- Email: [email protected]
Physical and chemical analysis of interaction between oxide fuel and pyrocarbon coating of coated particles
0360.5442i9l $3.00 + 0.00 Perpmon Press pk
,%qy Vol. 16. No. l/2. pp. 501-306. 1991 Printed in cheat Britaia
PHYSICAL AND CHEMICAL ANALYSIS OF INTERACTION BETWEEN OXIDE FUEL PYROCARBON COATING OF COATED PARTICLES
AND
R. A. LYUTXKOV, YU. F. KROMOV, and A. S. CHERNIKOV Scientific Industrial Association, Podolsk, 142100 Moscow
Region, USSR
Abstract - In terns of the model proposed the equilibrium pressure of gases (CO, Kr, Xe) in pyrocarbon-coated uranium dioxide fuel particles has been calculated, as function of the initial composition of the fuel (O/U), the design features of the coated particles, the fuel temperature, and the burnup. The possibility of reducing gas pressure in the particles by alloying the kernels with uranium carbide, and increasing the kernel capacity for retention of solid fission products by alloying the uranium oxide with aluminum-silicates, has been investigated. 1. INTRODUCTION The coating leak tightness is one of the main conditions, but not the only one, for retention of fission products inside the coated fuel particles (CP) for the hightemperature gas-cooled reactors. The degree of retention of solid fission products (SFP) inside CP essentially depends on their chemical state. The nuclides that form oxides or chemical compounds stable at the operating temperatures are almost corn-pletely retained by the coated particles. The nuclides that do not form solid solutions or chemical compounds migrate through the coating and contaminate the coolant. The possibility of maintaining the coating leak tightness and determining the conditions of maximum fission products binding inside CP can be estimated by the quantitative analysis of the physical and chemical processes taking place under irradiation. 2. ANALYTICAL STUDIES In the present work the available thermodynamic data were used to estimate the oxygen potential in uranium dioxide as a function of the CP design features and operating conditions (temperature, uranium burnup), stable noble gas pressure and, possibility of binding SEP to oxide compounds. In the coated particles with the oxide kernels the most important phenomenon is the reduction of the uranium dioxide by carbon, which results in the generation of the equilibrium pressure of the gaseous reaction product carbon monoxide. From the consideration of the minimum free energy of the reduction reactions of the oxide and analysis of He-C-O equation of state diagram, metal carbides were considered as the final product of the reduction of the uranium dioxide and the SFP oxides. The gas pressure level depends on the kernel oxygen potentisl, the CP design features (free volume to kernel mass ratio), the uranium burnup and the temperature. As a result of uranium fission the oxygen potential of the fuel increases.l The analysis of possible chemical reactions between CP components, taking into account the uranium fission products and the CP free volume change during irradiation, permitted the formulation of the equilibrium equation. This equation defines the equilibrium pressure of CO
501
R. A. LYUIWOV etal
502
inside CP as a function of the initial value of the kernel oxygen potential, CP design, uranium burnup, and temperature:
(1 =lg pk”oTR: wcc~
PO]
(x0 - xk)
.
(2xk
- x0)
+ AFX[
(238 - 3A + 16xk) xk
Tk
L _ N
(1 - AF) (XF - xk) xk + AF xf c
=
Qiyi
n
Vi - &I
c
Pi + R:
[o+(~-Po)~~il
i-l 0.5794
4.68
where
+ -
T
* 10I
4
,
(1)
Pg; = CO pressure inside CP,
= equilibrium pressure of oxygen over i-oxide,
pi*
x0 = O/U ratio of the uranium dioxide (initial), xk = O/U ratio of the uranium dioxide after coating deposition, xF = D/U ratio of the uranium dioxide after burnup of F (atomic fraction) uranium, A-
enrichment of uranium with U-235 (atomic fraction),
Ro = kernel radius, PO = kernel porosity, Pk = 1theoretical density of the kernel, n-
the number of pyrocarbon (PyC) coating layers under the layer SIC,
Ri-1, RI = :he inner and outer radii of the i-th PyC layer, Pi = ,oroeity of the i-th PyC layer, Ni = :he amount of long-lived solid fission products in the kernel after lranium burnup F (atomic fraction), N-
Qi =
:he amount of solid fission products, forming stable oxides at the riven oxygen potential inside CP, :he amount of the i-th element oxide formed in 1 mol uranium iieeion,
yi =
the OlHei ratio of the i-th element oxide,
4 =
the molecular weight of the i-th element,
Pi = the theoretical density of the i-th element oxide, T-
temperature, K,
Tk = 273 K = O'C,
Safety and licensing issues
= 2.24 * 104 cm3 - the volume (T = 273 K, P = 1.105 Pa).
