**1. Introduction**

The debate about the depth and characteristics of public policy intervention in encouraging renewable energy is more urgent than ever. Some of the literature has started to cast doubt on the strategies being pursued by countries to encourage renewables. These criticisms have been varied with regard to the costs of intervention and the consequences for the economy as a whole. The need to guarantee a continuous supply of electricity requires the existence of backup power, which is essentially based on fossil sources. Marques and Fuinhas (2012a) point out that the increase in renewables has been predominantly based upon direct public subsidies and intervention. Market-driven policies have been deprecated in favor of policydriven measures. Fossil sources are often identified as beneficiaries of subsidies, so renewa‐ ble sources should also be stimulated by these policy instruments. However, the way in which this argument is presented can lead to confusion. In fact, a substantial part of these subsidies for fossil fuels is a consequence of the strategy to develop renewables. Fossil fuels are used to provide backup power, such as that from coal plants or combined-cycle gas-fired plants, but they are turned off for long periods. Consequently, overcapacity and economic inefficiency arise, which is the primary reason for the current subsidies for fossil fuels. Some literature, such as Liao et al. (2011), sustains that all incentives/subsidies should be removed, both for fossil fuels and renewables. The authors then propose applying fees to fossil-based

© 2013 Marques et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Marques et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

products in order to pay for the emission of greenhouse gases. Despite being pragmatic and objective, this perspective is not easy to apply considering the current state of renewable en‐ ergy technology. In fact, several challenges remain, such as the problem of intermittent gen‐ eration, which will continue to require the use of fossil sources to offset it.

wind power. The ratio of the actual electricity output to maximum capacity is referred to as the capacity factor. Electricity demand throughout the day is volatile, especially in off-peak and peak-load periods. This may also influence the amount of idle capacity. This problem can force investment into pumped hydro during periods when there is wind overproduc‐ tion and low grid consumption and secondly into thermal plants like coal-based or gas-fired

On the Public Policies Supporting Renewables and Wind Power Overcapacity: Insights into the European Way Forward

http://dx.doi.org/10.5772/52159

53

The vast literature about renewable intermittency, both theoretical and case studies, has not explored the phenomenon of wind overcapacity in enough detail. Indeed, the empirical as‐ sessment of overcapacity in wind power merits much more attention. On the one hand, the phenomenon of overcapacity reflects the path taken by renewables and, on the other, since this phenomenon is a leading indicator, it should back the process of updating public guid‐ ance. The aim of this chapter is to provide empirical evidence on the drivers that contribute to explaining wind power overcapacity and, secondly, to identify empirically the causes for a panel of 19 countries. While Boccard (2009) addresses the issue of wind intermittency from the perspective of the capacity factors, this chapter is focused on the importance of intermit‐

tency and possible wind overcapacity, but using a non-used wind capacity approach.

**2. Renewables' intermittency context: The debate**

inefficiency.

sumers (Gómez et al., 2011).

The role played by several energy sources in creating wind power overcapacity is assessed, controlling for socio-economic drivers and public energy policies and measures. On the whole, this approach can be useful in highlighting the relevance of the intermittent nature of renewables for policymakers in order to deal with wind overcapacity. Econometric techni‐ ques of panel data were applied to deal with the energy and socio-economic characteristics of an economic bloc with environmental concerns and long-term energy targets. In particu‐ lar, the contribution of conventional energy sources to the wind power overcapacity in Eu‐ rope is appraised. Some light is shed on the public policies that might mitigate the economic

The expansion of renewables is the subject of hot debate in the literature regarding the im‐ plications of these energy sources, namely their advantages, consequences and prospects for growth. The implications of the unpredictability and inconstancy of wind energy generation prove relevant. In fact, this intermittency in generation makes it increasingly important to combine different energy sources, including fossil fuels, to backup energy supply. A rele‐ vant role is merited not only for conventional energy sources, but also for the mix of renew‐ ables. Moreover, it is crucial to understand the role that public policy and measures have played. Wind power installation has been strongly stimulated by public guidance and high‐ ly subsidized, namely by guaranteed prices under feed-in tariffs which will last for more than 25 years, as stated by Moreno and Martínez-Val (2011). Together with other drivers that promote renewables on a large scale, this creates distortions and increased costs for con‐

to provide backup power for wind power when necessary (Luickx et al., 2008).

The deployment of new energy sources is inevitable, which is why alternative energy sour‐ ces have emerged, resulting from the use of natural resources such as water, wind, sun, tides and heat from the earth. In the meantime, the international community has made several commitments to promoting greater deployment of renewable energy sources. Examples in‐ clude the Kyoto Protocol in 1997 or the recent European directive for climate and energy measures, known as the 20-20-20 targets. This directive aims to reduce greenhouse gas emis‐ sions by 20%, increase the share of energy consumption from renewable energy sources to 20% and promote energy efficiency by reducing primary energy use by 20%. Nevertheless, while the need to develop the use of new energy sources has been consensual, in view of the long-term depletion of fossil fuels and the issue of climate change, there has been no exten‐ sive evaluation of the consequences of renewable energy use. The continuous support for re‐ newables, particularly in Europe, has raised the debate about the levels of wind power installed capacity. It is well known that there is no kind of power plant that operates at 100% of its maximum capacity, particularly renewables due to their intermittent nature. Hence, a problem of structural inefficiency arises, which leads to high economic costs associated with the existence of idle capacity.

It is widely accepted that renewables, such as solar and wind, are at the heart of common instruments in reaching European goals of reducing energy dependence, as well as the re‐ duction of greenhouse gases. However, the growth in wind energy magnifies the problem of intermittency. As stated by Holttinen et al. (2009), it is crucial to properly estimate the costs of wind energy in the system as a whole when planning high wind power penetration. Fur‐ thermore, the analysis of renewables' intermittent generation is important for policymakers due to the great support for renewables in Europe, in the context of long-term energy goals. Faced with the problem of renewable intermittency, two possible solutions can be consid‐ ered: (i) energy storage for later use; and (ii) backup electricity generation with fossil fuels. However, the literature (e.g. Beaudin et al., 2010) suggests that energy storage costs are still very high, so upgrading the energy grid in this way is not yet attainable. As a consequence, it would seem more appropriate to combine other energy sources to backup power. Fossil fuel plants can startup and shut down in a short time to keep a secure energy supply and are an effective way of mitigating renewable intermittency (Isla, 1999; and Luickx et al., 2008). A consequence of the divergence between maximum capacity in full-time operation and the electricity actually generated in a given period of time is the idle capacity phenom‐ enon. Idle capacity is noticeable both for renewables, due to their intermittent nature, and for other energy sources since they are turned off more frequently.

We shall focus only on wind power overcapacity. The scarce research on this subject arouses curiosity about the high levels of idle capacity in wind power. Indeed, Boccard (2009), Fie‐ dler and Bukovsky (2011) and Yang et al. (2012) found that wind energy generation is rarely more than 25% of total capacity. This leads us to believe that there may be overcapacity in wind power. The ratio of the actual electricity output to maximum capacity is referred to as the capacity factor. Electricity demand throughout the day is volatile, especially in off-peak and peak-load periods. This may also influence the amount of idle capacity. This problem can force investment into pumped hydro during periods when there is wind overproduc‐ tion and low grid consumption and secondly into thermal plants like coal-based or gas-fired to provide backup power for wind power when necessary (Luickx et al., 2008).

products in order to pay for the emission of greenhouse gases. Despite being pragmatic and objective, this perspective is not easy to apply considering the current state of renewable en‐ ergy technology. In fact, several challenges remain, such as the problem of intermittent gen‐

The deployment of new energy sources is inevitable, which is why alternative energy sour‐ ces have emerged, resulting from the use of natural resources such as water, wind, sun, tides and heat from the earth. In the meantime, the international community has made several commitments to promoting greater deployment of renewable energy sources. Examples in‐ clude the Kyoto Protocol in 1997 or the recent European directive for climate and energy measures, known as the 20-20-20 targets. This directive aims to reduce greenhouse gas emis‐ sions by 20%, increase the share of energy consumption from renewable energy sources to 20% and promote energy efficiency by reducing primary energy use by 20%. Nevertheless, while the need to develop the use of new energy sources has been consensual, in view of the long-term depletion of fossil fuels and the issue of climate change, there has been no exten‐ sive evaluation of the consequences of renewable energy use. The continuous support for re‐ newables, particularly in Europe, has raised the debate about the levels of wind power installed capacity. It is well known that there is no kind of power plant that operates at 100% of its maximum capacity, particularly renewables due to their intermittent nature. Hence, a problem of structural inefficiency arises, which leads to high economic costs associated with

