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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 9, September 2011 1867

Polarization Dynamics and Non-Equilibrium

Switching Processes in Ferroelectrics
Marian Vopsaroiu, Paul M. Weaver, Markys G. Cain, Mike J. Reece, and Kok Boon Chong

Abstract—Time- and temperature-dependent effects are models is the failure to predict a relationship between the
critical for the operation of non-volatile memories based on fer- switching time to the applied electric field and tempera-
roelectrics. In this paper, we assume a domain nucleation pro-
cess of the polarization reversal and we discuss the polariza-
ture. Most of the published relations are based on empiri-
tion dynamics in the framework of a non-equilibrium statistical cal expressions derived from the study of domain wall mo-
model. This approach yields analytical expressions which can tion. Moreover, (1) contains no explicit dependence on the
be used to explain a wide range of time- and temperature-de- E field or temperature. Nucleation processes, as described
pendent effects in ferroelectrics. Domain wall velocity derived by KAI models, assume, in general, that they are gener-
in this work is consistent with a domain wall creep behavior in
ferroelectrics. In the limiting case of para-electric equilibrium,
ated with a certain probability followed by the fast rever-
the model yields the well-known Curie law. We also present sal of polarization, without giving a relationship between
experimental P-E loops data obtained for soft ferroelectrics the probability of nuclei formation and the driving forces
at various temperatures. The experimental coercive fields at (electric field, temperature, etc.). We represent the ferro-
various temperatures are well predicted by the coercive field electric sample as an assembly of N regions, which we call
formula derived in our theory.
elementary polar regions. Applying a statistical treatment
to the microscopic mechanisms responsible for nucleation
I. Introduction inside an elementary polar region, is our approach to de-

W hen an electric field is applied to a ferroelectric ma- rive the kinetic equations of the polarization switching in
terial, the reversal process occurs via a nucleation this paper. This theoretical approach was first proposed in
of domains, movement of domain walls, and subsequently [10] and applied to ferroelectric systems that display depo-
expansion and growth at the expense of the existing do- larization field effects. In this paper, we used a simplified
mains [1]. One of the fundamental models of the polariza- version of the model to derive the kinetic equations of
tion switching is the Kalmogorov-Avrami-Ishibashi (KAI) polarization reversal and to explain the experimental P-E
domain nucleation-switching model, which treats polar- loop data acquired at various temperatures. The model
ization reversal as a nucleation process [2] and it predicts makes the following assumptions: 1) the polarization
the following temporal dependence of polarization/electric reversal occurs via a domain nucleation process; 2) the
displacement during the switching process: nucleation process occurs independently inside regions of
material called elementary polar regions; 3) the nucleation
n
∆D(t) = 2p s ⋅ (1 − e −(t/t sw) ), (1) process is considered to be activated when the region of
reversed polarization reaches a critical volume V*; and 4)
where t is the experimental time; tsw is the switching time; the switching rate is controlled by the switching rate of
2ps is the amount of reversed polarization, where ps is the critical volume V*, rather than the rate of expansion
the spontaneous polarization at zero applied field E; and of the domain. If the volume of this region of reversed
n is the Avrami exponent. The KAI model of polariza- polarization is below a critical level, V*, the nucleus is
tion switching has successfully given a good description unstable and decays. Above the critical volume, it is ener-
of polarization kinetics of ferroelectric single crystals [3] getically favorable for the nucleus to grow. It is important
and some epitaxial thin films [4], but it is not fully ap- to mention that these assumptions are fully valid for re-
plicable to the reversal over larger time periods or the versal produced by applied electric fields much larger than
reversal of polycrystalline thin films [5]. Several studies the coercive field. When applied E fields are comparable
have attempted to improve the KAI model to increase to or smaller than the coercive field, reversal via domain
its applicability. The introduction of a distribution of re- wall movement becomes dominant and the total switching
laxation times [6], a nucleation-limited switching model time includes also the time taken for the domain wall to
[5], a statistical time-dependent depolarization field [7], expand to full reversal state. However, the proposed nucle-
size effects [8], and thermal effects [9] are a few of the ation model remains valid, because considerations of the
most notable published innovations. Despite all of these domain wall dynamics are complementary to it. Although
advances, one of the main limitations of the nucleation outside the scope of this model, this important issue is
also briefly discussed in Section IV.
Manuscript received October 14, 2010; accepted April 12, 2011.
M. Vopsaroiu, P. M. Weaver, and M. G. Cain are with the National
Physical Laboratory Teddington, UK (e-mail: mv1@npl.co.uk). II. Model Description
M. Vopsaroiu is currently known as Melvin M. Vopson.
M. J. Reece and K. B. Chong are with the Centre for Materials Re-
search, Queen Mary University of London, London, E1 4NS, UK. We assume that the switching of elementary polar re-
Digital Object Identifier 10.1109/TUFFC.2011.2025 gions is provided by the nucleation of a domain per el-

