Surface Imperfections in Crystalline Solid

Surface Imperfections

Surface imperfections are observed on the surfaces of the crystals. Surface, in broad sense, means a depth of few degree angstrom (oA) too. Due to finite size of crystals, bonds are broken on the, surfaces for want of neighboring atoms. The number of bonds broken per atom, on different planes, due to formation of one square meter (1m2) surface, are:

1/2r2    on  (100) plane,

√2/8r2  on  (110) plane, and

3√3/r2  on (111)plane.

where r is atomic radius.

Moreover during solidification, formation of new crystals in a polycrystalline material is random. Interaction of crystals between themselves inherits some imperfection on the inside of surface. We shall now deal with different types of surface imperfections in this article.

Grain Boundary

Mechanism of grain boundary defect: Polycrystalline solids consist of several crystals of different sizes oriented randomly with respect to each other. They grow during the process of re-crystallization. Growth of crystals is a direct consequence of addition of atoms.

If the number of atoms are more in a crystal, the size of crystal will be large. As shown in Figure 1, crystal marked A is smaller than crystal marked B because of lesser number of atoms joining the crystal A.

The crystals grow randomly and in doing so impinge upon each other. When adjoining crystals impinge together, some atoms marked C are caught in between them. These atoms are forced to join one or the other crystal. But they do not join any crystal due to their opposing forces. These atoms occupy positions at the junction of adjoining crystals.

Junction or the boundary region is distorted and behaves as non-crystalline material. This boundary region is the defect called grain boundary. Lines joining various atoms C are grain boundaries, and θ is the grain orientation angle.

Twin or Twinning

This defect is also called twin boundary. As the name implies, twin boundaries occur in pairs. The arrangement of atoms is such that one side of twin boundary is a mirror replica of the other side.

As shown in Figure 2, side A is a mirror image of side B. The zone CDEF is known as twinned zone. DE and FC are twin boundaries.

Annealing twin and deformation twin: Twins can form during the process of re-crystallization or during plastic deformation of materials. In the first case it is called annealing twin and in the other as deformation twin.

Occurrence of twins is common in brass and metallic sheets. Twins in crystalline solids can be visualized by an optical microscope. The twin planes and twin directions in different crystal structures are given in the following table:

Structure Twin plane Twin Direction Example
BCC (112) [111] Fe, W, V
FCC (111) [112] Cu, Al, Ag
HOP (101bar2) [101bar1bar] Mg, Ti, Zn

Low Angle Tilt Boundary

When crystals orientation is such that the orientation angle (Figure 3) is less than 10°, the structure is called low angle tilt boundary. Here the adjacent crystals are oriented at a small angle to each other.

Geometry of the tilt boundary h may be taken as a vertical distance between equally spaced edge dislocations of same kind (of inverted T) located one over the other. The schematic arrangement is shown in Figure 3.

A, B, C and D are like (positive) edge dislocations of the same kind. A relation between the geometrical dimensions b and h of edge dislocation gives

b/h = tanθ

For small angles (θ<4.5o) , it becomes

b/h = θ (approximately)

Here b is the Burgers vector and h is the vertical distance between two adjoining edge dislocations.

Other Crystal Boundaries

Besides the low angle tilt boundary discussed above, surface boundary imperfections also occur in other forms such as:

  1. high angle boundary,
  2. inter-phase boundary, and
  3. twist boundary.
  • Orientation between two adjoining crystals having q > 10° is referred to as high angle boundary.
  • Two crystals having either different crystalline configurations or different composition form an inter-phase or interface boundary.
  • Boundaries, formed by screw dislocations on small orientation angle θ are called twist boundaries.

Stacking Fault

The stacking sequence in FCC crystals, of ABCABCABC …. type,  and in HCP crystals of ABABAB …. type. However if any one or more stacking plane of atoms are missing, the solid configuration becomes faulty. The defect is then called stacking fault or piling-up fault. Typical stacking fault in FCC crystals is illustrated below

ABCAB*A*CA*BC….

and in HCP crystal as

ABA*AB*BAB

The * mark in above two stackings indicate the fault.

Volume Imperfections

Volume imperfections, also known as 3-dimensional imperfections are found inside the solids. These may form due to one or more of the following reasons.

  1. foreign-particle inclusions,
  2. regions of non-crystallinity,
  3. pores,
  4. dissimilar natured regions.

The dimensions of these are of the order of tens of oA. The inclusions, pores etc. may be randomly located at one or many positions in the volume of the material.

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