“The thermodynamic punishment must fit the structural crime.”
The core research themes: (i) Synthesis, (ii) Crystallography, (iii) Calorimetry and (iv) CALPHAD are broken down into actionable research objectives. These are discussed in detail below.
Objective 1: Synthesis: Complex Oxides, Carbides and Nitrides
Goal 1: To adapt the steric entrapment oxide method for carbide and nitride syntheses.
Goal 2: Crystal structures of new materials will be solved using X-ray and neutron powder diffraction in conjunction with charge flipping and/or simulated annealing.
Complex oxides, carbides, and nitrides have potential applications in many material systems: Thermal Barrier Coatings (TBC), electrode/electrolytes, radiation-resistant materials, plasma resistant materials and Phase Changing Materials (PCM). While oxides have been readily studied, only high symmetry cubic/hexagonal carbides and nitrides have been investigated. This hinders engineering development as an entire space for material selection has been ignored. This work aims to fix this problem by synthesizing and measuring fundamental materials data for new lower symmetry carbides and nitrides, so they too can be used for material selection. This, in particular, will be beneficial for space exploration, as carbides and nitrides tend to be high-temperature materials.
Steric entrapment  is a reliable synthesis technique for the production of stable homogenous complex oxides. This process involves the dissolution of cations, from salt or alkoxide precursors, in a solvent. A steric entrapping agent, such as polyvinyl alcohol (PVA) or ethylene glycol (EG) is then added, entrapping cations on the atomic scale (Figure 1). Once the solvent reaches a critical concentration, the cation-polymer mixture undergoes a gelation reaction forming a porous, nano-particulate, amorphous powder. This amorphous powder is then calcined in an air atmosphere causing the formation of oxides. This technique has proven to be quite versatile and has allowed the synthesis of many homogeneous and complex oxides with more than 5 different cations.
The air (high oxygen chemical potential) calcining atmosphere is key for the formation of these oxides. By adapting the chemical potential in the calcining step, the system can be altered to promote the formation of carbides and nitrides. For example, an ammonia-rich atmosphere can be used to increase the chemical potential of nitrogen to promote nitride formation. In comparison, methane, propane or even carbon monoxide atmosphere can be used to increase the chemical potential of carbon, promoting the formation of carbides. The chemical potential can also be tailored for the formation of oxy-nitrides and even oxy-carbides. The advantage of using this method is the starting material is nanoparticulate, nano-porous and amorphous, which all promote the acceleration of reaction kinetics with the gas phase. In addition, since the starting material is amorphous, metastable intermediates do not interfere during synthesis.
The crystal structure of new materials will be solved using X-ray powder diffraction at Argonne National Labs (ANL), Advanced Photon Source (APS) beamline 11-BM, and neutron diffraction at Oakridge national labs (ORNL), Spallation Neutron Source (SNS), POWGEN. X-ray and neutron powder diffraction data will be used in conjunction with charge flipping and simulated annealing to solve the structure of these new compounds .
Objective 2: Crystallography & Computation: Anisotropic Thermophysical Properties
Goal 1: To measure and characterize complex oxides, carbides, and nitrides in terms of their anisotropic thermal expansion α, compressibility κ, and their molar volume strain Vε.
Goal 2: To assess volume compatibilities for engineering applications: high temperature and energy storage.
Thermophysical properties (Table 1) of a material are those which are partial derivatives of the free energy and are related to the change in volume (lattice vectors), such as the thermal expansion α, compressibility κ and molar volume strain Ve (also represented as a partial molar volume of mixing Vmix). These values are typically tabulated in databases as single coefficients. While this is sufficient for high symmetry materials (cubic), this description is insufficient for lower symmetry materials. In general, a material requires up to 6 coefficients to describe either α, κ or Vε.
Anisotropic thermophysical properties can be measured from in-situ diffraction, where the temperature, isostatic pressure and/or composition is varied. α can be measured from room temperature up to melting by using a quadrupole lamp furnace (QLF) (200-2000 ±4 ˚C)  and a conical nozzle levitator (CNL) system (800-3400±25 ˚C) [4,5] at ANL, APS beamline 33-BM-C, and 6-ID-D, respectively [6,7]. κ can be measured using a diamond anvil cell at ANL, APS beamline 16-ID-B . Vε, can most easily be measured by varying composition and measuring the lattice vectors .
These measured thermophysical data has implications for both engineering applications and physical phenomena. The α, κ, and Vε are related to material strains, and thus affect how the shape of the material changes for perturbations of dT, dP, and dn. This thermophysical data is relevant across fields, from high-temperature applications to geological studies, and even energy storage: (i) Consider thermal barrier coating (TBC) for high-temperature engineering applications. TBC’s are typically made of simple oxides carbides or nitrides. If the α of the TBC and the surface material are not tailored, the TBC will crack due to internal strains. (ii) Geologists use κ to see how stress is distributed within the Earth. The κ of oxides and even the carbides and nitrides will be of use for predicting geological features on distant planets with atmospheres of nitrogen or carbon-based gases. (iii) In energy storage applications, if the Vε of the electrolyte and electrodes of solid-state batteries are not tailored or accounted for, the battery will crack and fail during charge and discharge. Thus, these anisotropic thermophysical properties are clearly important in a broad range of critical applications.
In some cases, one or all of the coefficients associated with a thermophysical property can be negative. This gives rise to the notorious negative thermal expansion/compressibility as well as potential directions of zero thermal expansion/compressibility  (Figure 2). These types of properties can be useful in the design of near-zero expansion materials, or optimally mixed composites.
