Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications
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dimensions are a ¼ 475:6 pm, b ¼ 102:1 pm, c ¼ 598:0 pm and the cell contains 4
formula units, i.e. 4(Mg
2
SiO
4
). [Answer: e
r
¼ 7:03]
18. A disc capacitor of thickness 1 mm carries circular electrodes of diameter 1 cm. The
real and imaginary parts of the relative permittivity of the dielectric are 3000 and 45
respectively. Calculate the capacitance and the power dissipated in the dielectric
when a sinusoidal voltage of amplitude 50 V and frequency 1 MHz is applied to the
capacitor. [Answer: 245 mW]
19. A capacitor in the form of a ceramic disc 10 mm diameter and 1 mm thick is
electroded to its edges. It has a capacitance of 2000 pF and a dissipation factor of
0.02. Calculate the relative permittivity of the dielectric, the dielectric loss factor, a.c.
conductance at 50 Hz and at 50 MHz, and the loss current flowing for an applied
sinusoidal voltage of 10 V (r.m.s.) at 1 kHz. [Answers: 2877; 57.5; 1:27 10
8
S;
1:27 10
2
S; 2.54 mA]
20. A dielectric is a fine interdispersion of two phases, one having a relative permittivity
of 20 and a TCC of 500 MK
1
and the other a relative permittivity of 8 and TCC of
100 MK
1
In what proportion should the two phases be mixed to give zero TCC, and
what is the relative permittivity of the mixture? [Answers: 16.7 vol% of phase with
TCC ¼500 MK
1
; e
r
¼ 9:3]
21. A simple circuit comprises a capacitor C shunted by a resistor R. Show that the
frequency response of the circuit impedance, plotted in the complex plane, is
represented by a semicircle of diameter R and with center at Z
1
¼
1
2
R:
Two such circuits are connected in series. In one the resistor and capacitor values
are respectively 3 kO and 3.3 nF and in the other 10 kO and 1 mF. Sketch the expected
frequency response of the impedance in the complex plane, marking the main
features of the curves with numerical values.
22. The quote from the monograph ‘Dielectric Relaxation’ (see p. 88) was written nearly
40 years ago. White a brief critical commentary, about the same length as the quoted
passage, giving your opinions on the aptness, or otherwise, of the views expressed to
present day materials’ research and development in the electroceramics context.
Bibliography
1. Cotton, F.A. and Wilkinson, G. (1980) Advanced Inorganic Chemistry, 4th edn, J. Wiley
and Sons, New York.
2. Shannon, R.D. and Prewitt, C.T. (1969) Effective Ionic Radii in Oxides and Fluorides.
Acta. Cryst. B. 25, 925–46 (Revised values in Acta. Cryst. B.26, 1970, 1046–8).
3. Newnham, R.E. (1975) Structure-Property Relations, Springer-Verlag, Berlin.
4. Smyth, D.M. (2000) The Defect Chemistry of Metal Oxides, Oxford University Press,
Oxford.
92 ELEMENTARY SOLID STATE SCIENCE
TEAMFLY
Team-Fly
®
5. Kittel, C. (1986) Introduction to Solid State Physics, 6th edn, John Wiley and Sons
Inc., New York.
6. Bleaney, B.I. and Bleaney, B. (1976) Electricity and Magnetism, 3rd edn, Oxford
University Press, Oxford.
7. Seuter, A.M.J.H. (1974) Defect chemistry and electrical transport properties of barium
titanate. Philips Research Reports, Supplement No. 3.
8. Daniels, J., Hardtl, K.H., Hennings, D. and Wernicke, R. (1976) Defect chemistry
and electrical conductivity of doped barium titanate ceramics . Philips Research Reports
31, 487–559.
9. Shannon, R.D. (1993) Dielectric polarizabilities of ions in oxides and fluorides.
J Appl. Phys. 73(1), 348–66.
10. Lines, M.E. and Glass, A.M. (1977) Principles and Applications of Ferroelectrics and
Related Materials, Clarendon Press, Oxford.
11. Herbert, J.M. (1985) Ceramic Dielectrics and Capacitors, Gordon and Breach, New
York.
