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Materials (Definitions (Structure of crystalline solids (Crystals and…
Materials
Definitions
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Imperfections in solids
Point defects
Vacancy
- All crystalline solids contain vacancies and, in fact, it is not possible to create such a material that is free of these defects. The necessity of the existence of vacancies is explained using principles of thermodynamics; in essence, the presence of vacancies increases the entropy i.e., the randomness) of the crystal.
- The equilibrium number of vacancies depends on and increases with temperature.
Self interstitial
- A self-interstitial is an atom from the crystal that is crowded into an interstitial site, a small void space that under ordinary circumstances is not occupied In metals, a self-interstitial introduces relatively large distortions in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated. Consequently, the formation of this defect is not highly probable, and it exists in very small concentrations, which are significantly lower than for vacancies.
Subtitutional and interstitial defects
- Both are point defects that form solid solution and therefore depends on atomic size, crystal structure, electronegativity and valences. (as described in the solid solution branch)
Solid solution
- It is just the dissolving ability of a foreign element in the host crystal. Here the element is commonly referred as solute and the host crystal as solvent. In other words, solvent represents the element that is present in the greatest amount. Solute represents the element that is present in a minor concentration. A solid solution forms when the solute atoms are added to the solvent provided that the solvent crystal structure is maintained. The dissolving ability of solute in the solvent is called solid solubility. However, the solubility of solute in the solvent critically depends on the parameters of the elements involved
- The crystal structure is maintained and no new structures are formed
Atomic size difference
- Appreciable amount of solute dissolves in the solvent if the difference between the atomic radii of two is less than +/- 15%. Other wise the solute atoms create significant lattice distortion of the solvent crystal and a new phase will form
Crystal structure
- For appreciable solid solubility the crystal structures of both the solute and the solvent must be same
Electronegativity of solvent and solute atoms
- The more electro-positive one element and the more electro-negative the other, such cases will form intermetallic compound instead of forming a substitutional solid solution. Thus, the electronegativities of the solute atom and solvent atom must be comparable.
Valences
- Other factors being equal, a metal will have more of a tendency to dissolve another metal of higher valency than one of a lower valency
Linear defects
- Permanent deformation of most crystalline materials are by the motion of dislocations. Dislocations are introduced during solidification, during plastic deformation and as a consequence of thermal stresses that result from rapid cooling
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Interfacial defects
- Interfacial defects are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations. These imperfections include external surfaces, grain boundaries, twin boundaries, stacking faults, and phase boundaries.
External surface
- One of the most obvious boundaries is the external surface, along which the crystal structure terminates. Surface atoms are not bonded to the maximum number of nearest neighbors, and are therefore in a higher energy state than the atoms at interior positions. The bonds of these surface atoms that are not satisfied give rise to a surface energy, expressed in units of energy per unit area (J/m2 or erg/cm2). To reduce this energy, materials tend to minimize, if at all possible, the total surface area. For example, liquids assume a shape having a minimum area—the droplets become spherical. This is not possible with solids, which are mechanically rigid.
Grain boundary
- Atoms are bonded less regularly along a grain boundary (e.g., bond angles are longer), and consequently, there is an interfacial or grain boundary energy similar to the surface energy described above. The magnitude of this energy is a function of the degree of misorientation, being larger for high-angle boundaries.
- Grain boundaries are more chemically reactive than the grains themselves as a consequence of this boundary energy. Furthermore, impurity atoms often preferentially segregate along these boundaries because of their higher energy state.
- The total interfacial energy is lower in large or coarse-grained materials than in fine-grained ones, since there is less total boundary area in the former. Grains grow at elevated temperatures to reduce the total boundary energy.
Diffusion
- Phenomenon of material transport by atomic motion; stepwise migration of atoms from site to site
- Two conditions must be met for diffusion:
- there must be an adjacent empty site
- the atom must have sufficient energy to break the bonds with its neighbour atom and then cause some lattice distortion during displacement. This energy is vibrational in nature
- Increases exponentially with temperature
Interdiffusion
- Atoms of one metal diffuse into another
Self-diffusion
- Occurs for pure metals, in which all atoms exchanging positions are of the same type
Mechanism
- Of the different models for atomic diffusion, two dominate for metallic diffusion
Vacancy diffusion
- Interchange of an atom from a normal lattice position to an adjacent vacant lattice site.
- Is a function of the number of vacancy defects that are present; significant concentrations of vacancies may exist in metals at elevated temperatures. Both self-diffusion and interdiffusion occur by this mechanism; for the latter, the impurity atoms must substitute for host atoms.
Interstitial diffusion
- The second type of diffusion involves atoms that migrate from an interstitial position to a neighbouring one that is empty. This mechanism is found for interdiffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen, which have atoms that are small enough to fit into the interstitial positions. Host or substitutional impurity atoms rarely form interstitials and do not normally diffuse via this mechanism. This phenomenon is appropriately termed interstitial diffusion.
- In most metal alloys, interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, since the interstitial atoms are smaller and thus more mobile. Furthermore, there are more empty interstitial positions than vacancies; hence, the probability of interstitial atomic movement is greater than for vacancy diffusion
Steady-state diffusion
- Diffusion is a time dependent process. The rate of diffusion, expressed as diffusion flux J, is:
\(J=M/At\),
where M is the mass of atoms diffusion through and perpendicular to a unit cross section area of solid per unit time
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