8
= 143.67 kcal/g-at.
In Table 11, room-temperature heats of sublimation obtained by secondand third-law calculations a r e shown, measured by several workers and
compiled by Ackermann and Rauh 111 I.
2.
2.1.
ZIRCONIUM FLUORIDES
Zirconium di- and trifluoride
Murad and Hildebrand 1151 have studied the equilibria between gaseous
species over mixtures of CaF, + Z r held in a graphite Knudsen cell, using
a - m a s s spectrometer. The multiplier efficiencies and ionization crosssections used by these investigators in calculating absolute p r e s s u r e s a r e
not reported. Since ZrF4 does not ionize to give a parent ion, i t s intensity
was calculated by subtracting from the ion intensity of ZrFQ a t 17.5 eV the
contribution due to ZrF3, assuming a linear variation of intensity with
electron energy above threshold. F r o m the results, the Gibbs energy changes
for the following reactions can be calculated in the temperature range
1665 - 1745 K:
(Ca) + (ZrF4) -. (CaF) + (ZrF3)
(1)
Since the derived Gibbs energies scatter (f1200 cal), meaningful second-law
heats and entropies cannot be derived from these results. The standard
Gibbs energy changes a t 1700 K accompanying reactions (1) and (2) a r e :
Murad and Hildebrand 1151 have derived third-law heats of the
reactions (1) and (2) and have combined these with available information
on the heats of formation of (CaF) and (ZrF4) to obtain the heats of formation
of gaseous zirconium di- and trifluoride a t 298 K:
ALCOCK et a1.
2.2.
2.2.1.
Zirconium tetrafluoride
Allotropy
Solid zirconium tetrafluoride exists in four different allotropic modifications (0, @, 7 and a n amorphous form) 116 1. The cr, 7 and amorphous forms
transform irreversibly to the @-form a t 723-773 K. The transition temperat u r e for the cr (tetragonal) to @ (monoclinic) transition i s 72 3 K 117]. No
other information is available on the temperature ranges of stability of the
various forms o r on the heats of transformation.
2.2.2.
Heat capacity
Westrum 1181 has measured the heat capacity of solid ZrF4 from 5 to
307 K by adiabatic calorimetry. The heat capacity a t 298 K is
24.79 cal/K* mol. McDonald e t al. 1191, using a copper block drop calorimeter, have measured the heat capacity from 284 to 1225 K. Smith et al. [20]
employed a Bunsen ice calorimeter in their study of the heat capacity of
ZrF4 in the range 273-1150 K. The agreement between the two s e t s of hightemperature heat capacity measurements is poor. The crystal structures
of the samples used in the two studies have not been specified. It i s possible
that the measurements relate to two different allotropic forms. Since the
heat capacity measured by McDonald et al. a t 298 K (24.74 cal/K mol) i s
in good agreement and joins smoothly with the low-temperature heat capacity
measurements of Westrum, their data a r e selected f o r internal consistency.
The heat capacity of solid Z r s can be represented by the following equation:
2.2.3.
Standard entropy
The standard entropy a t 298 K of solid ZrF4 calculated from the calorimetric heat capacity measurements of Westrum i s 25.00 (k0.05) c a l / ~ ' m o l .
TABLE 111. VAPOUR PRESSURE OF ZIRCONIUM TETRAFLUORIDE
lnvutigaton
Technique
Flrcher [ 221
-
Flrcher et al. [ 231
Bell method
Senre et a1. [ 24.251
Transpiration
Cantor et a1. [261
Quasi-tatlc method
Galkln et PI. [271
Knudsen cell
Aklrhin et al. [281 and
Sldorov et al. [291
Knudsen cell, mass
spectrometer
Selected value
-
Temp, range
(K)
-r
PART I.
THERMOCHEMICAL PROPERTIES
-(K)
FIG. 1. Vapour prulurer of ZrF,, shown as a functlon of reciprocal temperature.
2.2.4.
Heat of formation
Greenberg et al. L21.1 have determined the heat of formation of solid
ZrF4 by fluorine bomb calorimetry:
The product of synthesis in the calorimeter was primarily 0-ZrF4.
2.2.5.
Heat of fusion
The heat capacity measurements of McDonald e t al. [191 show that the
melting point is 1 2 0 5 k 2 K and the heat of fusion is 15.35 (k0.15) kcal/mol.
14
2.2.6.
ALCOCK et a1.
Gibbs energy of formation
Direct measurements of the Gibbs energy of formation of solid ZrF,
are not available. The Gibbs energy of formation calculated from the
thermal data referred to above can be represented by the following equation:
A ~ ~ ( c a l / m o= l-455
)
440 + 77.0 T (f400)(300-1205 K ) .
The corresponding standard Gibbs energy of formation of liquid ZrF, is
2.2.7.
Vapour pressure
The vapour pressure measurements are summarized in Table I11 and
compared in Fig.1. Galkin et al. [271 used a-ZrF4 as the starting material.
