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Density, thermal expansion of stainless steel and interfacial properties of UO2-stainless steel above 1690 K
Journal of Nuclear Materials 82 (1979) 172-178 o North-Ho~and Publish~g Company
DENSITY, THERMAL EXPANSION OF STAINLESS STEEL AND INTERFACIAL PROPERTIES OF UOz -STAINLESS STEEL ABOVE 1690 K P. NIKOLOPOULOS * and B. SCHULZ Ke~~~or~c~~~g~ze~~~~ Kurismhe, Institut fiir MateriaC und Festk~rperfors~hu~g,
Postfoch 3640,
7500 Kmlsmhe,
Fed, Rep. ~e~mun~
Received 13 November 1978
The sessile drop method was used for the determination of the density in liquid state. The results for stainless steel 1.4970 using uranium dioxide as substrate material in the temperature range 1690 K (liquidus temperature Tl) < T < 2120 K are p = 6.82 X lo3 - 10.25 x lo-’ (7’TI) kg/m3, and Q = 1.50 X 10-4K-‘. Below 1690 K the linear thermal expansion is given by Al/lo = 0.00204 + 7.1 lo X 10m6 T + 7.734 X 10d9 T2. Using the same method but not correlated with the density measurements the following interfacial properties of the system UO2 -stainless steel have been determined: surface energy of liquid steel ybv = 1.19 - 0.57 X 1O-3 (T- Tl) J/m2 and interfacial energy of liquid steel against UOz 7s~ = I.57 - 2.01 X 10e3 (T - Tl) J/m4 the results yield a contact angle e = 0” at T= 2515 K. Usingliterature data for the compressibility of liquid U02, an estimate of the surface energy of IJO in liquid state was performed. The estimated value at the melting point is: T~V = 0.522 J/m*. The mean value of the experimental data given by several authors is 0.513 f 0.085 J/m2. The estimated temperature dependence of the surface energy of liquid UO2 is given by dvbv/dT = -0.19 X 10m3 Jfm2.
1. Introduction
function of temperature in the liquid and solid state, and to use these data in the nuclear safety analysis of core meltdown accidents. In the case of two immiscible melts the density of the two liquids is of interest for considerations of the thermohydraulic behaviour of the core melts because of possible segregation and formation of layers,
Surface and interfacial properties are of basic interest for the theoretical treatment of a number of phenomena in two phase or multiphase materials, e.g., their strength, and problems related with powder metallurgy preparation technique. A further range of interest developed with the extension of nuclear safety analysis to hypothetical core meltdown accidents in the past years. Regarding the high temperatures under accident conditions, knowledge of materials properties is needed, especially in the liquid state. In the field of liquid metal fast breeders, the materials of interest are UOz, a representative for the real mixed oxide fuel, and stainless steel, especially I .4970. Up to now, experiments on the structure of core melts in LMFBR [I] do not indicate an interaction of these materials even at temperatures above the melting point of ur~ium dioxide. Thus, it is justified to measure or estimate the physical properties of components, as a
2. Density measurements Well established methods for liquid densitometry are the Archimedean, pyknometric and pressure methods [2]. In lieu of these, the apparatus which was constructed for contact angle measurements [3] was calibrated for liquid densitometry (fig. 1). 2.1. Experimental procedure Using a graphite susceptor, samples on the substrate material were heated to the desired temperature. The exis of the tube was used to photograph the sample as well as to measure the temperature by optical pyro-
* University of Patras, Institute of Physical Metailurgy, Greece. 172
173
P. Nikolopoulos, B. Schulz /Properties of U02-SS above 1690 K
pyrometer ›-
Silica tube 2. Guide sleeves 3 Pyrex-window G inductive heating coil 5. Graphite Susreptor 6. Graphite plate 7. Substrat material 8. Metal drop 9. Molybdenum -shielding 10. Molybdenum -pins
h Vacuum equipment
Fig. 1. Scheme of the apparatus for contact angle and density measurements.
metry. The temperature was measured in a bore of the graphite plate (ratio of diameter: depth = 1 : 4) simulating black body radiation. The pyrometer was adjusted to the melting points of gold, copper, iron, nickel, cobalt and platinum. The general uncertainty of the temperature measurements is +20 K. The atmosphere was highly purified argon (99.999). The density of the material in liquid state was determined by weighing the sample at the beginning of the experiment and measuring the volume of the droplet. The experiments were carried out within short times to avoid evaporation losses. As is well known from contact angle measurements, the molten droplet on a substrate material is deformed by the influence of gravity from a sphere to a spheroid. This deformation is negligible if the masses used (no more than 0.5 g) are small. The determination of the volume was always done on the assumption that the droplet is part of a sphere. This was proved by the measurement of the distances 2a, h and of the projected area F (fig. 2).
