Coupled Al/Si and O/N order/disorder in BaYb[Si4–xAlxOxN7–x]sialon

The fractions of aluminium, [Al]/[Al + Si], and oxygen, [O]/[O + N], in crystallographically distinct sites of BaYb[Si4–xAlxOxN7–x] oxonitridoaluminosilicate (space group P63mc, No. 186) were refined based on the results of neutron powder diffraction for a synthetic sample with the composition of x = 2.2(2) and simulated as functions of temperature for the compositions x = 2 and x = 2.3 using a combination of static lattice energy calculations (SLEC) and Monte Carlo simulations. The SLEC calcu lations have been performed on a set of 800 structures differing in the distribution of Al/Si and O/N within the 2 × 2 × 2 supercell containing 36 formula units of BaYb[Si4–xAlxOxN7–x]. The SLEC were based on a transferable set of empirical interatomic potentials developed within the present study. The static lattice energies of these structures have been expanded in the basis set of pair-wise ordering energies and on-site chemical potentials. The ordering energies and the chemical potentials have been used to calculate the configuration energies of the oxonitridoaluminosilicates (so-called sialons) using a Monte Carlo algorithm. The simulations suggest that Al and O are distributed unevenly over two non-equivalent T(Si/Al) and three L(N/O) sites, respectively, and the distribution shows strong dependence both on the temperature and the composition. Both simulated samples exhibit order/disorder transitions in the temperature range 500–1000 K to phases with partial long-range order below these temperatures. Above the transition temperatures the Si/Al and N/O distributions are affected by short-range ordering. The predicted site occupancies are in a qualitative agreement with the neutron diffraction results

Thermodynamics of mixing in diopside-jadeite, CaMgSi2O6-NaAlSi2O6, solid solution from staticlattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have beenperformed for a set of 800 different structures in a 2 2 4 supercell of C2/c diopside with compositionsbetween diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273?2,023 K and to calculate a temperature?composition phase diagram. The simulations predict the order?disorder transition in omphacite at1,150 20C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433?440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1?M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral83:419?433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600C

Rare-Earth Orthophosphates From Atomistic Simulations

Lanthanide phosphates (LnPO4) are considered as a potential nuclear waste form for immobilization of Pu and minor actinides (Np, Am, and Cm). In that respect, in the recent years we have applied advanced atomistic simulation methods to investigate various properties of these materials on the atomic scale. In particular, we computed several structural, thermochemical, thermodynamic and radiation damage related parameters. From a theoretical point of view, these materials turn out to be excellent systems for testing quantum mechanics-based computational methods for strongly correlated electronic systems. On the other hand, by conducting joint atomistic modeling and experimental research, we have been able to obtain enhanced understanding of the properties of lanthanide phosphates. Here we discuss joint initiatives directed at understanding the thermodynamically driven long-term performance of these materials, including long-term stability of solid solutions with actinides and studies of structural incorporation of f elements into these materials. In particular, we discuss the maximum load of Pu into the lanthanide-phosphate monazites. We also address the importance of our results for applications of lanthanide-phosphates beyond nuclear waste applications, in particular the monazite-xenotime systems in geothermometry. For this we have derived a state-of-the-art model of monazite-xenotime solubilities. Last but not least, we discuss the advantage of usage of atomistic simulations and the modern computational facilities for understanding of behavior of nuclear waste-related materials

Ion distribution models for defect fluorite ZrO2 - AO1.5 (A = Ln, Y) solid solutions : II: Thermodynamics of mixing and ordering

Thermodynamic mixing properties of AxB1-xO2-0.5xV0.5x, fluorite-type solid solutions (B = Zr, A = {Nd-Yb, Y}, V = oxygen vacancy) are modelled as functions of four parameters, ΔH1, ΔH2, ΔH3 and ΔH4, which correspond to the enthalpy effects of the reactions 6A + 8B = 7A + 7B (1), 6A + 8B = 8A + 6B (2), 6B + 8B = 7B + 7B (3) and 6A + 8A = 7A + 7A (4), involving six cation species, 6A, 7A, 8A, 6B, 7B and 8B. The model predicts that the disordered configuration containing all cation species evolves with the decreasing temperature such that 6-fold coordinated cations tend to vanish within 0 ≤ x ≤ 1/2 domain, while 8-fold coordinated cations become extinct within 1/2 ≤ x ≤ 1 domain. The further evolution within the intervals of 0 ≤ x ≤ 1/3, 1/3 ≤ x ≤ 1/2, 1/2 ≤ x ≤ 2/3 and 2/3 ≤ x ≤ 1 favours the extinction of 7A, 8B, 7B and 6A cation species, respectively. With the further decrease in the temperature 6-fold B and 8-fold A cations reappear within the domains of 1/3 ≤ x ≤ 1/2 and 1/2 ≤ x ≤ 2/3 via the reaction 7A + 7B = 8A + 6B. The configurational entropy reduces along with these transformations. The model fits structural and calorimetric data on Zr-based AxB1-xO2-0.5xV0.5x systems and provides hints to understanding of ionic conductivity and radiation susceptibility data

