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J. Phys. Soc. Jpn. 89, 024803 (2020) [6 Pages]
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Identification of the Sintering Mechanism of Oxide Nuclear Fuel through the Analysis of Experimental Pore Size Distributions

Yury N. Devyatko1 , Oleg V. Khomyakov1,2, , Andrey V. Tenishev1 , Maxim E. Matvenov1, and Dmitry P. Shornikov1
+ Affiliations
1National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse, 31, Moscow, 115409, Russia2Joint Stock Company “A.A. Bochvar High-technology Research Institute of Inorganic Materials” (JSC “VNIINM”), Rogova st. 5a, Moscow, 123069, Russia
Received August 27, 2019; Accepted December 26, 2019; Published January 30, 2020

The paper studies the sintering kinetics of pelletized oxide nuclear fuel in terms of various parameters (heating rate, sintering temperature, partial pressure of oxygen in sintering atmosphere). It considers calculated experimental pore size distributions in sintered fuel pellets. Study of the evolution of pore size distributions let us determined the physical mechanism of sintering of uranium dioxide. The sintering process is controlled by the mechanism of viscous flow under the influence of capillary forces and residual stresses.

©2020 The Physical Society of Japan
https://doi.org/10.7566/JPSJ.89.024803
1. Introduction

Currently, uranium dioxide is the main fuel for thermal neutron reactors. The melting point of uranium dioxide is very high — 3120 °C, and the initial stage of its production, including enrichment and conversion, ends with obtaining of a powder. As a consequence, the main method of industrial production of fuel pellets is sintering at considerably lower temperatures (\({\sim}1700{\text{--}}1750\) °C). Initially, pellets produced from uranium dioxide powder are pressed under load 200–250 MPa into a cylindrical compact with a density \({\sim}50{\text{--}}55\)% of the theoretical density (TD) of uranium dioxide (\(\rho_{0} = 10.96\) g/cm3). In the original powder, uranium dioxide has a nonstoichiometric (\(\text{O/U}>2\)) chemical composition. In order to produce a fuel with a composition close to the stoichiometric one, a compact is sintered in a reducing atmosphere — hydrogen flow (in industry) or in a gas mixture Ar+8%H2 (under laboratory conditions). A green compact of uranium dioxide has a developed internal surface. Shown in Fig. 1(a), the structure of the green pellet contains agglomerates of microcrystallites of uranium dioxide with characteristic sizes \({\sim}200{\text{--}}300\) nm. During sintering grains of powder combine into grains of fuel pellet. That is accompanied by rearrangement of the internal surface and formation of a closed pore system [see Fig. 1(b)]. Let us note that however the processes of formation and growth of grains and dissolution of pores goes in parallel during sintering they are not directly related to each other and are only concomitant ones.


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Figure 1. The microstructure of an oxide nuclear fuel pellet before sintering (a) (density 50–55%TD) and after sintering (b) (density 94–95%TD).

A primary feature of sintering is the specimen shrinkage, which occurs when pores dissolve inside the compact during its heating and isothermal annealing. Generally, the sintering process has 3 stages: initial, intermediate and final.3–5) Figure 2 shows the images (with different magnification) of microstructure of uranium dioxide pellet at each stage of sintering. The initial stage of the process is characterized by sintering of contacting grains of powder followed by the formation of necks at the zone of contact. The shrinkage at the initial stage, as a rule, is negligible and does not exceed 1–2% of the initial linear size of the green pellet. It should be noted that the initial stage of sintering is characterized by lack of porosity in the traditional sense of this term. The green pellet has only internal surface that coincides with the overall surface of all its constituent grains of powder.


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Figure 2. (Color online) Images of microstructure of uranium dioxide pellet at various stage of the sintering process (with different magnification).

At the intermediate sintering stage, the coalescence of grains of powder leads to the formation and growth of grains, resulting in the reduction of their common surface. At the same time the structure of the internal surface of the green pellet changes. The system of interconnected, open and isolated pores is being formed.

Let us define the types of pores. “Isolated pore” has closed surface and approximately spherical shape. “Interconnected pore” is pore having maximal linear size considerably exceeding its mean characteristic size. “Interconnected pore” as well as “isolated pore” has closed surface. Isolated and connected pores together form closed porosity. If pore has open surface then it is named by open pore.