Only negligible (-0.6%) deviation from a sphere give good agreements in calculating the projected area F by using 2u and h. In the case of nonwetting behaviour, i.e. contact angle >f~, the assumption was verified in using the relationships for spheroids [4]. The dimensions were taken from photo negatives with a Guinier viewer (Fa. Enraf Nonius) and calculated to the real size by using an optical standard (Fa. Zeiss). The depth in the focus of the optical system is
droplet
Fig. 2. Quantities for the determination the droplet and contact angle 8.
i
of the volume V of
P. Nikolopoulos,
174
B. Schulz /Properties
of UOz-SS
above 1690 K
Table 1 Chemical analysis of materials used uo2
O/U < 2.005 Al 8-10 ppm Cr S-10 cu 1 Fe 20-30 Mn S-10 Si50 Sn 10 (max)
Fe (wt%)
cu
c 0.007 Si < 0.01 P 0.02 S 0.018 Cr 0.007 N 0.01 02 0.07
a)
02 0.12
Ni
co
Ey}SOO ppm
b,
02
02
10 wm
Ni 5 (max) w5 Mg 5 MO2-3
0.19
AU
Pt
1.4970 ss (wt%)
99.999
99.999
c 0.095 Si 0.52 Mn 1.90 P 0.009 S 0.008 v 0.04 Cr 16.0 Ni 14.97 MO 1.15 Ti 0.57 B 0.0061 co 0.02 N 0.01 02 0.01
a) Impurities < 0.1 wt%. b, Impurities < 0.06 wt%.
the true limitation for the accuracy of the density measurements, which was determined as the standard deviation of + 3%. 2.2. Chemical composition of the materials The results of the chemical analysis of all materials used in this work is given in table 1. The droplets of the stainless steel were chemically analyzed especially with respect to a change in oxygen content and possible diffusion of uranium. The penetration of uranium was less than 0.1 wt%, while no change in oxygen content could be observed.
ment of the density and thermal expansion of the steel in liquid state was carried out yielding the results (fig. 5): - density at liquidus temperature 1690 K: 6.82 X lo3 kg/m3; - slope of the temperature function: -10.25 X10-l kg/m3 . K; - thermal expansion coefficient: t1.50 X 10e4 K-r. The temperature dependence can be compared with those on some iron-chromium-nickel melts [lo] (table 3). The comparison gives reasonable agreement.
2.3. Calibration and results To assure the correctness of the measurements of the dimensions, first the linear thermal expansion of stainless steel 1.4970 in the solid state was measured and compared with results using push-rod dilatometry with gold standards for calibration. The data are shown in fig. 3. As can be seen, the results of both methods agree well and complement each other. In liquid state the apparatus was calibrated with iron and copper (fig. 4 and table 2). The results agree with literature data regarding the standard deviation of the method. Thus the measure-
Fig. 3. Linear thermal expansion of solid stainless steel 1.4970.
175
P. Nikolopoulos, B. Schulz /Properties of UO2-SS above 1690 K Table 2 Comparison of the density measurements for iron and copper with literature data
Density at melting point PT1 kdm3)
cu
Fe
7.99 x lo3 [6] 8.10 x 103
7.01 7.23 7.04 6.85 1.20 1.72 2.08 1.58
Thermal expansion coefficient CY = -(l/pT$dp/dT)(K-‘1 T> T1
Table 3 Temperature dependence of the density of Fe-Cr-Ni [lo] compared to that of stainless steel 1.4970
x x x x x x x x
103 [7] lo3 [8] 10” [9] 103 104 (71 lo4 [8] lo4 [9] lo4
melts
-dp/dT &g/m3 * K)
Melt composition (wt%)
E
Cr
Ni
19.75 19.92 13.5 ss 1.4970
9.74 19.50 10.50
jj -S
-9 -13 -9 10.25
x x x X
10-l [lo] 10-l [lo] 10-l [lo] 10-l
7.6 t
1200
1300
1100
1500
1600
17w
1000
1900
2000
2100
Fig. 5. Density of stainless steel 1.4970 versus temperature.
