Example from Material Science

Due to its unique ability to directly image the local structure of a thin object with atomic resolution, HRTEM is an extremely powerful tool for materials research. Metals, ceramics, and semiconductors are some examples of prominent materials of interest. HRTEM imaging used to be a high-end research tool mostly used in academia, but has now become standard for a wide variety of applications from materials science research to defect analysis in industrial semiconductor fabrication lines. 

Boranes, boron clusters, and in particular, carboranes are of special interest due to their unique properties that cannot be found in organic counterparts. These uniqne properties are based either on the element boron, due to its electron deficiency, or on the structnral featnre of the cluster compound. Borane clusters as a class of materials have a wide range of potential applications. This is not only due to their unique electronic and nuclear features the fields of application, to name but a few, range from materials science through medical applications to catalysis, which will be described in more detail below [13]. Carboranes can be applied as liquid crystals in electro-optical displays [14], non-linear optics [15], and ion-selective electrodes [16] in the materials science arena. If carboranes are vaporized and fired at high temperatures they create boron films that are applied in Tokamak reactors for nuclear fusion [17]. Boranes have furthermore found application in airbag propellant systems in cars [18], as the stationary phase in gas chromatography [19] and in metal ion extraction systems, for example, for nuclear waste [20]. In medical applications, boron neutron capture therapy (BNCT), a special field of anti-cancer therapy, is noteworthy. 

Periodic models, notably the so called block copolymers are of central importance in application, for example in material science and in biology. We omit the extensive bibliography since it is too far from the mathematical aspects on which we focus. 

As an example, we show in Figure 3 a backscattering spectrum from GaAs (110), obtained vwth a 300-keV Li ion beam. This is a well-chosen test example of energy resolution, as the atomic numbers of the two constituents are quite close (31 and 33 for Ga and As, respectively). Not only are these two species well resolved, but the two common isotopes of Ga are also well separated. Note that the peaks are asymmetric due to contributions from lower layers. Resolving power of this kind surely will find many new applications in materials science. 

From strength of materials one can move two ways. On the one hand, mechanical and civil engineers and applied mathematicians shift towards more elaborate situations, such as plastic shakedown in elaborate roof trusses here some transient plastic deformation is planned for. Other problems involve very complex elastic situations. This kind of continuum mechanics is a huge field with a large literature of its own (an example is the celebrated book by Timoshenko 1934), and it has essentially nothing to do with materials science or engineering because it is not specific to any material or even family of materials. 

As we have repeatedly seen in this chapter, proponents of computer simulation in materials science had a good deal of scepticism to overcome, from physicists in particular, in the early days. A striking example of sustained scepticism overcome, at length, by a resolute champion is to be found in the history of CALPHAD, an acronym denoting CALculation of PHAse Diagrams. The decisive champion was an American metallurgist, Larry Kaufman. 

The modern discipline of Materials Science and Engineering can be described as a search for experimental and theoretical relations between a material s processing, its resulting microstructure, and the properties arising from that microstructure. These relations are often complicated, and it is usually difficult to obtain closed-form solutions for them. For that reason, it is often attractive to supplement experimental work in this area with numerical simulations. During the past several years, we have developed a general finite element computer model which is able to capture the essential aspects of a variety of nonisothermal and reactive polymer processing operations. This "flow code" has been Implemented on a number of computer systems of various sizes, and a PC-compatible version is available on request. This paper is intended to outline the fundamentals which underlie this code, and to present some simple but illustrative examples of its use. 

The approach in crystal engineering is to learn from known crystalline structures of, for example, minerals in order to design compounds with desired properties. Crystal engineering is considered to be a key new technology with applications in pharmaceuticals, catalysis, and materials science. The structures of adamantane and other diamondoids have received considerable attention in crystal engineering due to their molecular stiffness, derivatization capabilities, and their six or more linking groups [114-117]. 

Base catalysis is another area which has received a recent stimulus from developments in materials science and microporous solids in particular. The Merk company, for example, has developed a basic catalyst by supporting clusters of cesium oxide in a zeolite matrix [13]. This catalyst system has been developed to manufacture 4-methylthiazole from acetone and methylamine. 

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