It is widely accepted that renewables, such as solar and wind, are at the heart of common instruments in reaching European goals of reducing energy dependence, as well as the re‐ duction of greenhouse gases. However, the growth in wind energy magnifies the problem of intermittency. As stated by Holttinen et al. (2009), it is crucial to properly estimate the costs of wind energy in the system as a whole when planning high wind power penetration. Fur‐ thermore, the analysis of renewables' intermittent generation is important for policymakers due to the great support for renewables in Europe, in the context of long-term energy goals. Faced with the problem of renewable intermittency, two possible solutions can be consid‐ ered: (i) energy storage for later use; and (ii) backup electricity generation with fossil fuels. However, the literature (e.g. Beaudin et al., 2010) suggests that energy storage costs are still very high, so upgrading the energy grid in this way is not yet attainable. As a consequence, it would seem more appropriate to combine other energy sources to backup power. Fossil fuel plants can startup and shut down in a short time to keep a secure energy supply and are an effective way of mitigating renewable intermittency (Isla, 1999; and Luickx et al., 2008). A consequence of the divergence between maximum capacity in full-time operation and the electricity actually generated in a given period of time is the idle capacity phenom‐ enon. Idle capacity is noticeable both for renewables, due to their intermittent nature, and

We shall focus only on wind power overcapacity. The scarce research on this subject arouses curiosity about the high levels of idle capacity in wind power. Indeed, Boccard (2009), Fie‐ dler and Bukovsky (2011) and Yang et al. (2012) found that wind energy generation is rarely more than 25% of total capacity. This leads us to believe that there may be overcapacity in

for other energy sources since they are turned off more frequently.

eration, which will continue to require the use of fossil sources to offset it.

the existence of idle capacity.

52 New Developments in Renewable Energy

The vast literature about renewable intermittency, both theoretical and case studies, has not explored the phenomenon of wind overcapacity in enough detail. Indeed, the empirical as‐ sessment of overcapacity in wind power merits much more attention. On the one hand, the phenomenon of overcapacity reflects the path taken by renewables and, on the other, since this phenomenon is a leading indicator, it should back the process of updating public guid‐ ance. The aim of this chapter is to provide empirical evidence on the drivers that contribute to explaining wind power overcapacity and, secondly, to identify empirically the causes for a panel of 19 countries. While Boccard (2009) addresses the issue of wind intermittency from the perspective of the capacity factors, this chapter is focused on the importance of intermit‐ tency and possible wind overcapacity, but using a non-used wind capacity approach.

The role played by several energy sources in creating wind power overcapacity is assessed, controlling for socio-economic drivers and public energy policies and measures. On the whole, this approach can be useful in highlighting the relevance of the intermittent nature of renewables for policymakers in order to deal with wind overcapacity. Econometric techni‐ ques of panel data were applied to deal with the energy and socio-economic characteristics of an economic bloc with environmental concerns and long-term energy targets. In particu‐ lar, the contribution of conventional energy sources to the wind power overcapacity in Eu‐ rope is appraised. Some light is shed on the public policies that might mitigate the economic inefficiency.


**Abstract**

The circular economy is considered as an alternative model to the unsustainable linear "take–make–waste" approach that characterizes contemporary economic systems. It aims to achieve sustainable development by promoting the responsible and cyclical use of resources to maintain their value in the economy and minimize pressures on the environment. Biochar systems offer opportunities for operationalizing the CE model. They are multifunctional systems that can be used for bioenergy and biochar production using an extensive range of biomass feedstocks, including biowaste. They can contribute to climate change mitigation, as producing biochar and mixing it with soil is a means for sequestering atmospheric CO2. Moreover, the produced biochar has a wide range of applications, including its use for agricultural soil amendment, wastewater treatment, manufacturing of cement, and remediation of contaminated soils. This versatility of biochar systems creates great opportunities for developing circular models of waste management that can valorize different waste streams. This chapter provides an overview of the CE concept and describes biochar systems, focusing on systems for the synergistic valorization of wood waste and contaminated soils. It also discusses the role of these systems in the CE indicating that they can contribute to the transition toward the CE.

**Keywords:** circular economy, sustainable development, biochar systems, wood waste, contaminated soil


In this respect, the aging time dependences of some physical parameters directly related to the stability of colloidal dispersions must be explored and discussed. Two of the most im‐ portant parameters that should be taken into account are pH and the average particles size. The first one is determinant for fixing the thickness of the ionic layers surrounding any giv‐ en charged colloidal particle (Stern layers) while affecting, at the same time, the Zeta poten‐ tial, the electrophoretic mobility and the aggregation mechanisms as well as the apparent hydrodynamic particle size. As a consequence, the average particles size is the final result of the conjugate action of all the physicochemical variables hardly mentioned before. It is also the definitive experimental variable on which any post processing technique should be

4 2 2

*S Aq*

*Aq Aq Aq Aq t hrs*

'Universal' Synthesis of PZT (1-X)/X Submicrometric Structures Using Highly Stable Colloidal Dispersions...

~90

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331

http://dx.doi.org/10.5772/51996

*i*

Accordingly, bands located at 1280, 1370-1440 and 1530-1595 cm-1 in the crystals spectrum, shown in Figure 3, can be assigned to the ν(C-CH3:Acac), δ(CH3:Acac) and ν(C-C) + ν(C-O:Acac) vibrational modes, respectively [26].

**Figure 4.** Fully chelated metal-acetylacetonate complexes. (a) Zr(Acac)4 as reported by single crystal XRD charateriza‐ tion, (b) Zr(Acac)4 structure simulated by Materials Studio (MS) according to its crystallographic data and (c) Ti(Acac)2(OPr)2 simulated by MS according to its most probable configuration.

### *2.4.2. Chemical reaction*

As seen before, solution B can be thought as the resulting chelated metal complexes mixed with residual isopropanol. In this case, an appropriate chemical equation for the reaction could be:

$$\begin{aligned} &0.53Zr \Big(\text{O}^{i}\Pr\Big)\_{4\text{(A)}} + 0.47\text{Ti} \Big(\text{O}^{i}\Pr\Big)\_{4\text{(A)}} + 2A\text{acch} \mathbf{H}\_{\{\text{Aq}\}} \xrightarrow[t\to\text{4m}]{\text{T}\cdot\text{spt}\heartseq} 2\text{HO}^{i}\Pr\_{\{\text{Aq}\}} + yZr \Big(\text{Aac}\Big)\_{4\text{(A)}} \\ &+ \Big(1-2y\Big) \text{Ti} \Big(\text{Aac}\Big)\_{2} \Big(\text{O}^{i}\Pr\Big)\_{2\text{(Aq)}} + \Big(0.53-y\Big) \text{Zr} \Big(\text{O}^{i}\Pr\Big)\_{4\text{(Aq)}} + \Big(2y-0.53\Big) \text{Ti} \Big(\text{O}^{i}\Pr\Big)\_{4\text{(Aq)}} \end{aligned} \tag{2}$$

where we have assumed that all the acetylacetone reacts with the alkoxides thus forming the chelated organometallic complexes. As we see, there is still a fraction of nonchelated reac‐ tants due to the insufficient amount of acetylacetone needed for that purpose. Let us find now the exact amount of acetylacetone required for obtaining fully chelated organometallic complexes without any further byproducts. We could rewrite equation [2] as:

$$\begin{aligned} \text{(0.53Zr)} \left(\text{O}^{\text{i}}\text{Pr}\right)\_{\text{4\text{\textdegree{}}\text{(A\text{\textdegree{}})}} &+ 0.477\text{i}\text{\textdegree{}(\text{O}^{\text{i}}\text{Pr})}\_{\text{4\text{\textdegree{}(A\text{\textdegree{}})}} + (\text{Z} + \text{A})\text{AcacH}\_{\text{(A\text{\textdegree{}})}} \xrightarrow[\text{I}\text{\text{--}4\text{km}.}]{\text{T}\text{-}40\text{°C}} (\text{Z} + \text{A})\text{HO}^{\text{i}}\text{Pr}\_{\text{\textdegree{}(A\text{\textdegree{}})}} + \\ &+ 0.53Zr\text{(A\text{\textdegree{}}A\text{\textdegree{}})}\_{\text{4\text{\textdegree{}}\text{(}\text{})} + 0.477\text{i}\text{\textdegree{}(A\text{\textdegree{}}A\text{\textdegree{}})} \text{\textdegree{}(\text{O}^{\text{i}}\text{Pr})\_{\text{2\textdegree{}(A\text{\textdegree{}})}} \end{aligned} \tag{3}$$