The thermophysical data is related to the free energy of the compound and thus offers insight into the energetics for perturbations of dT, dP, and dn. Understanding these mechanisms will be extremely useful for bottom-up engineering of materials with tailorable volume expansion as a function of T, P, and n.
Objective 3: Crystallography & Computation: Symmetry Relations within Materials Systems
Goal 1: To describe phase transformations in terms of crystallographic orientation relations and lattice variant deformations (related to ΔV of transformation).
Goal 2: To determine symmetry relations among phases.
Goal 3: To assess material transformations for structural engineering; transformation toughening and shape memory in addition to energy storage; intercalation transformations.
Phase transformation symmetry relations can be elucidated by monitoring how thermophysical properties evolve during in-situ powder diffraction. In fact, they have been used to develop the “topotactic motif orientation extraction method”, a technique that allows for the calculation of the crystallographic orientation relation [OR] and lattice variant deformation [ε] between the parent and product phase of a symmetrically related transformation :
It is important to note that the [OR] and [ε] simply forces lattice points of the two structures to coincide and does not describe how the two crystallites in a microstructure are related. This is because the [ε][OR] does not take into account transformation kinetics/pathways (sometimes referred to as lattice correspondence and symmetry variants) or lattice invariant deformation. The crystallite orientation relation and any kinetic/pathway information can be obtained from microscopy. The [OR] and [ε] relations can be useful here as the microstructural orientation relation viewed in a microscope is a convolution of the lattice variant deformation, lattice invariant deformation, lattice correspondence, and crystallographic orientation relations.
For structural applications, if the lattice variant deformation is large, the transformation could potentially be used as a mechanism of toughening. If the lattice variant deformation corresponds to a low overall volume change but has a spontaneous shape change, it could potentially be used for a shape memory material [10–12]. This can also be translated to energy storage applications, as the lattice variant deformation during intercalation will dictate damage and thus the lifetime of the energy storage system.
By knowing the [OR] and [ε] at transformation, a symmetry decomposition can be performed between the two structures to show how they are related by symmetry distortions. While these distortions do not reveal kinetic information directly, they are useful in showing how phases are related to each other. For example, the Hf6Ta2O17 (S.G.=Ima2) complex oxide, which undergoes a peritectic transformation, is related to HfO2 (P4/nmc) + liquid by polyhedral rotations and coordination changes (Figure 3).
Since carbides and nitrides are also built on polyhedral networks like oxides, it suggests they too may possess similar symmetry relations between structures within their phase diagrams. By performing in-situ diffraction experiments as a function of temperature, pressure, and composition, this work aims to characterize any observed phase transformations in terms of their crystallographic orientation relations, lattice variant deformations and symmetry decompositions to gain a fundamental understanding of how the structure of these phases are related. The transformations will also be assessed for their applications as new oxide, carbide, and nitride structural and/or energy storage materials.
Objective 4: Calorimetry & Computation: Phase Equilibra
Goal 1: To make calorimetric measurements to validate observed in-situ phase equilibria.
Goal 2: To relate energetic measurements to symmetry relations and atomic motifs.
Goal 3: To use the CALPHAD method to build the Gibbs free energy functions, G(T,P,n), and develop accurate phase diagrams for these new complex oxides, carbides, and nitrides.
In-situ powder diffraction measurements have proven to be useful as a first step to identify phase equilibria in high-temperature systems. An example of this is the development of the HfO2-Ta2O5 phase diagram . These in-situ diffraction studies need to be complemented with calorimetry studies for verification of phase equilibria.
Solution drop calorimetry will be implemented to measure the formation enthalpies and enthalpies of mixing of the synthesized oxides, carbides and nitrides. The enthalpies of mixing will be used to complement the thermophysical parameter, Vε in an attempt to understand the energetics of the symmetry relations (Objective 3) observed in the phase diagrams. This information will be critical for the optimization of stable phases with tailorable volume and PCM.
High-temperature calorimetry will be used to determine accurate temperatures and enthalpies of transformation. These will be coupled with, and compared, to the lattice variant deformations and symmetry distortion of temperature-induced transformations. These will be related to currently known transformation toughening and shape memory ceramics in an attempt to design new varieties of complex oxide, carbide and nitride systems.
Finally, all the collected thermophysical and thermochemical data will be combined using the CALPHAD method to build the complete free energy, G(T,P,n), description of observed phases in the studied systems. This will be used to develop accurate phase diagrams and for the design of new high temperature, energy storage and structural material systems.
Currently, our thermodynamic databases are rich with data on metallic materials and materials with high symmetry, i.e. cubic. However, the amount of thermodynamic property data available starts to decrease as we move to complex oxides, carbides, and nitrides. Thermochemical properties such as the free energy of formation (ΔGf ), heat capacities (Cp), transformation enthalpies (ΔHT ) and enthalpies of mixing (ΔHmixing) are scarce and are only readily available for metals, simple oxides, carbides and nitrides within limited temperature ranges. In addition, these databases rarely include sufficient thermophysical properties such as thermal expansion (α), compressibility (κ) and molar volume strain (Vε), especially at their operating conditions. Even more frustrating is that this thermophysical property data is not even available for low symmetry materials, making them impossible to effectively engineer into material systems. This truly hinders our ability to engineer advanced material systems as we only have useable data for a small subset of materials.
The lasting contribution to science and engineering will be the population of thermophysical and thermochemical data on complex oxides, carbides, and nitrides. This data will allow the design of next-generation space exploration materials, including new high-temperature materials, radiation-resistant materials, plasma resistant materials, energy storage materials and structural materials (transformation toughening and/or shape memory).
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