Lecture handout including QS - Department of Materials Science ...

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Qu. Sheet 6 MATERIALS SCIENCE BQ2 Course B: Materials for Devices 3. A ceramic material has a piezoelectric coefficient of 250 pC N -1 and a dielectric constant of 500. A compressive stress of 5 MPa is applied across a 1 cm thick sample of the material. Calculate the voltage that will develop across the sample and determine whether this is sufficient to create a spark across a 1 mm air gap. [Breakdown voltage of air is ~ 3 MV m -1 ] 4. Pyroelectric infra-red detectors sense temperature change through a change in surface charge on a sheet of a pyroelectric crystal, and hence a change in measured voltage across the sheet. Write down an equation for the sensitivity of the detector (ΔV/ΔT) in terms of the pyroelectric coefficient, p, and the dielectric constant, κ. Hence explain briefly why BaTiO 3 is not an ideal material to be used in a pyroelectric detector. Using information provided in the databook, estimate the ΔV/ΔT response achieved from a polyvinylidene fluoride (PVDF) detector of 1 mm thickness. Comment on the value obtained. MT13
Qu. Sheet 7 MATERIALS SCIENCE BQ3 Course B: Materials for Devices Question Sheet 7 1. (a) Draw a plan of the perovskite BaTiO 3 structure projected onto (010), i.e. the x-z plane. Indicate mirror planes normal to the paper, and rotation axes parallel to [010]. What are the fractional coordinates of the mirror planes parallel to (010) What is the crystal system Is there a centre of symmetry and, if so, where What is the shape of the coordination polyhedra around Ti, and how are they linked (b) Re-draw the crystal structure with all the Ti cations displaced slightly along [001], towards the neighbouring oxygen (illustrate a displacement of about 1 / 5 th of the cell parameter). Which symmetry elements are lost, and which survive What is the new crystal system Is there now a centre of symmetry (c) If the Ti 4+ cation moves 0.2 Å along [001] with respect to other ions as a result of the ferroelectric phase transition in BaTiO 3 , what will be the dipole moment formed in a single unit cell (Note that this displacement is much less than that depicted in (b).) If the unit cell parameter of the cubic phase is 4.0 Å, and the volume of the tetragonal phase is almost the same as that of the cubic phase, what is the polarisation If the polarisation can be thought of as an effective charge density accumulating on either side of the sample, what is the potential difference across a sample of BaTiO 3 of thickness 0.1 mm and of dielectric constant 1000 2. By referring to the phase diagram of PZT in your Handout (BH35), answer the following: (a) What is the Curie temperature of PbTi 0.4 Zr 0.6 O 3 (b) What is the crystal structure of PbTi 0.6 Zr 0.4 O 3 at room temperature (c) What conditions of polarisation would result in a specimen of PbTi 0.6 Zr 0.4 O 3 after each of the following treatments: (i) Strong electric field applied at 750 K, held for some hours, & switched off. Specimen cooled to 300 K. (ii) Strong electric field applied at 620 K, held for some hours, specimen cooled to 300K, then field switched off. 3. The Bloch wall energy for Ni is about 10 -3 J m -2 . If a spherical Ni particle consists of two equal and opposite magnetic domains, write down an equation for the total domain wall energy of the particle, in terms of its radius, r. The stray field energy (given in Joules) of a small, single domain Ni particle of radius, r, is approximately 2×10 5 r 3 . Estimate the critical size of a Ni particle, below which magnetic domains will not form, stating your assumptions. MT13
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