“0 The possibility was determined
of binding the from the additional
i-th uranium unequality:
of
503
1 g-mol
nuclide
in
gas
under
normal
the
oxide
form
conditions
in kernels
(2)
where
= metallic
tIei
solid
The Eq. 1 represents oxide over the system
fission
products.
the dependence between the equilibrium pressure IJO2+,-SFP oxides-PyC and the free volume of the
of stable The pressure the CP was found by Eq.
gaseous fission products 3 after the value XF was
Pk”oT&‘F
pI3= Tk
I 2
i=l
where
Vi - &I
Pi
(238
-
(Xe, Kr, determined
are
the
The numerical solution the EC-1060 computer.
coatings
of
1:
t
(3)
+ R:
same as of
the
3A + 16XF) ’
Pg - pressure of stable gaseous fission products, the yield of the i-th GFP per uranium fission symbols
inside from Eq.
Qi
Qi -
The other
I)
of the carbon undamaged CP.
Eqs.
in Eq.
(relative
units).
1.
1 and 3 has
been
obtained
by the
Newton method on
Using Eqs. 1 through 3, the dependence of CO, Xe, Kr, and I pressure inside the CP has been calculated with the appropriate input parameters. As an example, Fig. 1 shows the results for uranium dioxide of initial composition O/U - 2.01, buffer PyC layer porosity of 60X, and a fuel burnup of 10% PIMA, calculated in the form of a nomograph in the coordinates: buffer layer thickness - CP free volume - equilibrium pressure of the gases (PCO + PXe Kr). The calculation has been carried out for CP with the kernel diameter 400 to $00 pm and the buffer layer thickness 20 to 120 pm in the temperature range 1473 to 1873 K. Using a nomograph the limits of the pressure variations in the CP of the same batch can be estimated if the spread in the values of separate parameters (kernel diameter, buffer layer thickness) are known. For example, in the CP with the kernel diameter 500 jhll, buffer layer thickness 80 pm, temperature 1200°C. and a burnup of 10% FIMA the gas pressure would be 320.105 Pa. An increase in the kernel diameter to 600 pm, with the other parameters being the same, is accompanied by the pressure rising to 410.105 Pa. The values of the estimated pressure levels are close to the critical pressures that resulted in the destruction of the weakest CP during the long-term in-pile tests of loosely packed CP (200 to 400.105 Pa) and of the consolidated CP in spherical fuel elements (“400 to 600.105 Pa). For different sets of the input parameters the rate of PCO increase as a function of uranium burnup depends on the amount of UCl.86 in the CP kernel, es was introduced in the kernel or was formed during the PyC coating deposition, according to the reaction: Uo,
SOY
IUI-l-HH
+ (1.86
+ X) c - uc1.,36
+ xc0
.
(4)
504
R. A. LYUTIKOV
et
a!
R,=250 2 m Ro=3 !X‘Pim R,o200~~m R,=300~tim \
& Ln
I
0 7 .
is
El20 6
0
Go0 2 G
1000
f
g
Fr 80
800
60
600
40
400
. 20
200
0
50
100
0 150
200
? free volume, pmFig. 1.
Dependence of the equilibrium pressure of gases (PcD+GFP) in coated particles on temperature and some of its design characteristics [vCP - CP free vofume (porosity) under carbide coating SiCi hbuf - thickness of PyC buffer layer, P - pressure). Calculation is carried out for O/U - 2.01; PO - 0.06~ R, = 200, 250, 300, and 350 /bm; porosity and thickness8 the PyC buffer layer - 60%; 40 to 120 Cm; medium density layer - 30%; 35 Cm; high density layer - 20%; 45 pm; a burnup of 10% FIMA. The guide dashed line is an example of using the nomograph. 1 - 3273lC,2 - 1473 K, 3 - 1573 K; 4 - 1673 K; 5- 1873 K.