3. Surface and interfacial energy I Kirshenbaum,CahiU 1962. IILucas
IIIBcnedacks
1960 lI 01
1930.
Nthtswork
6.6.
' a ' ' ' ' 1600 (900 2000 2100 2200 2300 TIKl -
' ' ZLOO 2500
Fig. 4. Density of liquid iron versus temperature.
As mentioned above, the apparatus used for these experiments was the same as for density measurements. The whole method, its problems and limitations is discussed in detail in [3]. Cylindrical samples of SS 1.4970 were used and molten on the substrate material uranium dioxide. Under the influence of gravity, the liquid phase forms a spheroid which cannot be assumed to be a sphere when determining the surface energy. Using the method described in [4] (determination of the maximum diameter) and tabulated data [5], the shape (p) and size (b) of the spheroid can be determined. From this it follows:
P. Nikolopoulos,
176
B. Schulz /Properties
of UOz-SS above 1690 K
Table 4 Contact angle (e), surface energy (7~“) of liquid steel and work of adhesion (Wa) in the system liquid steel-UOz T
I9
YLV
w, =
(W
(<)
(J/m*)
(J/m*)
1690 1840 1930
124.0 110.2 104.0
1.19 1.12 1.05
0.525 0.733 0.796
YLV(l + cos 0)
where p = density, g = acceleration due to gravity. This method is restricted to contact angles >90”. 3.1. Contact angles and surface energy of SS 1.4970 In the temperature range investigated, the following data were obtained (table 4). From this, one gets a linear relationship for the surface energy: yLv = 1.19 - 0.57 X 10V3 (T-
Tt)J/m*
,
with slope dyLv = -0.57 dT
TCKI +
Fig. 6. Surface energy (~Lv) of stainless steel 1.4970 and interfacial energy (7s~) of stainless steel - UOz.
Applying the Young equation
ysv = ysL
+ yLv
cose
(2)
1
one can determine the interfacial energy ys~ between stainless steel 1.4970 and uranium dioxide. It follows ys~ = 1.57 - 2.01 X low3 (T-
X 10T3 J/m* . K .
These data can be compared to those of Ahmad and Murr [ 1 l] measured in hydrogen atmosphere for SS 304 on Al2 0s as substrate material. They obtain (by a true analysis of their results): yLv=1.172-8.24X
10V3(T-
Tt)J/m*,
1748
dioxide is well
[T] = K .
T,)J/m*
.
From this, a total wetting (0 = 0) of uranium dioxide by the steel occurs at 25 15 K. Fig. 6 shows the results together with the surface energy of liquid steel. 3.3. Surface energy of liquid uranium dioxide With respect to the possible high temperature in LMFBR-core meltdown accidents, the surface energy of liquid uranium dioxide is of some interest. Its value at the melting point in liquid state is known [13-l 51, the mean of all data yield of: yLv = 0.513 f 0.085 J/m* Keeping in mind that the bonds in uranium dioxide are dominated by an ionic character [ 161, one can try to estimate the surface energy of liquid U02. The theory of the physical behaviour of ionic liquids was developed by Ftirth [17] and experimentally verified by Bockris and Richards [ 181, There the isothermal compressibility Kil in liquid state is given by: f
0.37
Kil
= Kf
Kis
.
Kis
being the compressibility
(3) in solid state at the
P. Nikolopoulos.
B. Schulz /Properties
of W-SS
melting point and K; a term due to the creation of holes in liquid state during melting. The volume of a hole ut, is given by:
177
above 1690 K
3.9
t ”
[ 171 ,
uh = 0.68(kT/yL”)“a
(4)
38.
,t E
(k = Boltmann’s
u
constant)
#
and the number of holes Nn by:
(5) (AV
=
increase in volume at the melting point).