Now, it is obvious that Δ = 1.06 implying an alkoxides: acacH molar ratio of 1:3.06 for full che‐ lation of metallic centers. Equation [3] can now be written for any given Zr:Ti ratio (1-x)/x:

$$\begin{aligned} \text{Tr}(\mathbf{1} - \mathbf{x}) \text{Zr} \Big( \mathbf{O}^{\dagger} \text{Pr} \Big)\_{\mathbf{4}\_{\{\!4\_{\emptyset}\}}} + \text{xlTi} \Big( \mathbf{O}^{\dagger} \text{Pr} \Big)\_{\mathbf{4}\_{\{\!4\_{\emptyset}\}}} + \text{2(2 - x)} \text{AacarH}\_{\{\!4\_{\emptyset}\}} \xrightarrow[\text{t-4km.}]{\text{T} \rightarrow \text{00} \text{°C}} \text{2(2 - x)} \text{HO}^{\dagger} \text{Pr}\_{\{\!4\_{\emptyset}\}} + \text{2(2 - x)} \text{H} \text{O}^{\dagger} \text{Ar} \\ + \text{(1 - x)} \text{Zr} \Big( \text{Aacar} \Big)\_{\mathbf{4}\_{\{\!4\}}} + \text{xlTi} \Big( \text{Aacac} \Big)\_{\mathbf{2}} \Big( \mathbf{O}^{\dagger} \text{Pr} \Big)\_{\mathbf{2}\{\!4\_{\emptyset}\}} \end{aligned} \tag{4}$$

This equation represents an extension for the initially proposed sol-gel based route in order to obtain fully chelated and no hydrolysable precursor solutions for PZT based ferroelectric materials. It allows us to synthesize PZT at any Zr:Ti ratio while maximizing solution stabili‐ ty and offering a noticeable repetitiveness for both small and large scale manufacturing and processing.

On the following section we will analyze some features of different sol-gel based PZT (1-x)/x precursors when synthesized using the universal 1:2(2-x) alkoxides: acacH molar ratio al‐ ready discussed above.

### **3. Some properties of the PZT precursors**

propoxide [18],[20]. Figure 4(c) shows a very simple Materials Studio 3D modeling for the most probable configuration of Ti(Acac)2(OPr)2 as determined by the Forcite package [25] on

Accordingly, bands located at 1280, 1370-1440 and 1530-1595 cm-1 in the crystals spectrum, shown in Figure 3, can be assigned to the ν(C-CH3:Acac), δ(CH3:Acac) and ν(C-C) + ν(C-

**Figure 4.** Fully chelated metal-acetylacetonate complexes. (a) Zr(Acac)4 as reported by single crystal XRD charateriza‐ tion, (b) Zr(Acac)4 structure simulated by Materials Studio (MS) according to its crystallographic data and (c)

As seen before, solution B can be thought as the resulting chelated metal complexes mixed with residual isopropanol. In this case, an appropriate chemical equation for the reaction

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

~4 . 4 4 4

where we have assumed that all the acetylacetone reacts with the alkoxides thus forming the chelated organometallic complexes. As we see, there is still a fraction of nonchelated reac‐ tants due to the insufficient amount of acetylacetone needed for that purpose. Let us find now the exact amount of acetylacetone required for obtaining fully chelated organometallic

( ) ( ) ( ) ( ) ( ) ( )

*i i T C i*

( ) ( ) ( ) ( ) ( )

4 2 2

*S Aq*

*Aq Aq Aq Aq t hrs*

+ + +D +D +

*Aq t hrs Aq S Aq Aq ii i*

2 24 4

~90

¾¾¾®

° + + + +

*Aq Aq Aq*

~90

¾¾¾®

°

*i*

(2)

(3)

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 2 Pr 0.53 Pr 2 0.53 Pr

*y Ti Acac O y Zr O y Ti O*

*Zr O Ti O AcacH HO yZr Acac*

a single step relaxation and energy minimization routine.

Ti(Acac)2(OPr)2 simulated by MS according to its most probable configuration.

0.53 Pr 0.47 Pr 2 2 Pr

+ - + - + -

*i i T C i*

complexes without any further byproducts. We could rewrite equation [2] as:

~4 . 4 4

+ +

0.53 Pr 0.47 Pr (2 ) (2 ) Pr

*Zr O Ti O AcacH HO*

0.53 0.47 Pr

*Zr Acac Ti Acac O*

*2.4.2. Chemical reaction*

330 Advances in Ferroelectrics

could be:

O:Acac) vibrational modes, respectively [26].

In the final step of the synthesis, when mixing Solutions A and B with 2-methoxyethanol, the dissolved lead acetate complex can react with 2-MOE forming a very stable acetate–me‐ thoxyethoxy lead complex [27] that, along with the chelated metal complexes already formed, may lead to turn this final solution into a hydrophobic sol, poorly hydrolysable and, therefore, very stable.

Stability issues tend to be crucial when using sol-gel based precursors in research, small scale applications and industry. Therefore, it is very important to keep control over some parameters that affects the solution stability and, most of all, the average particles size. Par‐ ticularly, particles size can be an indicator of some undesirable processes that could be tak‐ ing place in the sol: aggregation, flocculation and sedimentation; aggregation, even though is a reversible process, is a good indicator of instability since the other two processes, which are not reversible, generally follows after some time.

In this respect, the aging time dependences of some physical parameters directly related to the stability of colloidal dispersions must be explored and discussed. Two of the most im‐ portant parameters that should be taken into account are pH and the average particles size. The first one is determinant for fixing the thickness of the ionic layers surrounding any giv‐ en charged colloidal particle (Stern layers) while affecting, at the same time, the Zeta poten‐ tial, the electrophoretic mobility and the aggregation mechanisms as well as the apparent hydrodynamic particle size. As a consequence, the average particles size is the final result of the conjugate action of all the physicochemical variables hardly mentioned before. It is also the definitive experimental variable on which any post processing technique should be based on as it explicitly defines the size range of the so called "building blocks" for bottomup studies or applications.

fore, (c) to the small amount of alcohol that could be formed afterwards. After 4 months of aging, no noticeable changes in pH values were detected. Moreover, the stability of these solutions could be eye inspected by verifying neither the absence of sedimentation nor pre‐

'Universal' Synthesis of PZT (1-X)/X Submicrometric Structures Using Highly Stable Colloidal Dispersions...

http://dx.doi.org/10.5772/51996

333

**Figure 5.** a) pH vs. concentration dependencies for the PZT 53/47 samples understudy measured at different time in‐ tervals. Semi-log fittings to guide the eye are also drawn. (b) Aging effects on pH for the same samples. Three distinc‐

Particles size measurements were carried out by means of the dynamic light scattering (DLS) technique in a Zetasizer Nano ZS90 manufactured by Malvern Instruments Ltd. equipped with a HeNe laser source. Approximately 1.5 ml of as synthesized sols were stor‐ ed in polystyrene cells (DTS0012 cells) provided by the same manufacturer and then size distributions curves were recorded from the very first day until 125 days after synthesis. For this purpose, several solvent parameters were needed for further processing of dispersed light intensity, namely viscosity (η2-MOE ~ 1.5410 cP), dielectric constant (ε2-MOE ~ 16.9) and re‐ fraction index (n2-MOE ~ 1.33) [32]. After each measurement, a nonlinear least squares fitting (NLLSF) was made to the experimental data according to a log-normal distribution function:

> 1 ln 0 2

b

p b

b b

size intervals where unimodal distribution curves were measured.

(, ) exp ln 2 *i x f x x*

=+ -

3 2 2

b

are fitting parameters. It must be stressed that this fitting was carried out only for

1 1

2

(5)

b

é ù æ ö ê ú ç ÷ ê ú è ø ë û

tive stages were detected and are highlighted in the graph.

**3.2. Mean particle size**

Where *βI*

*3.2.1. Experimental technique*

cipitation of single particles or aggregates after almost 1 year of stocking.

Currently, there are no known extensive reports in the literature directly concerned to the study of the time dependence of the average particles size or pH in a PZT precursor sol. It must be noted that, in the case of magnetic nanoparticles, some studies have been carried out [28]-[30]and all of them stress the strong correlation between the size of the colloidal particle and the final properties of the conceived structure, whether it will be nano- or not.