Thermodynamic and Structural Modelling of Non-Stoichiometric Ln-Doped UO2 Solid Solutions,Ln = {La, Pr, Nd, Gd}

Available data on the dependence of the equilibrium chemical potential of oxygen on degrees of doping, z, and non-stoichiometry, x, y, in U1-zLnzO2+0.5(x-y) fluorite solid solutions and data on the dependence of the lattice parameter, a, on the same variables are combined within a unified structural-thermodynamic model. The thermodynamic model fits experimental isotherms of the oxygen potential under the assumptions of a non-ideal mixing of the endmembers, UO2, UO2.5, UO1.5, LnO1.5, and Ln0.5U0.5O2, and of a significant reduction in the configurational entropy arising from short-range ordering (SRO) within cation-anion distributions. The structural model further investigates the SRO in terms of constraints on admissible values of cation coordination numbers and, building on these constraints, fits the lattice parameter as a function of z, y, and x. Linking together the thermodynamic and structural models allows predicting the lattice parameter as a function of z, T and the oxygen partial pressure. The model elucidates contrasting structural and thermodynamic changes due to the doping with LaO1.5, on the one hand, and with NdO1.5 and GdO1.5, on the other hand. An increased oxidation resistance in the case of Gd and Nd is attributed to strain effects caused by the lattice contraction due to the doping and to an increased thermodynamic cost of a further contraction required by the oxidation

Subsolidus phase relations in the CaCO3–MgCO3 system predicted from the excess enthalpies of supercell structures with single and double defects

The thermodynamic mixing properties of a binary (AxB1?x)R solid solution are evaluated from the enthalpies of supercell structures Am?2B2Rm and Bm?2A2Rm, where m is the number of the exchangeable sites in the supercell. The excess enthalpies of these structures are converted into concentration-dependent pairwise effective cluster interactions Jn, i.e., the enthalpies of the intracrystalline reactions AA+BB?2AB acting at the n-neighbor distance within the supercell. The pairwise interactions calculated in this way for all possible distances within 3×3×1 supercells of R3? c calcite and magnesite (m=54) are combined to form an effective Ising-type Hamiltonian from which temperature-dependent enthalpies, entropies, and free energies of mixing are evaluated with the Monte Carlo method. The calculated phase diagram with two miscibility gaps separated by a field of stability of the R3? dolomite phase is in good agreement with available experimental data, thereby showing that the existence of the intermediate ordered compound can be predicted from the analysis of the supercell structures whose compositions approach the diluted limits.Materials Science and EngineeringMechanical, Maritime and Materials Engineerin

Pyrochlore Compounds From Atomistic Simulations

Pyrochlore compounds (A (2) B (2)O(7)) have a large applicability in various branches of science and technology. These materials are considered for use as effective ionic conductors for solid state batteries or as matrices for immobilization of actinide elements, amongst many other applications. In this contribution we discuss the simulation-based effort made in the Institute of Energy and Climate Research at Forschungszentrum Jülich and partner institutions regarding reliable computation of properties of pyrochlore and defect fluorite compounds. In the scope of this contribution, we focus on the investigation of dopant incorporation, defect formation and anion migration, as well as understanding of order-disorder transitions in these compounds. We present new, accurate simulated data on incorporation of U, Np, Pu, Am and Cm actinide elements into pyrochlores, activation energies for oxygen migration and radiation damage-induced structural changes in these materials. All the discussed simulation results are combined with available experimental data to provide a reliable description of properties of investigated materials. We demonstrate that a synergy of computed and experimental data leads to a superior characterization of pyrochlores, which could not be easily achieved by either of these methods when applied separately