In eq. (3). the term K; is correlated with the volume and the number of holes in the following way: 9 !!!& “’ = 14 kTVTS
[I)31
36 -
‘k-
(6)
3ioo --OL90
3150 1 tK1
-
Fig. 7. Measured compressibility and estimated surface energy of liquid UO2.
temperature
,
( VTS = molar volume at the melting point). Combining
31-
=e
dependence
d-n.v = -0.19 dT
(fig. 7) is given by:
X 10e3 J/m2 . K.
eqs. (4).-(6) 4. Conclusion 0.68
With the experimental results of the compressibility at the melting point in the solid and in the liquid state [ 191, of can be calculated. All data used are given in table 5, the solid state compressibility was obtained according to Kis = 3( I - 2V)/E,
(8)
v = Poisson’s ratio, E = Young’s modulus. The data for Young’s modulus and Poisson’s ratio were taken from [20]. As can be seen, the estimated value at the melting point is in good agreement with the measured one. The
In the system U02-stainless steel 1.4970, the following properties have been determined. (1) The linear thermal expansion of solid stainless steel I .4970. (A&) = 0.002o4 + 7.11 e X I 0e6 T t 7.734 X lO-9 T2 (2) Density of’liquid steel I .4970. p = 6.82 X 1O3 10.25 X IO-’ (T - T,) kg/m3; T, = 1690 K. (3) Surface energy of liquid steel. yLv = I .19 0.57 X 10s3 (T - T,) J/m2. (4) lnterfacial energy in the system U02-stainless steel 1.4970. ysL = 1.57 - 2.01 X 1O-3 (T - Tl) J/m’. (5) Surface energy of liquid U02 (estimated). yLv = 0.522 - 0.19 X low3 (T- Tt)J/m’; T, = 3125 K.
Table 5
Used data for the calculation of the surface energy of liquid UO2 T
Kis x
W
(m’/N)
10”
A VI VTS
Ki x
10”
(m’/N)
Kl x 10” (m2/N)
‘YLV (J/m’)
TLV (J/m’) measured
3125 3175 3225
0.72
0.136
I211
3.54 3.64 3.79
3.27 3.37 3.52
0.521 0.514 0.502
0.513 [13-151
178
P. Nikolopoulos,
B. Schulz /Properties
Aknowledgements The authors are obliged to the Analytical Chemistry Group for carrying out the chemical analyses. J. Biirkin assisted with interest in performing the experiments.
References [ 1 ] B. Schulz, Kernforschungszentrum Karlsruhe Report KfK 127712 (1977) 123-21. [ 21 J.L. White, Physicochemical Measurements at High Temperatures, eds. J.O’M. Bockris, J.L. White and J.D. Mackenzie (Butterworth, London, 1959) p. 193. [ 3 ] P. Nikopoulos, Kernforschungszentrum Karlsruhe Report KfK 2038 (1974) und Dissertation, UniversitLt Karlsruhe (1974). [4] L. Zagar and W. Bernhardt, Forschungsberichte des Landes N.R.W. Nr. 1733. [5] F. Bashfort and S.C. Adams, An attempt to test the theories of capillary actions (University Press, Cambridge, 1883). [6] B.C. Allen, Liquid Metals, ed. S.Z. Beer (Dekker, New York, 1972) p. 161.
of UOz-SS
above 1690 K
[ 71 A.D. Kirshenbaun and J.A. Cahill, Trans. AIME 224 (1962) 816. [S] C. Benedicks, N. Ericson and G. Ericson. Archiv Eisenhiittenwesen 3 (1930) 473. 191 L.D. Lucas, Compt. Rend. 250 (1960) 1850. [lOI P.P. Arsentb and B.G. Vinogradov, Steel in the USSR 5 (1975) 145. IllI U.M. Ahmad and L.E. Murr, J. Mat. Sci. 11 (1976) 224. [121 P. Nikolopoulos, S. Nazare and F. Thiimmler, J. Nucl. Mat. 71 (1977) 89. 1131 J.L. Bates, C.E. McNeilly and J.J. Rasmussen, Mat. Sci. Res. 5 (1971) 11. 1141 J.A. Christensen, BNWL-SAd84A (1966). iI51 H. Schins, J. Nucl. Mat. 78 (1978) 215. 1161 R.T. Sawbridge and E.C. Sykes, J. Nucl. Mat. 35 (1970) 122. iI71 R. Ftirth, Proc. Cambr. Phil. Sot. 37 (1941) 252. (181 J. O’M Bockris and N.E. Richards, Proc. Roy. Sot. 241 (1957) 44. [ 191 O.D. Slagle and R.P. Nelson, J. Nucl. Mat. 40 (1971) 349. [ 201 H.E. Schmidt, High Temperatures, High Pressures 3 (1971) 345. [21] Argonne National Laboratory Report ANLCEN-RSD76-1 (1976).
