MODELING OF INTERACTION LAYER GROWTH BETWEEN UMo PARTICLES AND AN Al MATRIX
 DOI : 10.5516/NET.07.2013.713
 Author: KIM YEON SOO, HOFMAN G.L., RYU HO JIN, PARK JONG MAN, ROBINSON A.B., WACHS D.M.
 Organization: KIM YEON SOO; HOFMAN G.L.; RYU HO JIN; PARK JONG MAN; ROBINSON A.B.; WACHS D.M.
 Publish: Nuclear Engineering and Technology Volume 45, Issue7, p827~838, 20 Dec 2013

ABSTRACT
Interaction layer growth between UMo alloy fuel particles and Al in a dispersion fuel is a concern due to the volume expansion and other unfavorable irradiation behavior of the interaction product. To reduce interaction layer (IL) growth, a small amount of Si is added to the Al. As a result, IL growth is affected by the Si content in the Al matrix. In order to predict IL growth during fabrication and irradiation, empirical models were developed. For IL growth prediction during fabrication and any followon heating process before irradiation, outofpile heating test data were used to develop kinetic correlations. Two outofpile correlations, one for the pure Al matrix and the other for the Al matrix with Si addition, respectively, were developed, which are Arrhenius equations that include temperature and time. For IL growth predictions during irradiation, the outofpile correlations were modified to include a fissionrate term to consider fission enhanced diffusion, and multiplication factors to incorporate the Si addition effect and the effect of the Mo content. The inpile correlation is applicable for a pure Al matrix and an Al matrix with the Si content up to 8 wt%, for fuel temperatures up to 200 ℃, and for Mo content in the range of 6 – 10wt%. In order to cover these ranges, inpile data were included in modeling from various tests, such as the US RERTR4, 5, 6, 7 and 9 tests and Korea’s KOMO4 test, that were designed to systematically examine the effects of the fission rate, temperature, Si content in Al matrix, and Mo content in UMo particles. A model converting the IL thickness to the IL volume fraction in the meat was also developed.

KEYWORD
UMo , UMo/Al , Dispersion Fuel , Interaction Layer , IL Growth , Modeling , Inpile Data

