1. PDT 153 Materials Structure And Properties
Chapter 4: Crystalline and Non Crystalline Materials
Prepared by: Dr. Tan Soo Jin

2. Single Crystal
For a crystalline solid, the periodic and repeated arrangement of atoms is perfect or extends the entirely of the specimen without interruption resulted single crystal.
All unit cells interlock in the same way and have the same orientation.
Exist in nature or produced artificially.
Shape is indicative of the crystal structure.
In engineering materials, single crystals are produced only under carefully controlled conditions.
Eg: Single crystal silicon is used in the fabrication of semiconductors.

3. Polycrystalline Materials
Polycrystalline- Composed of many small crystals or grains in most of the crystalline solid.
Normally when a material begins to solidify, multiple crystals begin to grow in the liquid and a polycrystalline (more than one crystal) solid forms.
Various stages of solidification (Refer to Figure 4.1):
(a) Small crystal nuclei form at various positions.
(b) Growth of crystallites; the obstruction of some grains that are adjacent to one another is also shown.
(c) Upon completion of solidification, grains having irregular shapes have formed.
(d) The grain structure as it would appear under the microscope (dark lines are the grain boundaries).

4. Solidification
Figure 4.1: Schematic diagrams of the various stages in the solidifications.

5. Single Crystal and Polycrystalline Materials
Single crystal: periodic array over entire material.
Polycrystalline material: many small crystals (grains) with varying orientations.
Atomic mismatch where grains meet (grain boundaries).

6. Polycrystalline Materials
Simulation of annealing of a polycrystalline grain structure

7. Anisotropy
The physical properties of single crystals of some substances depend on the crystallographic direction in which measurements are taken.
The directionality of properties is termed anisotropy, associated with the variance of atomic or ionic spacing with crystallographic direction.
Substances in which measured properties are independent of the direction of measurement are isotropic.

8. Anisotropy Different directions in a crystal have different packing.
For instance: atoms along the edge of FCC unit cell are more
separated than along the face diagonal.
Causes anisotropy in crystal properties
Deformation depends on direction of applied stress
If grain orientations are random  bulk properties are isotropic
Some polycrystalline materials have grains with preferred orientations (texture): material exhibits anisotropic properties.

9. Anisotropy
Properties of crystals may be different along different directions, because atomic periodicities are different.
E.g. in single crystal cubic system:

10. Non-Crystalline (Amorphous) Solids
In amorphous solids, there is no long-range order. But sometimes amorphous does not mean random, in many cases there is some form of short-range order.
Schematic Diagram of Amorphous SiO2

11. Non Crystalline Solids
In non crystalline solids (amorphous) , the constituent particles are not arranged in an orderly manner. They are randomly distributed.
They do not have directional properties and so they are called as `isotropic’ substances.
They have wide range of melting point and do not possess a regular shape.
Examples: Glass, Plastics, Rubber etc.,

12. Amorphous Vs Polycrystalline Vs Single Crystal
Schematics of three general types of crystals: (a) amorphous,
(b) polycrystalline, (c) single crystal.

13. Microstructure Specimen Preparation
Metal specimen preparation:
1. Cutting
When cutting a specimen from a larger piece of material, care must be taken to ensure that it is representative of the features found in the larger sample, or that it contains all the information required to investigate a feature of interest.
2. Mounting
Mounting of specimens is
usually necessary to allow
them to be handled easily.
It also minimizes the
amount of damage likely
to be caused to the
specimen itself.

14. Microstructure Specimen Preparation (Cont..)
3. Grinding
Surface layers damaged by cutting must be removed by grinding. The grinding procedure involves several stages, using a finer paper (higher number) each time. Each grinding stage removes the scratches from the previous coarser paper. Between each grade the specimen is washed thoroughly with soapy water to prevent contamination from coarser grit present on the specimen surface.

15. Microstructure Specimen Preparation (Cont..)
4. Polishing Polishing discs are covered with soft cloth impregnated with abrasive diamond particles and an oily lubricant or water lubricant. Particles of two different grades are used : a coarser polish (diamond particles 6 microns) to remove the scratches produced from the finest grinding stage, and a finer polish (diamond particles 1 micron) to produce a smooth and mirror like surface.

16. Microstructure Specimen Preparation (Cont..)
5. Etching
A dilute acid is react with the surface of the sample. This operation is called etching. After etching, the grain boundries are visible in microscope (reveal the microstructure).

17. Optical Microscope
An optical instrument that uses a lens or a combination of lenses to produce magnified images of small objects, especially of objects too small to be seen by the unaided eye.

18. Optical Microscope (Cont..)

19. Optical Microscope Parts and Functions
Eyepiece: contains the ocular lens, which provides a magnification power of 10x to 15x, usually. This is where you look through.
Nosepiece: holds the objective lenses and can be rotated easily to change magnification.
Objective lenses: usually, there are three or four objective lenses on a microscope, consisting of 4x, 10x, 40x and 100x magnification powers. In order to obtain the total magnification of an image, you need to multiply the eyepiece lens power by the objective lens power. So, if you couple a 10x eyepiece lens with a 40x objective lens, the total magnification is of 10 x 40 = 400 times.
Stage clips: hold the slide in place.
Stage: it is a flat platform that supports the slide being analyzed.
Diaphragm: it controls the intensity and size of the cone light projected on the specimen. As a rule of thumb, the more transparent the specimen, less light is required.
Light source: it projects light upwards through the diaphragm, slide and lenses.
Base: supports the microscope.
Condenser lens: it helps to focus the light onto the sample analyzed. They are particularly helpful when coupled with the highest objective lens.
Arm: supports the microscope when carried.
Coarse adjustment knob: when the knob is turned, the stage moves up or down, in order to coarse adjust the focus.
Fine adjustment knob: used fine adjust the focus.