DENSITY, THERMAL EXPANSION OF STAINLESS STEEL AND INTERFACIAL PROPERTIES OF UOz -STAINLESS STEEL ABOVE 1690 K P. NIKOLOPOULOS * and B. SCHULZ Ke~~~or~c~~~g~ze~~~~ Kurismhe, Institut fiir MateriaC und Festk~rperfors~hu~g,
Postfoch 3640,
7500 Kmlsmhe,
Fed, Rep. ~e~mun~
Received 13 November 1978
The sessile drop method was used for the determination of the density in liquid state. The results for stainless steel 1.4970 using uranium dioxide as substrate material in the temperature range 1690 K (liquidus temperature Tl) < T < 2120 K are p = 6.82 X lo3 - 10.25 x lo-’ (7’TI) kg/m3, and Q = 1.50 X 10-4K-‘. Below 1690 K the linear thermal expansion is given by Al/lo = 0.00204 + 7.1 lo X 10m6 T + 7.734 X 10d9 T2. Using the same method but not correlated with the density measurements the following interfacial properties of the system UO2 -stainless steel have been determined: surface energy of liquid steel ybv = 1.19 - 0.57 X 1O-3 (T- Tl) J/m2 and interfacial energy of liquid steel against UOz 7s~ = I.57 - 2.01 X 10e3 (T - Tl) J/m4 the results yield a contact angle e = 0” at T= 2515 K. Usingliterature data for the compressibility of liquid U02, an estimate of the surface energy of IJO in liquid state was performed. The estimated value at the melting point is: T~V = 0.522 J/m*. The mean value of the experimental data given by several authors is 0.513 f 0.085 J/m2. The estimated temperature dependence of the surface energy of liquid UO2 is given by dvbv/dT = -0.19 X 10m3 Jfm2.
1. Introduction
function of temperature in the liquid and solid state, and to use these data in the nuclear safety analysis of core meltdown accidents. In the case of two immiscible melts the density of the two liquids is of interest for considerations of the thermohydraulic behaviour of the core melts because of possible segregation and formation of layers,
Surface and interfacial properties are of basic interest for the theoretical treatment of a number of phenomena in two phase or multiphase materials, e.g., their strength, and problems related with powder metallurgy preparation technique. A further range of interest developed with the extension of nuclear safety analysis to hypothetical core meltdown accidents in the past years. Regarding the high temperatures under accident conditions, knowledge of materials properties is needed, especially in the liquid state. In the field of liquid metal fast breeders, the materials of interest are UOz, a representative for the real mixed oxide fuel, and stainless steel, especially I .4970. Up to now, experiments on the structure of core melts in LMFBR [I] do not indicate an interaction of these materials even at temperatures above the melting point of ur~ium dioxide. Thus, it is justified to measure or estimate the physical properties of components, as a
2. Density measurements Well established methods for liquid densitometry are the Archimedean, pyknometric and pressure methods [2]. In lieu of these, the apparatus which was constructed for contact angle measurements [3] was calibrated for liquid densitometry (fig. 1). 2.1. Experimental procedure Using a graphite susceptor, samples on the substrate material were heated to the desired temperature. The exis of the tube was used to photograph the sample as well as to measure the temperature by optical pyro-
* University of Patras, Institute of Physical Metailurgy, Greece. 172
173
P. Nikolopoulos, B. Schulz /Properties of U02-SS above 1690 K
pyrometer ›-
Silica tube 2. Guide sleeves 3 Pyrex-window G inductive heating coil 5. Graphite Susreptor 6. Graphite plate 7. Substrat material 8. Metal drop 9. Molybdenum -shielding 10. Molybdenum -pins
h Vacuum equipment
Fig. 1. Scheme of the apparatus for contact angle and density measurements.
metry. The temperature was measured in a bore of the graphite plate (ratio of diameter: depth = 1 : 4) simulating black body radiation. The pyrometer was adjusted to the melting points of gold, copper, iron, nickel, cobalt and platinum. The general uncertainty of the temperature measurements is +20 K. The atmosphere was highly purified argon (99.999). The density of the material in liquid state was determined by weighing the sample at the beginning of the experiment and measuring the volume of the droplet. The experiments were carried out within short times to avoid evaporation losses. As is well known from contact angle measurements, the molten droplet on a substrate material is deformed by the influence of gravity from a sphere to a spheroid. This deformation is negligible if the masses used (no more than 0.5 g) are small. The determination of the volume was always done on the assumption that the droplet is part of a sphere. This was proved by the measurement of the distances 2a, h and of the projected area F (fig. 2).