During densification the decreasing of fraction of open, interconnected porosity with increasing of fraction of closed, isolated porosity occurs. When density higher 90%TD the contribution of open porosity to the total porosity in the pellet decreases abruptly and conversely the contribution of closed porosity to the total porosity in the pellet sharply increases (see Fig. 3). Therefore, the density value 90–91%TD can be considered as the percolation limit for the pore system. Traditionally, the intermediate stage is believed to finish when the pore system reaches the percolation limit. At the intermediate sintering stage, relative volume change (\(\Delta\mathrm{V}/\mathrm{V}\)) is most significant and reaches \({\sim}35{\text{--}}40\)%. And only the rest 2–7% corresponds to the initial and final stage of sintering. During final stage of sintering the dissolution of isolated pores occurs.


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Figure 3. (Color online) The dependence of fractions of open, closed, and total porosity on the density of sintered pellets of oxide nuclear fuel.1,2)

Despite on that fact the sintering stages were established long ago. To date there is no unequivocal notion of the physical mechanism of that process (diffusion mechanism6,7) or viscous flow mechanism7,8)). Traditionally, the dilatometric methods are usually used to study the kinetics of sintering. At that only the integral macroparameter (its linear size or density for a preselected thermal program) of the studied sample is measured. Beside the composition of the sintering atmosphere is under controlled. In turn, the physical mechanism of sintering determines microstructure of the specimen — pore size distribution. Let us note that in case of the diffusion model of sintering, the rate of pore radius reduction is inversely proportional to the square of the pore radius, and in the viscous flow model of sintering, the same quantity does not dependent on pore size. Accordingly, the evolution kinetics of the pore size distribution for both sintering mechanisms should vary significantly.

Both the density of the specimen and its dimensions are integral values; therefore, it is not enough the knowledge of kinetics of changes of linear sizes of sample at sintering to univocally determine the sintering mechanism. In reality in order to determine the sintering mechanism it is required the data on the evolution of the pores distribution in specimen under sintering.

However, experimental methods for investigating the porous structure have restrictions concerning their applicability to the study of sintering stages. For example, on the images of microstructure obtained using method of electrons microscopy only pores cross-sections on the plane of polished section are shown. While the characteristics of the pore distribution (mean size and moments of higher orders) and mean pore density can only be calculated on the basis of the 3D pore size distribution.

The existing nowadays method of calculating 3D-distribution from the 2D-pore size distribution (Sheil–Saltykov method9,10)) can be applied only to the specimens in which there is closed porosity and the main fraction of the pores is isolated. According to Fig. 3, that kind of porosity is formed in the sintered green pellet of uranium dioxide at a density exceeding \({\geq}90\)%TD, i.e., after the percolation limit. In fact, the Sheil–Saltykov method is only used to study the porous structure of a sintered pellet of oxide fuel at the final stage of that process.

Accordingly, it is not possible to construct the evolution kinetics of the pore size distribution for all sintering stages at the current level of development of experimental methods to study the microstructure. It seems to be reasonable to research the evolution of pore size distributions in pellets after the long-term isothermal annealing when the density of pellets exceeds \({\geq}90\)%TD.

It has been experimentally established11) that the sintering kinetics of oxide nuclear fuel and its shrinkage depend on several of factors: oxygen potential, sintering temperature, and heating rate up to the sintering temperature. The evolution of the pore size distribution function should also depend on those factors.

The purpose of this study is to identify the sintering mechanism of oxide nuclear fuel by analyzing the experimental pore size distribution in oxide nuclear fuel pellets, which were sintered by varying sintering temperature and heating rate in atmospheres with different oxygen partial pressures.