### **3.1. pH**

For this study, we synthesized PZT (1-x)/x precursor solutions by using the same route de‐ scribed in 2.1 with the only difference being the propoxides: acacH molar ratio. In this case, and for the rest of our text, that ratio will be 1:2(2-x) for full chelation of the metal alkoxides.

As it was stated earlier, we will avoid again showing and discussing irrelevant data of sam‐ ples that showed no significant discrepancies between each other and, because of this, this section will analyze the pH vs. Concentration vs. aging time behaviors of several PZT 53/47 precursor solutions with concentrations ranging from 0.05 M to 0.37 M in a time interval of up to 4 months of stocking.

As can be seen in Figure 5, the acidity/basicity of the solutions clearly shows a tendency with both sols concentration and aging time. Figure 5(a) shows the measured pH vs concen‐ tration for the studied sols at several aging steps and, as expected, the more concentrated sample implies the more acidic medium which is consistent with the chemical reaction pro‐ posed for sols synthesis.

Figure 5(b), on the other hand, shows the measured pH vs. time behavior. As a general ten‐ dency, sols pH dependency with aging time can be divided in three stages which are high‐ lighted in the graph: (i) pH increases notably in the first days after which (ii) it decreases to values somehow close to the initial ones. In this moment, (iii) pH starts to rise again but with a slower time gradient than on stage (i). In our opinion, for the understanding of the pH vs. aging time behavior, we have to take into account the coexistence of different com‐ petitive processes right after sols were prepared. In this way, a qualitative description could be done as follows [31]: (i) Remnant unreacted acetic acid evaporates during the first days implying a decrement on the acidity of sols. At this point, (ii) particles are less positively charged and are able to aggregate via condensation reactions followed by the formation of small portions of alcohol (1-propanol) and thus implying a more acidic environment as seen in Figure 5. The number of polyanions per aggregate chain must be limited, however, by the high chemical stability of the chelated metal complexes and that is why the aggregation process does not imply polymerization and/or gelation as it has been reported for more hy‐ drophilic sols. Shortly after condensation rate vanishes, (iii) it is possible for the residual al‐ cohols to evaporate as solutions age thus allowing pH to rise slowly, as seen in Figure 5 for the more aged solutions.

At this scenario, however, hydrolysis is not expected due to (a) the complete chelation of the metal complexes, (b) to the short lengths of the already formed polymeric chains and, there‐ fore, (c) to the small amount of alcohol that could be formed afterwards. After 4 months of aging, no noticeable changes in pH values were detected. Moreover, the stability of these solutions could be eye inspected by verifying neither the absence of sedimentation nor pre‐ cipitation of single particles or aggregates after almost 1 year of stocking.

**Figure 5.** a) pH vs. concentration dependencies for the PZT 53/47 samples understudy measured at different time in‐ tervals. Semi-log fittings to guide the eye are also drawn. (b) Aging effects on pH for the same samples. Three distinc‐ tive stages were detected and are highlighted in the graph.

### **3.2. Mean particle size**

based on as it explicitly defines the size range of the so called "building blocks" for bottom-

Currently, there are no known extensive reports in the literature directly concerned to the study of the time dependence of the average particles size or pH in a PZT precursor sol. It must be noted that, in the case of magnetic nanoparticles, some studies have been carried out [28]-[30]and all of them stress the strong correlation between the size of the colloidal particle and the final properties of the conceived structure, whether it will be nano- or not.

For this study, we synthesized PZT (1-x)/x precursor solutions by using the same route de‐ scribed in 2.1 with the only difference being the propoxides: acacH molar ratio. In this case, and for the rest of our text, that ratio will be 1:2(2-x) for full chelation of the metal alkoxides. As it was stated earlier, we will avoid again showing and discussing irrelevant data of sam‐ ples that showed no significant discrepancies between each other and, because of this, this section will analyze the pH vs. Concentration vs. aging time behaviors of several PZT 53/47 precursor solutions with concentrations ranging from 0.05 M to 0.37 M in a time interval of

As can be seen in Figure 5, the acidity/basicity of the solutions clearly shows a tendency with both sols concentration and aging time. Figure 5(a) shows the measured pH vs concen‐ tration for the studied sols at several aging steps and, as expected, the more concentrated sample implies the more acidic medium which is consistent with the chemical reaction pro‐

Figure 5(b), on the other hand, shows the measured pH vs. time behavior. As a general ten‐ dency, sols pH dependency with aging time can be divided in three stages which are high‐ lighted in the graph: (i) pH increases notably in the first days after which (ii) it decreases to values somehow close to the initial ones. In this moment, (iii) pH starts to rise again but with a slower time gradient than on stage (i). In our opinion, for the understanding of the pH vs. aging time behavior, we have to take into account the coexistence of different com‐ petitive processes right after sols were prepared. In this way, a qualitative description could be done as follows [31]: (i) Remnant unreacted acetic acid evaporates during the first days implying a decrement on the acidity of sols. At this point, (ii) particles are less positively charged and are able to aggregate via condensation reactions followed by the formation of small portions of alcohol (1-propanol) and thus implying a more acidic environment as seen in Figure 5. The number of polyanions per aggregate chain must be limited, however, by the high chemical stability of the chelated metal complexes and that is why the aggregation process does not imply polymerization and/or gelation as it has been reported for more hy‐ drophilic sols. Shortly after condensation rate vanishes, (iii) it is possible for the residual al‐ cohols to evaporate as solutions age thus allowing pH to rise slowly, as seen in Figure 5 for

At this scenario, however, hydrolysis is not expected due to (a) the complete chelation of the metal complexes, (b) to the short lengths of the already formed polymeric chains and, there‐

up studies or applications.

332 Advances in Ferroelectrics

up to 4 months of stocking.

posed for sols synthesis.

the more aged solutions.

**3.1. pH**

### *3.2.1. Experimental technique*

Particles size measurements were carried out by means of the dynamic light scattering (DLS) technique in a Zetasizer Nano ZS90 manufactured by Malvern Instruments Ltd. equipped with a HeNe laser source. Approximately 1.5 ml of as synthesized sols were stor‐ ed in polystyrene cells (DTS0012 cells) provided by the same manufacturer and then size distributions curves were recorded from the very first day until 125 days after synthesis. For this purpose, several solvent parameters were needed for further processing of dispersed light intensity, namely viscosity (η2-MOE ~ 1.5410 cP), dielectric constant (ε2-MOE ~ 16.9) and re‐ fraction index (n2-MOE ~ 1.33) [32]. After each measurement, a nonlinear least squares fitting (NLLSF) was made to the experimental data according to a log-normal distribution function:

$$f\_{\ln}(\mathbf{x}, \boldsymbol{\beta}\_{i}) = \boldsymbol{\beta}\_{0} + \frac{\boldsymbol{\beta}\_{i}}{\sqrt{\pi \boldsymbol{\beta}\_{2}}} \frac{1}{\boldsymbol{x}} \exp\left[-\frac{1}{2\boldsymbol{\beta}\_{2}^{2}} \ln\left(\frac{\boldsymbol{x}}{\boldsymbol{\beta}\_{3}}\right)^{2}\right] \tag{5}$$

Where *βI* are fitting parameters. It must be stressed that this fitting was carried out only for size intervals where unimodal distribution curves were measured.

### *3.2.2. Concentration dependence*

Figure 6 shows the results obtained for particles size distribution for two concentrations un‐ der study (a PZT 53/47 precursor) after different time lapses that are also shown in the figure.

Zr(Acac)4 in 2-MOE, (III) to a dilution process while mixing A+ B, or (IV) to a combined ef‐ fect of all of the above. Must be noted that the less acidic solution (C = 0.20M) possesses, at the same time, the less unimodal distribution function which is an expected result in con‐

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Thus, it seems plausible to assume solution B as a dispersion containing the Ti(Acac)2(OPr)2 compound at molecular level and submicrometric aggregates of Zr(Acac)4 that do not pre‐ cipitate; these are redissolved afterwards when mixed with the acetate rich solution A and 2- MOE. After stirring the resultant sol for one day, the size of some percentage of the Zr(Acac)4 aggregates still ranges between 100 and 1000 nm; after 20 days, however, size is well below 10 nm. From these results, and somehow confirming our previous discussion, we can also see that the less concentrated solution features a considerable amount of parti‐ cles with sizes well above 50nm even after 100 days of stocking. For this reason, we will fo‐ cus our attention from now on in precursor solutions with 0.35 M aged during the first 30-35 days, a time period that, according to our results, seems to be critical in the colloidal stability

As it was said before, all samples under study featured a noticeable stabilization when aged for about 1 month. Figure 7 shows this aging behavior for two PZT (1-x)/x precursor solu‐ tions concentrated at 0.35 M. In all cases, it could be observed a similar time evolution as the

**Figure 7.** Aging behavior, as depicted by the time evolution of particles size distribution curves, for two PZT (1-x)/x

On the other hand, Figure 8 shows the whole dataset of the measured mean particles size for the synthesized solutions. Fitting curves shown here were determined by considering a time

in the van Dongen–Ernst approximation, describes appropriately a nongelling system of dis‐

*1/(1 -λ)+ C2* that, according to the classical Smoluchowski theory

precursor solutions concentrated at 0.35 M: (a) PZT 25/75 and (b) PZT 60/40.

cordance to the relationship between ionic strength and particles size.

of as synthesized sols.