0885–3010/$25.00 © 2011 IEEE

1868 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 9, September 2011

1, W1. Similarly, the reversal from state 2 to state 1 re-

quires a minimum energy barrier equal to the absolute
value of the energy of state 2, W2. From (2), imposing
E = 0 and differentiating the free energy F with respect
to ps, we find that the minimum energy corresponds to
a spontaneous polarization ps = −α/β and the energy
minima is derived as Fmin = −α2/4β. For the case E = 0,
the two minima states have equal energies: W1 = W2 =
−α2/4β, and the energy barrier to overcome them is WB
= α2/4β. The energy barrier is usually much larger than
the thermal energy kBT, so that only over very long peri-
ods of time can some reversal occur thermally. Although
not accounted for in this study, the energy barrier in real
Fig. 1. Energy profile as a function of the polarization for zero applied systems can be modified by crystal defects [5], charge tun-
electric field and an arbitrary negative E field. neling [1], depolarization effects, impurities, temperature,
etc., and can display a distribution of energies. However,
ementary polar region. Our model strictly applies to a when an electric field is applied, the energies of states 1
sample comprising multiple nucleation sites and it treats and 2 are substantially modified, facilitating the reversal
the essential features of the domain nucleation in a sim- from one state to another. Fig. 1 shows the change in the
plified way to retain an analytical description of the key energy states when an electric field is applied anti-parallel
dependencies. Although not necessary to specify where to the polarization. The resulting energy shift of states 1
the locations of the nucleation sites are, it is widely ac- and 2 is given to a good approximation by W1,2 = −WB
cepted that the preferred sites for nucleation are the do- ± psE. Because transitions between the two states are
main walls, crystal imperfections, or the electrodes. We physically permitted on a continuous basis, the nucleation
assume that the nucleation occurs at random locations site is fundamentally a non-equilibrium two-state system,
within each elementary polar region. The switching of so that the occupation probabilities P1 and P2 of states
the elementary polar region occurs once a critical domain 1 and 2 are also time dependent (P refers to occupation
(volume V*) has reversed polarization and can expand probability and p refers to electric polarization). The time
unrestrictedly under a large applied electric field E. Under evolution of the probabilities when a non-equilibrium sys-
this assumption, the time taken to reverse the polarization tem goes through different possible states are described by
(i.e., switching time tsw) is equal to the time required for the general Pauli master equation [12], which is a system
the critical domain nucleation site to reverse. Moreover, of first-order time differential equations:
the time required for the expansion of the domain until it  dP1 = a P + a P = υ (−P eW1/(k BT ) + P eW2/(k BT ))
reverses the entire polarization of the elementary polar re-  dt 11, 1 1,2 2 0 1 2

gion is negligible in comparison with the nucleation time. 

