Outline

• Metallic Solid Solutions

  1. Substitutional solid solutions

  2. Interstitial solid solutions

• Defects in Crystals

  1. Point defects

     1. vacancies
     2. self interstitials or interstitialcies
     3. Shottky defect;
     4. Frenkel defect;
     5. Dilute solid solutions;

  2. Line Defects (dislocations)

     1. Edge dislocations
     2. Screw dislocations
     3. Mixed dislocations

  3. Grain Boundaries (Planar defects)

     1. Metallography of grains
     2. Grain size

Discussion

Metallic Solid Solutions:

Pure metals tend to be soft and ductile and thus have limited usefulness. One of the most common ways of strengthening metals is to mix them with other chemical elements to form an alloy. The simplest type of alloy is one in which the minor component is randomly dispersed in the crystal structure of the major component. This is called a solid solution. There are two classes of solid solutions, substitutional solid solutions and interstitial solid solutions.

Substitutional solid solutions are those in which the atoms of the minor component (solute) are substituted for the atoms of the major component (solvent) on the lattice positions normally occupied by the solvent atoms. Usually there is a limit to the maximum amount of solute (solubility limit) that can be added to the solvent before the structure changes to a more complex form. There are a few binary (two component) alloy systems where the solubility limit is 100%. Obviously before this can occur the two components must have the same crystal structure and these systems are often referred to as isomorphous systems. An example is the Cu-Ni system where both copper and nickle have the FCC crystal structure. There are other requirements in order to have extensive solid solubility: the two components must have similar atomic radii, similar electronegativities, and similar number of electrons in their outer shells (similar number of valence electrons). It is difficult to quantify these requirements exactly but it is perhaps useful to study a few examples.

Cu-Ni(100% solid solubility); The atom sizes differ by about 2%, the electronegativities are the same, the crystal structures are the same, the valences are confusing since table 2.4 shows the electron configuration of Ni to be [Ar]3d⁸4s² and the electron configuration of Cu is [Ar]3d¹⁰4s¹. However, these configurations apply to isolated atoms. In the solid it is thought that one of the Ni 4s electrons occupies a d state since the magnetic moment of Ni in the solid is 0.6 Bohr magnetons instead of the 2 that would be expected if there were 2 unpaired d electrons.

Cu-Ag(limited solid solubility, <1% at room temperature). The atomic size difference is 12% and all other factors are favorable. Copper and silver both have the FCC structure, the electronegativities differ by 0.4, and the valences are similar.

Interstitial solid solutions are those in which the solute atoms occupy the intersitial positions (holes between the atoms) in the crystal lattice of the solute). Interstitial solid solutions always have limited solubility of the solute. One of the requirements for measureable solubility is that the solute atom must be small to fit into the intersitial positions of the solvent. Electronegativity differences are also important. For example carbon shows measureable interstitial solubility in iron while oxygen and flourine do not even though the atoms are smaller than the carbon atom.

Example problem 4.3 of the text shows how to calculate the largest interstitial void radius in the FCC lattice. In homework set 4 we calculated the diameter of the largest interstitial that would just fit into the tetrahedral interstitial void in BCC vanadium as 0.038nm. There is another type of intersitial position in the BCC which is an octaderal position located at the centers of each face and also at the edges of each face. This can be seen to have a maximum interstitial radius of (a-2R)/2 = a(1 - 3^1/2/2)/2 = .0699a = .0204nm for V.

1. Point defects

   1. vacancies
      1. Thermal equilibrium defect requires excess energy of approximately 1eV in metals like copper ,larger in higher melting metals.
      2. Introduction of vacancies increases the entropy (due to greater disorder) so the free energy of the system is lowered. Effect is greater with increasing temperature.
      3. Excess vacancies may be introduced by quenching from high temperature, mechanical deformation, neutron irradiation.
      4. Vacancies enable atomic diffusion to occur in most metals and are thus essential for many industrial proccessing of materials.
   2. self interstitials or interstitialcies
      1. Requires substantially greater energy than for vacancies so thermal equilibrium concentration is negligible in most metals.
      2. Are created by neutron irradiation of metals.
   3. Shottky defect; Anion - cation vacancy pair (maintains local charge neutrality in ionic crystals)
   4. Frenkel defect; cation vacancy -cation interstitial pair.
   5. Dilute solid solutions; the solute atoms act as point defects . Topic 6 Outline

2. Line Defects (dislocations) Dislocations are a type of crystalline defect that allows deformation of metals to take place by a slip process that explains the ductility and work hardening of metals and many other features of deformation. Taylor and Orowan are generally credited as inventing the concept of dislocations as an explanation for the slip process in about 1930. It wasn't until the late 1940's that experimental evidence was obtained to corroborate their theory. The first transmission electron micrographs of dislocation lines were published about 1956. Chapter 1 of Theory of Dislocations , John Price Hirth and Jens Lothe 1968 gives a historical discussion of the development of dislocation theory. In chapter 4 of the text the student is introduced to the concept of dislocations. Further use of these concepts will be made in the discussion of mechanical properties of metals and ceramics.

   1. Edge dislocations (may be conceived of as the edge of an extra half-plane of atoms)
      1. Burgers vector, b perpendicular to the dislocation line.
      2. Burgers vector defined by Burgers circuit around the dislocation line.
      3. Glide plane defined by b and dislocation line.

   2. Screw dislocations ( think of a spiral ramp around the dislocation line)
      1. b is parallel to the line.
      2. glide plane not defined by b and dislocation line.

   3. Mixed dislocations (b is conserved as the line direction changes)Topic 6 Outline

3. Grain Boundaries (Planar defects)

   1. Metallography of grains
      1. Etching effects: grain boundary grooving or faceted planes.

   2. Grain size
      1. ASTM grain size number, n defined by N=2^n-1 where N is the number of grains per square inch observed on a polished and etched structure at 100X magnification.
      2. Mean grain diameter.