Since the 8-phase is stable above 723 K , the a-phase presumably would
transform to the 8-phase during the vapour pressure measurements above
this temperature. The vapour pressure over the u-phase above 723 K would
be higher than true equilibrium pressure. The presence of the a-phase
probably explains the fact that the vapour pressures reported by Galkin et al.
are considerably higher than those of other investigators.
Akishin et al. [28] and Sidorov et al. [ 2 9 ] measured the vapour pressure
of 8-ZrF4 by following the time dependence of the ion intensity of ZrF3+ions
accompanying the complete evaporation of the material held in a graphite
Knudsen cell attached to a mass spectrometer. The absolute pressures
are calculated from the formula
where B = a J m , I' is the ion intensity. T is the absolute temperature
in K , V is the weight of ZrF, taken, a is the area of the Knudsen orifice,
R is the gas constant, M is the molecular weight and t represents time.
Sufficient information is not available to critically assess the accuracies
attainable by this technique. Akishin et al. [281 were able to detect ZrOF;
ions at 1300 K ; they estimate the partial pressure of ZrOFz as l o 9 torr at
this temperature.
'
Sense et al. L24.251 used a transpiration method. The vapour pressures
obtained by them are 10-30% lower than those obtained by static or quasistatic methods [22,23,261. This might be due to lack of saturation of the
inert gas with ZrF4 vapour. The two independent measurements using the
static method [22,231, and the measurements of Cantor et al. [ 2 6 ] using a
quasi-static method are in good agreement; the selected values are based
on these measurements. The heat of sublimation corresponding to the
selected values is 53 250 cal/mol and represents the average second-law
heat of sublimation obtained from all the experimental measurements in
the temperature range 650-1200 K. The selected values indicate a sublimation
temperature of 1177 f 5 K. Since this value is below the melting point.
PART I. THERMOCHEMICAL PROPERTIES
ZrF, sublimes before it melts.
formation a r e a s follows:
2.2.8.
15
The third-law heats of sublimation and
ZrF, in Zr-Na-F system
Sidorov et al. [30] carried out a mass-spectrometric study of the
ZrF4-NaF system. Apart from ZrF,, NaF and Na$, in the gas phase,
NaZrF, was found a s a mixed halide molecule. The calculated heat of dissociation for the reaction (NaZrF5)-. (NaF) + (ZrF, ) in the temperature
range 877-1167 K was
h
AH,,,,
= 62.2 f 4.6 kcal/mol
Estimating the heat capacities of gaseous ZrF,, NaF and N a Z r S ,
ACP = 2.5 c a l / K * mol is obtained; thus AHdlts., 298 = 60.6 kcal/mol.
3.
ZIRCONIUM CHLORIDES
3.1.
3.1.1.
Zirconium tetrachloride
Heat capacity
The heat capacity of solid ZrC1, was measured by Todd [31] from
53 to 297 K. Coughlin and King [32] measured the high-temperature heat
capacity from 336 to 567 K. By extrapolation of the results of Todd to 0 K,
the standard entropy of <ZrCl,> a t 298 K can be obtained a s 43.5 (f0.6)
cal/K-mol. The heat capacity of solid ZrCl, above 298 K can b e represented
by the following equation
3.1.2.
Heat, entropy and Gibbs energy of formation
Siemonsen and Siemonsen [331 measured the heat of formation of
< ~ r ~ la,s>-232.0 (f0.5) kcal/mol, by direct chlorination of the metal in
a n enamelled bomb calorimeter. Experimental details, purity of the
zirconium metal used, and analytical details a r e not fully discussed in their
publication s o that a critical assessment of their work is difficult.
Gross e t al. [34] obtained a value of -225.9 kcal/mol for the heat of reaction
of solid zirconium with liquid chlorine to form one mole of < ~ r ~ l , > .
A value of -234.7 (f0.4) kcal/mol may be calculated from these measureme@s for the standard heat of formation of <zrcl4>a t 298 K.
A m o r e detailed account of direct chlorination of high-purity zirconium
in a bomb calorimeter has been published by Gal'chenko et al. 1351. They
demonstrated by chemical analysis the completeness of the reaction and the
absence of lower chlorides of zirconium in the residues. Their value,
16
ALCOCK et a t
AH:^^
= -234.2 (k0.3) kcal/mol, is in good agreement with that of Gross
= -234.4 (k0.3) kcal/mol. The correset al. The selected value is
= -72.4 (k0.5) cal/K. mol,
ponding standard entropy of formation is
when the standard entropy of zirconium selected in this compilation is
combined with a value of sozg8
= 53.29 c a l / ~ . m o lfor (C12). The standard
Gibbs energy of formation of solid ZrC1, obtained from thermal data in
the temperature range 298-700 K can be represented by the following equation:
3.1.3.
