# Analytic Model for U-Nb Liquidus and U-6 Nb Melting Curve  
[PERSON]  
1  
1 Los Alamos National Laboratory, Los Alamos, NM 87545, USA; [EMAIL_ADDRESS] (D.L.P. );  
[EMAIL_ADDRESS] (A.A.G. )1  
1 2  
to alloy uranium (U) [1; 2; 3]. However, among those, only niobium (Nb) does not form intermediate (stoichiometric) compounds with U; hence, Nb has been traditionally used more than the other three. Also, the addition of Nb significantly increases the oxidation resistance of U, because Nb is distributed uniformly in the U matrix [4]. Studies of the early 1960s of the phase diagram of the U-Nb system indicated that this system was a logical choice for a high-\(T\) fuel [5]. However, the original idea of the requirement for strength at elevated \(Ts\), which automatically removed uranium-rich alloys from consideration and concentrated on the niobium-rich alloys instead, e.g., the 20 weight percent (wt.%) uranium-80 wt.% niobium (U-80 Nb) alloy considered in [5], was later on reconsidered in favor of the use of the U-rich alloys as a high-\(T\) fuel. Specifically, U-Nb alloys in the vicinity of the monotectoid composition of 6 wt.% Nb (U-6 Nb), namely, within the range from 5 wt.% (U-5 Nb) to 8 wt.% (U-8 Nb), exhibit the shape memory effect [1; 2; 6], which depends on strain conditions and \(T\). Specifically, the U-6 Nb alloy can recover up to 7% strain in tension by heating the material back into the high-\(T\)\(\gamma\) phase [6]. Another aspect of alloying U with Nb is the extension of the \(T\) range of the stability of its high-\(T\) body-centered cubic (bcc) structure, referred to as the \(\gamma\) phase, which is stable at (in K) \(1049\leq T\leq T_{m}=1408\) relative to that of the low-\(T\) orthorhombic (oS4) structure, referred to as the \(\alpha\) phase, which is stable in the 0-941 K range [7]. The intermediate tetragonal (tP30) structure of U, which is referred to as the \(\beta\) phase, is stable between 941 and 1049 K. From the material processing standpoint (machining, etc. ), \(\gamma\)-U is much more preferable to \(\alpha\) because of the brittle nature of the latter and its tendency to form uranium oxides. In fact, U-6 Nb is stable in the bcc structure, also referred to as the \(\gamma\) phase, already at \(T\stackrel{{>}}{{\sim}}600\) K. However, as the alloy is cooled down rapidly to room \(T\), it undergoes a two-stage transformation process: at \(\sim\) 570 K, the material exhibits the distorted cubic (i.e., tetragonal) structure referred to as the \(\gamma^{0}\) phase. At a lower \(T\) of \(\sim\)370-450 K, the alloy undergoes further transformation into the metastable monoclinic \(\alpha^{\prime\prime}\) structure. These transformations are discussed in detail in Refs. [8; 9]. With a Nb concentration of \(\sim\)60 to 100 wt.%, the U-Nb system forms a continuous solid solution of the bcc \((\gamma)\) structure in the entire \(T\) range [10]. 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-\(P\), where \(P\) stands for 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, and in this respect, the U-Nb system is no exception. At high \(T\), U and Nb form a continuous solid solution without any stoichiometric compound. The ambient phase diagram of the U-Nb system is summarized in Refs. [10; 11]. The high-\(T\) Nb-rich portion of this phase diagram is based on the experimental results of [PERSON] et al. of the late 1950s [12; 13], the accuracy of which has not been assessed. These old results have not been updated since then.