Safety and licensing
505
issues
The CP pressure remains constant up to complete oxidation of the UC1.86 by free oxygen. As described in Ref. 2, the amount of uC1.86 that must be introduced into the kernel to maintain the CO pressure at the end of the irradiation at the level 30 to 40.105 kPa. was evaluated for a burnup of 10% FIMA at 125O'C it proved to be "15 mol x uC1.86. Reduction of PcO inside the CP decreases the possibility of coating destruction caused by the internal gas pressure, but simultaneously the amount fission products bound in the kernel is limited. At the above mentioned CO pressure zirconium. strontium, barium, and rare earth nuclides could be oxidized. At the equilibrium CO pressure in nonalloyed CP (300.105 Pa) in accordance with Eq. 2:
(lgP;;I < (lgP;;i +
Mei
oy
I
.
molybdenum can be present in the oxidized form. All the cesium is practically fn the metal form. Complete oxidation of Cs to Cs20 is only possible at a CO pressure L108 Pa. Creation of the coatings capable of withstanding such loads does not seem reasonable. To increase the retention capability of Cs inside the CP it is necessary to decrease the equilibrium pressure PO over the Cs-containing compounds. This can be
achieved
when
the
oxide
The equilibrium pressure the oxygen stoichiormetry at 12OO’C does not exceed ~eacrlun of ce~lu~~ oxidat
kernel
is
al z oyed
with
aluminum
of CO in CP with aluminum of uranium dioxide, because 1 to 10.105 Pa, as indicated LOU
shifts to the right bccausc the compound Cs7O*Al203*4SlO2.
of
2cs
+ co
:
the
Cs7.0
is
cs20 strongly
siIicates.3*‘
silicate additions is defined by the PC, over aluminum silicates in Ref. 5. Nevertheless the
, found6
(5) in
aluminum
sflicatcr
1s
The temperature stability of Cs aluminum silicates depends 011 the CO pressure inside the CP. If the CO pressure is determined by the reactions of aluminum silicates with PyC. then the aluminum silicate fn the compound Cs20*A1203*4SI02 hetng the least stable will be stable up to 1550°C, as given in Ref. 5. The efficiency of retention of Cs in the kernel when it is bonded to aluminum silicates depends on the Al/S1 ratio in the alloying addition. 5 When the Al/Si ratio is unity, eutectic mixtures between Cs20 and tAl203*ySiO2 with a melting temperature of about 1lOO’C can be produced. The kernel alloying with the aluminum silicate addition with Al/Si = 4/l raises the eutectic melting temperature up to about 15OO”C, as indicated in Ref. 7. In this case the CP buffer layer will not interact with the silicate melt, which has a Cs partial pressure that is higher by two to four orders of magnitude compared with the pressures in other aluminum silicates.8
3. CONCLUSIONS The results obtained in the present work can be considered as approximation to the description of the real state in the systems under consideration. This is due to two reasons. First, the thermodynamical information used for the calculations is not always sufficiently accurate and complete. For a number of compounds (aluminum silicates SFP and some others) the temperature dependence of the isobar-isothermal potential (AZ) was established using approximated methods. Second, the kinetic factors, which in some cases can make it difficult to reach the equilibrium, were not considered in the work, For example, the CO pressures inside CP with the alloyed oxide fuel is about two to three times lower than the equilibrium pressure, necessary for Cs oxidation according to reaction.5 Under these conditions the relative fraction of atoms in the oxidized form can be low enough and the rate of formation of cesium aluminum silicates can be comparable with the rate of migration of Cs atoms through PyC. This analysis is to be supplied with experimental verification on obtaining the equilibrium conditions.
506
1. 2. 3. 4. 5. 6.
7.
8.
R.A.Lwn~ov
etal
REFERENCES J., Homan, H. Nabielek, et al., "Low-Enriched Fuel Particle Performance Review," Jiil-1502,KFA, August 1978. F. J. Homan, T. B. Lindemer, et al., Nucl. Technol., 35, 428 (1977). R. Fgrthmann, Ibid, 56, 81 (1982). Yu. F. Khromov, E. Svistunov, et al., Atomnaya Energiya, 2, Issue 5, 363 (1985) (in Russian). A. S. Chernikov, Yu. F. Khromov, et al., Atomnaya Energiya, B, Issue 3, 191 (1989) (in Russian). V. I. Babushkin, G. M. Matveev , et al., Thermodynamics of Silicates, Moscow, 352 (1965) (in Russian). R. Fgthmann, "Bestrahlungsverhalten von beschichteten Brennstoffteilchen mit spaltproduktbindenden Kernadditiven," Jill-1620, KFA, 1979. R. Odoj, K. Hilpert, and H. W. N&nberg, "Prgparation und massenspektrometrische Hochtemperaturuntersuchungen von Verbindungen des quasi-teriiren Systems Cs2O*Al2Oj'SiO2," Jiil-1460, KFA, 1977. thfe F.