Only negligible (-0.6%) deviation from a sphere give good agreements in calculating the projected area F by using 2u and h. In the case of nonwetting behaviour, i.e. contact angle >f~, the assumption was verified in using the relationships for spheroids [4]. The dimensions were taken from photo negatives with a Guinier viewer (Fa. Enraf Nonius) and calculated to the real size by using an optical standard (Fa. Zeiss). The depth in the focus of the optical system is
droplet
Fig. 2. Quantities for the determination the droplet and contact angle 8.
i
of the volume V of
P. Nikolopoulos,
174
B. Schulz /Properties
of UOz-SS
above 1690 K
Table 1 Chemical analysis of materials used uo2
O/U < 2.005 Al 8-10 ppm Cr S-10 cu 1 Fe 20-30 Mn S-10 Si50 Sn 10 (max)
Fe (wt%)
cu
c 0.007 Si < 0.01 P 0.02 S 0.018 Cr 0.007 N 0.01 02 0.07
a)
02 0.12
Ni
co
Ey}SOO ppm
b,
02
02
10 wm
Ni 5 (max) w5 Mg 5 MO2-3
0.19
AU
Pt
1.4970 ss (wt%)
99.999
99.999
c 0.095 Si 0.52 Mn 1.90 P 0.009 S 0.008 v 0.04 Cr 16.0 Ni 14.97 MO 1.15 Ti 0.57 B 0.0061 co 0.02 N 0.01 02 0.01
a) Impurities < 0.1 wt%. b, Impurities < 0.06 wt%.
the true limitation for the accuracy of the density measurements, which was determined as the standard deviation of + 3%. 2.2. Chemical composition of the materials The results of the chemical analysis of all materials used in this work is given in table 1. The droplets of the stainless steel were chemically analyzed especially with respect to a change in oxygen content and possible diffusion of uranium. The penetration of uranium was less than 0.1 wt%, while no change in oxygen content could be observed.
ment of the density and thermal expansion of the steel in liquid state was carried out yielding the results (fig. 5): - density at liquidus temperature 1690 K: 6.82 X lo3 kg/m3; - slope of the temperature function: -10.25 X10-l kg/m3 . K; - thermal expansion coefficient: t1.50 X 10e4 K-r. The temperature dependence can be compared with those on some iron-chromium-nickel melts [lo] (table 3). The comparison gives reasonable agreement.
2.3. Calibration and results To assure the correctness of the measurements of the dimensions, first the linear thermal expansion of stainless steel 1.4970 in the solid state was measured and compared with results using push-rod dilatometry with gold standards for calibration. The data are shown in fig. 3. As can be seen, the results of both methods agree well and complement each other. In liquid state the apparatus was calibrated with iron and copper (fig. 4 and table 2). The results agree with literature data regarding the standard deviation of the method. Thus the measure-
Fig. 3. Linear thermal expansion of solid stainless steel 1.4970.
175
P. Nikolopoulos, B. Schulz /Properties of UO2-SS above 1690 K Table 2 Comparison of the density measurements for iron and copper with literature data
Density at melting point PT1 kdm3)
cu
Fe
7.99 x lo3 [6] 8.10 x 103
7.01 7.23 7.04 6.85 1.20 1.72 2.08 1.58
Thermal expansion coefficient CY = -(l/pT$dp/dT)(K-‘1 T> T1
Table 3 Temperature dependence of the density of Fe-Cr-Ni [lo] compared to that of stainless steel 1.4970
x x x x x x x x
103 [7] lo3 [8] 10” [9] 103 104 (71 lo4 [8] lo4 [9] lo4
melts
-dp/dT &g/m3 * K)
Melt composition (wt%)
E
Cr
Ni
19.75 19.92 13.5 ss 1.4970
9.74 19.50 10.50
jj -S
-9 -13 -9 10.25
x x x X
10-l [lo] 10-l [lo] 10-l [lo] 10-l
7.6 t
1200
1300
1100
1500
1600
17w
1000
1900
2000
2100
Fig. 5. Density of stainless steel 1.4970 versus temperature.