 dP2
 W /(k T ) W /(k T )
To describe the dynamics of this process, we introduce the = a 2,1P1 + a 2,2P2 = υ 0(P1e 1 B
− P2e 2 B
),
 dt
1-D Landau-Devonshire free energy per unit volume of the (3)
elementary ferroelectric polar region i as [11]
where kBT is the thermal energy and υ0 is a constant equal
Fi = α/2 ⋅ Di 2 + β/4 ⋅ Di 4 − DiE, (2)
to the total number of trials per second to overcome the
where i = 1, 2, …, N, and higher-order energy terms have energy barrier. In our case, this is taken as 1013 Hz, which
been ignored. α and β are the Landau coefficients and is the frequency of the optical phonons in the crystal [7].
they are assumed to be equal for all N elementary po- P1(t) and P2(t) are the probabilities that the system is in
lar regions; D is the electric displacement. Assuming the the state 1 or 2 at the time t, respectively; a1,1, a1,2, a2,1,
system is in a ferroelectric state (i.e., T < Tc, α < 0), we and a2,2 are the transition rates per unit time between
now examine the free energy at zero applied electric field, the states 1 to 1, 2 to 1, 1 to 2, and 2 to 2, respectively.
which implies that Di = ps, where ps is the spontaneous Solving the equations (3) and imposing the normalization
polarization. Fig. 1 shows the energy dependence on the condition P1(t) + P2(t) = 1 at t = 0 and t = ∞, we obtain
polarization of a nucleation site at zero external applied the following time dependent probabilities:
electric field. This indicates only two possible stable en-
P1(t) = e −(t/t sw) + P1(∞) ⋅ (1 − e −(t/t sw)) (4)
ergy states: 1 and 2 corresponding to polarization up and
down, respectively. P2(t) = (1 − P1(∞))(1 − e −(t/t sw)), (5)
Assuming the nucleation polar region was poled in one
of the two directions initially, before the E field was re- where P1(0) is taken to be 1 because we assumed the
moved, then to reverse the polarization from state 1 to sample is initially poled into state 1, P1(∞) is the occupa-
state 2, the system must overcome a positive energy bar- tion probability of the state 1 at t = ∞ (equilibrium) and
rier equal to the absolute value of the energy of the state is given by
vopsaroiu et al.: polarization dynamics and non-equilibrium switching processes in ferroelectrics 1869

P1(∞) = (1 + e (W1 −W2)/k BT )−1, (6)

and tsw is the relaxation time of the system, or the switch-

ing time:

t sw = υ 0 −1 ⋅ e (W B −p sE )/k BT . (7)

A full derivation of (4) to (7) is given in [10]. It is use-

ful to observe that relation (7) predicts the existence of a
random distribution of the local switching times because
of the intrinsic randomness of the E field distribution in
the system or because of a distribution of energy barriers.
This is consistent with the inhomogeneous field mecha-
nism (IFM) model of polarization dynamics in ferroelec-
Fig. 2. Time dependence of the reversed polarization at E = 100 kV/cm
tric, which assumes the existence of a random distribution for different temperatures.
of the local switching times [13], [14].