12. Megaw, H.D. (1957) Ferroelectricity in Crystals, Methuen & Co. Ltd, London, p. 85.
13. Arlt, G. (1990) Twinning in ferroelectric and ferroelastic ceramics: stress relief.
J. Mater. Sci. 25, 2655–66.
14. Arlt, G. (1998) Strong ultrasonic microwaves in ferroelectric ceramics. IEEE Trans.
Ultrason. Ferroelectr. Freq. Control 45, 4–10.
15. Hall, D. (2001) Nonlinearity in piezoelectric ceramics. J. Mater. Sci. 36, 4575–601.
16. Lichtenecker, K. (1926) Die dielektrizita
¨
tskonstante natu
¨
rlicher und Ku
¨
nstlicher
Mischko
¨
rper. Physikal Z. 27, 115–158.
17. Macdonald, J.R. (Ed.) (1987) Impedance Spectroscopy, J Wiley and Sons, New York.
BIBLIOGRAPHY 93
3
PROCESSING OF CERAMICS
The following summary of ceramics’ processing technology can be supplemented
by reference to the monographs by J.S. Reed [1] and M.N. Rahaman [2]. Many
of the important aspects of present-day ceramics processing outlined below are
treated in depth in [3]. Access to a text concerned with elementary colloid science,
for example that by D.J. Shaw [4], may be advisable.
3.1 G eneral
The objectives of fabrication are to produce
1. a material with specific properties,
2. a body of a required shape and size within specified dimensional tolerances
and
3. the required component at an economic cost.
The material properties are basically controlled by the composition but will also
be affected by the grain size and porosity of the sintered ceramic, and the latter
features are affected by the method of fabrication.
Key stages in the fabrication of ceramics are calcination and sintering, which
are sometimes combined. During these processes the constituent atoms
redistribute themselves in such a way as to minimize the free energy of the
system. This involves a considerable movement of ions, their interdiffusion to
form new phases, the minimization of the internal surface area and an increase in
grain size. Usually the overall dimensions shrink and, from a practical viewpoint,
it is important that the shrinkage is reproducible so that pieces of specified
dimensions can be made. It is also necessary that the shrinkage should be
uniform within a given piece, otherwise the shape will be distorted. For this there
Electroceramics: Materials, Properties, Applications. 2nd Edition. Edited by A. J. Moulson and J. M. Herbert.
& 2003 John Wiley & Sons, Ltd: ISBN 0 471 49747 9 (hardback) 0 471 49748 7 (paperback)
must be a minimum variation in the density throughout the ‘green’ body. (The
term ‘green’ is widely used to describe the unfired ceramic.)
The fabrication process comprises five stages:
1. the specification, purchase and storage of raw materials;
2. the preparation of a composition in powder form;
3. forming the powder into a shape;
4. densification;
5. finishing.
3.2 Cost
A detailed consideration of the cost aspect is beyond the scope of this book but it
is vitally important. Factory space and plant cost money in rent and maintenance
so that, the longer they are occupied in producing a given number of items, the
higher is the cost of each. The number of people involved in a process, especially
if they are skilled, often accounts for a major part of the cost. The price of raw
materials may only contribute a small fraction to the ultimate cost but must be
kept to a minimum. An unnecessarily close specification for purity, dimensional
tolerances etc. may result in a large increase in price.
Scale of production can greatly affect cost since, if production levels warrant it,
the process can be highly automated; it must be borne in mind, however, that
automatic machinery is only economic when fully utilized.
Some indication of the relative costs of processes is given, but it has to be
emphasized that these are based on the present state of the art and that future
developments or changed circumstances may drastically modify them.
3.3 Raw Materials
The simple label on a laboratory container, e.g. ‘calcium carbonate’, gives only
an approximate indication of the composition of its contents. The labels on
analytical reagents may also give the maximum levels of certain impurities, which
is an adequate description of the contents for many purposes although it needs
checking. One aspect of the composition that is difficult to specify exactly is the
moisture content. It depends on the ambient humidity, the method of storage
and the particle size. It may vary from less than 0.1% to more than 1% for non-
hygroscopic materials and, of course, much more widely if they are hygroscopic.
