Materials Science and Engineering/Doctoral review questions/Daily Discussion Topics/01092008

GMR

in situ process
- cobalt can oxidize and deteriorate
- use sputtering to directly deposit alumina
a thin film corresponds to a small crystal size
there are surface energy terms

Heat Dissipation

$E=\int VIdt$
- $E=0\;$ - out of phase
- $E\neq 0$ - in phase

Graphite and Diamond

Why is one phase stable?

Size of the atom
- extra shell of electrons

Carbon and Silicon

Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in structure.

The outer electron orbitals of silicon (half filled subshell holding up to eight electrons) are of the same structure as in carbon and the two elements are very similar chemically.

Why is there not a similar structure of graphite in the case of silicon?

Hybridisation and Molecular Orbital Theory

Although the language and pictures arising from Hybridisation Theory, more widely known as Valence Bond Theory, remain widespread in synthetic organic chemistry, this qualitative analysis of bonding has been largely superseded by molecular orbital theory in other branches of chemistry. For example, inorganic chemistry texts have all but abandoned instruction of hybridisation, except as a historical footnote. One specific problem with hybridisation is that it incorrectly predicts the photoelectron spectra of many molecules, including such fundamental species such as methane and water. From a pedagogical perspective, hybridisation approach tends to over-emphasize localisation of bonding electrons and does not effectively embrace molecular symmetry as does MO Theory.

Molecular orbital (MO) theory uses a linear combination of atomic orbitals to form molecular orbitals which cover the whole molecule. These are often divided into bonding orbitals, anti-bonding orbitals, and non-bonding orbitals. Molecular orbitals are further divided according to the types of atomic orbitals combining to form a bond. These orbitals are results of electron-nucleus interactions that are caused by the fundamental force of electromagnetism. Chemical substances will form a bond if their orbitals become lower in energy when they interact with each other. Different chemical bonds are distinguished that differ by electron cloud shape and by energy levels.

Some allotropes of carbon: diamond, graphite, lonsdaleite, buckyballs (C60, C540, C70), amorphous carbon and a carbon nanotube.

MO theory provides a global, delocalized perspective on chemical bonding. For example, in the MO theory for hypervalent molecules, it is no longer necessary to invoke a major role for d-orbitals. In MO theory, any electron in a molecule may be found anywhere in the molecule, since quantum conditions allow electrons to travel under the influence of an arbitrarily large number of nuclei, so long as permitted by certain quantum rules. Although in MO theory some molecular orbitals may hold electrons which are more localized between specific pairs of molecular atoms, other orbitals may hold electrons which are spread more uniformly over the molecule. Thus, overall, bonding (and electrons) are far more delocalized (spread out) in MO theory, than is implied in VB theory. This makes MO theory more useful for the description of extended systems.

Allotrope

Allotropy (Gr. allos, other, and tropos, manner) is a behavior exhibited by certain chemical elements: these elements can exist in two or more different forms, known as allotropes of that element. In each different allotrope, the element's atoms are bonded together in a different manner. Allotropes are different structural modifications of an element.[1]

For example, the element carbon has two common allotropes: diamond, where the carbon atoms are bonded together in a tetrahedral lattice arrangement, and graphite, where the carbon atoms are bonded together in sheets of a hexagonal lattice.

Note that allotropy refers only to different forms of an element within the same phase or state of matter (i.e. different solid, liquid or gas forms) - the changes of state between solid, liquid and gas in themselves are not considered allotropy. For some elements, allotropes have different molecular formulae which can persist in different phases - for example, the two allotropes of oxygen (dioxygen, O2 and ozone, O3), can both exist in the solid, liquid and gaseous states. Conversely, some elements do not maintain distinct allotropes in different phases: for example phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.

Allotropes can exhibit quite different physical properties and chemical behaviours. The change between allotropic forms is triggered by the same forces that affect other structures, i.e. pressure, light, and temperature. Therefore the stability of the particular allotropes depends on particular conditions. For instance, iron changes from a body-centered cubic structure (ferrite) to a face-centered cubic structure (austenite) above 906 °C, and tin undergoes a transformation known as tin pest from a metallic phase to a semiconductor phase below 13.2 °C.

Ferromagnetic Domains

Several types of energy are included in the theory of domain structure of ferromagnetic materials. These include the exchange energy, $f_{ex}$ , anisotropy energy, $f_{K}$ , magnetoelastic energy, $f_{me}$ , and magnetostatic energy, $f_{mag}$ . Below are equations of energy density with regard to a cubic crystal.

  $f_{ex}=JS^{2}\sum _{i>j}\psi _{ij}^{2}$ 
  $f_{K}=K_{1}\left(\alpha _{1}^{2}\alpha _{2}^{2}+\alpha _{2}^{2}\alpha _{3}^{2}+\alpha _{3}^{2}\alpha _{1}^{2}\right)$ 
  $f_{me}={\frac {3}{2}}\lambda T\sin ^{2}\theta$ 
  $f_{mag}=-{\frac {1}{2}}\mathbf {H} \cdot \mathbf {I} {\mbox{ (self-energy)}}$