III. Switching Kinetics and Coercive Field barrier of 0.9 eV (1.44 × 10−19 J) for zero applied field
at room temperature and a spontaneous polarization of
For N elementary polar regions, we define N1(t) = 0.74 C/m2. For all calculations, the energy barrier has
P1(t) ⋅ N as the number of sites in state 1 at time t and been kept constant with the shifts in the energy resulting
N2(t) = P2(t) ⋅ N as the number of sites in state 2 at time only from the applied electric field. This is a rather rough
t, with N = N1 + N2. We now assume that the nucleation approximation because the energy barrier has, in fact, a
process occurs over a very short period of time and simul- strong dependence on the temperature and other intrinsic
taneously in all the elementary polar regions and that (4) or extrinsic factors.
and (5) describe the state of each polar nucleation region Modeling data obtained using (9) is presented in Fig.
at time t. We also assume that the sample has been poled 2 and shows that a faster polarization reversal occurs at
so that all polar sites are reversed into state 1 at the initial higher temperatures. The results of this study are very
state, P1(0) = 1, which results in N = N1(0) and N2(0) = important because they suggest a substantial thermal de-
0. We now apply instantaneously a constant electric field pendence of the switching time, which should be care-
E to reverse the polarization into state 2. Over a period of fully considered in the design, operation and stability
time t, the total amount of polarization (electric displace- considerations of memory devices based on ferroelectrics.
ment) switched from state 1 into state 2 is equal to: The coercive field derived from the standard Landau-
Ginzburg-Devonshire (LGD) model overestimates most of
∆D(t) = 2p s ⋅ N 2(t)/N = 2p s ⋅ (1 − P1(t)), (8) the experimental data. Many experimental studies showed
that the coercive field is very susceptible to the measure-
where ps is the spontaneous polarization. Using (4), the ment frequency [15] or the measurement temperature [1],
time-dependent expression for the switched polarization/ [16]. Our approach to the switching can explain such ef-
electric displacement is obtained: fects. Let’s assume again that the sample has been poled
at time t = 0 into state 1 [P1(0) = 1, positive polariza-
∆D(t) = 2p s ⋅ (1 − e −(t /t sw)) ⋅ (1 − P1(∞)). (9) tion]. We now apply an arbitrary constant negative E field
to the sample, opposite to the polarization direction. The
Eq. (9) is in good agreement to the KAI model when field will induce the nucleation and switching of elementa-
the Avrami exponent is n = 1. However, the expressions ry sites into state 2 (negative polarization). Under the ac-
derived in our model contain explicit dependence on the tion of the negative field, in time, enough sites will switch
E field and temperature via P1(∞) and tsw. Moreover, our into state 2 so that the total net polarization of the sample
relations, in comparison to those derived in the KAI mod- is zero. In terms of the hysteresis loop, the applied field at
el, contain the factor (1 − P1(∞)), which can take posi- which this condition is met is called the coercive field (Ec).
tive values from 0 to 1. This accounts for the amount of However, in terms of our switching model, the occupation
reversed polarization, which can be 0 if P1(∞) = 1 and 2ps probabilities of the two possible states are equal at the
if P1(∞) = 0 (i.e., full reversal). Fractional values 2ps(1 − coercive field: P1(t) = P2(t) at Ec. Because P1(t) + P2(t)
P1(∞)), are obtained for P1(∞) ≠ 0 or 1, which accounts = 1, P1(t) = 0.5. Using (4), the condition P1(t) = 0.5 and
for the fact that at equilibrium not all the polar sites are the fact that P1(∞) ≪ 1 for a large negative E field, we
necessarily reversed. For numerical simulations, we have determined that the coercive field can be written as [10]
used the following parameters: α = −11.57 × 107 V·m/C;
β = 2.1 × 108 V·m5/C3; kB = 8.61 × 10−5 eV/K (1.38
× 10−23 J/K); V* = 10−26 m3. This results in an energy E c(t,T ) ≅ W B/p s − k BT /V *p s ⋅ ln(υot ln(2)−1). (10)
1870 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 9, September 2011

cess, as demonstrated by Paruch et al. [17], Jin et al. [18],

and Damjanovic [19]. Moreover, pinning sites [20] (i.e.,
impurities, defects, etc.) can trap domain walls and a do-
main wall creep process can occur. Creep regime domain
wall propagation has been studied in detail via domain
dynamics observation using scanning probe microscopy
techniques [21]–[24]. In the framework of our model, as-
suming the case of polarization reversal inflicted by the
application of E fields smaller than the coercive field, the
theoretical non-equlibrium treatment of the domain nucle-
ation remains valid. However, the total polarization rever-
sal time of an elementary polar site (domain) is given by:

