U–Mo equilibrium phase diagram

An equilibrium phase diagram of an alloy allows one to predict its phase composition based upon its constituent contents and its temperature after all transformations have been completed. Even though the U–Mo alloy in the fuel is never in its equilibrium condition, the equilibrium phase diagram provides a starting point when studying the effects of composition on the fabrication and operation of the fuel.

2.2.1. Equilibrium phase diagram

The U–Mo equilibrium phase diagram published in 1990 by Massalski [21], and discussed in Section A.2.2 point (8) of the Appendix, has been the reference diagram for the current LEU U–Mo fuel development effort. Massalski’s diagram shows the eutectoid transformation of γ′ phase material (body centred cubic [bcc] –U containing Mo in solid solution) to form α phase material (orthorhombic –U containing Mo in solid solution) and tetragonal γ′ phase material (U2Mo) to occur at 550°C, instead of at 565°C as measured by Dwight during the most recent measurement [22]. This apparent discrepancy ultimately led to review of the data in Massalski’s phase diagram and tracing the data to their origins. The results of this effort are described in Section A.2 of the Appendix. The development of the U–Mo phase diagram was first reported by Ahmann et al. in 1945 [3]; however, that work and most other work on U–Mo were classified until the mid-1950s. Most of the work on the phase diagram until around 1960 was focussed on determining the phase boundaries and phase fields from ~60 to 100 wt% U and from room temperatures to temperatures above the uranium  phase to γ phase transition temperature (776°C). Saller et al. [23] proposed that the decomposition of the γ phase was a eutectoid reaction, and Bostrum and Halteman [24]

confirmed that proposed reaction. Haltemann [25] described the structure of the γ′ phase, and Dwight [22] published the last study of the U–Mo phase diagram below 19 wt% Mo and 900°C in 1960, reporting the eutectoid composition and temperature. Interestingly, the high-temperature (solidus and liquidus) data were provided either by Ahmann et al. [3] in 1945 or by Garg and Ackermann [26] in 1977, the earliest and the most recent studies, respectively.

Considerable information regarding the development of the U–Mo equilibrium phase diagram from around 1944 through 1990 is contained in Section A.2.1 and A.2.2 of the Appendix. Based on this information, a new phase diagram that more closely fits the measured data, shown in Fig. 1, has been developed; its use is recommended. Section A.2.4 of the Appendix provides a detailed description of how the proposed new phase diagram was constructed. The coordinates of the phase boundary junctions are shown on the diagram, and coefficients of the quadratic equations used to represent the phase transition boundaries are given in Table 8 found in section A.4.4 of the Appendix.

FIG. 1. Phase diagram of the uranium–molybdenum system developed during this work. The coordinates (atomic percent uranium, temperature) are shown for each transition-line junction (courtesy of James L. Snelgrove).

2.2.2. Melting temperature

An alloy generally does not melt at a single temperature upon heating; melting occurs progressively as the temperature increases from the solidus temperature (at which the first bit of solid melts, i.e. at which liquid first appears) to the liquidus temperature (at which the last of bit of solid melts and all is liquid). Those concerned with reactor design and safety usually think of the solidus temperature as the ‘melting’ temperature because that is the temperature at which the alloy begins to lose its integrity and begins to provide pathways through the liquid for the release of fission products. A fuel fabricator, on the other hand, might consider the liquidus temperature to be the ‘melting’ temperature since that is the temperature at which the alloy is fully molten, allowing rapid mixing of all constituents. The melting temperature of unalloyed uranium is 1134C, and the melting temperature of U–Mo increases with Mo content for alloys

lines in the U–Mo binary phase diagram shown in Fig. 1. The equations of the solidus line and liquidus line are given by Eqs (38) and (39) of the Appendix, respectively, and are reproduced here as Eqs (6) and (7):

TU–Mo solidus = 0.09982(x_a^U)² − 19.81(x_a^U) + 2117, (60.5 ≤ x_a^U ≤ 100) (6) TU–Mo liquidus= 0.1236(x_a^U)² − 25.87(x_a^U) + 2485, (69.5 ≤ x_a^U ≤ 100) (7) 2.2.3. Transformation kinetics

Cubic-structured γ phase U–Mo alloys are preferred for use in nuclear fuel because of the greater irradiation stability of the cubic structure compared to that of the orthorhombic structure of α phase uranium alloys. After high-temperature annealing at 800-1000^oC followed by quenching, U–Mo alloys above a certain Mo content will remain in the γ phase, but the γ phase will immediately begin to decompose into two phases at a temperature lower than the eutectoid reaction temperature. The rate of transformation of γ phase U–Mo solid solution to the α + γ′

phases below the eutectoid temperature (~565°C) decreases with increasing molybdenum content.