,%qy Vol. 16. No. l/2. pp. 501-306. 1991 Printed in cheat Britaia
PHYSICAL AND CHEMICAL ANALYSIS OF INTERACTION BETWEEN OXIDE FUEL PYROCARBON COATING OF COATED PARTICLES
AND
R. A. LYUTXKOV, YU. F. KROMOV, and A. S. CHERNIKOV Scientific Industrial Association, Podolsk, 142100 Moscow
Region, USSR
Abstract - In terns of the model proposed the equilibrium pressure of gases (CO, Kr, Xe) in pyrocarbon-coated uranium dioxide fuel particles has been calculated, as function of the initial composition of the fuel (O/U), the design features of the coated particles, the fuel temperature, and the burnup. The possibility of reducing gas pressure in the particles by alloying the kernels with uranium carbide, and increasing the kernel capacity for retention of solid fission products by alloying the uranium oxide with aluminum-silicates, has been investigated. 1. INTRODUCTION The coating leak tightness is one of the main conditions, but not the only one, for retention of fission products inside the coated fuel particles (CP) for the hightemperature gas-cooled reactors. The degree of retention of solid fission products (SFP) inside CP essentially depends on their chemical state. The nuclides that form oxides or chemical compounds stable at the operating temperatures are almost corn-pletely retained by the coated particles. The nuclides that do not form solid solutions or chemical compounds migrate through the coating and contaminate the coolant. The possibility of maintaining the coating leak tightness and determining the conditions of maximum fission products binding inside CP can be estimated by the quantitative analysis of the physical and chemical processes taking place under irradiation. 2. ANALYTICAL STUDIES In the present work the available thermodynamic data were used to estimate the oxygen potential in uranium dioxide as a function of the CP design features and operating conditions (temperature, uranium burnup), stable noble gas pressure and, possibility of binding SEP to oxide compounds. In the coated particles with the oxide kernels the most important phenomenon is the reduction of the uranium dioxide by carbon, which results in the generation of the equilibrium pressure of the gaseous reaction product carbon monoxide. From the consideration of the minimum free energy of the reduction reactions of the oxide and analysis of He-C-O equation of state diagram, metal carbides were considered as the final product of the reduction of the uranium dioxide and the SFP oxides. The gas pressure level depends on the kernel oxygen potentisl, the CP design features (free volume to kernel mass ratio), the uranium burnup and the temperature. As a result of uranium fission the oxygen potential of the fuel increases.l The analysis of possible chemical reactions between CP components, taking into account the uranium fission products and the CP free volume change during irradiation, permitted the formulation of the equilibrium equation. This equation defines the equilibrium pressure of CO
501
R. A. LYUIWOV etal
502
inside CP as a function of the initial value of the kernel oxygen potential, CP design, uranium burnup, and temperature:
(1 =lg pk”oTR: wcc~
PO]
(x0 - xk)
.
(2xk
- x0)
+ AFX[
(238 - 3A + 16xk) xk
Tk
L _ N
(1 - AF) (XF - xk) xk + AF xf c
=
Qiyi
n
Vi - &I
c
Pi + R:
[o+(~-Po)~~il
i-l 0.5794
4.68
where
+ -
T
* 10I
4
,
(1)
Pg; = CO pressure inside CP,
= equilibrium pressure of oxygen over i-oxide,
pi*
x0 = O/U ratio of the uranium dioxide (initial), xk = O/U ratio of the uranium dioxide after coating deposition, xF = D/U ratio of the uranium dioxide after burnup of F (atomic fraction) uranium, A-
enrichment of uranium with U-235 (atomic fraction),
Ro = kernel radius, PO = kernel porosity, Pk = 1theoretical density of the kernel, n-
the number of pyrocarbon (PyC) coating layers under the layer SIC,
Ri-1, RI = :he inner and outer radii of the i-th PyC layer, Pi = ,oroeity of the i-th PyC layer, Ni = :he amount of long-lived solid fission products in the kernel after lranium burnup F (atomic fraction), N-
Qi =
:he amount of solid fission products, forming stable oxides at the riven oxygen potential inside CP, :he amount of the i-th element oxide formed in 1 mol uranium iieeion,
yi =
the OlHei ratio of the i-th element oxide,
4 =
the molecular weight of the i-th element,
Pi = the theoretical density of the i-th element oxide, T-
temperature, K,
Tk = 273 K = O'C,
Safety and licensing issues
= 2.24 * 104 cm3 - the volume (T = 273 K, P = 1.105 Pa).
