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Lab 2: Crystallography

June 1 2000


1.0 Procedure

This Lab has been performed in accordance with the procedures outlined in the ME 215 – Structure and Properties of Materials Laboratory Manual, spring 2000, provided by the mechanical engineering department of University of Waterloo.

2.0 Viewing The Specimen

(1)   The metallic specimen is mounted on to the Bakelite base

(2)   Specimen is sliced to a small thickness

(3)   The specimens is gradually sanded to fine grade 

(4)   The specimen is polished

(5)   The specimen is etched with acid

(6)   The specimen is levelled accurately on the base


The specimen is placed beneath the objective lens.  A light sources with variable intensity is focused on the specimen.  The reflected light is used to magnify the image, which is transferred on to a computer via a digital camera.


The image observed has areas of different darkness.  This is caused by minute inclusions on the material.


Chemical etch is used on polished specimens to eat in to grain boundaries and other impurities.  The acid eats in to the metal in different depths  eats in to different imperfections


Chemical etch is used on polished specimen to remove any impurities and grin boundaries.

3.0   Results and Observations

Grain boundaries: A grain boundary is a surface that separates individual grains.   The lattice has a different orientation on either side of the grain boundary. 

Low angle boundaries: Is an array of dislocations that produces a small misorientation between the adjoining lattices.  Small angle boundaries formed by edge dislocations are called tilt boundaries and those caused by screw dislocations are called twist boundaries.

 Vacancy:  Is produce when an atom is missing from a normal site.  They are introduced into a crystal during solidification, at high temperatures, or as a consequence of radiation damage.

Substitution atom: Substitution atom occurs where there is a substitutional defect.  A substitutional defect is introduced when a different type of atom in a lattice replaces one atom. Substitution atoms may either be larger or smaller than the normal atoms in the lattice.

Edge dislocation: is line defect when an “extra half plane” of atoms is introduced into the lattice

Indices Of The Most Closely Packed Planes: Using MSE software, and observing models it was found that BCC has closely packed directions, whereas HCP and FCC crystal structures has close packed planes. BCC has eight close packed directions. They are in the family of <111> direction, and {110} plane. HCP has two families of closely packed directions, and they are in the direction <100> and <110>. HCP crystal structures also have two families of closely packed planes. They are {0001} and {0002} planes. It was also found that FCC has twelve closely packed directions four closely packed planes, and they are in the family of {111} planes. Furthermore, FCC crystal structures have four closely packed planes, and they are in the family of {111} planes. The most closely packed direction in a BCC crystal structure is <111> with a low index set of planes {110}.

The following table summarises the close packed planes and directions of the three crystal structures, namely BCC, FCC, and HCP.











<110>, <100>, or <1120>

{0001}, {0002}

Table 1: Close-packed planes and directions [Ask eland]

For a BCC and a FCC structure there are two possible interstitial site formations.  The two formations are tetrahedral [1, ½, ¼] and octahedral [½,1, ½].  The brackets indicate the interstitial site location on the unit cell.

Crystal and site Type

Maximum radius

BCC octahedral

(a0 – 2r)/2

BCC tetrahedral

Ö2a0 –2r

FCC octahedral

(a0 – 2r) / 2

FCC tetrahedral

(a0 /2Ö2 ) -r




Table 2: Interstitial sites

 Thus for a given lattice parameter the largest interstitial site in a BCC is larger than that in a BCC.

4.0 Discussion

4.1       Aspects of Dislocation motion:

In order to study different aspects of dislocation motion in real crystals various models were used. For example, a soap bubble model was helpful to visualise grain boundaries, substitutional atoms, vacancies, and other 2-D properties. However, it falls short to explain certain concepts such as slip direction versus the Burger’s vector orientation for edge versus screw dislocations. Consequently, graphics program and 3-D models were used to explain these concepts. From 3-D models, it was observed that in an edge dislocation, dislocation motion is perpendicular to the Burger’s vector. On the other hand, in a screw dislocation, dislocation motion is parallel to the Burger’s vector. The 3-D models also helped to visually understand interstitial sites and slip planes.

4.2              Fe-C Phase Diagram:

From the Fe-C equilibrium “phase diagram”, it was observed that the solubility of carbon in FCC-Fe is higher than BCC-Fe. The largest available radius of the interstitial site radius is

0.07nm. The radius of the interstitial site in BCC-Fe is 0.0361nm, whereas that of FCC-Fe is 0.0522nm. Consequently, carbon atoms can fit in FCC-Fe with relative ease when compared to BCC-Fe. Hence, it can be concluded that solubility of substitutional atoms (carbon in this case) is directly related to the size of the interstitial sites.

4.3       Dislocations in ionic crystals:

NaCl is an ionic crystal, which is a combination of two FCC structures, which makes it a strong crystal.  The movement of dislocations in these types of crystals is difficult and usually causes the crystal to break.  The movement of dislocation will break the ionic bonds and causes atoms with likes charges to line up, which results in repulsive force between the ions.  This repulsive force causes the breakage of the crystal.

The metallic bonds that form crystals in metals are relatively weak when compared with those that form ionic crystals.   Metallic bonds are also elastic because the bonds can be stretched.  This, and the fact that metallic bonds have little repulsion between atoms, allows dislocations to be move more easily than in ionic crystals.