96 PROCESSING OF CERAMICS
However, it is usually quite easy to determine as a loss in weight after heating to
a suitable temperature.
Chemical composition is only one aspect of the specification of a raw material.
Particle size and degree of aggregation are often important, and are more difficult to
specify and to agree on with a supplier. It is even more difficult to specify the
‘reactivity’ of a material but it can be of primary importance. Reactivity depends on
particle size and the perfection of the crystals comprising the particles. Many raw
materials are subjected to heat treatment during their preparation, and variations in
the temperature and duration of this may affect reactivity. These raw material
parameters are modified by the subsequent processing so that corrections can be
made for some variations in them provided that the magnitude of the variations is
known. The more detailed is the specification the more expensive is the material, so
that a balance has to be kept between the elaboration of the specification and the
cost of testing and correcting for variations during processing.
The ultimate test for a starting material is that when it is put through a
standard process it yields a product with specified properties. The assumption is
often made that the process used in production is sufficiently standard to be used
as a basis for raw material testing. This assumption needs careful confirmation
since wear and tear causes changes in the behaviour of plant and machinery.
Frequently a model production line is set up in the laboratory with a closely
controlled and consistent performance and bearing a well-established relation-
ship to the large-scale production line. This can serve as a check on the
production process. Such a line is a necessity when introducing a new process but
may be expensive to maintain. Most commercial operations employ a mixture of
analytical and physical tests coupled with laboratory and manufacturing trials in
an endeavour to achieve an economical compromise. The difficult factor to
estimate is the possible cost of a breakdown in production leading to a high scrap
level or a loss of orders.
The storage of materials is important. The cheapest method is a heap in the open,
which may be adequate for coal for a furnace. The most expensive is a room in which
the humidity and temperature are controlled. The importance of controlling
moisture content is the most relevant factor determining the amount spent on storage
space. The quantity of material kept in store has significant economic consequences.
On the one hand it represents idle capital; on the other each of a succession of small
batches needs handling and testing, both involving expense. It may seem superfluous
to mention that every batch of every material should be clearly identified and
accessible, but such details can lead to much trouble if neglected.
3.4 Powder Preparation ^ Mixing and Grinding
The first step is to weigh out the raw material with due allowance for impurity
and moisture content. Many modern weighing machines record each weighing;
POWDER PREPARATION ^ MIXING AND GRINDING 97
otherwise the only safeguard against normal human fallibility is to have every
weighing checked by a second person.
The next step is mixing, eliminating aggregates and/or reducing the particle
size. If compound formation is to occur during calcining or firing, the matter of
neighbouring particles must interdiffuse and the time taken to complete the
process will be proportional to the square of the particle size. The process will
clearly be considerably slower if the particles consist of aggregates of crystals
rather than individual crystals. Even where there is only a single component,
aggregates that are present during sintering usually densify more rapidly
internally than with neighbouring aggregates, with a resulting residue of pores in
the spaces originally between the aggregates. Apart from breaking up
agglomerates and forming an intimate mixture of the constituents, a milling
process introduces defects into the crystals which may enhance diffusion and
accelerate sintering.
The most commonly used method of initial mixing is wet ball-milling. A ball-
mill is a barrel (usually of ceramic material) that rotates on its axis and is
partially filled with a grinding medium in the form of spheres, cylinders or rods.
The grinding medium is in such quantity that the rotation of the mill causes it to
cascade, rather like the breaking of a wave on the shore, so that both a shearing
and a crushing action is applied to any material lying between the milling
elements. For efficient action the real volume of material to be milled should be
about a third of that of the milling media. The volume of liquid must be sufficient
to form a freely flowing cream, usually between 100 and 200% of the volume of
the powder. The addition of surface-active agents reduces the amount of water
needed for a given fluidity and assists in the dispersion of the softer aggregates.
The ball charge normally contains a range of sizes with the largest diameter being
of the order of a tenth of the diameter of the barrel. The optimum quantity of
balls, their sizes and composition, the quantity of ‘slip’ and the rate of rotation
are normally defined by the supplier of the plant but require adjustment for
particular applications. Ball-mills are slow but mechanically simple and robust.