“0 The possibility was determined
of binding the from the additional
i-th uranium unequality:
of
503
1 g-mol
nuclide
in
gas
under
normal
the
oxide
form
conditions
in kernels
(2)
where
= metallic
tIei
solid
The Eq. 1 represents oxide over the system
fission
products.
the dependence between the equilibrium pressure IJO2+,-SFP oxides-PyC and the free volume of the
of stable The pressure the CP was found by Eq.
gaseous fission products 3 after the value XF was
Pk”oT&‘F
pI3= Tk
I 2
i=l
where
Vi - &I
Pi
(238
-
(Xe, Kr, determined
are
the
The numerical solution the EC-1060 computer.
coatings
of
1:
t
(3)
+ R:
same as of
the
3A + 16XF) ’
Pg - pressure of stable gaseous fission products, the yield of the i-th GFP per uranium fission symbols
inside from Eq.
Qi
Qi -
The other
I)
of the carbon undamaged CP.
Eqs.
in Eq.
(relative
units).
1.
1 and 3 has
been
obtained
by the
Newton method on
Using Eqs. 1 through 3, the dependence of CO, Xe, Kr, and I pressure inside the CP has been calculated with the appropriate input parameters. As an example, Fig. 1 shows the results for uranium dioxide of initial composition O/U - 2.01, buffer PyC layer porosity of 60X, and a fuel burnup of 10% PIMA, calculated in the form of a nomograph in the coordinates: buffer layer thickness - CP free volume - equilibrium pressure of the gases (PCO + PXe Kr). The calculation has been carried out for CP with the kernel diameter 400 to $00 pm and the buffer layer thickness 20 to 120 pm in the temperature range 1473 to 1873 K. Using a nomograph the limits of the pressure variations in the CP of the same batch can be estimated if the spread in the values of separate parameters (kernel diameter, buffer layer thickness) are known. For example, in the CP with the kernel diameter 500 jhll, buffer layer thickness 80 pm, temperature 1200°C. and a burnup of 10% FIMA the gas pressure would be 320.105 Pa. An increase in the kernel diameter to 600 pm, with the other parameters being the same, is accompanied by the pressure rising to 410.105 Pa. The values of the estimated pressure levels are close to the critical pressures that resulted in the destruction of the weakest CP during the long-term in-pile tests of loosely packed CP (200 to 400.105 Pa) and of the consolidated CP in spherical fuel elements (“400 to 600.105 Pa). For different sets of the input parameters the rate of PCO increase as a function of uranium burnup depends on the amount of UCl.86 in the CP kernel, es was introduced in the kernel or was formed during the PyC coating deposition, according to the reaction: Uo,
SOY
IUI-l-HH
+ (1.86
+ X) c - uc1.,36
+ xc0
.
(4)
504
R. A. LYUTIKOV
et
a!
R,=250 2 m Ro=3 !X‘Pim R,o200~~m R,=300~tim \
& Ln
I
0 7 .
is
El20 6
0
Go0 2 G
1000
f
g
Fr 80
800
60
600
40
400
. 20
200
0
50
100
0 150
200
? free volume, pmFig. 1.
Dependence of the equilibrium pressure of gases (PcD+GFP) in coated particles on temperature and some of its design characteristics [vCP - CP free vofume (porosity) under carbide coating SiCi hbuf - thickness of PyC buffer layer, P - pressure). Calculation is carried out for O/U - 2.01; PO - 0.06~ R, = 200, 250, 300, and 350 /bm; porosity and thickness8 the PyC buffer layer - 60%; 40 to 120 Cm; medium density layer - 30%; 35 Cm; high density layer - 20%; 45 pm; a burnup of 10% FIMA. The guide dashed line is an example of using the nomograph. 1 - 3273lC,2 - 1473 K, 3 - 1573 K; 4 - 1673 K; 5- 1873 K.