20. Polymorphism or Allotropy
Metals exist in more than one crystalline form. This is called polymorphism or allotropy.
Temperature and pressure leads to change in crystalline forms.
Example:- Iron exists in both BCC and FCC form depending on the temperature.
-2730C
9120C
13940C
15390C
α Iron
BCC
γ Iron
FCC
δ Iron
Liquid
Iron

21. Crystal Structure Analysis
Information about crystal structure are obtained using X-Rays.
The X-rays used are about the same wavelength ( nm) as distance between crystal lattice planes.
35 KV
(Eg:
Molybdenum)

22. X-Ray Spectrum of Molybdenum
X-Ray spectrum of Molybdenum is obtained when Molybdenum is used as target metal.
Kα and Kβ are characteristic of an element.
For Molybdenum Kα occurs at wave length of about 0.07nm.
Electrons of n=1 shell of target metal are knocked out by bombarding electrons.
Electrons of higher level drop down by releasing energy to replace lost electrons

23. X-Ray Diffraction Crystal planes of target metal act as mirrors
reflecting X-ray beam.
If rays leaving a set of planes
are out of phase (as in case of
arbitrary angle of incidence)
no reinforced beam is
produced.
If rays leaving are in phase,
reinforced beams are
produced

24. Uses of X-Ray Diffraction
Identification of single-phase materials – minerals, chemical compounds or other engineered materials.
Identification of multiple phases in microcrystalline mixtures (i.e., rocks)
Determination of crystal structure of identified materials
Recognition of amorphous materials in partially crystalline mixtures

25. Issues to Express
Crystalline substances (e.g. minerals) consist of parallel rows of atoms separated by a ‘unique’ distance
Diffraction occurs when radiation enters a crystalline substance and is scattered
Direction and intensity of diffraction depends on orientation of crystal lattice with radiation.

26. X-Rays to Determine Crystal Structure
intensity
(from
detector) q c
d =
n l
2 sin
Measurement of critical angle, qc, allows computation of planar spacing, d.
• Incoming X-rays diffract from crystal planes.
Adapted from Fig. 3.19, Callister 7e.
reflections must
be in phase for
a detectable signal
spacing
between
planes d
incoming
X-rays
outgoing X-rays
detector l
extra
distance
travelled
by wave “2”
“1”
“2”

27. X-Ray Diffraction (Cont..)
For rays reflected from different planes to be in phase, the extra distance traveled by a ray should be a integral multiple of wave length λ .
nλ = MP + PN
(n = 1,2…)
n is order of diffraction
If dhkl is interplanar distance,
Then MP = PN = dhkl.Sinθ
Therefore, λ = 2 dhkl.Sinθ

28. Interpreting Diffraction Data
We know that
Since
Note that the wavelength λ and lattice constant a are the same
For both incoming and outgoing radiation.
Substituting for d,
Therefore

29. Interpreting Diffraction Data (Cont..)
For planes ‘A’ and ‘B’ we get two equations
Dividing each other, we get
(For plane ‘A’)
(For plane ‘B’)

30. X-Ray Diffraction Analysis
Powdered specimen is used for X-ray diffraction analysis as the random orientation facilitates different angle of incidence.
Applications include structural characterization, quantification of strain and relaxation in multilayer structures.

31. Diffraction Condition for Cubic Cells
For BCC structure, diffraction occurs only on planes whose miller indices when added together total to an even number.
I.e. (h+k+l) = even Reflections present
(h+k+l) = odd Reflections absent
For FCC structure, diffraction occurs only on planes whose miller indices are either all even or all odd.
I.e. (h,k,l) all even Reflections present
(h,k,l) all odd Reflections present (h,k,l) not all even or all odd Reflections absent.

32. X-Ray Diffraction Patternz x y a b c

33. Interpreting Experimental Data (Cont..)
For BCC crystals, the first two sets of diffracting planes are {110} and {200} planes.
Therefore
For FCC crystals the first two sets of diffracting planes are {111} and {200} planes

34. Crystal Structure of Unknown Metal (Cont..)
Crystallographic
Analysis
FCC
Crystal
Structure
BCC

35. Summary (Chapter 2-4) • Atoms may assemble into crystalline or
amorphous structures.
• We can predict the density of a material, provided we
know the atomic weight, atomic radius, and crystal
geometry (e.g., FCC, BCC, HCP).
• Common metallic crystal structures are FCC, BCC, and
HCP. Coordination number and atomic packing factor
are the same for both FCC and HCP crystal structures.
• Crystallographic points, directions and planes are
specified in terms of indexing schemes.
Crystallographic directions and planes are related
to atomic linear densities and planar densities.

36. `
Summary (Cont..)
• Some materials can have more than one crystal
structure. This is referred to as polymorphism (or
allotropy).
• Materials can be single crystals or polycrystalline.
Material properties generally vary with single crystal
orientation (i.e., they are anisotropic), but are generally
non-directional (i.e., they are isotropic) in polycrystals
with randomly oriented grains.
• X-ray diffraction is used for crystal structure and
interplanar spacing determinations.