They mix and eliminate aggregates and can reduce the particle size to around
10 mm.
The milling media are inevitably abraded by the charge and therefore
contaminate it. Contamination is minimized by adhering to well-established
practice which will optimize the time of milling, by using hard materials for the
grinding media, e.g. flint, alumina or tungsten carbide, or by using materials of
the same composition as one of the constituents of the charge, e.g. alumina for
aluminous porcelains or steel for ferrites. The contamination may be less than
0.1% but can rise to 1 or 2% under adverse conditions. It is important that the
media are inspected periodically and undersized pieces discarded since they will
eventually be smashed by impact with larger pieces and contribute excessive
contamination. The barrel is normally made of aluminous porcelain and will also
be abraded. It can be coated internally with an abrasion-resistant polymer or
98 PROCESSING OF CERAMICS
formed entirely of a polymer, and any contamination from this will be burned
away in subsequent firing stages; however, larger pieces of polymer that survive
up to the final sintering may result in large pores.
Wet ball-milling is faster than dry-milling and facilitates the separation of the
milling media from the charge. Its disadvantage is that the liquid must be
removed, which is most economically achieved by filtration, but any soluble
constituent will be removed with the liquid. If this is undesirable the alternative is
to evaporate the liquid which can be effected by spray-drying if the liquid is
water. Evaporation can also take place in shallow trays in ovens; in this case
soluble material may appear as a skin on the surface and heavy coarse particles
may settle out.
The liquid used is usually water since it is available with adequate purity at low
cost and is non-flammable and non-toxic. However, because it results in a
powder with a very thoroughly hydrated surface which may have a significantly
reduced reactivity during the sintering process, dry-milling is sometimes
preferred. In this case it is usually necessary to add a surface-active material
such as a stearate containing an inorganic cation to prevent the powder forming
a cake on the mill walls. Dry-milling can be combined with the continuous
removal of fine particles by forcing air over the surface of the rotating charge and
filtering out the entrained material.
Alternatives to ball-mills include vessels with rotating paddles and rotating
barrels that contain baffles that ensure that the powder is tossed about. These
have no grinding action so that the particle size is unaltered. They also have little
effect on aggregates.
So-called ‘vibro-energy’ mills are machines for vibrating vessels filled with
grinding media at amplitudes up to approximately 5 cm. The interstices are filled
with a slip containing the material to be ground. Size reduction is far more rapid
than in ball-mills and the particle size can be regulated to some extent by the size
of the media elements; 3-mm alumina balls give a size range of 1–3 mm. Similar
results are obtained by having a paddle rotating through the grinding media in a
stationary vessel – the ‘attritor’ mill. In this case the heat generated must be
removed by water cooling. Such methods can yield powders in which a high
proportion of particles have sizes below 1 mm.
Contamination by the milling media can be largely avoided by the use of fluid
energy mills. In these the powder is entrained in two streams of high-velocity air
which are made to impinge on one another so that the particles are broken up by
impact. The feedstock must already be ground to within a factor of 10 of the final
size required and adjustments are necessary to suit particular materials.
Very good mixing on an atomic scale can be achieved by chemical methods [5],
and in the context of electroceramics the production of high purity, sub-micron
barium titanate-based powders for the manufacture of multilayer capacitors (see
Section 5.4.3) is of paramount importance. Tight control over powder chemistry
has a direct and significant influence over capacitor failure rates. Also, the strong
POWDER PREPARATION ^ MIXING AND GRINDING 99
interest in ferroelectric random access memories (FeRAMs) and in new ceramics
for dynamic random access memories DRAMS (see Section 5.7.5) has stimulated
demand for precursors for the fabrication of thin films that can be incorporated
into integrated circuits.
If the cations of interest, Ba
2+
and Ti
4+
in the case of barium titanate, can be
obtained in solution in the correct ratio then precursors to the final required
product can be formed. Subsequent heating of the precursors leads to the
formation of BaTiO
3
(BT) involving the minimum of ion diffusion distances.