2. Materials, Facilities, and Methods

In this work, UO2 green pellets containing additive Al(OH)3 were used as research samples. Specimens represented cylinders with generatrix \(L_{0}\) and radius \(r_{0}\). Green pellets were sintered in a high-temperature horizontal dilatometer NetzschDIL 402C (Germany). During sintering it was directly measured the time dependence of generatrix length of the specimen \(L(t)\). Based on the measurement results the kinetics of specimen shrinkage [the time dependence of the relative change of specimen generatrix length \(y(t)=\Delta L(t)/L_{0}\)] was calculated for a preselected sintering thermal program. The specimens were sintered in atmosphere Ar+8%H2. In order to control the oxygen potential in sintering atmosphere the method of a solid electrolyte galvanic cell ZirconiaM (Russia) was used. The solid electrolyte of cell is yttria-stabilized ZrO2 and the reference electrode is Ni/NiO.

In that work, the initial and final density of specimens (before and after sintering) were determined both by hydrostatic weighing methods in the filtered water and by measuring geometric sizes and mass of the specimen. Mass was measured using an electronic balance Satorius CPA225D (Germany), whose measurement error is \(\pm 0.01\) mg. The absolute error in determining the fuel density by hydrostatic weighing is \(\pm 0.03\) g/cm3.

After sintering, the specimens were prepared for microstructure studies. For this purpose, the sintered pellet was cut in half along the generatrix using a precision diamond cut-off machine. Subsequently, the cut surface was ground on the grinding and polishing machine using two types of abrasive paper with a grain size 600 and 1000, then polished with a diamond paste. At the final stage of preparation, the polished surface was cleaned in an ultrasonic bath and wiped with spirits. A scanning electron microscope JEOL JSM-6610LV (Japan) was used to obtain images of the microstructure of sintered UO2 pellets.

Using the “VIDEOTEST” program, the depicted areas of pores cross-sections were counted and a histogram of pores cross-sections distribution was calculated for each image of the microstructure.

Then the Scheil–Saltykov method9,10) was used to calculate 3D-pore size distribution functions based on known histograms of pores cross-sections distributions. A method of calculation of pores size distribution in an oxide nuclear fuel pellet based on the analysis of images of their cross-sections is described in the co-named paper.1)

3. Pore Size Distribution in Specimens Heated up to Sintering Temperature with Various Rates and Sintered at the Same Temperature

Uranium dioxide specimens were heated at rates 4, 6, and 8 K/min up to a maximum temperature 1600 °C and annealed at this temperature for the same time interval 465 min. The sintering temperature regime and sintering curves are shown in Fig. 4(a). Figure 4(b) shows the temperature dependence of specimen shrinkage for the same sintering conditions. Figure 4(b) also shows that the shrinkage curves almost coincide. It means that the shrinkage \(y(t)\) is slightly dependent on time directly and is a composite function of temperature \(y(t)\approx y(T(t))\). Table I gives the initial and final densities of the sintered specimens. It follows from Table I that the final density of the sintered pellets of uranium dioxide coincides within the error.


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Figure 4. (Color online) Kinetics of shrinkage and the temperature regime of sintering of samples heated up to annealing temperature at rates 4, 6, 8 K/min (a); temperature dependence of shrinkage (b).

Data table

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Table I. Specimen density determined by various methods before and after sintering.

Figure 5 shows a pore size distribution function in specimens heated at rates of 4, 6, and 8 K/min and sintered at a temperature of 1600 °C in a gas mixture Ar+8%H2. The same figure shows the mean pore density in specimen and the pores mean diameter. It follows from Fig. 5 that pores with smaller diameter have the highest density. As the pore size increases, the pores density monotonically decreases. In fact, the distribution histograms do not have pronounced maxima and minima on a logarithmic scale. It can also be seen that the mean pore diameter does not depend on the heating rate up to the maximum temperature. This result is consistent with the fact that the value of the final shrinkage of the samples does not depend on their heating rates. Thus, the average characteristics of the pores ensemble are identified only by the temperature and duration of annealing of green pellet if regime of pressing and powder composition remain unchanged.


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Figure 5. (Color online) Pore size distribution in specimens heated at various rates and sintered at temperature 1600 °C.