AH^^^
AS^^^
Vapour p r e s s u r e
The vapour p r e s s u r e of ZrC1, has been measured by Palko e t al. [361
in the temperature range 480-750 K, using three different techniques:
the diaphragm method for the pressure range 10-1000 mmHg, the capillary
bridge method for the p r e s s u r e range 1000-9000 mmHg, and a molten-tin
manometer for p r e s s u r e s above 10 000 mmHg. Static vapour p r e s s u r e
methods have been used by Rahlfs and Fischer [371 (535-607 K), Nisellson
e t al. [38] (711-773 K), and Denisova e t al. [39, 401 (626-708 K). The vapour
p r e s s u r e s obtained in these investigations agree within k 15%. The leastmean-squares fit t o a l l the experimental data points gives the following
equations for the variation of the vapour p r e s s u r e with temperature:
< z r c 1 4 > : log p (mmHg) = -5409 T-' + 11.78
{ZrCl,):
log p (mmHg) = -3580 T-'
+ 9.21
C
*
(400-710 K)
(710-800 K)
<
The melting point of ~ r ~ 1 ,is) 710 K [36,37,391. The sublimation temperat u r e is 608 K. The liquid phase is therefore thermodynamically unstable.
The vapour p r e s s u r e equations given above, when combined with the heat
capacities and the estimated entropy of (ZrCl,), equal to 88 c a l / ~ . m o l ,
yield a third-law value of 26.5 (k0.3) kcal/mol for the standard heat of
sublimation a t 298 K. When the heat of sublimation is combined with the
heat of formation of solid ZrCl,, the standard heat of formation of gaseous
ZrC1, a t 298 K is -207.9 (k0.4) kcal/mol.
3.2.
Zirconium trichloride
Turnbull and Ways [41] determined the equilibrium p r e s s u r e s for the
reaction
in the temperature range 613-723 K, using a cooling curve modification
of the dew-point method,
log p (mmHg) = -6246 T-'
+ 11.632 (k0.05)
More recent work by Copley and Shelton [42], using a thermogravimetric
effusion method, indicates that in the range 388-573 K,<ZrC13> disproport i o n a t e ~a s follows:
>
6 <zrc13
-,
5<zrc12. 8> + (ZrClJ
log p (mmHg) = -6138
T-l
+ 12.29
c'
18
A K O C K et al.
-155 (f1.7) kcal/mol. Rahlfs and F i s c h e r [371 report 723 K a s the melting
point of < ~ r B r , > . Since the sublimation temperature i s lower than the
melting point, the liquid phase i s thermodynamically unstable.
4.2.
Zirconium di- and tribromide
Schlafer and Skoludek [46] have measured the p r e s s u r e of (ZrBr, )
over samples of < z r B r 3 in spiral quartz manometers. They assumed
that the disproportionation reaction was
>
There i s a considerable difference between the measured p r e s s u r e s at the
end of the disproportionation of each sample of ZrBr, and the pressure
calculated assuming the validity of the ideal gas laws. The deviation
increases with the weight of < z r ~ r , >
taken o r the pressure of (ZrBr,)
a t the end of disproportionation. This cannot be explained in t e r m s of
the non-ideal behaviour of (ZrBr,). Tsirelnikov [47] has suggested the
presence of ( Z r B r 3 ) above the product of disproportionation, which
explains the differences between measured and calculated p r e s s u r e s
adequately.
) 500 T-I
log K = log ( P ; , ~ , , / P ~ , ~=~-16
5.
+
22-58
ZIRCONIUM IODIDES
5.1.
Zirconium tetraiodide
5.1.1.
Heat capacity
The heat capacity of ZrI, has not been measured. Kelley [441 has
estimated the high-temperature heat capacity of solid ZrI,, which can be
represented by the following equation:
Cp (cal/K mol) = 26.3 + 12.3 X
T
The heat capacity of gaseous Zr14 has been estimated [441 a s 22 cal/K
5.1.2.
Heat of formation
Turnbull [45] has measured the heat changes associated with the
following reactions of Zr1,with alkaline solutions:
>
from reaction (1) i s
The standard heat of formation of < z ~ I , deduced
-115.6 f 0.8 kcal/mol, while the value obtained f r o m reaction (2) i s
.mol.
PART I. THERMOCHEMlCAL PROPERTIES
-SELEFTw
+
VALUE
I
lo3
FIG. 2. Vapour prururu of ZrI,. plotred against the reclpmcal temperature.
*
-116.3 0.8 kcal/mol. An average value of -115.9
selected for AH^^^.
5.1.3.
* 1.0 kcal/mol is
Vapour p r e s s u r e
Rahlfs and Fischer [371 measured the vapour p r e s s u r e of solid ZrII
in the temperature range 558-671 K, using a boiling-point method. Sale
and Shelton [481 measured the vapour p r e s s u r e using a nickel Knudsen
503 K. The calculated vapour
effusion cell in the temperature range 423
p r e s s u r e s were found to be dependent on the orifice size. The saturation
vapour p r e s s u r e s were deduced by extrapolating the measured p r e s s u r e s
to zero orifice area. The Zr14 used in this study was prepared by direct
-
20
ALCOCK et al.
synthesis and purified by sublimation. The results of the Knudsen and
boiling-point measurements a r e compared in Fig.2 with the selected value,
which can be represented by the following equation:
log p (mmHg) = -6280 T-'
+ 11.84
This corresponds to a sublimation temperature of 701 K, which i s below
the melting point, 772 K, reported by Rahlfs and Fischer [37]. The liquid
phase is therefore unstable a t unit atmospheric pressure. The secondlaw heat of sublimation of Zr14 is 28.73 kcal/mol. Because of a lack of
heat capacity data on ZrI,, an accurate third-law evaluation of the heat
of sublimation cannot be made.
