Stability of Bulk Metal Oxides

As an initial example of using DFT calculations to describe phase stability, we will continue our discussion of bulk metal oxides. In this chapter, we are interested in describing the thermodynamic stability of a metal, M, in equilibrium with gas-phase O2 at a specified pressure, Po2, and temperature, T. We will assume that we know a series of candidate crystal structures for the metal 

Thermodynamically, we would like to know which material minimizes the free energy of a system containing gaseous 02 and a solid at the specified conditions. A useful way to do this is to define the grand potential associated with each crystal structure. The grand potential for a metal oxide containing NM metal atoms and No oxygen atoms is defined by 

We can interpret the internal energy in the grand potential as simply the total energy from a DFT calculation for the material. It is then sensible to compare the grand potentials of the different materials by normalizing the DFT energies so that every DFT calculation describes a material with the same total number of metal atoms. If we do this, Eq. (7.1) can be rewritten as 

The grand potential defined in Eq. (7.2) has one crucial and simple property The material that gives the lowest grand potential is also the material that minimizes the free energy of the combination of gaseous 02 and a solid. In other words, once we can calculate the grand potential as shown in Eq. (7.2), the thermodynamically stable state is simply the state with the lowest grand potential. 

When comparing crystalline solids, the differences in internal energy between different structures are typically much larger than the entropic differences between the structures. This observation suggests that we can treat the entropic contributions in Eq. (7.2) as being approximately constant for all the crystal structures we consider. Making this assumption, the grand potential we aim to calculate is 

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If we were only interested in bulk copper and its oxides, we would not need to resort to DFT calculations. The relative stabilities of bulk metals and their oxides are extremely important in many applications of metallurgy, so it is not surprising that this information has been extensively characterized and tabulated. This information (and similar information for metal sulfides) is tabulated in so-called Ellingham diagrams, which are available from many sources. We have chosen these materials as an initial example because it is likely that you already have some physical intuition about the situation. The main point of this chapter is that DFT calculations can be used to describe the kinds of phase stability that are relevant to the physical questions posed above. In Section 7.1 we will discuss how to do this for bulk oxides. In Section 7.2 we will examine some examples where DFT can give phase stability information that is also technologically relevant but that is much more difficult to establish experimentally. 

Another difference between Co and Fe is their sensitivity towards impurities in the gas feed, such as H2S. In this respect, Fe-based catalysts have been shown to be more sulfur-resistance than their Co-based counterparts. This is also the reason why for Co F-T catalysts it is recommended to use a sulphur-free gas feed. For this purpose, a zinc oxide bed is included prior to the fixed bed reactor in the Shell plant in Malaysia to guarantee effective sulphur removal. Co and Fe F-T catalysts also differ in their stability. For instance, Co-based F-T systems are known to be more resistant towards oxidation and more stable against deactivation by water, an important by-product of the FTS reaction (reaction (1)). Nevertheless, the oxidation of cobalt with the product water has been postulated to be a major cause for deactivation of supported cobalt catalysts. Although, the oxidation of bulk metallic cobalt is (under realistic F-T conditions) not feasible, small cobalt nanoparticles could be prone to such reoxidation processes. 

The precipitation and colloid formation of different metal oxide hydroxides is known in soils when the concentration of the ions reaches the value of stability products. In this case, the precipitation can be explained by the thermodynamic properties of the bulk solution. In the lead ion/calcium-montmorillonite system, however, the production of lead enrichments cannot be explained by the... 

Research on supported Ni catalysts, used for steam reforming and other applications " , has dealt with factors affecting their activity and stability. Catalyst formulation and the extent to which interaction occurs between NiO and the support are important factors influencing the reduction of NiO to Ni in the catalyst and the catalysts subsequent behavior. The influence of the support on the metal is illustrated by NiO on AI2O3 or MgO. It is well known that NiO deposited on oxide supports is less readily reduced than bulk NiO. Furthermore, growth of crystallites of the metal oxide can be retarded by a suitable support. For instance, the presence of MgO retards the growth of NiO. When NiO is calcined at 500°C for 4 h, NiO crystallites increase to about 30 nm, whereas in a NiO/40% MgO solid solution, the crystallites grow to only 8 nm (Fig. 1). ... 

Recent publications show that there is actually no solid absorbent based on bulk metal oxides available that meets the conditions formulated above for application in high-temperature desulfurization processes. Absorbents that have been developed all show one or more undesired characteristics. Disintegration due to a poor mechanic and chemical stability is commonly found. Metal sulfate formation during regeneration with O2 is a considerable problem [5]. Furthermore, absorbents based on bulk metal oxides display a relatively low activity towards the removal of H2S from coal gas. 

They doubtless owe their stability to the bulk of the aryl thiolate ligand they have tbp structures with equatorial nitrile that can be displaced by CO to give rare carbonyls of a metal in the +4 oxidation state. 

Bulk structures of oxides are best described by assuming that they are made up of positive metal ions (cations) and negative O ions (anions). Locally the major structural feature is that cations are surrounded by O ions and oxygen by cations, leading to a bulk structure that is largely determined by the stoichiometry. The ions are, in almost all oxides, larger than the metal cation. It does not exist in isolated form but is stabilized by the surrounding positive metal ions. 

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