MATS31501
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© The University of Manchester, 2022
One and a half hours
Non-programmable electronic calculators may be used, provided that they
cannot store text.
Graph paper available on request.
UNIVERSITY OF MANCHESTER
BSc DEGREE, THIRD YEAR EXAMINATION
MEng DEGREE, THIRD YEAR EXAMINATION
FUNCTIONAL MATERIALS & DEVICES
28 January 2022
14:00 - 15:30
Answer FOUR questions out of SIX in total.
Use a SEPARATE ANSWER BOOK for each QUESTION.
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© The University of Manchester, 2022
Answer FOUR questions out of SIX in total.
1. Piezoelectric sensors and actuators.
(a) Define the direct and converse piezoelectric effects, giving an equation to
represent the relationship in each case. Define all the parameters used and
explain the meaning of any indices. (5 marks)
(b) Selected dielectric and piezoelectric properties of 2 different PZT
ceramics, denoted PZ26 and PZ29, are given in Table 1 below.
(i) Identify which of these materials would be classified as hard or soft
PZT ceramics. In each case, give examples of typical compositional
modifications (dopants) that are used to achieve these types of
functional behaviours and explain briefly the mechanisms involved. (4 marks)
(ii) Give 2 examples of piezoelectric devices that could be manufactured
using hard or soft PZT ceramics (one in each case), indicating which
properties are most important. (2 marks)
(c)
(i) Calculate the piezoelectric voltage coefficient, g33, for both PZ26
and PZ29 (permittivity of free space, e0 = 8.854 x 10-12 F m-1). (2 marks)
(ii) Identify which of these materials would be most suitable for use in a
piezoelectric spark generator and calculate the electric field that
would be induced by an applied uniaxial stress of 10 MPa. (2 marks)
(iii) Calculate the voltage induced in the spark generator for a stress of 10
MPa if the piezoelectric component is a cylinder having a length of
20 mm. (1 mark)
(d) A multilayer electro-mechanical actuator is manufactured using 800 layers
of a piezoelectric ceramic material, with an individual layer thickness of
80 mm.
(i) Calculate the total length of such an actuator and use this to
determine the mechanical strain required to achieve an axial
displacement of 100 mm. You can neglect the thickness of the
internal electrode layers in this calculation. (1 mark)
Table 1. Selected properties of Ferroperm piezoceramics
Material
Type
er tand d33 / pC N-1 d31 / pC N-1
PZ26 1330 0.003 328 -128
PZ29 2840 0.016 573 -237
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© The University of Manchester, 2022
(ii) Identify which of the materials listed in Table 1 would be most
suitable for use in a such a multilayer piezoelectric actuator, giving
reasons for your choice. (1 mark)
(iii) For the material that you identified in part d(ii) above, calculate the
electric field and hence the applied voltage required to achieve the
axial displacement given in part d(i). (2 marks)
(a) Define the term ferroelectric. (2 marks)
(b) Describe the main characteristic features of typical perovskite-type
ferroelectric ceramics, with respect to the following factors:
(i) Spontaneous polarisation and its origin; (5 marks)
(ii) Polymorphic phase transformations, including ONE example of the
temperature-dependent changes in crystal structure for a typical
ferroelectric ceramic and a sketch of the resulting dielectric
permittivity-temperature relationship; (4 marks)
(iii) Ferroelectric domains, including the driving force for domain
formation and typical domain patterns in tetragonal perovskites; (4 marks)
(iv) Ferroelectrics hysteresis. Include in your answer a consideration of
the polarisation-electric field and strain-electric field relationships.
Explain briefly the mechanism responsible for hysteresis and its
significance to the poling process for piezoelectric devices. (5 marks)
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3. Lead-free piezoelectrics.
(a)
(i) Briefly explain the background reasons for the recent expansion of
research on lead-free piezoelectrics. (3 marks)
(ii) Describe the types of lead-free ferroelectric solid solution systems
that have been selected for investigation, including consideration of
morphotropic phase boundaries (MPBs) and polymorphic phase
transformations (PPTs). (4 marks)
(b)
(i) Explain the meaning of the term Goldschmidt tolerance factor, t, for
perovskite compounds and show how the relationship given in
equation 1 below is derived using geometric considerations of the
ions in a unit cell.
(1) (4 marks)
(ii) Using the data given in Table 2 below, calculate the tolerance factors
of the perovskite compounds, KNbO3 and NaNbO3. From these
results, predict whether a tetragonal or rhombohedral crystal
structure should be most stable for each of these compounds in the
region below the Curie temperature.