Larsen and Leddy [49 1 have studied the reaction
from 473 to 973 K and a t 5 to 15 atm pressure and report data on fractional
reaction. The authors express doubt about the attainment of equilibrium.
These results have not been used to calculate the thermodynamic properties
of ( Z r h ) o r <zr13>.
Sale and Shelton [501 have shown that the disproportionation of < z ~ I , >
proceeds to the di-iodide via an intermediate phase:
1
2
log p (mmHg) = -8700 T-1 + 12.47
log p (mmHg) = -26 367 T-I
6.
+ 37.70
ZIRCONIUM-OXYGEN SYSTEM
The phase diagram of the Z r - 0 system published by Domagala and
McPherson [51] shows ZrOz a s the only stable solid compound. At high
temperatures, vapour species of both ZrO and ZrOz have been shown to
be present over condensed ZrOz. Phase.transitions and relevant temperatures in the Z r q system a r e shown in Fig.3 1521. The melting point of
ZrOz of near stoichiometric composition was found by Latta et al. 1531 to
be 2953 f 15 K.
6.1.
Zirconium-oxygen alloys and oxygen-deficient ZrQZ
The structure of the zirconium-oxygen system, up to 2 at.% oxygen,
has been studied by Holmberg and Dagerhamn 1541 who showed various degrees
of ordering in the solid solution.
Komarek and Silver [55] measured the oxygen activities in alloys of
oxygen and zirconium by equilibration with known partial pressures of
magnesium o r calcium and their respective oxides, making use of the Gibbs
energies of formation of MgO and CaO, respectively, in their calculations.
The partial molar Gibbs energy of oxygen in zirconium is obtained a s follows:
6
PART I.
-273
0
1W
21
THERMOCHEMlCAL PROPERTIES
3000
20a)
TEMPERATURE
4000
(OC
FIG.3. Schematic diagram of the effect of total external pressure
on the stable and the metastable phases of Z r q .
The equations of the f r e e energy of formation of MgO and CaO employed
in these measurements a r e a s follows:
Boureau and Gerdanian [561 measured the partial molar heat of solution
of oxygen in Z r - 0 alloys and in non-stoichiometric zirconia by means of
a Tian-Calvet microcalorimeter at 1300°C. Their results a r e in good agreement with the Z r - 0 phase diagram a t the low oxygen content end and they
found no change in the value of the partial heat of solution of oxygen a c r o s s
the a - Z r / Z r O z y phase boundary. In the oxygen-deficient region of Z r 0 2 ,
near the stoichiometric composition, the Gq curve has a maximum and a
minimum, which suggests that there a r e two different mechanisms of defect
accommodation in this oxide, each dominating at different defect concentrations. The values of the oxygen potential in Z r - 0 alloys measured by
Komarek and Silver [551 a r e combined with the partial heats of solution
determined by Boureau and Gerdanian [561 t o calculate the partial molar
entropy of solution of oxygen in this sytem and a r e shown in Table IV.
46
ALCOCK et al.
TABLE XIII. INTEGRAL PROPERTIES OF ZIRCONIUM
FOR THE Zr-H SYSTEM
xZr(a) +
N ~ r
16.3.
-
(H2)
ZrXH1?
A G (900 K)
(cal/g-at. )
AS
( c a l m . g-at.
)
Gibbs energy of formation
Numerous studies on the hydrogen pressures in equilibrium with solid
Zr-H alloys in the a-, P- and 6-phases, reported in the literature, a r e
summarized in Table X. Since the chemical potentials of hydrogen calculated from these measurements do not differ by more than 570, average
values have been derived for the chemical potential and the partial molar
heat of solution of hydrogen, giving greater weight to the results obtained
with purer materials. Several investigators have shown that oxygen in
the alloys has a significant effect on hydrogen solubility. The average
values were plotted a s a function of composition, and the chemical potentials
and partial molar heats of hydrogen were obtained from the smoothed curve
a t regular intervals of composition. The results a r e shown in Table XI.
Sievert's law i s obeyed by hydrogen in a - Z r alloys. Measurements
of McQuillan and Wallbank [1481 indicate that Sievert's law i s not obeyed
in dilute P-phase alloys in the temperature range 1150-1220 K. It i s
interesting to note (Fig.7) that the partial molar heat of solution of hydrogen
is found to become more negative in 8-phase alloys with increasing hydrogen
concentration.