*3.2.3. Aging time dependence*

one described earlier for Figure 6.

dependence given by *<d>= C1t*

According to what is shown, an appropriate discussion relaying on the acidity/particles size dependence cannot be easily established: oscillations in the pH values, see Figure 5, during aging are not followed by oscillations in the mean particles size values. Even though this feature is not fully understood, it may be due to the short lengths of the oligomeric chains present in the solution and to the weak sensitivity of the completely chelated metal com‐ plexes to the ionic strength of the solvent medium. Another possible explanation could be given in terms of the irreversibility associated to the formation of these chains when the sol‐ vent medium is not acidic enough to break the corresponding bonds and/or coordinations.

As can be seen, as prepared sols featured multimodal distributions with some small percent of particles that could even have sizes higher than 1μm. As solutions are aged, these distri‐ butions tend to be unimodal featuring a mean particles size well below 10 nm. We consider that this is a remarkable result of this work as it shows that there is no rule of thumb closely related to the need of using fresh, as prepared solutions for synthesizing several kinds of nanodimensional systems by means of electrophoretic deposition(EPD) or simple template immersion, [33]-[36]. Moreover, in this case we could have chosen solutions aged for 20 days or more for bulk, thin films or nanostructures synthesis due to the better homogeneity re‐ garding particles size distribution in both cases under study.

**Figure 6.** Particles size distribution functions for the analysed PZT 53/47 precursor solutions and for several aging times in the whole measurement range. Log-normal fittings for the more populated size intervals are also depicted.

This behavior could be explained, in principle, on the basis of the chemical reaction which was described for obtaining what we called solution B, see Section 2.4. As we stated, by the end of this step we observed the crystallization of the compound Zr(Acac)4. Such crystalliza‐ tion does not occur after mixing solutions A and B in the presence of 2-MOE which can be attributed (I) to the higher acidity of the final A+B+2-MOE solution, (II) to the solubility of Zr(Acac)4 in 2-MOE, (III) to a dilution process while mixing A+ B, or (IV) to a combined ef‐ fect of all of the above. Must be noted that the less acidic solution (C = 0.20M) possesses, at the same time, the less unimodal distribution function which is an expected result in con‐ cordance to the relationship between ionic strength and particles size.

Thus, it seems plausible to assume solution B as a dispersion containing the Ti(Acac)2(OPr)2 compound at molecular level and submicrometric aggregates of Zr(Acac)4 that do not pre‐ cipitate; these are redissolved afterwards when mixed with the acetate rich solution A and 2- MOE. After stirring the resultant sol for one day, the size of some percentage of the Zr(Acac)4 aggregates still ranges between 100 and 1000 nm; after 20 days, however, size is well below 10 nm. From these results, and somehow confirming our previous discussion, we can also see that the less concentrated solution features a considerable amount of parti‐ cles with sizes well above 50nm even after 100 days of stocking. For this reason, we will fo‐ cus our attention from now on in precursor solutions with 0.35 M aged during the first 30-35 days, a time period that, according to our results, seems to be critical in the colloidal stability of as synthesized sols.

### *3.2.3. Aging time dependence*

*3.2.2. Concentration dependence*

334 Advances in Ferroelectrics

Figure 6 shows the results obtained for particles size distribution for two concentrations un‐ der study (a PZT 53/47 precursor) after different time lapses that are also shown in the figure. According to what is shown, an appropriate discussion relaying on the acidity/particles size dependence cannot be easily established: oscillations in the pH values, see Figure 5, during aging are not followed by oscillations in the mean particles size values. Even though this feature is not fully understood, it may be due to the short lengths of the oligomeric chains present in the solution and to the weak sensitivity of the completely chelated metal com‐ plexes to the ionic strength of the solvent medium. Another possible explanation could be given in terms of the irreversibility associated to the formation of these chains when the sol‐ vent medium is not acidic enough to break the corresponding bonds and/or coordinations. As can be seen, as prepared sols featured multimodal distributions with some small percent of particles that could even have sizes higher than 1μm. As solutions are aged, these distri‐ butions tend to be unimodal featuring a mean particles size well below 10 nm. We consider that this is a remarkable result of this work as it shows that there is no rule of thumb closely related to the need of using fresh, as prepared solutions for synthesizing several kinds of nanodimensional systems by means of electrophoretic deposition(EPD) or simple template immersion, [33]-[36]. Moreover, in this case we could have chosen solutions aged for 20 days or more for bulk, thin films or nanostructures synthesis due to the better homogeneity re‐

**Figure 6.** Particles size distribution functions for the analysed PZT 53/47 precursor solutions and for several aging times in the whole measurement range. Log-normal fittings for the more populated size intervals are also depicted.

This behavior could be explained, in principle, on the basis of the chemical reaction which was described for obtaining what we called solution B, see Section 2.4. As we stated, by the end of this step we observed the crystallization of the compound Zr(Acac)4. Such crystalliza‐ tion does not occur after mixing solutions A and B in the presence of 2-MOE which can be attributed (I) to the higher acidity of the final A+B+2-MOE solution, (II) to the solubility of

garding particles size distribution in both cases under study.

As it was said before, all samples under study featured a noticeable stabilization when aged for about 1 month. Figure 7 shows this aging behavior for two PZT (1-x)/x precursor solu‐ tions concentrated at 0.35 M. In all cases, it could be observed a similar time evolution as the one described earlier for Figure 6.

**Figure 7.** Aging behavior, as depicted by the time evolution of particles size distribution curves, for two PZT (1-x)/x precursor solutions concentrated at 0.35 M: (a) PZT 25/75 and (b) PZT 60/40.

On the other hand, Figure 8 shows the whole dataset of the measured mean particles size for the synthesized solutions. Fitting curves shown here were determined by considering a time dependence given by *<d>= C1t 1/(1 -λ)+ C2* that, according to the classical Smoluchowski theory in the van Dongen–Ernst approximation, describes appropriately a nongelling system of dis‐ persed clusters. Moreover, in the same approximation, the small values of *λ*(*λ<<1*) are usual‐ ly associated with a Brownian diffusion limited aggregation process vastly dominated by collisions between larger clusters with smaller ones [31].

Our samples were also characterized by the High Resolution Transmission Electron Micro‐ scopy (HR-TEM) technique. A few drops of the synthesized sols were deposited on copper grids, evaporated afterwards and put under a JEOL JEM2200 microscope with Omega filter and a spherical aberration corrector; some of the obtained images are shown in Figure 9 for a PZT 95/05 precursor solution. As expected, particles are likely to coalesce as the solvent evaporated prior to characterization, see Figure 9(a) and (b), and some of those nanoparti‐ cles are shown in higher magnification images in Figure 9(c) and (d). Most of the features regarding particle size that were discussed earlier were corroborated by means of this tech‐

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At this point, and considering what has been discussed until now, it must be highlighted that a rigorous control of the chelation rate, pH and aging time could give us a chance to "tune" the average nanoparticles size and/or the colloidal stability as desired. By looking back at Figure 5 through Figure 8 one may feel free to choose to explore several "working points" according to our research or technological needs for every (1-x)/x Zr:Ti ratio in the

**Figure 9.** HR-TEMimages at different magnifications for a PZT 95/05 precursor solution, with C = 0.35 M and aged for

nique for all the precursor solutions.

PZT system.

2 months.

Another view of the aging process could be illustrated by means of the dimensionless nor‐ malized distribution curves, not shown here. In that representation, the broadening of the distribution curves with aging is an indicator of very likely aggregation processes and some‐ how will help to complete the kinetic analysis that we have been through in this section.