Safety and licensing
505
issues
The CP pressure remains constant up to complete oxidation of the UC1.86 by free oxygen. As described in Ref. 2, the amount of uC1.86 that must be introduced into the kernel to maintain the CO pressure at the end of the irradiation at the level 30 to 40.105 kPa. was evaluated for a burnup of 10% FIMA at 125O'C it proved to be "15 mol x uC1.86. Reduction of PcO inside the CP decreases the possibility of coating destruction caused by the internal gas pressure, but simultaneously the amount fission products bound in the kernel is limited. At the above mentioned CO pressure zirconium. strontium, barium, and rare earth nuclides could be oxidized. At the equilibrium CO pressure in nonalloyed CP (300.105 Pa) in accordance with Eq. 2:
(lgP;;I < (lgP;;i +
Mei
oy
I
.
molybdenum can be present in the oxidized form. All the cesium is practically fn the metal form. Complete oxidation of Cs to Cs20 is only possible at a CO pressure L108 Pa. Creation of the coatings capable of withstanding such loads does not seem reasonable. To increase the retention capability of Cs inside the CP it is necessary to decrease the equilibrium pressure PO over the Cs-containing compounds. This can be
achieved
when
the
oxide
The equilibrium pressure the oxygen stoichiormetry at 12OO’C does not exceed ~eacrlun of ce~lu~~ oxidat
kernel
is
al z oyed
with
aluminum
of CO in CP with aluminum of uranium dioxide, because 1 to 10.105 Pa, as indicated LOU
shifts to the right bccausc the compound Cs7O*Al203*4SlO2.
of
2cs
+ co
:
the
Cs7.0
is
cs20 strongly
siIicates.3*‘
silicate additions is defined by the PC, over aluminum silicates in Ref. 5. Nevertheless the
, found6
(5) in
aluminum
sflicatcr
1s
The temperature stability of Cs aluminum silicates depends 011 the CO pressure inside the CP. If the CO pressure is determined by the reactions of aluminum silicates with PyC. then the aluminum silicate fn the compound Cs20*A1203*4SI02 hetng the least stable will be stable up to 1550°C, as given in Ref. 5. The efficiency of retention of Cs in the kernel when it is bonded to aluminum silicates depends on the Al/S1 ratio in the alloying addition. 5 When the Al/Si ratio is unity, eutectic mixtures between Cs20 and tAl203*ySiO2 with a melting temperature of about 1lOO’C can be produced. The kernel alloying with the aluminum silicate addition with Al/Si = 4/l raises the eutectic melting temperature up to about 15OO”C, as indicated in Ref. 7. In this case the CP buffer layer will not interact with the silicate melt, which has a Cs partial pressure that is higher by two to four orders of magnitude compared with the pressures in other aluminum silicates.8
3. CONCLUSIONS The results obtained in the present work can be considered as approximation to the description of the real state in the systems under consideration. This is due to two reasons. First, the thermodynamical information used for the calculations is not always sufficiently accurate and complete. For a number of compounds (aluminum silicates SFP and some others) the temperature dependence of the isobar-isothermal potential (AZ) was established using approximated methods. Second, the kinetic factors, which in some cases can make it difficult to reach the equilibrium, were not considered in the work, For example, the CO pressures inside CP with the alloyed oxide fuel is about two to three times lower than the equilibrium pressure, necessary for Cs oxidation according to reaction.5 Under these conditions the relative fraction of atoms in the oxidized form can be low enough and the rate of formation of cesium aluminum silicates can be comparable with the rate of migration of Cs atoms through PyC. This analysis is to be supplied with experimental verification on obtaining the equilibrium conditions.
506
1. 2. 3. 4. 5. 6.
7.
8.
R.A.Lwn~ov
etal
REFERENCES J., Homan, H. Nabielek, et al., "Low-Enriched Fuel Particle Performance Review," Jiil-1502,KFA, August 1978. F. J. Homan, T. B. Lindemer, et al., Nucl. Technol., 35, 428 (1977). R. Fgrthmann, Ibid, 56, 81 (1982). Yu. F. Khromov, E. Svistunov, et al., Atomnaya Energiya, 2, Issue 5, 363 (1985) (in Russian). A. S. Chernikov, Yu. F. Khromov, et al., Atomnaya Energiya, B, Issue 3, 191 (1989) (in Russian). V. I. Babushkin, G. M. Matveev , et al., Thermodynamics of Silicates, Moscow, 352 (1965) (in Russian). R. Fgthmann, "Bestrahlungsverhalten von beschichteten Brennstoffteilchen mit spaltproduktbindenden Kernadditiven," Jill-1620, KFA, 1979. R. Odoj, K. Hilpert, and H. W. N&nberg, "Prgparation und massenspektrometrische Hochtemperaturuntersuchungen von Verbindungen des quasi-teriiren Systems Cs2O*Al2Oj'SiO2," Jiil-1460, KFA, 1977. thfe F.