The compatibility of the selected values with the phase diagram i s
demonstrated in Fig.8, where the composition dependence of the chemical
potential of hydrogen i s superimposed on the boundaries of the singlephase and two-phase regions at 900 K. The partial molar properties of
zirconium in Zr-H alloys obtained by Gibbs-Duhem integration a r e
summarized in Table XII. The calculated integral properties of zirconium
for the Zr-H system a r e shown in Table XIII.
Measurements of Morton and Stark [I411 indicate that the dissociation
pressure of deuterium in the Zr-D system i s higher by a factor of four
than the corresponding pressure in the Zr-H system a t 700 K. The secondlaw heats of solution of hydrogen and deuterium a r e the same within experimental e r r o r . The zirconium used by Morton and Stark contained 2 2.870
oxygen. More recent measurements by Ricca [1471, using purer materials
-
,
PART I.
THERMOCHEMICAL PROPERTIES
47
at 773 K and No =
to lom4,show that the pressures of deuterium and
hydrogen a r e the same (*lo/a). At higher temperatures (1150-1200 K),
McQuillan and Wallbank [1481 have shown that the partial Gibbs energy of
deuterium i s more negative by 4 to 6 kcal/g-at. for ND = 3 X
to 0.5
than the partial Gibbs energy of hydrogen a t equivalent compositions. In
view of the apparent discrepancy in the information now available, values
for the Zr-D system a r e not tabulated.
17. Zr-X-H SYSTEMS
Katz and B e r g e r [1491 have measured the composition dependence of
the hydrogen pressure in four alloys, ZrHfoe3,ZrHfo.5, ZrHfie4 and ZrHf4.,,,
in the range 0-60 at.% H and a t 773 - 1173 K. Their results indicate
significant deviations from Sievert's law for dilute alloys and do not extrapolate through zero, indicating the absorption of hydrogen a t defect sites
like dislocations and pores. The addition of hafnium appears to increase
the activity coefficient of hydrogen in a-Zr. Since corrections for hydrogen
interaction with the defect structure cannot be estimated from the reported
data, meaningful thermodynamic information cannot be derived from them.
17.2. Zr2Cu-H, ZrCrz-H, ZrV2-H, Z%Ni-H and ZrMq-H
Pebler and Gulbransen [150, 1511 have measured the composition
dependence of the hydrogen pressure in some intermetallic compounds of
zirconium. They classify the intermetallic compounds into four categories,
based on the nature of their reaction with hydrogen:
(a) The intermetallic compound (e.g. Zr2Cu) decomposes after forming
a saturated solid solution of hydrogen, resulting in a mixture of zirconium
hydride and a zirconium-deficient intermetallic compound. In the c a s e of
the Zr-Cu-H system, the composition and structure of the zirconiumdeficient phase a r e unknown. At N,/N,,
+ Nc, = 0.62, a l l the Zr2Cu i s
consumed by the reaction.
(b) The intermetallic compound forms a ternary hydride phase after
being saturated with hydrogen (e.g. ZrNiH o r ZrN%) [152].
(c) The intermetallic compound absorbs l a r g e amounts of hydrogen
without any change in crystal structure. The Laves-type phases ZrCr2,
ZrV2 and ZrMo2 belong to this group.
(d) The intermetallic compound neither dissolves, nor reacts with,
hydrogen (e.g. ZrFe2, ZrCo2).
Pebler and Gulbransen [150,15 11 have corrected their data f o r the
initial absorption of hydrogen by defects in the lattice of the intermetallic
compound to obtain the t r u e solubility of hydrogen. The corrected values
show that Sievert's law i s obeyed in the a-phase alloys:
48
ALCOCK e t al.
TABLE XIV. THERMODYNAMIC DATA FOR (r-SOLID SOLUTIONS OF
HYDROGEN IN INTERMETALLIC COMPOUNDS OF ZIRCONIUM
Intermetallic
compound
AHH
(kcal/g-at. )
ASH
AGH. 773 K
Temperature
(cal/K - g - a t . )
(kcal/g-at. )
(K)
Composition
range
(at. 70H)
where p ~ i, s the hydrogen pressure in atrn, kH is the Sievert's law constant,
AGH, ASH and AHH a r e the Gibbs energy, entropy and enthalpy of solution
) the intermetallic compound. The chemical potential of hydrogen
of $ ( H ~ in
over the alloys is related to AGH by the relation
The infinitely dilute solution i s chosen a s the reference state such that the
activity of hydrogen equals its mole fraction (NH). F r o m the variation of
the Sievert's law constant with temperature, the partial enthalpy and entropy
of solution of hydrogen in the intermetallic compound were calculated.
The value for AHH and ASH obtained from the measurements of Pebler
.
respectively,
and Gulbransen [150] in 0-Zr a r e -14.4 and - 13.8 c a l / ~ g-at.,
which compare with the values of 13.75 and 13.13 cal/K g-at. selected
in this compilation. F o r the sake of internal consistency, the values of
AHH and ASH calculated from the measurements have been normalized
using the selected values for the Zr-H system. The normalized values
a r e shown in Table XIV, along with the temperature range of measurement
and the composition range in which Sievert's law is obeyed.