4.4       Polystyrene vs. Polyethylene

Polystyrene is more difficult to crystallise because it is an amorphous polymer structure with benzene side groups [1]. This polymer, formed from non-symmetrical repeat units arranged randomly, is called atactic polymers.  When it crystallises the benzene acts like a hook preventing the formation of a highly ordered crystal structure.  This causes the crystal to have characteristics such as poor packing low-density low strength, and low stiffness [1].

4.5       Heated Fe wire:

Some materials change their crystal structure when they are heated or cooled. Such a crystal structure change involves rearrangement of the atoms in the crystal. As part of the crystallography laboratory this material property is demonstrated by heating an iron wire using electrical current, and observing the change in its length, measured by a simple indicator.

As the wire is heated, it expands and this is observed as a rise on the indicator. The current is then turned off, subsequently the wire cools down and contracts. This is seen as a dip on the indicator dial. When the temperature drops to 912 °C, the indicator dial shows a sudden increase in volume. This is due to the fact that at 912 °C Fe changes its molecular structure from FCC to BCC.

FCC and BCC cells have different packing factors that can be calculated using the following formula:

 FCC cells have a packing factor of 0.74, whereas BCC cells have that of 0.68, which means that there is more space available for same number of unit cells [ ]. Therefore Fe shows an increase in volume for a fraction of time, while cooling down.

4.6       Twinning

Twinning is a type of surface grain boundary defect in which a crystal is joined to its mirror image.  Twins can be produced when a shear force causes the atoms to shift out of position.  “Mechanical” twins are caused by mechanical deformation, whereas “annealing” twins are formed during heat treatment. Metals such as tin and zinc twin when mechanically deformed because, unlike many other metals they are of HCP structure.  Twinning can be easily identified under the metallurgical optical microscope by the sets of darker parallel lines

4.7       Viewing Specimen in an optical microscope

(7)   The metallic specimen is mounted on to the Bakelite base

(8)   Specimen is sliced to a small thickness

(9)   The specimens is gradually sanded to fine grade 

(10)  The specimen is polished

(11)   The specimen is etched with acid

(12)   The specimen is levelled accurately on the base

The specimen is placed beneath the objective lens.  A light sources with variable intensity is focused on the specimen.  The reflected light is used to magnify the image, which is transferred on to a computer via a digital camera. The image observed has areas of different darkness.  This is caused by the different surface defects on the material.   Chemical etch is used on polished specimens to help identify surface defects, such as grain boundaries, and other impurities.  The chemical etch “eats” in to the metal at different atomic depths, depending on the defect or impurity.   The different depths causes the light to diffract differently, which is visible on the optical microscope as darker sections.  For example dark black lines are grain boundaries.

 Scanning Electron Microscope:

The Scanning Electron microscope (SEM) uses electrons instead of light to form an image. A heating metallic element is placed at the top of the microscope that produces a beam of electron. The beam follows a vertical path through the column of the microscope, and makes its way through electromagnetic lenses, which focus and direct the beam down toward the sample.


Once it hits the sample, other electrons are ejected. Detector collects the back-scattered electrons, and converts them to a signal that is sent to a viewing screening.



Figure: Electron Microscope


There are many advantages to using the SEM over optical microscope. The SEM has a large depth of field, which allows a large amount of the sample to be in focus at one time. The SEM also produces images of high resolution, which means that closely spaced features can be examined at a high magnification. Preparation of the samples is relatively easy since most SEMs only require the sample to be conductive. The combination of higher magnification, larger depth of focus, greater resolution, and ease of sample observation gives SEM an edge over optical microscopes.



The purpose of this lab was to become familiar with the concepts of crystal structures and their defects, and to get a first hand experience with the various microscope.

Crystal structures have two types of dislocations.  Edge dislocation occurs when an “extra half plane” of atoms is added, whereas a screw dislocation is the skewing of a crystal one atomic space.  It was determined that both these dislocations can be identified using burger's vectors. Furthermore it was also found that the burgers vector runs perpendicular to a screw dislocation and parallel to an edge dislocation.  The ability of a dislocation to travel across the crystal relates to the strength of the material.   Examples of surface defects are twinning, and grain boundaries, whereas examples of point defect are vacancies, substitution atoms, and interstitial sites. Both surface defects and point defects add to the strength of the material as they prevent the movement of dislocations, however these defects add to the brittleness.

Some materials change their crystal structure when they are subjected to temperature changes. As iron changes form FCC to BCC crystal structure at 912°C, the volume in changes to accommodate more interstitial carbon atoms, thereby increasing the strength of the iron.

The crystallisation of polymers, which have randomly placed side groups, such as polystyrene, are hard to crystallise because the tangle up the carbon chain.

Twinning occurs only with metals with a HCP structure.  It is visible under an optical microscope by recognizing darkened parallel lines.

In order to view a specimen under an optical microscope several steps must be taken.  The specimen should be sanded to a fine grain, polished and then etched with chemical to remove surface inclusions.

An advantage of using a scanning electron microscope over an optical microscope is that specimens can be viewed at a higher magnifications, and larger depth of focus.