# Mechanical and Thermal Properties for Uranium and U-6 Nb Alloy from First-Principles Theory
## 1 Introduction  
Uranium is an essential metal that has many different applications. Of course, its nuclear attributes are important, but its material properties are also very relevant. It is a heavy (high-density) metal that is mechanically strong relative to other nuclear materials but is prone to oxidation (corrosion). Uranium's mechanical properties are to a degree a consequence of its rather unusual crystal structure (orthorhombic) that induces greater anisotropy than materials with higher symmetry structures, such as the d-transition metals. The material properties and the anisotropy are reflected in the elastic moduli that represents the character and strength of the atomic bonding, that in the case of uranium is dominated by delocalized and bonding 5f electrons [1]. The anisotropy is also revealed in an anomalous and poorly understood negative thermal expansion (contraction) of one of its orthorhombic lattice constants. Adding solid-solution elements from the series of d-transition metals has a beneficial effect on corrosion resistance and improves the mechanical properties. Typically, these alloying elements are soluble at higher temperatures in the body-centered cubic (bcc) phase, \(\gamma\)-uranium, but they can be retained in other phases through quenching [2], as we will discuss below. It has been shown that for U-Nb-specific alloys, the alloying improves the mechanical properties, including ductility, relative to pure uranium [3, 4]. Additionally, the addition of niobium to uranium is particularly beneficial, as it significantly increases oxidation resistance because the niobium metal is distributed uniformly in the uranium matrix [5]. These uranium-niobium alloys furthermore exhibit a shape memory effect (SME) that depends on temperature and strain conditions. Considerable numbers of studies have been conducted, particularly for the U-Nb alloys, focused on the equilibrium phase diagram, metastable phases, phase transitions, thermodynamics, microstructures, mechanical properties, equation of state, aging, and corrosion [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. The equilibrium U-Nb phase diagram has been presented and discussed in numerous papers [6; 7; 8; 9; 10; 11]. There is a complete solubility across the equilibrium U-Nb phase diagram in the high-temperature \(\gamma\) phase but below the critical temperature, T\({}_{c}\) = 950 \(\pm\) 20 \({}^{\circ}\)C, the uranium-niobium phase diagram displays a \(\gamma\)-phase miscibility gap (\(\gamma\)(bcc) \(\rightarrow\)\(\gamma_{1}\)(bcc) + \(\gamma_{2}\)(bcc)) with decomposition of the \(\gamma_{1}\)-phase according to the monotectoid reaction \(\gamma_{1}\rightarrow\gamma_{2}+\alpha\) at 647 \({}^{\circ}\)C, where the \(\gamma_{1}\) and \(\gamma_{2}\) phases contain 13.3 and 70 \(\pm\) 2 at.% Nb, respectively, while the \(\alpha\) phase has less than 1 at.% Nb in solution. Because this scenario represents the equilibrium U-Nb phase diagram, the decomposition of \(\gamma_{1}\) is diffusional, forming a two-phase structure with unalloyed \(\alpha\) uranium and niobium-rich \(\gamma_{2}\)-phase. The resulting mixture suffers degraded corrosion resistance and ductility [3; 4; 11; 12; 13; 14; 15] due to the lack of niobium in solid solution. It also promotes microscopic anodic and cathodic regions [15]. [PERSON] [16] mentioned, relating to [PERSON]'s theoretical argument [26], that during the described eutetoid decomposition the equilibrium composition of the product phases could only happen in the ideal case when the reaction rate approaches zero. Based on the mechanism suggested by [PERSON] [16], [PERSON] et al. [18] and [PERSON] et al. [11] concluded that the phase transition from the high-temperature \(\gamma\) phase to the low-temperature equilibrium \(\alpha\) uranium- and niobium-rich \(\gamma_{2}\)-phase occurs through metastable (quenched) phases: \(\gamma^{0}\) (tetragonal), \(\alpha^{\prime\prime}\) (monoclinic), and \(\alpha^{\prime}\) (orthorhombic).