-
-
<
18. BINARY ALLOY SYSTEMS WITH ZIRCONIUM
The binary alloys of zirconium have not been studied extensively. In
some cases, the solubilities have been determined a t a few temperatures
only. T h e r e a r e also several systems which were subjected to wider thermodynamic investigations. In this section, the available solubility data and
other thermodynamic information a r e compiled f o r the following systems:
PART I.
THERMOCHEMICAL PROPERTIES
49
Zr-Al: Gibbs energies and heats of formation of three Al-Zr intermetallic
compounds
Zr-Bi:
Partial molar Gibbs energies of solution of zirconium in liquid
bismuth
Zr-Cd:
Partial molar Gibbs energies of solution of cadmium in zirconium
Zr-Fe:
Gibbs energy of formation of Fe2Zr
Zr-Ga:
Gibbs energy of formation of ZrGa,
Zr-Mg: Solubility of zirconium in liquid magnesium
Zr-Na:
Solubility of zirconium in liquid sodium
Zr-Ni: Activity coefficient of zirconium in liquid nickel
Zr-Pt:
Gibbs energy and heat of formation of ZrPt,
Z r - r a r e earth metals: Heats of solution
Zr-Ti:
Activity coefficient of titanium in liquid zirconium
Zr-Zn:
Gibbs energies of formation of Zr-Zn compounds
18.1.
Zirconium-aluminium svstem
The Gibbs energies of formation of some of the intermetallic compounds
in the systems Zr-Fe and Zr-A1 were calculated from the solubility products,
which were determined by means of liquid magnesium solution calorimetry
by Schneider e t al. [1531. They calculated the Gibbs energies of formation
from the elements of three Zr-A1 intermetallic compounds; these were
measured a t one temperature only (740°C):
Argent and P e r r y [1541 determined the heats of formation of zirconium
aluminides using the small furnace calorimeter of Kubaschewski and Dench.
Their measurements can be summarized a s follows:
Compound
18.2.
AH1,,,
(kcallg-at.)
Remarks
'ZrAl,'
-10.6 f 0.4
not quite homogeneous
ZrA12
-10.6 f 0.4
homogeneous
'Zr2A131
-7.4
not homogeneous
Zirconium-bismuth system
The solubility of zirconium in bismuth a t 973 K was measured by
Wiswall and Egan [155 1. The activity of zirconium in a dilute {Zr-Bi)
solution was determined by measuring the emf of a zirconium concentration
T A B L E XV.
VAPOUR P R E S S U R E AND R E L A T I V E P A R T I A L MOLAR F R E E E N E R G Y O F
CADMIUM I N Z r - C d ALLOYS
A
~
C
~
in B-Zr
(cal/g-at.)
15.4
11.0
8.227
7.545
- 5720 T - I
- 21.695T
+453
8.040
+ 5.751 T logT
- 6340
7.654 - 6200 T-'
7.918
7.410
3.0
6.915
2.1
7.150
1.0
5.690
- 6000 T - I
- 5660 T-'
- 6150 T-'
- 4800 T-'
- 6250 T'
+ 5.751TlogT
7.5
5.0
- 6310 T-'
-828
- 22.312T
+I27
- 24.577 T + 5.751 T log T
7.227
-1514
- 23.502 T + 5.751 T logT
7.168
+4662
- 30.181 T + 5.751 T log T
6.880
T-I
- 5960 T-1
- 6100 T-'
- 6100 T-I
- 18.575 T + 5.751 Tlog T
-1972 - 19.430 T + 5.751 T log T
-2384 - 19.988 T + 5.751 T log T
-2246
- 21.196 T + 5.751 T log T
- 23: 150T + 5.751 T log T
Temp. range of
transformation
(K)
1158-1166
R
.=
E
1152-1160
-645
1150-1162
- 23.419T + 5.751 T log T
-1286 - 24.737 T + 5.751 Tlog T
-
1167-1173
1165-1170
-1743
-1286
k
1149-1160
1147-1160
PART I.
51
THERMOCHEMICAL PROPERTIES
cell with a NaF.ZrF4 electrolyte, a t 973 K. Their results a r e summarized
below:
%I
= RT log azr
(kcal/mol)
log azr
in {Bi)
RT log 7
= A
(kcal/mol)
0.0015
-20.85
-4.68
-8.28
0.0040
-19.65
-4.41
-8.75
0.0064
-18.45
-4.15
-8.53
0.0194
-16.61
-3.73
-8.80
0.0220
-15.59
-3.50
-8.01
G~,
Mean -8.47
The measurements indicate that Henry's law i s obeyed up to a t least
2 at.70 of zirconium in solution, with the mean value of the activity coefficient
The partial molar heat of solution of zirconium in bismuth
y = 1.05 X
in this concentration range and around 973 K i s -8.6 f 0.4 kcal/mol.