t = t sw + t d, (11)
Fig. 3. Time-dependent coercive field for different temperatures. The
where tsw is the switching nucleation time given in (7) and
increase in both the measurement time and the temperature has the ef-
fect of lowering the Ec. td is the expansion time of the reversed domain. If vd is
the velocity of the domain wall, then in the time interval
td = t − tsw the domain will expand by the distance vd(t
This analytical expression allows studying the time and − tsw). The area of the expanded domain can be written
temperature dependence of the coercive field of ferroelec- in general as [25]
tric materials. It is important to mention that this relation
can be applied to any type of energy barrier WB, including Ad = C d[v d(t − t sw)]n, (12)
complex energy barrier distributions. V* is the volume of
the elementary nucleation site, which is taken as 10−26 m3 where n is related to the dimensionality of the shape of the
in this work (although it doesn’t appear in previous equa- reversed domain. For a 1-D domain, the reversed area is
tions, any relation containing an energy term is, in fact, Ad = 2vd(t − tsw) and for a 2-D domain, it is Ad = πvd2(t
the product of energy ⋅ V*, because the energies are ex- − tsw)2. It has been shown that in the case of inhomoge-
pressed in energy per unit volume). neous nucleation, the domain wall velocity is proportional
Fig. 3 shows the calculated time dependence of the co- to tsw (see [20], [25]):
ercive field at different temperatures, when the time var-
ied from 1 ms to 5 s (frequency of 1 kHz to 0.2 Hz). For v d ∝ 1/t sw. (13)
the calculations, we have used the same numerical param-
eters defined previously in this section. Using relations (7) and (13), we obtain the wall veloc-
The data shows a consistent decrease of the Ec when ity as
the measurement time increases (i.e., faster measurement
v d ∝ e −W B/k BT × e γ ⋅E , (14)
results in larger Ec) and a reduction of the Ec at higher
temperatures. For example, we calculated a reduction of
where γ = ps/kBT. Eq. (14) is consistent with a creep be-
almost 50% of the coercive field when the measurement
havior of the domain wall movement [21]–[24]. The wall
time increased from 1 ms to 5 s at room temperature.
velocity depends strongly on the activation energy (i.e.,
More substantial variations are also observed when the
energy barrier), temperature, and increases rapidly with E
measurement temperature increases, with reductions of up
field. For very small E fields, the velocity reduces dra-
to 500% when the temperature was increased from 200K
matically, reaching the lower limit of vd ∝ e −W B/k BT for E
to 350K at constant measurement frequency.
= 0. This shows that in the low-field regime, thermal ac-
tivation plays an important role in the domain wall dy-
namics and, consequently, in the polarization dynamics.
IV. Domain Wall Velocity
Energy terms related to the domain wall energy and elas-
tic interactions at pinning sites can be incorporated into
The existing model makes the assumption that the po-
the energy barrier expression as a further development of
larization switching time is dominated by the nucleation
the model by including such energy terms in the initial
time (i.e., the time taken by the critical volume V* to
energy functional equation (2).
reverse its polarization in our model) and that the time
taken by the domain wall expansion to reach full polariza-
tion reversal is negligible. This assumption is only correct
for applied E fields much larger than the coercive field and V. The Equilibrium Susceptibility
for cases of ideal materials with perfect crystal structures
and no impurities. In reality, this is not the case at all, We now impose the equilibrium para-electric conditions
and the movement of the domain wall is an important pro- to equations (3): dP1/dt = dP2/dt = 0, resulting in
vopsaroiu et al.: polarization dynamics and non-equilibrium switching processes in ferroelectrics 1871

P1eW1/k BT = P2eW2/k BT , (15)

where T is a temperature larger than the Curie tempera-

ture (T > Tc); to reflect this condition, it can be replaced
by (T − Tc). For N elementary polar sites, we defined N1
= P1 ⋅ N as the number of sites in state 1 at time t and
N2 = P2 ⋅ N. Using these relations and noting that W1,2
= −WB ± psE, (15) becomes

N 1e p sE /k B(T −Tc) = N 2e −p sE /k BT (T −Tc), (16)

where T > Tc. The exponentials in (16) can be expressed

using the following approximation (ex ≈ 1 + x and e−x
≈ 1 − x, which are valid approximations for x ≪ 1). Eq.
Fig. 4. P-E loops as a function of temperature at 1 Hz frequency.
(16) becomes

N 1(1 + p sE /k B(T − Tc)) = N 2(1 − p sE /k B(T − Tc)).

