Computer algebra removes much of the drudgery from mathematics; it allows users to formulate models by using the language of mathematics and to have those models evaluated with little effort. This symbolic form of representation is often thought of as being separate to dedicated computational programs such as Rietveld refinement. These dedicated programs are often written in low level languages; they are relatively inflexible in what they do and modifying them to change functionality in a small manner is often a major programming task. This paper describes a symbolic system that is integrated into the dedicated Rietveld refinement program called TOPAS. The symbolic component allows large functional changes to be made at run time and with a relatively small amount of effort. In addition, the system as a whole reduces the programming complexity at the developmental stage.

We describe for the first time the full 3D atomic structure of room-temperature α-La2Mo2O9. The material, despite its simple chemical formula, has a remarkable 312 crystallographically unique atoms and is thus one of the most complex oxide structures reported to date. Despite this complexity, the structural results offer significant insight into the O2- migration pathway in the anion conducting high-temperature form, β-La2Mo2O9. The material contains a mixture of 4, 5, and 6 coordinated Mo sites, suggesting that variable Mo coordination number is a key factor in providing a low-energy O2- conduction pathway. We provide quantitative analysis showing that the positions in the ordered array of 216 oxygen sites of α-La2Mo2O9 are directly related to the average sites occupied in β-La2Mo2O9, providing compelling evidence that the high-temperature conducting form of the material has a time-averaged version of the low-temperature structure.

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Oxide ion conductors are technologically important materials because of their potential applications in oxygen sensors and pumps, as dense membranes for oxygen permeation, catalysts, and as electrolytes for solid oxide fuel cells (SOFCs). [1][2][3][4] To be efficient in various applications, candidate materials should possess a conductivity of at least 10 À2 S cm À1 at deviceoperating temperatures; currently commercially used yttriastabilized zirconia (YSZ) reaches this target at 700 8C.[1]Given the drive towards lowering device-operating temperatures, there is a strong impetus and a great challenge for materials chemists to develop materials with enhanced ionic mobility and superior low-temperature oxide ion conductivity. [5,6] A better understanding of generic structural features and pathways which facilitate ionic mobility at lower temperature is a key step in reaching this goal.Here we report a remarkably high oxide ion conductivity at low temperatures (300-500 8C) in an ordered pseudo-cubic 3 3 3 [8,9] By contrast and unusually, our materials crystallize as stable ordered superstructures, and do not undergo phase transitions to lower symmetry and lower conductivity polymorphs. Our ab initio molecular dynamics (AIMD) simulations reveal the structural features and mechanisms which facilitate the high oxide ion mobility at low temperatures, and provide conceptual insight readily applicable to other materials and structure types.The high-temperature cubic fluorite-type bismuth oxide, d-Bi 2 O 3 , with intrinsic oxygen vacancies, shows the highest oxide ion conductivity measured in any material (around 1 Scm À1 at 750 8C); [10] however, it is only thermodynamically stable in the narrow range between 730 and 824 8C.[11] There has been considerable interest in stabilizing the highly conducting d-Bi 2 O 3 phase by isovalent or aliovalent cation substitution to preserve oxide ion conductivity at lower temperatures. For example, 20 % substitution of Er into Bi 2 O 3 results in oxide ion conductivity of 2 10 À2 S cm À1 at 500 8C and 0.4 S cm À1 at 700 8C.[12] Double cation substitution has yielded even higher conductivities at low temperatures (300-500 8C); the best examples include Dy-W, [13] Pr-V, [7] and the recently reported La-Re [8] À3 -10 À2 S cm À1 at 300-400 8C, approaching the Cu-doped layered Bi 2 VO 5.5 (BICUVOX), which itself has the disadvantage of two-dimensional, anisotropic conductivity. Although the relative chemical instability of Bi oxides under reducing conditions has so far hampered their applications in SOFCs, the use of bilayer electrolytes can overcome this issue. [14] In addition to high oxide ion conductivity, bismuthbased oxides show electrocatalytic activity and therefore also have great potential for applications in electrochemical oxygen separation. [15,16] A common structural feature in the best d-Bi 2 O 3 -based oxide ion conductors reported so far is that doping stabilizes simple cubic structures with a % 5.5 and space group Fm " 3m. [7][8]13] By comparison, doped d-Bi 2 O 3 material...

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. ABSTRACT:We describe the synthesis and characterization of a family of materials, Zr 1-x Sn x Mo 2 O 8 (0 < x < 1) whose isotropic thermal expansion coefficient can be systematically varied from negative to zero to positive values. These materials allow tunable expansion in a single phase as opposed to using a composite system. Linear thermal expansion coefficients, α l , ranging from -7.9(2) × 10 -6 K -1 to +5.9(2) × 10 -6 K -1 (12 to 500 K) can be achieved across the series; contraction and expansion limits are of the same order of magnitude as the expansion of typical ceramics. We also report the various structures and thermal expansion of "cubic" SnMo 2 O 8 , and use time-and temperature-dependent diffraction studies to describe a series of phase transitions between different ordered and disordered states of this material.