18.3. Zirconium-cadmium svstem
The properties of the zirconium-rich section of the Zr-Cd system were
studied by F r y e et al. [1561. The cadmium vapour p r e s s u r e over Zr-Cd
alloys of various composition was determined by the dew-point method.
/3 transformation
These authors also investigated the extent to which the a
of zirconium is affected by the cadmium solid solution in the alloy.
Table XV shows the cadmium vapour p r e s s u r e s measured by F r y e e t al.
and the relative partial molar Gibbs energy of cadmium in the alloy calculated therefrom. The value of the vapour pressure over pure liquid
cadmium used in the calculation was compiled by Kubaschewski e t al. [120].
The a//3 transformation temperature ranges observed in the course of the
vapour pressure measurements differ by about 10 degC from those reported
in the phase diagram of Zr-Cd.
*
18.4 Zirconium-iron system
Schneider et al. [I531 measured the Gibbs energy of formation of Fe,Zr
in their liquid magnesium calorimetry studies. It is described by the
equation: A G O (cal/mol) = -17 700 5.2 T (1023 K).
The activity coefficient of iron in liquid zirconium was determined a t
only one temperature by Peyzulayev e t al. [1571 by means of the Langmuir
f r e e evaporation method a s applied to spherical surfaces. The measurements were taken at 2475 K, and the concentration of iron in liquid zirconium
was 0.16 at.70 and 1.62 at.70. The mean activity coefficient found was a s
follows:
-
yFe = 0.15 f 0.04 for 0.16 at.70 F e
yFe = 0.23 f 0.04 for 1.62 at.% F e
55
THERMCCHEMICAL PROPERTIES
PART I.
TABLE XVI. VAPOUR PRESSURE OF ZINC OVER Zn-Zr ALLOYS
log pZn (aun) = a ~ -+' c
Temp. range
Phases in equilibrium
a
c
(K)
-12 918
9.603
800-1180
ZrZn,
ZrZb
-8 440
6.401
940-1225
ZrZn,.
ZrZn,
-8792
7.053
900-1200
ZrZn,. Z ~ Z Q
-7448
6.488
650-1200
Z ~ Z Q . ZrZn,,
-7 171
6.441
750-820
Zr. ZrZn
18.11. Zirconium-titanium system
Peyzulayev e t al. [I571 measured the activity coefficient of titanium
in liquid zirconium a t 2475 K by the Langmuir f r e e evaporation method.
The titanium concentration in zirconium was 1.89 at.% and 0.19 at.%,
respectively. They found nearly ideal behaviour with the mean activity
~ , ) 0.19.
coefficient for [ ~ i ] ~= 0.92
*
18.12. Zirconium-zinc svstem
The thermodynamic properties of the zirconium-zinc system were
studied by Chiotti and Kilp [165] employing the dew-point method and the
Knudsen cell technique. The temperature range investigated was 750-1225 K.
Combining the measured zinc vapour pressures over the two phase equilibria
with the standard Gibbs energy of vaporization of zinc, given by Kelley [44],
the standard Gibbs energies of formation of the intermetallic compounds of
zinc and zirconium were calculated. Constants for the equations describing
vapour p r e s s u r e and o,ther thermodynamic quantities a r e given in Tables XVI
and XVII. The authors claim an e r r o r limit of rt500 cal on the Gibbs energy
values.
19. TERNARY ZIRCONIUM SYSTEMS
19.la.
Zirconium
+ iron + oxygen
Buzek and Hutla [1661 measured the effect of zirconium addition on
dissolved oxygen in molten iron. The measurements were carried out at
1800°C in an atmosphere of argon, and the zirconium content was varied
between 0.007% and 1.55%. An average value for the interaction coefficient
= -800 (f300).
is
€8
19.lb.
Zirconium
+ iron + nitroeen
Evans and Pehlke [77] have measured the effect of zirconium on the
solubility and activity coefficient of nitrogen in liquid iron a t 1600°C. F r o m
their measurements the first- and second-order interaction parameters
= a2 1nyN/a~2Zr
= 145.
may be calculated: c$ = alnyN/aNZr= -240;
pir
T A B L E XVII.
THERMODYNAMIC FUNCTIONS F O R T H E REACTION < ~ r+)x {Zn) -. < Z r ~ n , >
AGO
(cal/mol) = A
Compound
ZrZs
A
B
ZrZn
-28 198
-1.096
+ BT + DTlog T + E'?
A@ (calfmol) = A + BT+ E T ~
.
E x lo4
A
B
6.03
2.75
-28 198
-2.62
D
E X lO'
-2.75
AS' (cal/K. mol) = A
A
-1.524
-5.5 x l o - d
-6.030
x
x
-12.060
-35 909
-16.842
12.06
5. 50
-35 909
-5.24
-5.50
11.60
-11. 0
ZrZn,
-45 231
-29.605
18.09
8.25
-45 230
-7.86
-8.25
21.745
-16.5
-15.72
-16.50
-36.68
-38.50
-54749
-75.646
36.18
16.50
-54 749
ZrZn14
-69 993
-200.150
84.42
38.50
-69 990
59.926
163.47
c
B
Zr Zn,
Zr Zn,
+ BT + C l o g T
10-
-18.09
-33. 0 x lo-d
-36.18
-77. 0 x lo-d
-84.42
PART I.