In a way of summarizing our results, it could be said that, just after synthesis, several popu‐ lations of particles were detected until homogenized a few days later; then particles tend to grow very slowly with time according to an almost linear law (corresponding to that de‐ scribing a nongelling system) and aggregation is expected. Moreover, these cases fit very well in the Brownian diffusion limited aggregation type where smaller clusters stick to big‐ ger ones when they collide. The slow but evident increase in the mean cluster size, as well as the noticeable broadening in the distribution peaks, must warn us about an undesirable and irreversible precipitation process for, hypothetically, t → ∞.

The high stability shown by our samples even after 4months of stocking and the small val‐ ues for mean particles size (well below 10 nm) are good indicators that the complete chela‐ tion of the organometallic compounds plays a key role in keeping short, and poorly reactive, oligomeric chains. An aggregation process dominated exclusively by Brownian motion is highly desirable when solution stability needs to be maximized.

**Figure 8.** Mean particles size vs. aging time dependence for the systems under study. Fitting curves obeying a *t1/(1*  λ)scaling law are depicted.

Our samples were also characterized by the High Resolution Transmission Electron Micro‐ scopy (HR-TEM) technique. A few drops of the synthesized sols were deposited on copper grids, evaporated afterwards and put under a JEOL JEM2200 microscope with Omega filter and a spherical aberration corrector; some of the obtained images are shown in Figure 9 for a PZT 95/05 precursor solution. As expected, particles are likely to coalesce as the solvent evaporated prior to characterization, see Figure 9(a) and (b), and some of those nanoparti‐ cles are shown in higher magnification images in Figure 9(c) and (d). Most of the features regarding particle size that were discussed earlier were corroborated by means of this tech‐ nique for all the precursor solutions.

persed clusters. Moreover, in the same approximation, the small values of *λ*(*λ<<1*) are usual‐ ly associated with a Brownian diffusion limited aggregation process vastly dominated by

Another view of the aging process could be illustrated by means of the dimensionless nor‐ malized distribution curves, not shown here. In that representation, the broadening of the distribution curves with aging is an indicator of very likely aggregation processes and some‐ how will help to complete the kinetic analysis that we have been through in this section.

In a way of summarizing our results, it could be said that, just after synthesis, several popu‐ lations of particles were detected until homogenized a few days later; then particles tend to grow very slowly with time according to an almost linear law (corresponding to that de‐ scribing a nongelling system) and aggregation is expected. Moreover, these cases fit very well in the Brownian diffusion limited aggregation type where smaller clusters stick to big‐ ger ones when they collide. The slow but evident increase in the mean cluster size, as well as the noticeable broadening in the distribution peaks, must warn us about an undesirable and

The high stability shown by our samples even after 4months of stocking and the small val‐ ues for mean particles size (well below 10 nm) are good indicators that the complete chela‐ tion of the organometallic compounds plays a key role in keeping short, and poorly reactive, oligomeric chains. An aggregation process dominated exclusively by Brownian motion is

**Figure 8.** Mean particles size vs. aging time dependence for the systems under study. Fitting curves obeying a *t1/(1 -*

collisions between larger clusters with smaller ones [31].

336 Advances in Ferroelectrics

irreversible precipitation process for, hypothetically, t → ∞.

highly desirable when solution stability needs to be maximized.

λ)scaling law are depicted.

At this point, and considering what has been discussed until now, it must be highlighted that a rigorous control of the chelation rate, pH and aging time could give us a chance to "tune" the average nanoparticles size and/or the colloidal stability as desired. By looking back at Figure 5 through Figure 8 one may feel free to choose to explore several "working points" according to our research or technological needs for every (1-x)/x Zr:Ti ratio in the PZT system.

**Figure 9.** HR-TEMimages at different magnifications for a PZT 95/05 precursor solution, with C = 0.35 M and aged for 2 months.

This, in fact, is a powerful tool provided by the physicochemical phenomena and mecha‐ nisms previously discussed and, generally speaking, could be extended to other material systems of technological interest at a moderate cost.

### **4. Crystallization route**

The final A + B + 2-MOE solutions were dried at 100°C for several days and, after that, they were thermally treated in order to analyze the phase evolution from the amorphous PZT sol-gel network to the expected final Perovskite structure. Due to fundamental similarities among the different samples we will be discussing only the case where Zr:Ti ratio is 53/47, concentrated at 0.35 M and aged for 2 months.

### **4.1. Experimental techniques**

Crystallization was monitored by means of FT-IR and Raman vibrational spectroscopies, see Sections 2.2.1 and 2.2.2, and by X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) techniques after treating the samples for 12 hours at certain temperatures that were previously chosen. For the sake of clarity, we decided to divide the crystallization study in two temperature intervals: (i) 100 ≤ T ≤ 510° C and (ii) 550 ≤ T ≤ 900° C. At this point, it is im‐ portant to say that, for powders heated at 850° C and 900° C, the treatment was carried out for just 2 hours due to the high volatility of lead for 850° C and beyond.

**Figure 10.** Phase transformations for 100 °C≤ T≤ 510 °C as registered by Raman (a) and FT-IR (b) vibrational spectros‐ copies; in this case, remnant vibrations due to the presence of acetate and chelated metal complexes are highlighted.

are almost the same and, on the other hand, Raman spectra featured no signal given the strong presence of π-bonded organic species. Afterwards, IR spectra revealed the almost complete decomposition of acetates and a decrement of Metal:Acac complexes while any no‐

assigned to a PZT 53/47 started to show up. After treating at this temperature, the FT-IR spectra reveals the formation and definition of the A1(3TO) vibrational mode (~600 cm-1)

Another view of the whole process in this temperature range could be given, as seen in Fig‐ ure 11, by means of XRD characterization. XRD patterns clearly illustrate the phase transfor‐ mation exhibited by an amorphous material turning into crystalline; as for the Raman

These maxima are usually associated to an intermediate metastable phase belonging to the Fluorite crystal system (F) which is mainly characterized by the spatial disarrangement of the oxygen atoms, vacancies and metal cations while coexisting with some carbonates and/or oxides that still remain in the material. Afterwards, when carbonates and oxides re‐ act, a new metastable phase is formed but this new arrangement tends to be more ordered than the previous fluorite. This intermediate phase is considered as belonging to the Pyro‐ chlore crystal system (P or Pyr) and consisting of a 2 x 2 x 2 ordered fluorite cell with oxygen and metallic vacancies or, from another point of view, consisting of a 2 x 2 x 2 non stoichio‐ metric Perovskite (Per) cell. This rigorous differentiation between Fluorite and Pyrochlore is not always considered in literature and it can be subtle sometimes, especially when working

ticeable Raman signal is still absent. Just after T = 450°

which is also characteristic for this compound [38]-[41].

spectra, crystallinity starts to get noticed at T = 450°

existence of well defined peaks near 28°

C, IR spectra showed no variation; the intensity ratios between the detected modes

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C. However, these patterns revealed the

that disappear almost entirely at 510°C.

Until 225°

Scanning Electron Microscopy (SEM) was carried out on fine ground powders in a Leica Cambridge Stereoscan 440 microscope and the X-Ray powder diffraction patterns were re‐ corded over a 20-60° 2θ range on a Bruker D8 Advance diffractometer with filtered CuKα radiation. In this technique, the identified phases were indexed by comparing the resulting diffraction patterns with those of similar compositions reported in the International Union of Crystallography (IUCr) JCPDS-ICDD database.

### **4.2. 100 ≤ T ≤ 510 °C**

In this temperature range the material goes through very noticeable phase transformations; the initial amorphous powder starts to show some crystallinity for about 500° C, right after the combustion of the remaining organic species. Figure 10 shows these first crystallization stages as recorded by the Raman (a) and FT-IR (b) vibrational spectroscopies. The vibration‐ al modes associated to the remnant organic compounds coexisting after heat treating at 100 °C are also highlighted in this graph, Figure 10(b), and it must be noticed that they corre‐ spond, basically, to the lead acetate and to the completely chelated organometallic com‐ plexes. More explicitly, numbered modes in Figure 2(b) have been assigned to: (1)Pb(OAc)2:ρ(COO), (2)Pb(OAc)2:δS(COO), (3)Pb(OAc)2:νS(C-C), (4)Ti(OPr)2(Acac)2:Ti-Acac, (5)Zr(Acac)4:Zr-Acac,(6)Pb(OAc)2:δS(CH3), (7)Ti(OPr)2(Acac)2/Zr(Acac)4:δ(CH3:Acac) + Pb(OAc)2:νS(CO)and (8)Ti(OPr)2(Acac)2/Zr(Acac)4:[ν(C-C) + ν(C-O:Acac)] + Pb(OAc)2:νA(C=O)[26],[37].