(17)
m2. ps was estimated by taking the saturated polarization,
Noting that N = N1 + N2 and the electric polarization is from the saturated P-E loops and multiplying it by the
given by p = (N1 − N2) · ps, after some algebraic rear- geometric factor, 1/0.83 (we used the value relevant for
rangement of (17) we obtain a tetragonal structure), required to account for the fact
that ps in a polycrystalline ceramic is not equal to ps in a
p = Np s 2E /k B(T − Tc). (18) single crystal. For P-E hysteresis loop measurements, the
electric field was applied using a triangular wave func-
The relationship between polarization, the electric field, tion at a frequency of 1 Hz [9]. The sample was placed
and the electric susceptibility is: p = ε0 · χ · E, which in a silicone oil bath container in which the temperature
combined with (18) results in the following expression of could be varied between 1°C and 220°C (274K to 493K).
the electric susceptibility: To ensure the repeatability of results, the following proce-
dure was carried out: after testing the specimen at a given
χ = (1/T ) ⋅ Np s 2/k Bε 0 = C /(T − Tc). (19)
frequency and temperature, a P-E loop was repeated at a
reference frequency of 1 Hz and temperature of 300K to
Eq. (19), derived in the context of our model in the limit- verify that exactly the same loop was recovered after each
ing case of equilibrium conditions, is the well-known Curie test. Fig. 4 shows the experimental P-E loops data ac-
law, with C = Nps2/kBε0. The fact that our non-equilibri- quired at 1 Hz measurement frequency. The coercive field
um switching model converges at the equilibrium case to consistently changed with temperature from 1.10 MV/m
a well-established classical result is a further confirmation at 1°C (274K) to 0.088 MV/m at 220°C (493K), which
of the validity of our approach. is a ~90% decrease. The values of the coercive field at
different temperatures have been extracted from the P-E
loops and plotted as a function of temperature (Fig. 5).
VI. Experiment Our model predicts that the coercive field measured at
constant time and variable T is expected to vary linearly
To test some of the predictions of the model we have versus T with a negative slope [see (10)]. This is exactly
measured standard P-E loops at various temperatures. what has been observed in our experiment, which confirms
The material chosen for the study was a soft PZT-5H, the theoretical equation (10). We performed a linear fit of
which has a morphotropic phase boundary composition the experimental data using (10), which is Ec(T) = a − b
(Zr/Ti = 52/48). X-ray diffraction analysis revealed the × T, where a = WB/ps and b = kB/(V* ⋅ ps) × ln(ν0 ⋅ t/
predominance of tetragonal phase with the coexistence of ln(2)). From the linear fit, we have determined that a =
some rhombohedral phase. 2.206 and b = 4324. Using these values, we extracted the
This material was chosen because it exhibits a very energy barrier of the nucleation, WB, and the nucleation
consistent and reproducible poling behavior, producing activation volume, V*, by introducing the experimentally
very stable recoverable hysteresis loops. measured value of ps = 0.32 C/m2, the measurement time
The sample was disk-shaped with a diameter of 10 mm, t = 1 s (frequency 1 Hz), and kB = 1.38 × 10−23 J/K. The
thickness of 1 mm, and with platinum electrodes. The rel- values obtained are V* = 3 × 10−25 m3 and the energy
ative dielectric permittivity for unpoled material is 1827, barrier of nucleation at zero applied field WB = 0.7 eV.
the Young’s modulus in open circuit, Y33D = 111 GPa, The V* calculated from our model compares well with the
which gives a shear modulus of μ = 50 GPa, and the spon- V* calculated for the same sample using a different ther-
taneous polarization, ps, at room temperature is 0.32 C/ mal model (V* = 1.62 × 10−25 m3) [9].
1872 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 9, September 2011