57
THERMOCHEMICAL PROPERTIES
TABLE XVIII. PARTIAL MOLAR F R E E ENERGIES, E N T H A L P E S AND
ENTROPIES OF SOLUTION OF OXYGEN IN UyZrlyOz+, at 1250 K
Y
x
(kcal/mol)
(kcal/mol)
( c a l m . mol)
( c a l k mol)
58
ALCOCK e t al.
19. lc. Zirconium + iron + s d ~ h u r
Banya and Chipman [l66a] have measured the effect of zirconium on
the activity coefficient of sulphur in liquid iron a t 1600°C. The results may
= -20.
be expressed a s
19.ld.
Zirconium
+ nickel + nitrogen
The effect of zirconium on the activity coefficient of nitrogen dissolved
in liquid nickel at 1600°C can be obtained from the solubility measurements
= -90;
= 50.
of Tripolitov et al. [161b] :
&
19.2. Double oxides with zirconia
19.2.1.
Li20.Zr02, and oxide of alkaline earth metals + Z r 9
Kubaschewski [167] in his assessment of the properties of double
oxides gives the heats of formation of the alkaline earth metal-zirconium
double oxides formed from the oxides, based on calorimetric work by
Lvova and Feodosev [168]. The values of estimated entropy contents a r e
also listed.
AH^^^ (kcalfmol)
sig8( c ~ / K m0l)
.
LiQ.Zr02
-15.2 f 1.5
21.9 f 2.0 (estim.)
Ca0.Zr02
-7.3 f 2.0
22.4 f 2.0 (estim.)
Sr0.Zr02
-17.8 f 2.5
26.0 f 2.0 (estim.)
BaO. Z r 0 2
-28.6 f 2.5
TABLE XM. HEATS OF FORMATION OF RARE-EARTH ZIRCONATES
Structure
Zirconate
tYPe
Pymchlore
x
Fluorite
Pyrochlore
Pyrochlore
Pyrochlore
Fluorfte
Fluorite
Fluorfte
Pyrochlore
(kcal/mol)
(from oxides)
-&Il,
- A @ , (kcal/mol)
(from elements)
PART I.
THERMOCHEMICAL PROPERTIES
59
The thermodynamic properties of urania-zirconia solid solutions were
measured by Aronson and Clayton [1691 by means of high-temperature emf
measurements. These authors estimate the limits of solid solubility a t
13 molo/o zirconia, based on e a r l i e r studies, but state that Zr0,-UO, solid
solutions of much higher zirconia content (=30 mol%) a r e metastable when
quenched from 1700°C, with no phase segregation appearing, even after
prolonged heating a t 1000°C. The partial molar quantities were determined
for UyZrly02+, These compounds were prepared from powdered oxides
a t T > 1700°C in hydrogen and then equilibrated a t 800°C in a controlled O2
atmosphere to dissolve the required excess oxygen. The results a r e shown
in Table XVIII. Aronson and Clayton proposed a model in which the excess
oxygen ions take random interstitial positions and th_e us+ions a r e distributed
randomly. The partial molar entropy of solution, ASq, based on this model,
then incorporates the configurational entropies of 012,;and u5+and the
vibrational entropies :
The value of Q, according to this model, i s expected to be reasonably constant
'
for a given U:Zr = y:(l-y) and independent of the amount of excess oxygen
present. However, when plotting Q ( c a l / K W
mol) versus x, curves with a
minimum around x = 0.08 a r e obtained instead of a straight line. Later
experiments by W i l l i s [1701 on UOz+xshow the formation of groups
of defects within the U02 matrix. It is probable that similar defect i n t e r
actions occur in the UyZrl- 02+xsystem,thus invalidating Aronson and
Clayton's model for the calculation of contributors to the partial molar
entropy of solution of oxygen.
19.3.
Rare-earth zirconates and CaZrOg
The heats of formation of rare-earth zirconates were determined by
Korneev e t al. [I711 from zirconium and the respective rare-earth oxide
by combustion in an oxygen bomb calorimeter. They also determined a
value for the heat of formation of CaZrO, which is in good agreement with
that of Lvova and Feodosev [168]. However, their value for the heat of
formation of ZrOz is more than one kcal below the value recommended in
the present assessment. The heats of formation a s determined by
Korneev et al. a r e given in Table XM. The heats of formation, standard
entropy and other important thermochemical values (where available) of
all the compounds discussed in this assessment a r e listed in Table XX.
TABLE
n.
SUMMARY O F THERMOCHEMICAL VALUES OF ZIRCONIUM AND ITS COMPOUNDS
,:s
( d K mol)
TrdounaUon
temperature
AHt
Melting
point a
(K)
!cal/mol)
(K)
PART I.
THERMOCHEMICAL PROERTIES
62
ALCOCK e t al.
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111
121
131
141
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