The first compositional diagram for the uranium-silicon system was based on studies performed by Kaufmann et al., in the 1940s at the Massachusetts Institute of Technology (Cullity, 1945). The original phases reported were U₁₀Si₃, U₅Si₃, USi, U₂Si₃, USi₂, and USi₃ (Katz and Rabinowitch, 1951). In 1949, Zachariasen (1949) further refined the original composition diagram by correcting the identification of several compounds; U₁₀Si₃ was actually U₃Si, U₅Si₃ was U₃Si₂, and U₂Si₃ (β-USi₂) was an isostructural form of USi₂ (α-USi₂).

Later, in 1957, Kaufmann et al. (1957) published the phase diagram shown in Figure 1A, which contains the compounds U₃Si (ε), U₃Si₂ (δ), USi (ζ), U₂Si₃ (η), USi₂ (θ) and USi₃ (ι). Kaufmann et al. (1957) claimed that the ε phase has a very narrow composition range near 23 at% Si, rather than a stoichiometric ratio of U₃Si and also that the α-USi₂ phase did not transform at high temperature to β-USi₂ and formed the compound U₂Si₃ in its place. U₃Si forms at 1203 K through the peritectic reaction between U₃Si₂ and γ-uranium-silicon solid solution. A eutectic exists between γ-uranium and U₃Si₂ at 9 at% Si and a temperature of 1258 K. The compound U₃Si₂ congruently melts at 1938 K. The USi compound incongruently melts at 1848 K and there is a eutectic between U₃Si₂ and USi at 1843 K. The U₂Si₃ compound incongruently melts at 1883 K and the USi₂ compound is reported to melt congruently at approximately 1973 K. USi₃ is shown to have an incongruent melting point at 1783 K. There is a eutectic at 87 at% Si between USi₃ and silicon at 1588 K. There was appreciable solid solubility of silicon in uranium.

The phase diagram that is currently referenced is shown in Figure 1B and was published in 1990 in ASM international (Massalski, 1990). This phase diagram is characterized by seven intermetallic phases, U₃Si, U₃Si₂, USi, U₃Si₅, USi_1.88, USi₂, and USi₃. The 0–50 at% Si region remained as previously reported by Kaufmann et al. (1957) except for the temperature where the eutectic reaction occurs between U₃Si₂ and USi. The phase identified as U₂Si₃ by Kaufmann, or β-USi₂ by Zachariasen (1949), is represented as U₃Si₅. In 1959 Brown and Norreys (1959) reported that the U₂Si₃ phase was in fact a modification of the α-USi₂ compound; however, the composition was located between 62–63 at% Si (U₃Si₅). Brown and Norreys (1961) also reported that the phase considered as α-USi₂ is actually USi_1.88, forming at 65 at% Si and has high melting point. They further claimed that the compound at exact 1:2 stoichiometry does not exist above 723 K.

In an attempt to elucidate the controversy regarding the phases between the 40 to70 at% silicon region of the U-Si system, Vaugoyeau et al. (1972) reexamined the system within this region. The existence of compounds USi, U₃Si₅, U₃Si₂ and USi_1.88 were confirmed (Vaugoyeau et al., 1972). Vaugoyeau et al. (1972) reported: The USi phase forms at 1853 ± 10 K from a peritectic reaction between liquid and U₃Si₅. The temperature of the eutectic reaction between USi and U₃Si₂ was 1813 ± 10 K, which is approximately 20 K lower than that reported by Kaufmann et al., (Kaufmann et al., 1957). The melting of U₃Si₅ occurred congruently at 2043 ± 10 K instead of incongruently at 1883 K. The USi_1.88, reported by Brown and Norreys (1961) forms through a peritectic reaction between liquid and U₃Si₅ at 1983 ± 10 K. The stoichiometric USi₂ compound was not observed by Vaugoyeau et al. (1972).