This, in fact, is a powerful tool provided by the physicochemical phenomena and mecha‐ nisms previously discussed and, generally speaking, could be extended to other material

The final A + B + 2-MOE solutions were dried at 100°C for several days and, after that, they were thermally treated in order to analyze the phase evolution from the amorphous PZT sol-gel network to the expected final Perovskite structure. Due to fundamental similarities among the different samples we will be discussing only the case where Zr:Ti ratio is 53/47,

Crystallization was monitored by means of FT-IR and Raman vibrational spectroscopies, see Sections 2.2.1 and 2.2.2, and by X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) techniques after treating the samples for 12 hours at certain temperatures that were previously chosen. For the sake of clarity, we decided to divide the crystallization study in

Scanning Electron Microscopy (SEM) was carried out on fine ground powders in a Leica Cambridge Stereoscan 440 microscope and the X-Ray powder diffraction patterns were re‐ corded over a 20-60° 2θ range on a Bruker D8 Advance diffractometer with filtered CuKα radiation. In this technique, the identified phases were indexed by comparing the resulting diffraction patterns with those of similar compositions reported in the International Union

In this temperature range the material goes through very noticeable phase transformations;

the combustion of the remaining organic species. Figure 10 shows these first crystallization stages as recorded by the Raman (a) and FT-IR (b) vibrational spectroscopies. The vibration‐ al modes associated to the remnant organic compounds coexisting after heat treating at 100 °C are also highlighted in this graph, Figure 10(b), and it must be noticed that they corre‐ spond, basically, to the lead acetate and to the completely chelated organometallic com‐ plexes. More explicitly, numbered modes in Figure 2(b) have been assigned to: (1)Pb(OAc)2:ρ(COO), (2)Pb(OAc)2:δS(COO), (3)Pb(OAc)2:νS(C-C), (4)Ti(OPr)2(Acac)2:Ti-Acac, (5)Zr(Acac)4:Zr-Acac,(6)Pb(OAc)2:δS(CH3), (7)Ti(OPr)2(Acac)2/Zr(Acac)4:δ(CH3:Acac) + Pb(OAc)2:νS(CO)and (8)Ti(OPr)2(Acac)2/Zr(Acac)4:[ν(C-C) + ν(C-O:Acac)] +

the initial amorphous powder starts to show some crystallinity for about 500°

C and (ii) 550 ≤ T ≤ 900°

C and beyond.

C and 900°

C. At this point, it is im‐

C, right after

C, the treatment was carried out for

systems of technological interest at a moderate cost.

concentrated at 0.35 M and aged for 2 months.

two temperature intervals: (i) 100 ≤ T ≤ 510°

portant to say that, for powders heated at 850°

just 2 hours due to the high volatility of lead for 850°

of Crystallography (IUCr) JCPDS-ICDD database.

**4. Crystallization route**

338 Advances in Ferroelectrics

**4.1. Experimental techniques**

**4.2. 100 ≤ T ≤ 510 °C**

Pb(OAc)2:νA(C=O)[26],[37].

**Figure 10.** Phase transformations for 100 °C≤ T≤ 510 °C as registered by Raman (a) and FT-IR (b) vibrational spectros‐ copies; in this case, remnant vibrations due to the presence of acetate and chelated metal complexes are highlighted.

Until 225° C, IR spectra showed no variation; the intensity ratios between the detected modes are almost the same and, on the other hand, Raman spectra featured no signal given the strong presence of π-bonded organic species. Afterwards, IR spectra revealed the almost complete decomposition of acetates and a decrement of Metal:Acac complexes while any no‐ ticeable Raman signal is still absent. Just after T = 450° C the active Raman modes normally assigned to a PZT 53/47 started to show up. After treating at this temperature, the FT-IR spectra reveals the formation and definition of the A1(3TO) vibrational mode (~600 cm-1) which is also characteristic for this compound [38]-[41].

Another view of the whole process in this temperature range could be given, as seen in Fig‐ ure 11, by means of XRD characterization. XRD patterns clearly illustrate the phase transfor‐ mation exhibited by an amorphous material turning into crystalline; as for the Raman spectra, crystallinity starts to get noticed at T = 450° C. However, these patterns revealed the existence of well defined peaks near 28° that disappear almost entirely at 510°C.

These maxima are usually associated to an intermediate metastable phase belonging to the Fluorite crystal system (F) which is mainly characterized by the spatial disarrangement of the oxygen atoms, vacancies and metal cations while coexisting with some carbonates and/or oxides that still remain in the material. Afterwards, when carbonates and oxides re‐ act, a new metastable phase is formed but this new arrangement tends to be more ordered than the previous fluorite. This intermediate phase is considered as belonging to the Pyro‐ chlore crystal system (P or Pyr) and consisting of a 2 x 2 x 2 ordered fluorite cell with oxygen and metallic vacancies or, from another point of view, consisting of a 2 x 2 x 2 non stoichio‐ metric Perovskite (Per) cell. This rigorous differentiation between Fluorite and Pyrochlore is not always considered in literature and it can be subtle sometimes, especially when working with a well known compound as PZT is. Anyway, in Figure 11 we have denoted by F (Fluo‐ rite) and P (Pyrochlore) the diffraction maxima associated with each of these phases and ac‐ cording to the indexed cubic structures reported in reference [42] (a = 5.25 Å) and in reference [43] (a = 10.48Å), respectively.

Up to this point, we have seen the almost complete elimination of organic ligands with heating as well as the amorphous/crystalline phase transformation going through two intermediate metastable phases. In the next subsection we will carry on a similar study for higher tempera‐ tures while exploring the formation of pure Perovskite phase with morphological quality.

**Figure 12.** Phase transformations for 550 °C≤ T≤ 900 °C as registered by Raman (a) and FT-IR (b) vibrational spectros‐

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**Figure 13.** Thermal evolution of the powders under study when 550 °C ≤ T ≤ 900 °C as evidenced by XRD patterns in

the 20 - 60 deg. 2θ interval. Regions where the most intense Pyr peak showed up are denoted by P.

copies.

**Figure 11.** Thermal evolution of PZT 53/47 precursor powders when100 °C≤ T≤ 510 °C as recorded by XRD patterns.

### **4.3. 550≤ T ≤ 900 °C**

Figure 12 shows Raman (b) and FT-IR (b) spectra for heat treated powders in the 550 – 900 °C range. Unlike the previously studied temperature range, vibrational spectra did not show drastic or very noticeable changes. The FT-IR spectra features the only IR active band for aPZT-R3m in the 400-1500 cm-1 range (A1(3TO)); this band, associated to the extensional vi‐ brations of the Perovskite BO6 octahedra, shifts slightly to higher frequencies while gets nar‐ rower as temperature increases. This shifting suggests a more compact octahedral structure while a narrower band could be the evidence of a better 'environment' around the octahe‐ dron or, in other words, a better local stoichiometry [44] that seems to be minimum for T = 800° C, an indicative of an optimum crystallization. Raman spectra featured vibrational modes that tend to define better as temperature increases.

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with a well known compound as PZT is. Anyway, in Figure 11 we have denoted by F (Fluo‐ rite) and P (Pyrochlore) the diffraction maxima associated with each of these phases and ac‐ cording to the indexed cubic structures reported in reference [42] (a = 5.25 Å) and in

Up to this point, we have seen the almost complete elimination of organic ligands with heating as well as the amorphous/crystalline phase transformation going through two intermediate metastable phases. In the next subsection we will carry on a similar study for higher tempera‐ tures while exploring the formation of pure Perovskite phase with morphological quality.

**Figure 11.** Thermal evolution of PZT 53/47 precursor powders when100 °C≤ T≤ 510 °C as recorded by XRD patterns.

Figure 12 shows Raman (b) and FT-IR (b) spectra for heat treated powders in the 550 – 900 °C range. Unlike the previously studied temperature range, vibrational spectra did not show drastic or very noticeable changes. The FT-IR spectra features the only IR active band for aPZT-R3m in the 400-1500 cm-1 range (A1(3TO)); this band, associated to the extensional vi‐ brations of the Perovskite BO6 octahedra, shifts slightly to higher frequencies while gets nar‐ rower as temperature increases. This shifting suggests a more compact octahedral structure while a narrower band could be the evidence of a better 'environment' around the octahe‐ dron or, in other words, a better local stoichiometry [44] that seems to be minimum for T =

C, an indicative of an optimum crystallization. Raman spectra featured vibrational

modes that tend to define better as temperature increases.

reference [43] (a = 10.48Å), respectively.