Table I presents a comparison of the density of specimens after sintering calculated by the pore size distribution, with the same value but measured by the experimental methods. The difference between the density calculated from the pore size distribution and the one identified by other experimental methods (hydrostatic weighing or measuring the specimen's volume and mass) may be caused by several reasons. Firstly, it may be due to an insufficient microscope magnification, at which images of the specimen microstructure were captured. Not all pores remaining in the sintered pellet with a size of less than 1 µm could be identified in the images of the specimen microstructure. Therefore, a difference 2–3%TD could be contained in submicron pores with a diameter of less than 0.1 µm. Secondly, in calculating the pore size distribution by the Sheil–Saltykov method, it is impossible to account for the contribution made by open porosity to the total calculated density of the fuel pellet. For example, according to Fig. 1, when a pellet density is 94–95%TD, the contribution from open pores to the total porosity makes \((0.9{\text{--}}0.8)\pm 0.3\)%. Finally, the present work might have insufficient statistics on the analyzed images of the microstructure, which does not allow us to identify the specimen density with an error of less than 2–3%TD. We assume all these factors to have contributed to the resultant error in calculating the density.

4. Pore Size Distribution in Specimens Sintered at Various Sintering Temperature

To study the fuel microstructure evolution as a function of temperature, within the scope of this research work, there was a set of long-term isothermal annealing of UO2 green pellets at temperatures 1300 °C, 1400 °C for 40 h and at a temperature 1500 °C for 8 h. A more long time annealing was not carried out at 1500 °C since the shrinkage curve reaches saturation at increasing sintering time. Figure 6 shows the time dependence of the shrinkage of those specimens. It can be seen that the pellet sintered at a higher temperature attained the highest density. The density of pellets after sintering is shown in Table II.


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Figure 6. (Color online) Shrinkage curves and temperature program of sintering for UO2 specimens annealed at 1300 °C, 1400 °C, 1500 °C.

Data table

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Table II. Parameters of specimens after sintering.

Figure 7 shows a histogram of the size distribution of pores in specimens sintered at 3 different temperatures. It also shows the mean porosity, mean diameter of pores and sintering temperature of the corresponding specimen. It follows from Fig. 7 that mean porosity decreases at increasing sintering temperature that is consistent with the shrinkage curves in Fig. 7. It should be noted that in case of the specimen sintered at a temperature 1500 °C the pores density in range of sizes \(0.19\leq D\leq 0.35\) µm higher than that one sintered at 1400 °C. During sintering the value of pore density \(n_{k}\) in an arbitrary size interval \(D_{k-1}\leq D\leq D_{k}\) is determined by the rivalry of processes of their dissolution and growth due to dissolution of larger pores with \(D>D_{k}\). An increase in the concentration of small pores (\(0.19\leq D\leq 0.35\) µm) with sintering temperature means that their concentration growth due to dissolution of large pores exceeds the concentration loss due to their complete dissolution. In the remaining size range, however, there is only a general decrease in the pore concentration with increasing of annealing temperature.


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Figure 7. (Color online) Pore size distribution function in UO2 specimens sintered at various temperatures.

An increase in the concentration of small pores during sintering means that the pores growth rate is an increasing function of their radius: \(d\dot{R}/dR\geq 0\). If the pore dissolution rate increases with its radius, then the accumulation of pores in the submicron size range will be due to a decrease in the radius/diameter of pores which belong to the right tail of distribution function.

There are 2 main different approaches to description of the sintering at intermediate and final stages of that process — diffusion theory of sintering and viscous flow theory.

Diffusion theory of sintering7)

The pore surface has curvature considerably exceeding of that quantity for flat surface of solid. Over pore surface there is always an equilibrium (temperature) vacancy concentration proportional to it curvature. Hence, in the sintering sample there is the gradient of vacancy concentration. Therefore, at higher temperature the vacancy flow from pore to the surface of sintered sample appears. This flow leads to the decreasing of vacancy concentration near pore surface. That process is accompanied by emission of vacancy from pore surface in the amount needed to maintenance their equilibrium (temperature) concentration. Emission of vacancies results in decreasing of pore radius. In such way all pores in the heating green pellet are overgrown.

According to the diffusion sintering theory,7) the dissolution rate of isolated pore in a sintered specimen is inversely proportional to the square of its radius. Subsequently, the smallest pores have a maximum dissolution rate, and large pores practically do not dissolute during sintering. Therefore, under these assumptions, the average radius/diameter would shift toward large pores, the density of small pores would decrease sharply, and the density of large pores would change slightly. Meanwhile, it follows from Fig. 7 that the average diameter remains practically unchanged as the annealing temperature rises. Thus, the diffusion mechanism of pore dissolution is not realized during the sintering process of oxide nuclear fuel.