Additional research since the publication of the phase diagram in Figure 1B shows the need for updates. The U₃Si phase was reported to undergo an allotropic transition at 1043 K (Dwight, 1982). A new phase, U₅Si₄, was reported by Noёl et al. (1998) and Berche et al. (2009) claimed that the phase is formed through a peritectic reaction between the liquid phase and U₃Si₂ at 1840 ± 10 K and participates in the eutectic reaction between the liquid phase and the USi phase at 1820 ± 10 K. The stoichiometric USi₂ phase was reported as metastable (Sasa and Uda, 1976; Dwight, 1982; Remschnig et al., 1992; Noordhoek et al., 2016) and the U₃Si₅, U₃Si₂, and USi_1.88 phases were each reported to have a narrow composition range (Dwight, 1982). A phase transition at 773 K was noted for the U₃Si₅ phase (White et al., 2015).

The crystal structure properties including the structure types, space groups, prototypes, lattice parameters for the various uranium silicide phases are summarized Table 1. The U₃Si crystal structure reported by Zachariasen (1949) in 1949 was often reproduced (Kaufmann et al., 1957; Dwight, 1982; Remschnig et al., 1992). Kimmel et al. (Kimmel et al., 1980), established that the space group reported earlier (Zachariasen, 1949) was correct; but the assignment of the uranium and silicon lattice sites was incorrect. Noël et al. (2023) also reported that the tetragonal structure undergoes an orthorhombic distortion at 120 K. Dwight, (1982) reported that the tetragonal U₃Si transforms to a cubic Cu₃Au-type structure at 1038 K.

The U₃Si₂ compound has a primitive tetragonal structure belonging to the P4/mbm space group and is a prototype for binary ternary rare earth compounds (Pöttgen, 1994; Lukachuk and Pöttgen, 2003). While all published experimental data are in agreement with the early work of Zachariasen (1949), DFT calculations fail to predict the experimental P4/mbm as the most stable structure (Noordhoek et al., 2016).

The U₅Si₄ phase reported in 1998 by Noёl et al. (1998) has a hexagonal unit cell, P6/mmm space group, with lattice parameters a = 10.468 Å and c = 3.912 Å and is isostructural to the U₂₀Si₁₆C₃ ternary phase (Lopes et al., 2019; Noël et al., 2023). The crystal structure of the equiatomic compound, USi, is the most controversial of the binary silicides. The compound was reported by Zachariasen (1949) to be orthorhombic of the FeB structure type. His results were based on diffractometer data taken on a powder sample. In later work, Bihan et al. (1996) reported that pure USi has a tetragonal structure with an I4/mmm space group as determined from a Weissenberg pattern on a small single crystal. Bihan et al. (1996) further state that the orthorhombic structure by found by Zachariasen (1949) is stabilized by 0.5–1.0 wt% oxygen. Remschnig et al. (1992) and Noordhoek et al. (2016) also reported an orthorhombic structure; however, both differ from the work of Zachariasen, (1949) and each other as the structure by Remschnig et al. (1992) belongs to the Pnma space group while the one by Noordhoek et al. (2016) belongs to the Imma Space group.

The compound USi₂ with exact 1:2 stoichiometry has all silicon sites occupied and exists in one of two structure types, either AlB₂ or ThSi₂, belonging to the P6/mmm or the I4 ₁ /amd space group. The compound U₃Si₅ is hexagonal, hP3, A1B₂-type structure which was reported to undergo an orthorhombic distortion when slightly rich in silicon (63 at% Si) to form the structure belonging to the Pmmm space group (Remschnig et al., 1992). The USi_1.88 phase is tetragonal of the ThSi₂-type and experiences an orthorhombic distortion when slightly silicon poor (64 at% Si) (Remschnig et al., 1992).

The silicon-rich compound USi₃ has the cubic Cu₃Au-type structure.