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vopsaroiu et al.: polarization dynamics and non-equilibrium switching processes in ferroelectrics 1873

Melvin Vopson (formerly known as Marian the development of a prototype SEM-based instrumented indentation
Vopsaroiu) received his B.Sc. and M.Sc. degrees in system, and he joined NPL in 1997 to lead the Functional Materials
physics from the University of Bucharest. Melvin Research group. Research activity includes the development of measure-
received his Ph.D. degree in physics from the Uni- ment methods to elucidate materials behavior in ferroelectric and piezo-
versity of Central Lancashire in 2002. He worked electric ceramics and thin film materials, and more recently in multifer-
as postdoctoral research fellow of the University of roic materials and materials metrology for Spintronics and Energy
York for almost 4 years, followed by an appoint- Harvesting. The focus of his research is materials metrology, and he has
ment as senior R&D engineer at Seagate Technol- published more than 80 peer-reviewed scientific papers in the field. He
ogy. Melvin joined NPL in 2006, and his research chairs the IOM3 Smart Materials and Systems Committee. He is Knowl-
interest currently revolves around experimental edge Leader for the Materials Division at NPL and Principal Research
and theoretical studies of solid-state physics with Scientist for the Multifunctional Materials technical area and also a
emphasis on ordered and multifunctional systems. Melvin has authored member of the Institute of Physics. In 2009, he was awarded the Institute
or co-authored more than 35 scientific articles with major contributions of Materials’ Verulam medal for outstanding contributions to ceramic
in the fields of thin film growth technologies, optical techniques of char- science, and is Visiting Professor at Queen Mary, University of London.
acterization of solids, and development of novel metrologies and innova-
tions involving ferroic materials.

Mike J. Reece did his Ph.D. degree research on

the microstructures of synthetic and natural fer-
Paul Weaver is principal research scientist with rites. This was followed by postdoctoral research
the multi-functional materials research group at on fracture and fatigue crack growth in structural
the UK’s National Physical Laboratory. Research ceramics at room and high temperature. Between
interests include the development of novel electro- 1989 and 1992, he worked at the National Physi-
mechanical devices and the application of piezo- cal Laboratory on problems associated with the
electrics and ferroelectrics for sensing and actua- mechanical and microstructural characterization
tion. He is a visiting Reader at Southampton of structural and functional ceramics. Currently,
University; he holds an M.A. degree in Natural Mike is a Professor at Queen Mary University of
Science from Cambridge University, and a Ph.D. London (QMUL) and his research interests are fo-
degree from Southampton University. He is a cused on the processing and electromechanical properties of functional
chartered engineer and member of the IET. ceramics and thin films. He is also a Director of Nanoforce Technology
Ltd., a spin-out company of QMUL.

Markys Cain graduated with his Ph.D. degree

from Warwick University in 1990 and spent the Kok Boon Chong obtained his Ph.D. degree in
next 2 years in the Materials Department of the 2007 from Queen Mary University of London un-
University of California, Santa Barbara, studying der sponsorship of National Physical Laboratory
thin film epitaxial science. Subsequent research in CASE Awards. He joined The Open University in
ceramic composite materials technology in the UK 2009. He has a particular interest in developing
utilized many of the principles learned at Santa theoretical models, that link microstructure prop-
Barbara in the deployment of new interfacial fiber erties of ferroelectrics to their polarization switch-
coatings for advanced high-temperature ceramic ing, phase transformation and transition, relax-
matrix composites for gas turbine applications. ation, and creep.
Research with an Oxford-based company led to

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