Theory of viscous flow8,12)

The green pellet of oxide nuclear fuel is made from grains of powder by its pressing under load 200–250 MPa, therefore in the green pellet the grains of powder are in the stress state even after removing of external load. If pore is located in viscous medium then under the influence of surface tension force and residual stress the flow of substance appears. This flow is directed to the pore and, accordingly, leads to its overgrowing.

The value of residual stress ∼20 MPa by an order exceeds the surface tension of pore (\({<}2\) MPa at typical pore radius \({>}0.2\) µm).12) Therefore, at an intermediate stage of sintering the process of pore overgrowing in a viscous medium proceeds mainly under the influence of residual stress. During sintering the relaxation of residual stresses occurs. To the beginning of final stage of sintering the residual stresses practically absence and following pore overgrowing occurs only under influence of forces of surface tension (classical Frenkel's theory8)).

It follows from the theory8) that the dissolution rate of isolated pore does not depend on its size and is defined only by the viscosity of the sintered substance. The viscous flow mechanism8) is most precise in describing the observed microstructure evolution of that sintered ceramic.

Nevertheless, it should be noted that besides surface tension in the green pellet there are also residual stresses between the compressed grains of powder.12) The presence of residual stresses leads to an additional contribution to the pores dissolution rate proportional to their radius.12) It is the mechanism of viscous flow of the substance under the influence of residual stresses and capillary forces that determines the sintering process of oxide nuclear fuel heated to a temperature exceeding its brittle-to-ductile transition temperature.12)

At room temperature all ceramics are brittle substances. Their strain-stress diagram is linear, and proportionality limit coincides with ultimate stress. But at temperatures higher than temperature of their brittle-ductile transition, on the strain-stress diagram the nonlinear dependence of stress from strain appears that corresponds to the plastic deformation. In the plastic (viscous) state the solid has finite viscosity. Therefore, according to the theory of viscous flow the sintering of ceramics (including uranium dioxide) occurs only at temperatures exceeding the temperature of their brittle-ductile transition. For uranium dioxide such temperature is 1100 °C.12) Let us note that according to diffusion theories of sintering the green pellet is sintered at arbitrary temperature because the diffusion proceeds at arbitrary temperature. But at low temperature the rate of that process (defined by Arrhenius law) is negligible.

5. Pore Size Distribution in Specimens Sintered in Atmospheres with Various Oxygen Potentials

The onset sintering temperature11) is known to depend on the oxygen potential of the gaseous environment where the process takes place. This value is shifted toward higher temperatures in gaseous environments with an extremely low partial oxygen pressure. Moreover, the deviation from the stoichiometric composition of the sintered pellet UO\(_{2+x}\) depends on the oxygen partial pressure in the sintering atmosphere. Figure 8 shows the sintering curves for UO2 specimens annealed for 20 h at a temperature 1300 °C in atmospheres with various oxygen potentials.


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Figure 8. (Color online) Shrinkage curves and temperature regime of sintering for specimens of uranium dioxide annealed at 1300 °C in sintering atmospheres with various oxygen potentials.

In Fig. 8 the value of the oxygen potential of the gaseous environment where the specimen was being sintered is corresponded to each sintering curve. It can be seen from Fig. 8 that the fuel pellet, sintered at the highest oxygen potential, has attained the greatest densification. Table III presents the density values of specimens whose sintering curves are shown in Fig. 8.

Data table

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Table III. Parameters of specimens after sintering.

Figure 9 illustrates pore size distribution functions in these specimens. From Fig. 9 it follows that the highest densification value was obtained due to a reduction in the pore density of the submicron size \(D<1\) µm. Even a slight increase in the partial pressure of oxygen in the sintering atmosphere can lead to an increase in the dissolution rate of pores of all sizes in a heated green pellet. It should be noted that the average value of the pore diameter is slightly dependent on the sintering atmosphere.


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Figure 9. (Color online) Pore size distribution in UO2 specimens sintered at 1300 °C in atmospheres with various oxygen potentials.