1. INTRODUCTION
UMo alloy fuel is a prime candidate for conversion of highpower research and test reactors, from HEU cores to LEU cores, thanks to its high density and advantageous irradiation performance. Two forms of UMo alloy fuel have been studied in the U.S. GTRICONVERT program (formerly known as RERTR): One is UMo particle dispersion in an Al matrix (UMo/Al dispersion fuel); the other is direct bonding of UMo thin foil to Alalloy cladding (UMo monolithic fuel) (Fig. 1). In this paper, because modeling the interaction layer growth between the UMo particles and Al matrix was concerned, we focused only on the dispersion fuel form.
One of the intrinsic characteristics of the UMo/Al dispersion fuel is perhaps the interaction layer (IL) growth between the UMo fuel particles and matrix Al. Interaction layer growth is due to interdiffusion between the fuel particle (U and Mo) and matrix (Al). Hofman and coworkers [1] reported the first observation of IL growth in UMo/Al from an irradiation test, where they also proposed a correlation
[Fig. 1.] Schematic Illustration of Cross Section Views of Dispersion Fuel and Monolithic Fuel Forms
for IL growth expressed as a function of the fission rate, temperature, and time. Hayes [2] later incorporated this model in a computer model PLATE. Ryu and coworkers [3] systematically measured the kinetics of IL growth and obtained the activation energy for IL growth for outofpile heating tests.
UMo/Al dispersion fuel performed well in irradiation tests at lower power and burnup, so its qualification appeared near [4]. However, later tests adopting higher power, i.e., higher fission rate and higher burnup, showed enhanced fuelmeat swelling, which was caused by massive IL growth, and in some cases, by large pore formation in the fuel meat [5],[6]. The pores were distinguishable from the fission gas bubbles in the fuel particles, in that they mostly formed outside of fuel particles, i.e., in the ILs, although both were commonly filled with fission gases. The formation of IL results in a net volume increase and a net thermal conductivity decrease in the meat. The low thermal conductivity of IL provides adverse feedback for higher IL growth by further increasing the fuel meat temperature. While UMo particles and Al are crystalline, ILs formed between UMo and Al are amorphous during irradiation [7],[8]. The amorphous nature of the ILs is believed to be the reason for large pores formed outside of fuel particles [9]. Fission gas diffusivity in the amorphous ILs is higher than in its crystalline state, and viscosity is lower, both of which promote fissiongaspore formation in the ILs.
A remedy was needed to reduce the IL growth rate and strengthen the IL to resist against pore formation and growth. Noticing the low IL growth between U_{3}Si_{2}/Al dispersion that did not form pores in the IL until full LEU burnup (see [10],[11]), it was proposed at ANL that a small amount of silicon be added to the aluminum matrix [12],[13]. An ample number of studies, both outofpile ([14][25]) and inpile ([26][42]), have been conducted to examine the effectiveness and better application of the remedy. The common findings were that Si addition to Al not only reduced IL growth, but also delayed pore formation and growth in the IL. Hence, overall performance of this fuel was improved.
Since IL growth is one of the deciding performance variables for UMo/Al dispersion fuel, an accurate model is also required. The studies for interaction layer (IL) growth modeling for inpile applications includes two cases: one for the pure Al matrix case [1],[2],[43],[45], and the other for the Siadded matrix case [28],[48]. The most uptodate correlation for the pure Al matrix case was by Wachs [45], which was confirmed as accurate by Kim [48]. The correlation for the Siadded matrix case, developed mostly on lowtemperature miniplate test data, was applied for all Si contents larger than 2 wt%. There was no need to provide a separate factor to consider the effect as a function of the Si content, because in the low temperature tests the addition of 2 wt% Si virtually suppresses IL growth to the lowest possible level. However, it has been noticed that the modeling underpredicts the high temperature test results from the RERTR9 and KOMO4. The high temperature test KOMO4 showed that a Si content higher than 2 wt% had different IL growth kinetics [39],[49]. Therefore, a model applicable to the high temperature regime and a Si content higher than 2 wt% was necessary. Another objective of the present work is to unify the existing separate models for the pure Al matrix and the Al matrix with Si addition.
An interaction layer can also grow during fabrication and the followon blister test when the fuel plates undergo heat processes. An IL growth model in this step was also required.
2. MODELS FOR OUTOFPILE INTERACTION LAYER GROWTH
2.1 Al Matrix with no Si Addition
IL growth during fuel fabrication and any followon heating test is modeled in this section. The interaction layer growth between UMo and Al is a typical interdiffusion process between U and Mo atoms versus Al atoms. Hence, in this paper, interaction and interdiffusion are used interchangeably. In addition, the ratecontrolling process in interaction layer growth is interdiffusion, not the reaction product formation [11]. The outofpile IL growth takes the following modified Arrhenius correlation because interdiffusion is due to thermal activation:
