As oxide research moves toward the discovery of new materials with increasing structural and compositional complexity, it is equally becoming more difficult to isolate such compounds by purely synthetic methods. Large and complex materials experimentally face two main problems, firstly, finding the composition at which a new structure can and will form for multiple element system can result in synthesis at a wide range of compositions and conditions with no guarantee that a new compound has not been missed. Secondly, even when new materials are formed, with large and complex structures, identifying the structure is a difficult task. Chapters 3 and 4 investigate the use of theoretical methods to calculate compositions at which new compounds can be formed, whereas chapter 5 focuses on using theoretical techniques to aid in the identification of a new complex oxide material.
Increasingly, theoretical methods have been developed in order to attempt to help with both of the problems presented above, in addition to the traditional contributions from theory such as the
Chapter 1. Introduction
calculations of band structures and corresponding density of states. The aid provided by theory covers a wide range of challenges utilising varying amounts of experimental information. At one end of the scale, where large amounts of experimental information is available are problems such as the most stable distribution of a set of cations for a given crystal structure and composition. At the opposite end, are problems where very little experimental information is known such as attempting to predict the contents of a compositional phase diagram in order to help guide future experimental synthesis. Although it should be noted that the level of experimental information available to use in the computational problem does not necessarily define problems complexity as the difficulty of the task is also reliant on the system size and number of different calculations required.
Given an infinite amount of computational power and infinite time, it would be possible to predict the structure of any compound by sheer brute force, i.e. to generate every possible permutation of a selection of atoms and to then calculate the corresponding free energy of every configuration. However in reality, in order to be able to perform calculations within a reasonable time frame and with the available computer resources, a number of different methods have been developed in order to efficiently aid experimental investigations. Although, each method either attempts to be as broad as possible or make a number of assumptions, resulting in limitations as to which systems a particular method can be applied to.
Before analysis of computed structures can be performed, the ground state structure must first be computed and methods for achieving this have become common place. Typically, the ground state structure is defined as the arrangement of a structure that has the lowest potential energy. Several different methods for finding a minimum energy structure can be reasonably performed
Chapter 1. Introduction
using modern computing resources, with the most suitable depending on the size of the system and what information is required.
In order to find a minimum energy structure, two things are required; a method by which to calculate the energy of the system and a method by which to alter the structure in order to search the energy landscape of the system43-46.
For calculating the energy of a system, there are three main levels of theory; ab-initio
calculations, classical mechanics and semi-empirical methods. With ab-initio calculations the energy of the system is computed with as few parameters as possible, with little information provided by the user apart from the atomic structure plus the number and type of atoms, with a common example of this being density functional theory (DFT, details given in the methods chapter). At the heavily parameterised end of theory is classical mechanics, whereby the energy of the system is calculated from completely parameterised atomic interactions also referred to as force fields (FF), a number of different types of force field are commonly used in simulation packages, details for the methods used in this thesis given in the methods chapter. In between these two types of theory are semi-empirical methods which combine elements from both of the above levels of theory. The most computationally expensive level of theory is the ab-initio
methods, with force fields being the cheapest and semi-emperical methods lying somewhere in- between depending on the level of parameterisation used. All of the calculations performed in this thesis fall into either classical mechanics or ab-initio, with a more detailed description presented in the experimental methods chapter.
Once the energy of a system is calculated, methods can be applied in order to reduce the energy of the structure, most common methods focus on attempting to find the nearest energy minimum.
Chapter 1. Introduction
To find the nearest minimum structure (also referred to as structure relaxation), the program may attempt to find the combination of inter-atomic distances that yields the lowest energy for example (assuming that each bond length will have an energy minimum as a function of distance). There exists a larger problem however; there is the possibility that the structure that is relaxed may not be the lowest possible energy structure for the system, i.e. it may be trapped into a local minima by large energy barriers preventing the energy minimisation finding it. However, relaxing a selection of local minima may be sufficient for specific systems, such as those studied in chapters 3 and 4. A number of levels of theory have been developed in order to find this lowest possible minimum structure, also known as the global minimum structure. In addition to attempting to approximate a brute force method, three common routines have been developed addressing the issue of finding the global minimum without resorting to the generation of as many structures as possible; Monte-Carlo sampling, molecular dynamics and genetic algorithms (which are discussed in the next section).
A substantial challenge in the field of materials chemistry is the ability to be able to predict the formation of new materials or the modification of existing compounds. Computational predictions range from predicting how different cation types order within a system47 to predicting new structures45. Each method will inevitably have its own advantages and drawbacks and so thus far no one method can be deemed universally applicable, each method will have systems for which it is best suited. In the following section some previously reported methods for making predictions in solid state materials are presented and summarised.
Chapter 1. Introduction