Non-stoichiometry Effects and Phase Equilibria in the Uranium-Carbon-Nitrogen Ternary System
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PRACTICAL demands initiated rigorous studies of the ternary uranium-carbon-nitrogen (U-C-N) system as early as the late 1950s.[3,4] This research continues, and recently the focus has been on the synthesis of uranium carbonitride, U(C, N),[5–10] and analysis of the corresponding phase diagrams of the system. The most extensive phase equilibria datasets are available from Austin and Gerd,[3] Leitnaker,[11] Henry and Blickensderfer,[12] Cordfunke and Ouweltjes,[13] Naoumidis and Sto¨ker,[14] and Katsura et al.[15] Typically, UC/UC2, UN, and C powders exposed to N2 atmosphere are used as starting materials, and equilibrium phases as well as the lattice parameters are identified by XRD.[16] To the best of our knowledge, the entire set of experimental data[3,11–15] have never been analyzed and screened for the obvious outliers based on rigorous theoretical models. This is the goal of the present paper. The nitrogen partial pressure and temperature are the most important control variables for a material scientist designing a synthesis pathway for U(C, N) materials. We, therefore, pay a special attention to the analysis of [1,2]
Artur A. Salamatin, Fei Peng, and Konstantin G. Kornev are with the Department of Materials Science and Engineering, Clemson University, 515 Calhoun Drive, 161 Sirrine Hall, Clemson, SC 29634. Contact e-mail: [email protected] Keith Rider is with BWX Technologies, Inc., Lynchburg, VA 24504. Manuscript submitted October 8, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
available experimental data and theoretical predictions related to the studies of phase equilibria in terms of these variables. Various theoretical descriptions of the ternary systems have been developed to explain the complexity of the multiphase equilibria that are observed in experiments[13,14,17,18]; thermodynamic treatment of each distinguished phase is not unanimously accepted. The equilibrium, i.e., the point of minimum of the overall thermodynamic potential (such as Gibbs or Helmholtz free energies) of a heterogeneous system, is, in general, uniquely determined by a set of stable phases and their compositions.[19,20] Mathematically, the potential is considered as an objective function of composition of every phase and their amounts. One obtains phase diagrams by tracing the phase domain boundaries repeatedly solving the minimization problem for different overall compositions and thermodynamic conditions.[21–23] The approach requires P an analytical expression for the Gibbs energy G ¼ si¼1 GðiÞ of any heterogeneous realization of the ternary system under consideration. It is given as a sum of energies G(i) of all phases. Here, the index i = 1..s spans over all s phases. The crucial step that bridges theory and experimentally available information is to suggest realistic and convenient parametric models for each phase to approximate their constitution. Eventually, this allows for the calculation of Gibbs energies G(i) for any thermodynamic condition given by temperature T and externally applied pressure P.[24–26]
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