4280 Structure of Materials 2006

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CMET 4280F I R S T P U B L I C E X A M I N A T I O N

Preliminary Examinat ion in Materials SciencesM ater ial s Science 1:S t r u c t u r e of Mater i a l s

' TRINITY TERM 006

Tuesday 6th June 2006,9:30 am- 12:30pmTime allowed 3 hours

Answ erfive questions onlyAll questions carry equal total weigh1

The numbers in the right hand margin indicate the weight w hich themoderators expect to assign to each part of the question

General InformationPermittivity of free space (E,) = 8.85 x 10-'* Fm-'Speed of light, c= 2.998 x 108ms-'Elementary charge, e = 1.602 x 1O-I' C

Do not tur n the page unt i l you ar e to ld that you may do so

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1 (a) Define the terms line direction, Burgers vector and glide plane for an edgedislocation and explain how these can be used to describe a slip system. ~4x21(b ) Sketch and exp lain the stable equilibrium configuration for 2 perfect edgedislocations with the sam e line direction in each of the follow ing two cases:

( i) Both have B urgers vectors a/2[1701 and lie on (1 11) planes separatedby 10nm; .(ii) One has Burgers vector a/2[17 01 and the other a/2[i 01 and they lie onthe same (1 11) plane. ~2x41

(c) Explain why it is energetically favourable for an a/2[1101 dislocation in a facecentered cubic crystal to d issociate, and give a possible dissociation reaction forthis dislocation. [41

(a) Explain what is meant by e ach of the following kinds of binary alloys, givingtwo examples of each kind:(i) Interstitial phase;(ii) Electron compound;(iii) Normal valency compound;(iv) Superlattice structure.

(b) Explain why superlattice structures are not observed at all temperatures. [41(c) Why are interstitial phases of the type M X generally harder and have highermelting temperatures than the parent metal M even though the m etal-metal atomdistance in these phases is larger than in the metal? [41

(a) Define the term electronegativity and explain how it can control the character ofa bond in a binary crystal. Describe the general trend of electronegativity acrossa row and down a group in the Periodic Table, and how this controls the natureof bonding in NaC1, ZnS and GaAs. [81(b) Sketch the crystal struc ture of NaC1, and give the lattice type, coordina tionnumber and the number of atoms per unit cell. How does diffusion of chlorineoccur in NaCl? [61(c) Why does NaCl not have the same structure as CsCl? (Ionic radii: Na+0.095nm , Cs' 0.169 nm, C1- 0.18 1 nm). [61CM ET 280

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4 (a) Sketch the frequency dependence of the intensity of black body radiation for twodifferent temperatures and explain how Plancks proposition that the radiation isquantised into packets of energy is able to account for the spectra.

(b) Describe how the photoelectric effect demonstrates the particle-like character ofwaves.(c) An experiment is performed in which sodium is irradiated with 400 nm and 300nm radiation. The energy of the photoelectrons emitted is found to be 0.750eV

and 1.826eV respectively. Use this data to calculate values for Plancks constantand the work function of sodium giving your answers to 3 significant figures.

5 Copper has a cubic F Bravais lattice with one atom on each lattice site. A needle-shaped crystal of copper is grown with side faces ( 1 1 1), (1 10) and (001).- - -

(a) On which of these three faces are the surface atoms close-packed?(b) What are the indices of the other close packed planes of atoms?(c) Sketch the poles for these faces onto a stereographic projection, with thedirection of the axis of the needle at the centre of the stereogram, and index the

three poles and the needle axis direction.(d) Insert on the same stereogram the four three-fold axes of the crystal and indexthem consistently.(e) A thin slice of the crystal is cut with its normal parallel to the axis of the needle.An electron diffraction pattern is obtained using lOOkV electrons, with the

electrons incident along the direction of the needle axis. Sketch the electrondiffraction pattern and index the eight reflections closest to the centre of thepattern. Indicate on your sketch the approximate distances of these indexedreflections from (000)

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Explain the meaning of the brackets used in the following symbols { 1 O } , (1 O ),[1101 and for a cubic crystallographic system. [41Give the conditions on the lattice parameters a, b, c and on the angles a , p, y forthe hexagonal Bravais lattice. [31In a hexagonal lattice with lattice parameters a = b = 0.40nm and c = 0.60nm,what is the interp lanar spacing (to 2 significan t figures) of the (loo), (110) and(002) planes? [41The W urtzite form of ZnShas a hexagonal Bravais lattice, with S atoms at(O,O,O) and (2/3, 1/3, 1/2) and Zn atoms at (0, 0,518) and (2/3, 1/3, US).

(i) How many atom s are there in the hexagonal unit cell? [21(ii) Draw a [OOOl] projection of the atoms in a unit cell showing the atomswith their fractional coordinates. [31(iii) On a stereographic projection, with [OOOl] at the centre, sketch thepositions of the poles corresponding to the directions from the S atom at(O,O,O) to its four nearest neighbour Zn atoms. [41

Describe the main differences between the three main types of engineeringpolymers, thermosets, thermoplasticsand elastomers,giving examples of each. [61For a composite consisting of a m atrix with elastic modulus 100 GPa andparticles of elastic modulus 400 GPa, show how the elastic modulus of thecomposite will vary with the volume fraction of particles, and determine the ,composition range over which the elastic modulus of the com posite will be 150GPa. [71Com pare the processes of hand spray up, compression moulding and pultrusionin the fabrication of polymer matrix composites. Which m ethod would youchoose to prepare composites for use under m ulti-axial loading? [61

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8 (a) Write down Braggs Law of diffraction from crystals, defining all the terms. [31(b ) For the bcc and fcc B ravais lattices, certain reflections hkl which satisfy theBragg Law d o not appear in diffraction patterns. For both of these latticetypes what are the conditions on hkl which determine these reflections? [41(c) The figure below shows an experiment in which X-rays with a wavelength of0.17 nm are used to form a powder diffraction pattern of a polycrystallinecub ic material on a circular film strip. The film is placed at a distanc e of 15cm from the polycrystalline material. Reflections (arcs) are observed atdistances of 11.30 cm, 13.17 cm, an d 19.34 cm from the position of theundeflected beam.

(i) Wh at is the Bravais lattice of the materia l? 151(ii) What is its lattice parameter? P Inext arc appear? [31

(iii) At w hat distance from the undeflected beam along the film will the

Give all answers to 2 significant figures.

Unc eflectedFilm strip

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4280 Structure of Materials 2006