(4 marks)
(c) Sketch the form of the strain-electric field relationship for a NBT-BT-
KNN (Na0.5Bi0.5TiO3-BaTiO3-K0.5Na0.5NbO5) ceramic in comparison with
that of a conventional PZT piezoelectric ceramic, stating the advantages
and disadvantages of each material. Briefly explain the mechanism
responsible for the giant electrostrain of NBT-BT-KNN. (5 marks)
Table 2. Effective ionic radii of certain ions for perovskites
Ion type O2- K+ Na+ Nb5+
Reff / nm 0.140 0.164 0.139 0.064
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(a) Band formation and electrical conductivity in metal oxides.
(i) Sketch the temperature dependence of electrical resistivity of a
normal metal. State which factors limit the minimal possible
resistivity. (2 marks)
(ii) A pure and stoichiometric metal oxide crystal demonstrates a
significant increase in electrical conductivity if placed into an
oxygen-rich atmosphere. Explain the reason behind this increase and
discuss the associated type of charge carriers. (3 marks)
(iii) A doped spinel crystal is known to have polaron conductivity.
Calculate the activation energy of the polaron mobility, ���ℎ, if this
spinel's electrical resistivity at temperature 497 K is ten times
smaller than at 300 K. Give the answer in meV. (Boltzmann constant
������ = 1.38×10-23 J/K, electron charge is ��� = 1.602×10-19 C). (5 marks)
(b) PTC Thermistors.
(i) Figure 1 shows the temperature-dependent resistance of an accurate
BaTiO3 PTC thermistor doped with Nb. Using this plot, estimate the
Curie temperature of the BaTiO3 ceramics this thermistor is made of.
Explain your answer.
Figure 1 (adapted from Ceram. Int. 17, 227 (1991)) (2 marks)
(ii) The charge on the surface of a tetragonal BaTiO3 grain is completely
compensated. The normal component of the polarisation at the grain
boundary is 8 µC/cm2. Calculate the charge density on the surface of
this grain when it is heated above the Curie point (Electron charge is
��� = 1.602×10-19 C). (3 marks)
(iii) Explain why a PTC thermistor cannot be built out of a single bulk
ferroelectric crystal. (5 marks)
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© The University of Manchester, 2022
(a) Fuel cells.
(i) Write the two half-cell chemical reactions in a solid oxide fuel cell
(SOFC) that uses hydrogen as fuel. (2 marks)
(ii) With the help of Kroger-Vink notation, identify the conduction
mechanism and charge carrier type in yttria-stabilised zirconia. (3 marks)
(iii) In a typical SOFC, the anode material is made of Nickel-YSZ
cermet. Explain the role of Nickel in this cermet and factors
determining its volume fraction. (5 marks)
(b) Surge protection and self-heating.
(i) With the help of a diagram, explain how a varistor is used for the
overvoltage protection of the circuit. (2 marks)
(ii) Figure 2 shows the I-V curve of an actual NTC thermistor. Using this
plot, determine the range of driven currents suitable for this
thermistor to be used as the temperature sensor. Explain your
answer.
Figure 2 (adapted from
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© The University of Manchester, 2022
(iii) Estimate the relative inaccuracy due to self-heating of the
temperature measurement taken at 35°C with the NTC thermistor
specified in Table 3.
Table 3
Parameter Value
Exponent, B 3500 K
Reference resistance, R0 1.5 kOhm
Reference temperature, T0 25 °C
Heat dissipation constant, C 1.2 mW/°C
Nominal operating current, I 405 µA (5 marks)
(a) Gas sensors.
(i) State what the reference O2 partial pressure is in the galvanic gas
sensor used in an automobile to monitor the air-to-fuel ratio. Explain
your answer. (2 marks)
(ii) Write down the expression for the electrical conductivity of
semiconducting metal oxide in an oxygen-containing atmosphere.
Using this expression explain the operation principle of a bulk
resistive gas sensor. (3 marks)
(iii) Explain the similarities and differences in the operational principles
of a PTC thermistor and a porous ceramic gas sensor. (5 marks)
(b) NTC Thermistors.
(i) Explain why the resistance of an NTC thermistor depends
exponentially on temperature. (2 marks)
(ii) A commercial NTC thermistor has the exponential parameter
3960 K, and the reference resistance measured at 25°C is 1 kOhm.
Find the temperature corresponding to a thermistor resistance of 69
Ohm. (3 marks)
(iii) Define the Temperature Coefficient of Resistance (TCR). Show that
for a polaron conductor, TCR is always negative. (5 marks)
END OF EXAMINATION