where Y_{Al} is the average IL thickness (μm) in a pure Al matrix, i.e., Al matrix without any intentional Si addition, T is the fuel meat temperature in K, and t is the time in s. The constants have been fitted using the data taken from Ryu [3] (Table 1). Only data from dispersion fuel tests were used. The IL thickness was measured using optical micrographs of the cross section of a sample. From an optical micrograph, several IL thicknesses were measured, and the average value was used as the nominal value. The method to obtain the true IL thickness is explained elsewhere [50]. Generally, in an optical micrograph, the common thinnest IL on the largest particle was taken to represent the true IL thickness.
The RERTR testplates were fabricated using the hot rolling technology [51], in which the heat processes involved were much shorter, ~1 h, but at a much higher temperature, 500 ℃, than inpile tests (Table 2, Table 3). For example, the test duration for the RERTR4 test was 257 d, and the lifeaverage fuel temperature was ~100 ℃.
IL growth during fabrication is hard to assess, so the correlation given in Eq. (1) is for an average value. The largest uncertainty during fabrication is due to the irregular contact pressure between particles with the matrix. For a typical rolling process used for RERTR test plates [51], the bonding between the UMo particles and matrix is poor during the preheating and first pass, so IL growth during these steps is virtually negligible. Meaningful bonding is achieved after the second pass and subsequent IL growth occurs during the last heating ~15 min (see [51] for detailed time and temperature for each step). The most IL growth takes place during the subsequent blisterannealing test at 485 ℃ for an hour. Using Eq. (1), we estimated an average of ~1.5 μm of IL growth during fabrication. The test
samples of the KOMO4 test from KAERI were produced using an extrusion process taking 0.5 hour at 400 ℃, for which Eq. (1) predicts negligible IL thickness. Table 2 compares the heat processes and IL growth involved during fabrication of some RERTR tests and the KOMO4 test.
The Mo content of the UMo particles is in the range of 6 – 10 wt%. However, the most common Mo contents are 7 wt% and 10 wt% in the RERTR irradiation tests. In the Mocontent 10 wt%, the thermodynamic equilibrium phase of the UMo is the αU + δU_{2}Mo dual phase at temperatures below ~550 ℃. For other Mo content in the range of 6 – 10 wt%, the phase boundary is slightly higher and another phase (α+γ) exists. Therefore, during fabrication, some parts of the metastable γU particle transform to αU. The γU has a lower swelling rate during irradiation than the αU (see [52][54]for details) and has a lower IL growth rate [17]. When the γU is partially transformed to the αU during fabrication and the subsequent blister test, a thicker IL grows on the αU while a thinner IL grows on the γU, which results in nodular type IL growth on the same UMo particle. In this situation, expressing IL in volume is more appropriate than in thickness.
2.2 Al Matrix with Si Addition
Measured data for UMo/AlSi dispersion, i.e., UMo dispersion in a Siadded Al matrix, are scarce from outof pile tests and scatter with considerable uncertainties. Iltis [23] measured the IL thicknesses of Siadded plates fabricated at a lower fabrication temperature than typical RERTR plates (Table 2) and then heated for two or four hours. As given in Table 2, 4 wt% Si and 6i plates show no clear correlation between the Si content and IL thickness, implying that the effect of Si content on IL growth in the outofpile heating test is negligible. Keiser and coworkers [24] also reported an outofpile heating test result of plates with Si addition. Using images in Ref. [24], we measured IL thicknesses as given in Table 1. The Keiser data also confirm that there is no clear correlation between the Si content and IL thickness. This uncertainty is chiefly because of the irregular IL thickness, which is caused by the decomposition of the metastable γphase UMo particles.
It is typical that considerable parts of the UMo surfaces have extremely thin ILs while some parts have thicker ILs, including some nodular type ILs. As discussed in sect. 2.1, this nodular type of IL is known to form on the parts of the UMo surface transformed to α+γ' during the heating steps. Because of the much higher IL growth rate of the α phase [17], the fuel surface with γtoα+γ' phase transformation shows higher IL growth. Once formed, the thick IL on the αU precludes Si diffusion to the fuel
surface and formation of a Sibarrier on the fuel surface to block Al diffusion. This further contributes to the formation of more irregular ILs in UMo/AlSi dispersions than UMo/ Al dispersions after inpile tests. Hence, considerable uncertainty is inevitably involved in the IL thickness of a plate with Si addition.
Park et al. [39] annealed a UMo/Al5Si dispersion sample at 580 ℃ for ~1 h and observed an average IL thickness of ~8 μm (see also Ref. [49]). Because the temperature was much higher, but still below the γphase boundary, it is probable that the decomposition of the metastable γphase UMo particles was higher in Park’s test, so his datum may be exaggerated. However, the extent of IL growth reported by Park is lower than those of U3Si/Al and U_{3}Si_{2}/Al dispersion fuels [11], suggesting that at the annealing temperature the UMo fuel surface forms an excellent barrier that effectively blocks Al diffusion into UMo. This result also implies that the effect of the presence of the Mo in UMo/AlSi is to synergistically reduce IL growth as in USi intermetallic dispersion in Al with a small addition of Mo, as reported by Ugajin [55].