340 Advances in Ferroelectrics

**4.3. 550≤ T ≤ 900 °C**

800°

**Figure 12.** Phase transformations for 550 °C≤ T≤ 900 °C as registered by Raman (a) and FT-IR (b) vibrational spectros‐ copies.

**Figure 13.** Thermal evolution of the powders under study when 550 °C ≤ T ≤ 900 °C as evidenced by XRD patterns in the 20 - 60 deg. 2θ interval. Regions where the most intense Pyr peak showed up are denoted by P.

XRD patterns depicted in Figure 13 allow us to notice the temperature evolution of the dis‐ tinctive Perovskite diffraction peaks. Peaks indexing has been done according to a PZT 53/47, FR(HT); sym: R3m. Besides, regions where the most intense Pyr peak showed up (~28.5° ) are denoted by P; the Pyr phase is present in a small percentage (%Pyr ~ 1 %) except for powders treated at T = 800°C which must be chosen as the appropriate crystallization tem‐ perature for this material. The final Perovskite phase homogenizes and tends to be predomi‐ nant as temperature increases until lead losses become noticeable.

On the other hand, Figure 15 shows SEM micrographs of crystallized PZT (1-x)/x powdered samples. As illustrated, a granular structure of fair morphological uniformity is found in all cases along with a remarkable submicrometric average grain size. Another interesting fea‐ ture is the low porosity found in all compositions, somehow resembling the granular struc‐ ture of sintered bulk samples, which certainly favors the formation of a high density

'Universal' Synthesis of PZT (1-X)/X Submicrometric Structures Using Highly Stable Colloidal Dispersions...

http://dx.doi.org/10.5772/51996

343

As it was said at the beginning of this chapter, this kind of sub-micron granular structures, or nanoceramics, allows the technological exploitation of dielectric and ferro/piezoelectric size related features. It is not shown here, but that very same samples have been resynthe‐ sized a couple of times with starting reactants being bought to different companies and final results showed almost the same granular and morphological quality. Repetitiveness is also a bonus when working with chemical routes of synthesis that tend to be less straightforward,

**Figure 15.** SEM micrographs showing the morphological quality of the PZT (1-x)/x powders when crystallized at 800

°C: (a) PZT 25/75, (b) PZT 60/40, (c) PZT 80/20 and (d) PZT 95/05.

ferroelectric material.

even though cheaper, than physical ones.

The rest of the PZT compositions that were chosen for this study, PZT (1-x)/x with C = 0.35 M and 2 months aged, were also treated at 800 °C in order to obtain the appropiate Perov‐ skite phase; Figure 14 shows the corresponding XRD patterns for each one of them. As seen in the graph, all samples attained a perfect crystallization in the corresponding phase and the proper pattern indexing as well as the phase indentification are also shown.

**Figure 14.** XRD patterns for PZT (1-x)/x under study: (a) PZT 25/75, (b) PZT 60/40, (c) PZT 80/20 and (d) PZT 95/05.

On the other hand, Figure 15 shows SEM micrographs of crystallized PZT (1-x)/x powdered samples. As illustrated, a granular structure of fair morphological uniformity is found in all cases along with a remarkable submicrometric average grain size. Another interesting fea‐ ture is the low porosity found in all compositions, somehow resembling the granular struc‐ ture of sintered bulk samples, which certainly favors the formation of a high density ferroelectric material.

XRD patterns depicted in Figure 13 allow us to notice the temperature evolution of the dis‐ tinctive Perovskite diffraction peaks. Peaks indexing has been done according to a PZT 53/47, FR(HT); sym: R3m. Besides, regions where the most intense Pyr peak showed up (~28.5°

are denoted by P; the Pyr phase is present in a small percentage (%Pyr ~ 1 %) except for powders treated at T = 800°C which must be chosen as the appropriate crystallization tem‐ perature for this material. The final Perovskite phase homogenizes and tends to be predomi‐

The rest of the PZT compositions that were chosen for this study, PZT (1-x)/x with C = 0.35 M and 2 months aged, were also treated at 800 °C in order to obtain the appropiate Perov‐ skite phase; Figure 14 shows the corresponding XRD patterns for each one of them. As seen in the graph, all samples attained a perfect crystallization in the corresponding phase and

**Figure 14.** XRD patterns for PZT (1-x)/x under study: (a) PZT 25/75, (b) PZT 60/40, (c) PZT 80/20 and (d) PZT 95/05.

the proper pattern indexing as well as the phase indentification are also shown.

nant as temperature increases until lead losses become noticeable.

342 Advances in Ferroelectrics

)

As it was said at the beginning of this chapter, this kind of sub-micron granular structures, or nanoceramics, allows the technological exploitation of dielectric and ferro/piezoelectric size related features. It is not shown here, but that very same samples have been resynthe‐ sized a couple of times with starting reactants being bought to different companies and final results showed almost the same granular and morphological quality. Repetitiveness is also a bonus when working with chemical routes of synthesis that tend to be less straightforward, even though cheaper, than physical ones.

**Figure 15.** SEM micrographs showing the morphological quality of the PZT (1-x)/x powders when crystallized at 800 °C: (a) PZT 25/75, (b) PZT 60/40, (c) PZT 80/20 and (d) PZT 95/05.

### **5. Chapter remarks**

Through this chapter, we tried to expose some relevant results directly concerned with a fea‐ sible 'universal' controlled synthesis of nano/submicrometric grain-sized PZT (1-x)/x piezo‐ electric structures that, technically speaking, potentially enhance the performance of current commercially bulk based devices by exploiting the size effects related phenomena that arise, as is commonly accepted, for grain sizes below 1 μm. Under the light of this study, the tenta‐ tive bottom-up "design" of any desired nano/submicrometric PZT (1-x)/x structure seems to be a plausible and successful task that, methodologically at least, could be expanded to more complex materials systems.

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Further reading regarding the work that has been shown here can be found in references [45]-[48]. On the other hand, references [49]-[60] will also provide the reader with very re‐ cent research papers in this field that undoubtedly extend the applicability and versatility of what has been discussed.

### **Author details**

2 CCADET-UNAM, Cd. Universitaria, Coyoacán, México D.F., México

3 Fac. de Física/IMRE, San Lázaro y L, Univ. de la Habana, Habana , Cuba

### **References**

[6] Wang ZL. The new field of nanopiezotronics. Materials Today 2007;10(5) 20-28.

**5. Chapter remarks**

344 Advances in Ferroelectrics

complex materials systems.

what has been discussed.

**Author details**

A. Suárez-Gómez1

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**Chapter 16**

**Phase Transitions, Dielectric and Ferroelectric**

Ferroelectric perovskites based on Na0.5Bi0.5TiO3 (NBT) are considered among the most promising lead-free candidate materials to substitute Pb(Zr*1-x*Ti*x*)O3 (PZT) in devices de‐ signed to respect standards and environmental laws. Taking into account the toxicity of lead-based systems, there are numerous lead-free piezoelectric materials under investigation in worldwide spread laboratories for replacing PZT in future devices. Constant efforts are

Solid-solution systems based on lead-free perovskites like Na0.5K0.5NbO3 (NKN), BaTiO3 (BT), Na0.5Bi0.5TiO3 (NBT) or bismuth layered-structured SrBi2Ta2O9 (SBT), and SrBi2Nb2O9 (SBN) are considered as viable alternatives for replacing lead-based materials. For example, (K,Na)NbO3–LiTaO3–LiSbO3 alkaline niobate ceramics exhibit a *d 33* piezoelectric coefficient up to 416 pC/N together with Curie temperature Tc around 526 K, as reported by Saito *et al* [1]. Sodium/bismuth titanate (NBT) belongs to the bismuth-based perovskites in which the A-site atom is replaced. The crystalline structure, phase transitions and physical properties have been intensively studied since the discovery of the material in 1960 by Smolensky *et al* [2]. NBT has a relatively high depolarization temperature, Td = 470 K, high remanent polari‐

high value of the coercive field and high electrical conductivity, NBT cannot be easily polar‐ ized, therefore different A-site substitutions have been attempted to avoid this drawback.

and reproduction in any medium, provided the original work is properly cited.

and piezoelectric coefficient d33 = 125 pC/N [3]. However, owing to the

© 2013 Scarisoreanu et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

made to find viable replacements for all these materials containing harmful elements.

**Properties of Lead-free NBT-BT Thin Films**

N. D. Scarisoreanu, R. Birjega, A. Andrei, M. Dinescu,

Additional information is available at the end of the chapter

F. Craciun and C. Galassi

http://dx.doi.org/10.5772/ 52395

**1. Introduction**

zation, 38 *μ*C/cm2