## 1 Introduction
### Ambient Melting Behavior  
Of all the physical properties of a material, melting behavior is a fundamental property closely related to its structure and thermodynamic stability, and therefore has always been a crucial research subject. The ambient (zero pressure) melting point (\(T_{m}\)) is also an important engineering parameter as it defines the operational limits of a material in its application environment. It becomes critical in nuclear engineering where the thermo-mechanical stability of a nuclear fuel element is a key factor determining fuel performance and safety. Furthermore, PuO\({}_{2}\) and UO\({}_{2}\) are two endpoints of the phase diagram of MOX; therefore, their ambient \(T_{m}\)s are fundamental reference points. The current knowledge of \(T_{m}\) of MOX is limited and controversial as the literature studies do not converge on the unique behavior of \(T_{m}\) as a function of \(x\). Specifically, studies [2; 3] produced \(T_{m}\) as a monotonically decreasing function of \(x\) such that, with \(T_{m}\) of UO\({}_{2}\) (\(x=0\)) of 3150 K, \(T_{m}\) of PuO\({}_{2}\) (\(x=1\)) is \(\sim\)2650-2700 K, while studies [4; 5; 6; 7] resulted in \(T_{m}\) having a local minimum at \(0.5<x<1\) such that \(T_{m}\) of PuO\({}_{2}\) is \(\sim\)3000-3050 K, so that the difference between the two values of \(T_{m}\) is as high as 350 K.  
This controversy in the melting behavior of MOX is directly related to the ambiguity in the value of the ambient melting point of PuO\({}_{2}\) as well as the melting behavior of MOX with high Pu content. Since the 1960s, several groups have reported measurements of \(T_{m}\) of PuO\({}_{2}\) using various experimental techniques. Most of them are summarized in a review by [PERSON] et al. [2] who recommended a value of 2701 \(\pm\) 35 K based on measurements circa 1960s using the thermal arrest technique on tungsten-encapsulated samples. More recently, [PERSON] et al. [3] recommended a value of 2660 K based on published data and the thermodynamic modeling of the Pu-O system. However, in the same year, [PERSON] et al. presented their experimental study [4; 5] in which the then-commonly-accepted value of \(T_{m}\) for PuO\({}_{2}\) was called into question, and a considerably higher value of \(\sim\)3000 K was proposed. While using essentially the same thermal arrest technique as in the 1960s, [PERSON] et al. paid particular attention not only to maintaining the exact O/M ratio, as the previous investigators did, but also to the effect of sample-containment interactions. In this way, they could attribute lower values of \(T_{m}\) in the previous studies to extensive interactions between PuO\({}_{2}\) samples and tungsten, typical crucible material in this range of \(T\). The most recent experimental values of \(T_{m}\) for PuO\({}_{2}\) are \(3017\pm 28\) K [6] and \(3050\pm 59\) K [7]. The difficulties with the experimental determinations of the melting behavior of the stoichiometric MOX as well as the shortcomings of the experimental techniques used for these determinations are summarized in the recent review by [PERSON] et al. [8]. Specifically, (i) the interaction of the U\({}_{1-x}\)Pu\({}_{x}\)O\({}_{2}\) samples of high Pu content with tungsten crucibles, and in some \(x>0.5\) cases with rhenium crucibles, drive the corresponding \(T_{m}\) systematically lower; (ii) Pu content affects the \(T_{m}\) measurements such that laser heating which is currently the most widely used technique causes a non-ideal behavior of the UO\({}_{2}\) and PuO\({}_{2}\) partitions of MOX which results in a distinct minimum of \(T_{m}\) as a function of \(x\) at \(0.4<x<0.8\); (iii) the measured values of \(T_{m}\) are affected by the O/M ratio which varies in the atmosphere during the experiments, so that it is not clear whether the measured \(T_{m}\) corresponds to an O/M of close to 2 in the stoichiometric case or if it is much less than 2. Hence, the clarification of the behavior of \(T_{m}\) as a function of \(x\) requires further study.