Some diffusioncouple test data are available in the literature [17],[18]. In a typical diffusioncouple test to measure interdiffusion between UMo and Al, a UMo block is welded with an Al block, and the metal couple, UMo versus Al, is isothermally heated. In the posttest analysis, the interaction layer thickness is measured. The contact pressure between UMo and Al in a diffusioncouple test is higher than that of a dispersion sample, so the IL growth rate is generally higher in the diffusioncouple test than in the outofpile test of dispersion fuel. For this reason, the diffusioncouple test data cannot be used with the dispersion test data.
Using the data provided in Table 1, we performed a data fitting to the Arrhenius equation and the IL growth correlation is obtained as follows (R^{2}=0.67):
where Y_{AlSi} is the IL thickness (μm) in an Al with a Si addition, T in K and t in s.
Using Eqs. (1) and (2), the IL growth during fabrication and the followon blister test for the RERTR test plates, and KOMO4 test were calculated and given in Table 2. Once IL growth before irradiation is assessed by using Eq. (1) or Eq. (2), the total IL growth accumulating during fabrication and irradiation can be obtained by
where Y is the total IL thickness, Y_{fab} is the fabrication IL thickness calculated by Eq. (1) or Eq. (2), and Y_{i} is the IL thickness during irradiation. The model for IL thickness prediction during irradiation is described in the following section.
3. MODEL FOR INTERACTION LAYER GROWTH DURING IRRADIATION
3.1 Inpile Test Data
The irradiation test data used in the model development are summarized in Table 3. While the RERTR test samples are miniplates having the meat thickness of ~0.64 mm, KOMO4 test samples have rodtype geometry with the meat diameter of 6.4 mm. Because of the much greater distance of heat transport and the higher heat flux, the KOMO4 test samples have much higher temperatures than the RERTR test samples for the same power.
For the RERTR test plates, the fuel temperatures were calculated at BOL and EOL, and arithmetic averages were taken to represent the test samples (Table 3). For the KOMO4 test, the timedependent fuel temperatures were calculated and lifeaverage values were obtained. The testsample power, and hence the fission rate, decreases due to depletion of fissile atoms in the sample. On the other hand, fuel temperatures tend to increase as the meat thermal conductivity degrades due to IL growth and the formation of fission gas pores. These two factors somewhat compensate for each other, and as a result, the change in fuel temperature over test life is insignificant. In the RERTR miniplate tests, although the temperature and fission rate (i.e., power) are each independent variables to each other, they are still coupled. In this regard, the KOMO4 test data are valuable because they have higher temperatures than the RERTR test data while the fission rates are similar.
IL thicknesses were measured at several locations in an optical micrograph and the average value was used as the nominal value. The method to obtain the representative IL thickness is illustrated in Fig. 2. Two cross sections are shown for illustration. The cut surface A is off of the equator B. Therefore, the IL thickness L1 measured in the cut surface A is thicker than L2 measured in the equator. Generally, on a metallographic picture, the common thinnest IL is more likely to be the true IL thickness, because it is more likely to be on a plane close to the equator of the fuel particle.
In Fig. 3 and Fig. 4, posttest micrographs of RERTR 6 and KOMO4 samples are shown, respectively. The RERTR6 is a test having relatively low temperatures and low fission rates. Although temperatures vary by ~18 ℃, all test plates consistently show that IL thickness decreases as the Si content increases. This trend is more noticeable in the KOMO4 test, which has less temperature variability.
The ILs of the RERTR samples were measured at the plate transverse (width) center to exclude possible influence
of pores forming in the matrix, and fuel creep occurring in the fuel meat loaded closer to the ATR core center, a phenomenon reported previously [56],[57]. For the KOMO 4 test, measurements were made at the meat center and meat midradius regions, by which two IL thicknesses at different temperatures with the same fission rate were obtained (Table 3).
The measurement errors, given in Table 3, stem largely from the irregular IL thicknesses. The errors tend to be larger for the samples with a Siadded matrix than the
pure Al matrix samples. PIE images also showed locally thick, nodular type, ILs, the cause for which originated from the α+γ' transformation during fabrication and the following blister test. On the other extreme, PIE images showed that ILs on some UMo particles were still thinner than the average IL thickness during fabrication. This indicates either that some parts of the fuel surface had poor contact from fabrication to the end of irradiation, or that large Si particles contacting the fuel particle effectively blocked Al diffusion. The asfabricated IL thickness was subtracted from the postirradiation IL, which means the predicted results by the new correlations are for those during irradiation.
3.2 Correlation Development for Irradiation
3.2.1 Basic Correlation
The IL growth correlation during irradiation is a modified Arrhenius equation from Eq. (1), and an additional term with the fission rate is multiplied to account for fissionenhanced diffusion (FED):
where ḟ is the fission rate, and A and q are empirical constants. The power, p, to the fission rate was empirically determined as p=0.5 [11],[44].