3. Surface and interfacial energy I Kirshenbaum,CahiU 1962. IILucas
IIIBcnedacks
1960 lI 01
1930.
Nthtswork
6.6.
' a ' ' ' ' 1600 (900 2000 2100 2200 2300 TIKl -
' ' ZLOO 2500
Fig. 4. Density of liquid iron versus temperature.
As mentioned above, the apparatus used for these experiments was the same as for density measurements. The whole method, its problems and limitations is discussed in detail in [3]. Cylindrical samples of SS 1.4970 were used and molten on the substrate material uranium dioxide. Under the influence of gravity, the liquid phase forms a spheroid which cannot be assumed to be a sphere when determining the surface energy. Using the method described in [4] (determination of the maximum diameter) and tabulated data [5], the shape (p) and size (b) of the spheroid can be determined. From this it follows:
P. Nikolopoulos,
176
B. Schulz /Properties
of UOz-SS above 1690 K
Table 4 Contact angle (e), surface energy (7~“) of liquid steel and work of adhesion (Wa) in the system liquid steel-UOz T
I9
YLV
w, =
(W
(<)
(J/m*)
(J/m*)
1690 1840 1930
124.0 110.2 104.0
1.19 1.12 1.05
0.525 0.733 0.796
YLV(l + cos 0)
where p = density, g = acceleration due to gravity. This method is restricted to contact angles >90”. 3.1. Contact angles and surface energy of SS 1.4970 In the temperature range investigated, the following data were obtained (table 4). From this, one gets a linear relationship for the surface energy: yLv = 1.19 - 0.57 X 10V3 (T-
Tt)J/m*
,
with slope dyLv = -0.57 dT
TCKI +
Fig. 6. Surface energy (~Lv) of stainless steel 1.4970 and interfacial energy (7s~) of stainless steel - UOz.
Applying the Young equation
ysv = ysL
+ yLv
cose
(2)
1
one can determine the interfacial energy ys~ between stainless steel 1.4970 and uranium dioxide. It follows ys~ = 1.57 - 2.01 X low3 (T-
X 10T3 J/m* . K .
These data can be compared to those of Ahmad and Murr [ 1 l] measured in hydrogen atmosphere for SS 304 on Al2 0s as substrate material. They obtain (by a true analysis of their results): yLv=1.172-8.24X
10V3(T-
Tt)J/m*,
1748
dioxide is well
[T] = K .
T,)J/m*
.
From this, a total wetting (0 = 0) of uranium dioxide by the steel occurs at 25 15 K. Fig. 6 shows the results together with the surface energy of liquid steel. 3.3. Surface energy of liquid uranium dioxide With respect to the possible high temperature in LMFBR-core meltdown accidents, the surface energy of liquid uranium dioxide is of some interest. Its value at the melting point in liquid state is known [13-l 51, the mean of all data yield of: yLv = 0.513 f 0.085 J/m* Keeping in mind that the bonds in uranium dioxide are dominated by an ionic character [ 161, one can try to estimate the surface energy of liquid U02. The theory of the physical behaviour of ionic liquids was developed by Ftirth [17] and experimentally verified by Bockris and Richards [ 181, There the isothermal compressibility Kil in liquid state is given by: f
0.37
Kil
= Kf
Kis
.
Kis
being the compressibility
(3) in solid state at the
P. Nikolopoulos.
B. Schulz /Properties
of W-SS
melting point and K; a term due to the creation of holes in liquid state during melting. The volume of a hole ut, is given by:
177
above 1690 K
3.9
t ”
[ 171 ,
uh = 0.68(kT/yL”)“a
(4)
38.
,t E
(k = Boltmann’s
u
constant)
#
and the number of holes Nn by:
(5) (AV
=
increase in volume at the melting point).
