## 1 Introduction
The Gibbs energy schematic put forward by [PERSON] [25] illustrates the generation of competing common tangent equilibria, but in all cases the common tangent between \(\alpha\) and \(\gamma^{\prime}\) is always metastable with respect to the \(\alpha\) and \(\gamma_{2}\) equilibrium. [PERSON] [25] mentioned that, upon [PERSON]'s theoretical argument [26], during eutectoid decomposition the equilibrium composition of the product phases could only be achieved in the ideal case when the reaction rate approaches zero. As has been mentioned here and in Ref. [3], solid solution additions of elements, such as niobium, titanium, and zirconium metals, significantly improve uranium's resistance to corrosion  
Figure 2: (a) Schematic representation of discontinuous monotectoid decomposition in the uranium-niobium system; and, (b) schematic energies describing [PERSON]’s hypothesis, taken from Ref. [20]. and substantially alter its mechanical properties. In practice, prior to machining, these alloys are typically heat-treated in the \(\gamma\)-phase (to form uranium alloy solid solutions) and then rapidly quenched to room temperature. Quenching uranium-niobium alloy compositions containing less than 9 at.% Nb to room temperature suppresses diffusion-controlled transformations to the equilibrium phases, resulting in an orthorhombic phase similar to unalloyed U. Because this phase is _supersaturated_ and its lattice parameters differ from the pure metal, it has been designated \(\alpha^{\prime}\). Uranium alloys containing between 10 and 16 at.% Nb form additional supersaturated metastable phases [5]. At room temperature after quenching, alloys containing 15.2 at.% Nb form a monoclinic distortion of the orthorhombic \(\alpha\) phase (\(\alpha^{\prime\prime}\)) and those with -16.6 at.% Nb formed a tetragonal distortion of the BCC \(\gamma\) phase (\(\gamma^{0}\)) [5]. The reactions producing \(\alpha^{\prime\prime}\) and \(\gamma^{0}\) are generally regarded as _martensitic_ in nature, occurring by shear and/or displacive mechanisms requiring only cooperative, short-range motions of the atoms [5; 7; 27]. The _highly supersaturated metastable_\(\alpha\)-phase solid solution exhibits far better corrosion resistance than unalloyed uranium and it is amenable to subsequent age hardening, permitting a wide range of mechanical properties through the selection of aging temperature and time [16; 28]. In several investigations [5; 7; 15; 29; 30; 31; 32] evidence was presented suggesting that the reaction path for these diffusion-less transitions proceeded progressively as:  
\[\gamma(\text{BCC})\rightarrow\gamma^{0}(\text{tetragonal})\rightarrow\alpha^{ \prime\prime}(\text{monoclinic})\rightarrow\alpha^{\prime}(\text{orthorhombic}) \tag{2}\]  
where the notations, \(\alpha^{\prime}\), \(\alpha^{\prime\prime}\), and \(\gamma^{0}\) has been suggested by [PERSON] and [PERSON] [33]. Multiple variations of the \(\alpha\) and \(\gamma\) phases are known to exist depending on the Nb content [13; 16; 29]. However, equilibrium conditions are not achieved without extended heat treating due to the low diffusivity of Nb in U. Because of this, metastable phase variants of \(\alpha\) and \(\gamma_{2}\), depending on the alloy content, form as indicated in Figure 3[16; 29]. In this figure, corresponding paired lines represent the martensite start (M\({}_{\text{S}}\)) and martensite finish (M\({}_{\text{F}}\)) temperatures on cooling. Higher cooling rates favor martensitically-formed metastable phases by avoiding _diffusional_ decomposition of \(\gamma\) solution during cooling to room temperature. Because of the sluggish solid-state diffusion in this system, the monotectoid reaction is usually bypassed at even moderate cooling rates (20 \({}^{\circ}\)C/s or greater), which are easily achieved during water quenching [3; 29].