There have been several other correlations that take a similar form to Eq. (4) but with different constants [44], [45],[48],[58]. In order to fit both the RERTR and KOMO data, the fitting constants here were revised from those of Refs. [44] and [45]. The best fit was obtained with A= 2.6x10^{8} and q=3850 K for plates with U7Mo in a pure Al matrix. In Table 3, the predicted and measured IL thicknesses are compared. Therefore, the correlation for the samples with a pure Al matrix is:
where Y is in μm, ḟ in f/cm^{3}s, T in K, and t in s.
The effects of Si addition and Mo content are considered by multiplying additional factors to Eq. (5) as follows:
where f_{Si} is the reduction factor by Si addition in the Al matrix and f_{Mo} is the factor to assess the Mo content other than 7 wt% in the UMo alloy particles. The modeling of these factors is described in the following subsections.
3.2.2 Factor for Siaddition Effect, f_{Si}
The addition of Si in the Al matrix results in an exponential reduction of IL thickness that varies with the Si content. Comparing the results from the lower temperature test RERTR6 and the higher temperature test KOMO4, it is noticeable that the Si addition effect on IL growth also depends on temperature. For the RERTR6 test, the Si effect is virtually saturated at 2 wt% Si (Fig. 5). However, the KOMO4 test shows that the IL reduction effect continues up to 8 wt% Si without saturation. Fitting the IL reduction versus the Si content for two different temperatures given in Fig. 5, we obtained the IL reduction factor by Si addition in Al as
where T is the fuel meat temperature in K (≤ 473 K) and W_{Si} is the Si content in the matrix in wt% (≤ 8 wt%). f_{Si} is in the range 0.002 ≤ f_{Si} ≤ 1. The minimum occurs at the Si content of 8 wt%, whereas the maximum occurs for the pure Al.
3.2.3 Factor for Mo Content Effect, f_{Mo}
It is known that as the Mo content increases, the IL growth rate decreases [2],[54],[14], so cases with a Mo content other than 7 wt% need to be considered. The current understanding is that the metastable γphase UMo more readily decomposes to the α+γ' if the Mo content in the alloy is reduced. Although the αphase transforms back to the γphase soon after irradiation starts [59],[60],[61], once formed, the αphase produces a thicker IL during fabrication and the subsequent blister test. The thicker IL formed on the a phase weakens the Si addition effect, and the result is an increase in the overall IL growth rate during irradiation. In the thick IL, as the Si concentration decreases, so does its activity [43]. Mirandou [19] also found a weakened Si effect in the thick IL from an elevatedtemperature outofpile test and argued that it was owing to the formation
of the αphase, on which U_{4}Mo_{6}Al_{43}+UAl_{3} phases form, excluding Si.
In the RERTR experiment modeling [2], we observed that the IL growth rate decreased linearly with the Mo content in the range of 6 – 10 wt%. This effect was similarly formulated as follows:
where W_{Mo} is the Mo content in fuel particles in wt%. f_{Mo} varies between 0.85 (at 10 wt% Mo) and 1.05 (6 wt% Mo). A Mocontent beyond 10 wt% is not considered in the US RERTR program.
4. DISCUSSION
One of the objectives of the development of the present model was to unify the two independent IL growth correlations applicable either to a pure Al matrix, or to an Al matrix with up to 8wt% Si and temperatures up to 200 ℃. In addition, IL formation before irradiation is included, so the model can be used for fuels produced by various fabrication methods.
The observations from the KOMO4 test [39] showed that Si tends to accumulate mostly at the ILmatrix interface due to Si diffusion from the matrix. It is known that Si contained only in the fissionfragment recoil zone produces Si diffusion flux. As the IL grows, the overlapping volume fraction of the recoil zones increases and, hence, there is a decrease in the
effective amount of Si per unitfuelsurface area available for diffusion.For the RERTR9 test, the fuel plates were made with smaller fuel particles and higher Uloading, which yielded more recoilzone overlapping during the test, and in turn reduced the effective Si amount available per unitfuelsurface area. Contrarily, the KOMO4 test samples had larger fuel particles sizes and relatively lower Uloading in the meat (see Table 3). As a result, smaller recoilzone overlapping was made, so the effective Si amount per unitfuelsurface area was higher. As Uloading increases, not only the matrix volume decreases and the depletion of the matrix occurs earlier, but homogeneity in fuel particle spatial distribution also tends to decrease. Regions with higher UMo particle densities occur, where the effective Si amount per unitfuelsurface area decreases. Hence, even for the same Si content in the matrix, the IL growth rate can be different.
In the meat, the homogeneity of fuelparticle spatial distribution may also affect the effective Si availability. For example, a higher homogeneity in fuelparticle spatial distribution improves the effect of Si addition.
An additional consideration in the efficacy of Si is how Si is added to the matrix Al. The finer the Si precipitates, the more effective is the Si addition: Hence, a lower IL growth rate. At present, there are two viable methods of adding Si to the matrix. One is adding Si to the Al as an alloying element, and the other is directly adding the Si powder to the Al powder during fuel fabrication. The former was considered the better method to provide finer Si particles in the matrix.