Because of this the oxides can be formed at relatively low temperatures, for
example 500 8C rather than the usual 41000 8C necessary to effect the solid
state reaction between mixed oxides.
An example of this approach is the co-precipitation of mixed oxides,
hydroxides and carbonates from aqueous solution. Another approach is for
the cations of interest to be complexed to form an organometallic compound, an
alkoxide, for example. Subsequent hydrolysis and heat treatment of the
precursors yields the required oxide. Cations can also often be incorporated
into sols and gels and the mixed oxides produced by dehydration.
There are four principal routes to producing barium titanate powders.
3.4.1 The ‘mixed oxide’ or solid state route
This route is the solid state reaction at temperatures above 1100 8C of a mixture
of BaCO
3
and TiO
2
– together with ‘modifiers’. The calcination is followed by
comminution to reduce the particle size to approximately 1 mm.
Although the route is still widely used for commercial scale production, as the
demands for ‘modified’ powders having precisely controlled physical and
chemical characteristics intensifies, so there will be a progressive move away
from the ‘mixed oxide’ toward the ‘chemical’ routes.
3.4.2 The oxalate route
Well-crystallized particles of barium titanyl oxalate (BaTiO(C
2
O
4
)
2
4H
2
O;
‘BTO’) are precipitated from acidic (HCl) solutions of TiOCl
2
and BaCl
2
with
oxalic acid (C
2
O
4
H
2
). The chemical precipitation conditions can be adjusted to
control the Ba/Ti ratio. Calcination at 1000 8C leads to the development of sub-
micron BT crystallites strongly bonded together in aggregates as large as 10 mm.
These have to be milled down to the primary BT sub-micron particle size
Dopants can be co-precipitated with the BTO.
The fully developed route is capable of producing powders of closely
controlled stoichiometry, composition and particle size on a large scale
commercial basis.
100 PROCESSING OF CERAMICS
3.4.3 The alkoxide route
Essentially this route involves mixing a solution of Ba(OH)
2
with Ti (C
3
H
7
O)
4
(titanium isopropoxide). Depending upon the reaction conditions, extremely fine
(50 nm) single crystal particles can be formed. The route is suited to large scale
commercial production.
3.4.4 Hydrothermal sy nthesis
This is a relatively low-temperature, water-based route capable of producing
submicron, spherical and uniform sized particles of either high purity or
chemically modified BT. Essentially barium, titanium and dopant compounds
are reacted in a basic aqueous medium to form hydroxides. Under the
hydrothermal conditions, typically in the temperature and pressure ranges
100–250 8C and 100 kPa–3 MPa (30 atm) respectively, sub-micron particles
of either pure or modified barium titanate are precipitated. There are many
variables which need careful control, especially the reactive areas of the
precursors and the degrees of supersaturation of the various species.
Not surprisingly ‘water’ in the form of hydroxyl groups can become
incorporated into the titanate structure and the evolution of this during
subsequent processing stages towards the sintered ceramic has to be planned for.
In its fundamentals the situation is identical to that described in Section 4.6.1
concerning the development of proton conductors.
Developments of the process permit coatings of a range of dopants to be
applied to the surfaces of the particles which, during sintering, produce the ‘core-
shell’ structure leading to X7R characteristics (see Section 5.7.1). The coatings
may also consist of sintering aids.
It is also possible to retain the hydrothermally produced barium titanate
particles in aqueous suspension to form the basis of a tape-casting slurry capable
of producing 53 mm dielectric layers. This route avoids the risk of the formation
of hard agglomerates on drying the precipitates.
Hydrothermal synthesis is being increasingly adopted for the commercial
production of compositionally tailored barium titanates for MLCCs.
3.5 Calcination
In some cases (e.g. certain grades of barium ferrite) a powder can immediately be
formed into a shape and sintered without prior heat treatment, but usually there
is an intermediate calcination at a lower temperature. Calcination causes the
constituents to interact by interdiffusion of their ions and so reduces the extent of
the diffusion that must occur during sintering in order to obtain a homogeneous
CALCINATION 101