The tabulated enthalpies of formation for the different U-Si phases are summarized in Table 2. The enthalpies of formation of USi₃, USi₂, USi and U₃Si₂ were measured as −33.05 kJ mol^-1, -43.51 kJ mol^-1, -40.17 kJ mol^-1 and -33.89 kJ mol^-1 by Gross et al. (1962) by measuring the heats evolved in the direct combination of the elements. The enthalpies of formation for USi₃, USi₂, and USi were verified by measuring the heats of reaction of tellurium with the preformed compounds and comparing them with those obtained from reacting equivalent quantities of the uncombined elements with tellurium. The enthalpy of formation for USi₃, USi₂, and USi were measured as −32.22, −42.69, and −43.52 kJ mol ^-1, respectively (Gross et al., 1962). Alcock and Grieveson (1961) measured silicon vapor pressure above the mixtures USi-U₃Si₅, U₃Si₅–USi₂, USi₂–USi₃ and USi₃–Si from the weight loss of a Knudsen cell. From these measurements, the Gibbs energy of U₃Si₅, USi₂ and USi₃ were directly derived. Activities of uranium and silicon for the U–U₃Si₂ mixture were determined from the chemical analysis of the condensate formed from the vapor effusing from the cell. Because of small associated values of uranium activity, a solid/liquid equilibration method using liquid gold–uranium alloys were used for the U₃Si₂–USi mixture. The Gibbs energies of formation of the compounds were derived from the silicon and uranium activity measurements. The results reported by Gross et al. (1962) and Alcock and Grieveson (1961) are in good agreement. OHare et al. (1974) reported the enthalpy of formation of U₃Si as −26.05 ± 4.8 kJ mol-atom^-1 using fluorine bomb calorimetry. The enthalpy of formation for U₃Si₅ and the tetragonal USi were measured as −43.8 ± 9.0 kJ mol ^-1 and −43.2 ± 6.2 kJ mol ^-1 for using oxidative drop calorimetry (Chung et al., 2018). The heat capacity as a function of temperature for U₃Si, U₃Si₂, USi and U₃Si₅ were measured by White et al. (2015); White et al. (2016) using differential scanning calorimetry from room temperature to 1150 K, 1773 K, 1673 K, and 1773 K, respectively. To the authors knowledge, there are no experimental efforts reported for obtaining the thermodynamic properties of the liquid phase.

The CALPHAD method is commonly used for calculating phase diagrams and predicting thermodynamic properties of a given system through critical assessment of available experimental and/or theoretical data. The CALPHAD method uses mathematical models with adjustable parameters to represent Gibbs energy functions of the phases as a function of temperature, pressure, and composition and calculates the thermodynamic equilibrium by minimizing the Gibbs energy of the system (Kaufman and Bernstein, 1970; Lukas et al., 2007). These functions are stored in a database and are used to calculate phase diagrams and thermodynamic properties. These databases are constructed by incorporating phase diagram data, thermochemical data, and physical and crystallographic properties of the phases (Perrut, 2015).

The first step in the CALPHAD method is to perform a thorough literature search and critically evaluate all the available data. The type of data to search for include; i) experimentally measured thermodynamic quantities such as enthalpies and heat capacity data, ii) the phase diagram data such as the liquidus temperatures and the phase transition reactions, iii) crystallographic information of solid phases (Ferro and Cacciamani, 2002), and first-principles calculations of total energies (Liu, 2009). When evaluating the experimental data, critical attention is paid to the experimental technique, experimental conditions, sample purity, quantities measured, phases present within the system, and accuracy of the measurements as there are many types of equipment utilized to collect the same information. First-principles data are normally used when there are no available experimental data. During the literature search, the possibility of finding previous assessments for the system of interest exists. In such cases, careful examination of the Gibbs energy models used for describing the system is necessary as it may be possible to improve the system. The second step is to develop a mathematical model for G (T, P, composition) for each phase (liquid, solid phases, gas … ) and to optimize model parameters simultaneously using all available thermodynamic and phase equilibrium data obtained from the first step. The third step is to use the models to calculate phase diagrams and other thermodynamic properties by minimization of the Gibbs energy. The fourth and final step is to use the calculated phase equilibria to develop a database.

The Gibbs energy of a phase can be expressed as follows in Eqs 1, 2: G m = G ref m + G id m + G E m + G p h y m (1) G id m = − T i d S (2)

Where G ref m is the “surface of reference”, which represents the Gibbs energy of the mechanical mixture of the constituents of the phase. ^idG_m is the contribution of configuration entropy to the Gibbs energy. T is the absolute temperature in Kelvin and ^idS is the configuration entropy, which is determined by the number of possible arrangements of the constituents in a phase. ^EG_m is the excess Gibbs energy, the Gibbs energy change from the ideal solution to the real solution. ^phyG_m represents the Gibbs energy contribution of physical phenomena, such as magnetic transitions.