In order to have more accurate modeling, consideration of the parameters discussed above (Uloading, homogeneity in fuelparticle spatial distribution and Si precipitate size in the matrix) may also be necessary. In the present modeling, however, these parameters are not explicitly considered.
The Si concentration in the IL tends to decrease during irradiation. As the Si concentration decreases, the Si’s strength to reduce the IL growth rate also decreases. However, the change in the Si effect during irradiation is not included in the present model.
The comparison between the measured data and predicted IL thicknesses are given in Table 3. Considering uncertainties in temperatures and measurement errors, a fair agreement was generally achieved, except for some cases. The uncertainty in the meat temperatures is believed to be caused by the uncertainty in the meat thermal conductivity at high burnup. Measurement errors were primarily due to the irregular IL thickness.
5. CONVERSION OF IL THICKNESS TO IL VOLUME
IL growth data given in thickness are often more convenient than those given in IL volume, because they do not need supplemental data such as Uloading and UMo particle size. However, for high IL growth cases, the thickness is not only difficult to measure, but it is also less meaningful. For these circumstances, data on IL volume fraction is a better metric. Consequently, a conversion model from IL thickness to IL volume was developed, assuming that fuel particles had a uniform size and were distributed in an FCC array.
Fig. 6 illustrates the configuration of two neighboring fuel particles and the IL formed around them. The distance,
d, between the surfaces of two neighboring particles is
where a is the FCC unit cell edge length, and r is the fuel particle radius. The fuel volume fraction in the meat is defined as
where V_{m} is the meat volume and V_{f} is the fuel volume in the unit cell, respectively. Because there are four fuel particles in the unit cell, V_{f} is given by
where r is the average fuel particle radius known from the fabrication data. From Eqs. (9) – (11), d can be found by
where the applicable range of V_{f} is less than 0.74, which is the FCC packing fraction. The fuel volume fraction V_{f} is usually calculated with known fabrication data (Uloading), because V_{f} =w_{U}/ρ_{U} where w_{U} is Uloading, and ρ_{U} is Udensity in the fuel particle. For example, V_{f} for 8 gU/cm^{3} of U7Mo is calculated by V_{f}= w_{U}/ρ_{U} = 8/16.3=0.49 where ρ_{U} = 17.5 ^{*} (1 – 0.07). The physical density of U7Mo alloy is 17.5 g/cm^{3}.
In Fig. 6, the overlapping part of the IL volume of the righthandside fuel particle, by the neighbor particle, is a partial sphere with height, h, of which the volume is
where h = Y – d/2 and R= r + Y. Here Y is the IL thickness. When the IL overlaps with neighboring fuel particles, i.e., Y is greater than d, as marked by the darker gray region in Fig. 6, and this volume must be subtracted from the large cap volume given in Eq. (13). Because there are two symmetric caps, two of these small caps must be considered.
where g = (Y– d)/2.
The IL volume can be calculated considering only one fuel particle surrounded by 12 neighboring ones by
The IL volume fraction v_{IL} in the fuel meat can be calculated by
where V_{IL} is given by Eq. (15) and V_{f} given in Eq. (11).
Fig. 7 shows the model predictions for IL volume fraction versus IL thickness for 6 gU/cm^{3} and 8 gU/cm^{3} Uloading cases with a fuel particle size of 70 μm. Also included is a case for the KOMO4 test, for which fuel loading is 5 gU/cm^{3} with fuel particle size of 150 μm. Fuel swelling and fuel consumption by the interdiffusion layer growth are not considered. However, these two factors somewhat tend to compensate for each other to give reasonably acceptable model predictions. A more detailed model is necessary for an accurate result, but the model described here is suitable for approximate estimates.
6. CONCLUSIONS
In the US GTRIconvert program (formerly known as RERTR), UMo alloy particle dispersion in Al is a primary fuel form being studied for use in converting HEUfueled research and test reactors to LEUfueled ones. In order to achieve sufficient total uranium densities, high fuelvolume loading is pursued. One of the largest obstacles to good fuel performance is interaction layer (IL) growth between the UMo particles and matrix Al, which needs to be minimized.
For an accurate fuel performance analysis, a prediction model for IL growth is therefore necessary. Two empirical IL growth correlations were developed for outofpile fabrication and possible subsequent testing: One is for the pure Al matrix, and the other for the matrix with Si addition. The IL growth correlations are Arrhenius equations.
The inpile growth correlation, developed using the RERTR4, 5, 6, 7 and 9 data, as well as KOMO4 data, takes a form similar to the outofpile correlations. For the inpile correlation, the outofpile IL growth was augmented by fissionenhanced diffusion (FED). The FED effect was modeled by the squareroot of the fuelparticle fission rate.
The inpile correlation was further enhanced to include the effect of Si addition in the Al and the effect of the Mo content. The model is applicable for Si contents in the matrix up to 8 wt%, for fuel temperatures up to 200 ℃, and for Mo content in fuel particles in the range of 6 – 10 wt%.
An approximate analytical method to convert IL thickness to IL volume fraction in the fuel meat was proposed. For a more accurate conversion, the volume changes in fuel and matrix caused by their consumption by IL growth must be considered together with the volume expansion by fissionproductinduced fuel swelling, which was not considered in the present work.