It is useful to know the minimum Mo content required for U–Mo to retain its γ phase structure following quenching to room temperature. In 1951 Saller et al. [23] reported that U–

Mo alloys with Mo content 12 at.% (5.2 wt%) decomposed during furnace cooling. In 1957 Bostrum and Halteman [24] reported that U–Mo with Mo content >7 wt% (15.7 at.%) retained the γ phase,⁶ while U–Mo with Mo content from 2–7 wt% (4.8 – 15.7 at.%) underwent a diffusionless phase transformation following quenching. McGeary [4] had reported in 1955 that the diffusionless transformation does not occur consistently for Mo content between 5 and 7 wt%, a phenomenon he attributed to a dependence on quenching rate. In 1960 Dwight reported that his 12.7 at.% (5.54 wt%) specimen, as well as those with higher Mo content, had retained the γ phase. Beghi [2] reported the minimum Mo content for retaining the γ phase after quenching to be 5.4 wt% (12.4 at. %, citing a 1963 report by Repas et al., But, it was not clear where Repas et al. obtained this lower limit. Because it was stated so exactly, however, this value likely came from Van Thyne and McPherson [27], who had published a TTT curve for a 5.4 wt% alloy in 1959.

At temperatures below ~565°C, this γ phase alloy will gradually decompose into the α+γ′

phases, hence the γ phase is metastable. During research reactor operation this is not an issue, because although U–Mo fuel is used at temperatures well below 565°C in research reactors, fission-induced processes stabilize the γ phase during irradiation [28]. In contrast, for fuel fabrication it is particularly important to understand metastable behaviour, since temperatures approaching the eutectoid temperature are used.

Of particular interest is the time required for an isothermally heated alloy to show the first sign of decomposition; such data are typically reported as time-temperature-transformation (TTT) diagrams, or TTT curves. Beghi [2] has provided a good summary of the results of a number of investigations of U–Mo decomposition rates performed in the 1950s and 1960s.

Manually digitized data obtained from these TTT diagrams at temperatures between 450 and 550°C are plotted in Fig. 2. These data were originally produced by: Van Thyne and McPherson [27] Bellot et al. [29] (obtained from Beghi’s [2] fig. 7), Donze and Cabane [30] (obtained from Beghi’s fig.8), McGeary [4], Peterson et al. [31], and Repas el al. [32]; using primarily the

6 Parida et al. [47] quoted Bostrum and Halteman’s value of 7 wt% [24], but mistakenly reported it as 7 at.% (2.94 wt%). Burkes et al. [35] also reported Parida’s erroneous value, as did Leenaers [36].

following measurement techniques, respectively: dilatometry, metallography; metallography, combination of resistivity, hardness, and metallography; and combination of metallography, hardness, and dilatometry.

The reconstructed TTT diagrams shown in Fig. 2 are not as smooth as the original diagrams because of the limited number of temperatures at which digitization was performed;

nevertheless, the basic characteristics of the diagrams can be seen. There is considerable spread in the positions and shapes of the diagrams for a given alloy from different investigators, especially for the 7 and 8 wt% alloys, much of which results from the measurement techniques used. As discussed briefly in Section A.3 of the Appendix, certain measurement techniques are better suited to detect the onset of transformation than others, depending on the speed of the transformation mechanism at the temperature of interest. Therefore, one could consider making a composite TTT diagram for each of the different alloys shown in Fig. 2 by tracing along the smallest-time portions of intersecting curves of a given color. The change of the color of the groups of curves from left to right clearly shows that increasing the Mo content significantly increases the time required for the transformation to begin. An expanded discussion of U–Mo TTT diagrams can be found in Section A.3 of the Appendix.

FIG. 2. TTT diagrams developed by various investigators during the 1950s and 1960s. The molybdenum content of the alloy and the investigator are listed in the legend. Note that the diagrams are color-coded by Mo content and investigator-coded by curve type and methodology coded by line type (metallography – solid, resistivity +hardness + metallography – long dashes, metallography + hardness – short dashes dilatometry – dots) coded by line type (courtesy of Argonne National Laboratory).