In eq. (3). the term K; is correlated with the volume and the number of holes in the following way: 9 !!!& “’ = 14 kTVTS
[I)31
36 -
‘k-
(6)
3ioo --OL90
3150 1 tK1
-
Fig. 7. Measured compressibility and estimated surface energy of liquid UO2.
temperature
,
( VTS = molar volume at the melting point). Combining
31-
=e
dependence
d-n.v = -0.19 dT
(fig. 7) is given by:
X 10e3 J/m2 . K.
eqs. (4).-(6) 4. Conclusion 0.68
With the experimental results of the compressibility at the melting point in the solid and in the liquid state [ 191, of can be calculated. All data used are given in table 5, the solid state compressibility was obtained according to Kis = 3( I - 2V)/E,
(8)
v = Poisson’s ratio, E = Young’s modulus. The data for Young’s modulus and Poisson’s ratio were taken from [20]. As can be seen, the estimated value at the melting point is in good agreement with the measured one. The
In the system U02-stainless steel 1.4970, the following properties have been determined. (1) The linear thermal expansion of solid stainless steel I .4970. (A&) = 0.002o4 + 7.11 e X I 0e6 T t 7.734 X lO-9 T2 (2) Density of’liquid steel I .4970. p = 6.82 X 1O3 10.25 X IO-’ (T - T,) kg/m3; T, = 1690 K. (3) Surface energy of liquid steel. yLv = I .19 0.57 X 10s3 (T - T,) J/m2. (4) lnterfacial energy in the system U02-stainless steel 1.4970. ysL = 1.57 - 2.01 X 1O-3 (T - Tl) J/m’. (5) Surface energy of liquid U02 (estimated). yLv = 0.522 - 0.19 X low3 (T- Tt)J/m’; T, = 3125 K.
Table 5
Used data for the calculation of the surface energy of liquid UO2 T
Kis x
W
(m’/N)
10”
A VI VTS
Ki x
10”
(m’/N)
Kl x 10” (m2/N)
‘YLV (J/m’)
TLV (J/m’) measured
3125 3175 3225
0.72
0.136
I211
3.54 3.64 3.79
3.27 3.37 3.52
0.521 0.514 0.502
0.513 [13-151
178
P. Nikolopoulos,
B. Schulz /Properties
Aknowledgements The authors are obliged to the Analytical Chemistry Group for carrying out the chemical analyses. J. Biirkin assisted with interest in performing the experiments.
References [ 1 ] B. Schulz, Kernforschungszentrum Karlsruhe Report KfK 127712 (1977) 123-21. [ 21 J.L. White, Physicochemical Measurements at High Temperatures, eds. J.O’M. Bockris, J.L. White and J.D. Mackenzie (Butterworth, London, 1959) p. 193. [ 3 ] P. Nikopoulos, Kernforschungszentrum Karlsruhe Report KfK 2038 (1974) und Dissertation, UniversitLt Karlsruhe (1974). [4] L. Zagar and W. Bernhardt, Forschungsberichte des Landes N.R.W. Nr. 1733. [5] F. Bashfort and S.C. Adams, An attempt to test the theories of capillary actions (University Press, Cambridge, 1883). [6] B.C. Allen, Liquid Metals, ed. S.Z. Beer (Dekker, New York, 1972) p. 161.
of UOz-SS
above 1690 K
[ 71 A.D. Kirshenbaun and J.A. Cahill, Trans. AIME 224 (1962) 816. [S] C. Benedicks, N. Ericson and G. Ericson. Archiv Eisenhiittenwesen 3 (1930) 473. 191 L.D. Lucas, Compt. Rend. 250 (1960) 1850. [lOI P.P. Arsentb and B.G. Vinogradov, Steel in the USSR 5 (1975) 145. IllI U.M. Ahmad and L.E. Murr, J. Mat. Sci. 11 (1976) 224. [121 P. Nikolopoulos, S. Nazare and F. Thiimmler, J. Nucl. Mat. 71 (1977) 89. 1131 J.L. Bates, C.E. McNeilly and J.J. Rasmussen, Mat. Sci. Res. 5 (1971) 11. 1141 J.A. Christensen, BNWL-SAd84A (1966). iI51 H. Schins, J. Nucl. Mat. 78 (1978) 215. 1161 R.T. Sawbridge and E.C. Sykes, J. Nucl. Mat. 35 (1970) 122. iI71 R. Ftirth, Proc. Cambr. Phil. Sot. 37 (1941) 252. (181 J. O’M Bockris and N.E. Richards, Proc. Roy. Sot. 241 (1957) 44. [ 191 O.D. Slagle and R.P. Nelson, J. Nucl. Mat. 40 (1971) 349. [ 201 H.E. Schmidt, High Temperatures, High Pressures 3 (1971) 345. [21] Argonne National Laboratory Report ANLCEN-RSD76-1 (1976).