42. Izhutov A., Alexandrov V., Novosyolov A., Starkov V., Sheldyakov A., Shishin V., Iakovlev V., Dobrikova I., Vatulin A., Kulakov G., Suprun V. 2010 “The Main Results of Investigation of Modified Dispersion LEU UMo Fuel Tested in the MIR Reactor” [Proc. Int. Meeting on Reduced Enrichment for Research and Test Reactors (RERTR)]

[Fig. 1.] Schematic Illustration of Cross Section Views of Dispersion Fuel and Monolithic Fuel Forms

[Table 1.] IL Growth between UMo a and Al from Outofpile Heating Tests, RERTR Tests and KOMO4 Test during Fabrication and Followon Blister Test

[Table 2.] Heat Processes during Fabrication and Followon Blister Test and Predicted IL Growth before Irradiation for RERTR Tests and KOMO4 Test

[Table 3.] Test Data and Comparison of IL Thicknesses between the Measured and Predicted from RERTR4, 5, 6, 7, 9 and KOMO4 Tests

[Fig. 2.] Schematic Illustration of the Measurement Method of Interaction Layer Thickness. A and B are Cross Section Planes.

[Fig. 3.] Post Irradiation Micrographs Showing Microstructures of RERTR6 plates. The Burnup is in Percent Fission Per Initial Heavy Metal Atom (FIHMA).

[Fig. 4.] Post Irradiation Micrographs Showing Microstructures of KOMO4 Samples. The Burnup is in Percent Fission Per Initial Heavy Metal Atom (FIHMA).

[Fig. 5.] Comparison of IL Reduction Factors Obtained for the Lowtemperature RERTR6 Test (at LifeavErage T ~100 ℃) and the Hightemperature KOMO4 Test (at Lifeaverage T ~180 ℃), where the IL Reduction Factor is Defined as the Square of IL Thickness Divided by the Square of IL Thickness for a Pure Al Matrix at the Same Irradiation Condition.

[Fig. 6.] Schematic Showing Configuration of Two Neighboring Particles with IL Formed on the Surfaces and IL Overlapping.

[Fig. 7.] Prediction of IL Volume Fraction as a Function of IL Thickness for 6 gU/cm3 and 8 gU/cm3 Udensity in the Meat (Average Fuel Particle size = 70 μm) and for 5 gU/cm3 UDensity in the Meat (Average Fuel Particle Size = 150 μm).