6. Conclusions

Green pellets of oxide nuclear fuel have been sintered with variation of:

•

heating rate during ramp up to the sintering temperature;

•

sintering temperature;

•

oxygen potential of sintering atmosphere.

The dilatometric method was used to experimentally determine the kinetics of specimen shrinkage during sintering. The density of the sintered pellets was measured by the hydrostatic weighing method in water and by measuring the volume and mass of the sintered pellet. Microstructure of the sintered specimens was studied by means of scanning electron microscopy. A histogram of the pore size distribution cross-sections over area of polished section was constructed. The Sheil–Saltykov method1) was used to calculate 3D-pore size distributions, the average diameter and porosity of the specimens.

From the experimental 3D pore size distributions, it has been found that:

•

the main fraction of pores at the intermediate sintering stage of oxide nuclear fuel belongs to the submicron region of characteristic sizes \(0.1<D<2\) µm;

•

pore size distribution in the sintered UO2 pellet is not dependent on its heating rate to the sintering temperature, but is determined by the value of the sintering temperature and duration, as well as the oxygen potential value of the sintering atmosphere;

•

specimen shrinkage occurs due to a decrease in the density of pores of all sizes, and the shrinkage increases with sintering temperature and the oxygen potential of sintering atmosphere;

•

absolute value of pore dissolution rate is a non-decreasing function of pores diameter.

The kinetics of evolution of pore size distributions has allowed us to unambiguously establish the sintering mechanism of oxide nuclear fuel:
•

at the final sintering stage the process is controlled by Frenkel mechanism of viscous flow under the action of capillary forces and residual stresses;

•

the diffusion mechanism is not being realized during the sintering process of oxide nuclear fuel.

Acknowledgment

The research work was supported by the State task of the Ministry of Education and Science of the Russian Federation (Project 11.2594.2017/4.6).

References

  • 1 Y. N. Devyatko, O. V. Khomyakov, A. V. Tenishev, V. V. Mihalchik, and D. P. Shornikov, J. Phys. Soc. Jpn. 88, 074802 (2019). 10.7566/JPSJ.88.074802 Link, Google Scholar
  • 2 B. A. Kalin, Fizicheskoe materialovedenie. Uchebnik dlya vuzov pod red. B.A. Kalina. t. 6 (2). YAdernye toplivnye materialy (Physical material science. Textbook for universities V. 6 (2). Nuclear fuel materials) (MEPhI, Moscow, 2008) p. 604 [in Russian]. Google Scholar
  • 3 R. L. Coble, J. Appl. Phys. 32, 787 (1961). 10.1063/1.1736107 Crossref, Google Scholar
  • 4 R. L. Coble, J. Appl. Phys. 32, 793 (1961). 10.1063/1.1736108 Crossref, Google Scholar
  • 5 D. L. Johnson, J. Appl. Phys. 40, 192 (1969). 10.1063/1.1657030 Crossref, Google Scholar
  • 6 B. Ya. Pines, J. Tech. Phys. 16, 137 (1946) [in Russian]. Google Scholar
  • 7 B. Ya. Pines, Usp. Fiz. Nauk 52, 501 (1954)10.3367/UFNr.0052.195404a.0501 [in Russian]. Crossref, Google Scholar
  • 8 Ya. I. Frenkel, J. Exp. Theor. Phys. 16, 29 (1946) [in Russian]. Google Scholar
  • 9 E. Scheil, Z. Anorg. Allg. Chem. 201, 259 (1931) 10.1002/zaac.19312010123[in German]. Crossref, Google Scholar
  • 10 S. A. Saltykov, Stereometrische Metallographie (Stereometric metallography) (VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1974) p. 397 [in German]. Google Scholar
  • 11 V. G. Baranov, Yu. N. Devyatko, A. V. Tenishev, and O. V. Khomyakov, Phys. At. Nucl. 78, 1345 (2015). 10.1134/S1063778815120029 Crossref, Google Scholar
  • 12 V. G. Baranov, Yu. N. Devyatko, A. V. Tenishev, A. V. Khlunov, and O. V. Khomyakov, J. Nucl. Mater. 432, 52 (2013). 10.1016/j.jnucmat.2012.07.050 Crossref, Google Scholar

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