The chemical composition of the PZT-PZN-PMnN ceramics.
\r\n\t
",isbn:"978-1-83969-561-2",printIsbn:"978-1-83969-560-5",pdfIsbn:"978-1-83969-562-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"65f2a1fef9c804c29b18ef3ac4a35066",bookSignature:"Dr. Luis Loures",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10756.jpg",keywords:"Urban Processes, Urban Patterns, Redevelopment Strategies, Landscape, Land Transformation, Urban Models, Urban Evolution, Urban Organisation, Legislation, Sustainable Development, Green Infrastructure, Regional Planning",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 23rd 2021",dateEndSecondStepPublish:"March 22nd 2021",dateEndThirdStepPublish:"May 21st 2021",dateEndFourthStepPublish:"August 9th 2021",dateEndFifthStepPublish:"October 8th 2021",remainingDaysToSecondStep:"13 days",secondStepPassed:!1,currentStepOfPublishingProcess:2,editedByType:null,kuFlag:!1,biosketch:"Dr. Loures has worked on pioneering research on circular planning applied to post-industrial landscape redevelopment. Since he graduated he has published several peer-reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA) and at the University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"108118",title:"Dr.",name:"Luis",middleName:null,surname:"Loures",slug:"luis-loures",fullName:"Luis Loures",profilePictureURL:"https://mts.intechopen.com/storage/users/108118/images/system/108118.png",biography:"Luís Loures is a Landscape Architect and Agronomic Engineer, Vice-President of the Polytechnic Institute of Portalegre, who holds a Ph.D. in Planning and a Post-Doc in Agronomy. Since he graduated, he has published several peer reviewed papers at the national and international levels and he has been a guest researcher and lecturer both at Michigan State University (USA), and at University of Toronto (Canada) where he has developed part of his Ph.D. research with the Financial support from the Portuguese Foundation for Science and Technology (Ph.D. grant).\nDuring his academic career he had taught in several courses in different Universities around the world, mainly regarding the fields of landscape architecture, urban and environmental planning and sustainability. Currently, he is a researcher both at VALORIZA - Research Centre for Endogenous Resource Valorization – Polytechnic Institute of Portalegre, and the CinTurs - Research Centre for Tourism, Sustainability and Well-being, University of Algarve where he is a researcher on several financed research projects focusing several different investigation domains such as urban planning, landscape reclamation and urban redevelopment, and the use of urban planning as a tool for achieving sustainable development.",institutionString:"Polytechnic Institute of Portalegre",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"8",totalChapterViews:"0",totalEditedBooks:"2",institution:{name:"Polytechnic Institute of Portalegre",institutionURL:null,country:{name:"Portugal"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"10",title:"Earth and Planetary Sciences",slug:"earth-and-planetary-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"205697",firstName:"Kristina",lastName:"Kardum Cvitan",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/205697/images/5186_n.jpg",email:"kristina.k@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"53522",title:"The Use of Control Charts in the Study of Bitcoin’s Price Variability",doi:"10.5772/66360",slug:"the-use-of-control-charts-in-the-study-of-bitcoin-s-price-variability",body:'\nBitcoin is a virtual currency and a quite new phenomenon. It was created in 2008 by Satoshi Nakamoto, who published an article "Bitcoin: A Peer-to-Peer Electronic Cash System” in 2008, in which he described a concept of virtual, decentralized and independent means of payment, which is based on a cryptographic blockchain protocol [1]. His main idea was to build a currency based not on trust but on an algorithm, which cannot be influenced or manipulated. It was thought to be independent of any legal or governmental body. After the first release of bitcoin, by generating the ‘block genesis’ in 2009, this currency was gaining rapidly in popularity.
\nAs in September 2015 ca. 667 crypto currencies were established.[1] - Among them, bitcoin is considered to be the most popular and the most widely used. According to data published on bitinfocharts.com, bitcoin has the highest market capitalization of more than $7 billion, representing 89% of the total capitalization of all cryptocurrency. Further down are the Ethereum $574 million (7.1%), litecoin $179 million (2.2%) and Dash $39 million (0.5%). Data published by blockchain.info at the beginning of 2012 indicated that bitcoin had ca. 400 users. This number increased by ca. 970 k at the beginning of 2014 and reached ca. 8.5 m in September 2016 [2].
\nWithin 4 years since its creation, the European Central Bank (ECB) and other financial institutions still have not come to a final conclusion, as to the classification of bitcoin and other cryptocurrencies. They have not recognized virtual currency as money or as a commodity. As such, the current legislation does not regulate events resulting thereof. The official definition of a ‘virtual currency’ was set up by a European Central Bank in 2012 for the first time, according to which ‘a virtual currency is a type of unregulated, digital money, which is issued and usually controlled by its developers and used and accepted among the members of a specific virtual community’ [3]. This definition associated virtual currency with a virtual world in a strict sense and the connection to the real economy was nearly neglected. Nowadays, bitcoin is similar to other virtual currencies that can be traded or exchanged for real money and goods and is accepted by many merchants all over the world. That is why in 2016, the International Monetary Fund (IMF) has extended the definition specifying, that ‘virtual currencies can be obtained, stored, accessed and transacted electronically and can be used for a variety of purposes, as long as the transacting parties agree to use them’ [4].
\nAccording to the IMF, the impact of virtual currencies on the real economy and the financial system is limited. It is, however, possible that with the increase of trading volume and acceptability, virtual currencies can become a serious threat to the financial and banking sector. One of the obstacles to the development of bitcoin named by IMF is its unstable variability.
\nThe purpose of this study is to assess the validity of whether the dollar (USD) is more stable than the bitcoin (BTC) using xbar-s and CUSUM control charts. Depending on the outcome thereof, it will evaluate the concerns of sceptics pertaining to bitcoin and its further development and acceptance in the long term. If it turns out that the volatility of bitcoin does not deviate significantly from the volatility of dollar, then the fears of some financial institutions might appear to be valid.
\nBitcoin is gaining much more popularity not only among financiers but also among scientists. However, a limited number of scientific papers pertaining to cryptocurrency have been published. Given the above, the proposed content will be an important contribution to studies of both control cards and bitcoin. Current scientific achievements can be divided into four main fields of interest.
\nA general and theoretical background concerning the origin, formation and characteristics of bitcoin, e.g. [5–9].
A number of reports focusing mainly on issues relating to acquisition (mining), trade and broadly understood security, e.g. [10–15].
The third large group of articles concerns the regulatory environment, including tax-specific policies and possible solutions that regulate the functioning of cryptocurrency in the financial area, e.g. [16–18]. This group also includes various types of reports, publications or banks, financial institutions and government statements on bitcoin, i.e. European Central Bank [19–21] Congressional Research Service acting on the needs of the US Congress [22, 23], Canadian Central Bank [24–26].
The last group of papers focuses on the application of quantitative methods in the study of Bitcoin.
Generalized autoregressive conditional heteroscedasticity models (GARCHs) were applied to investigate similarities between bitcoin and both US dollar and gold [27, 28]. It was found that bitcoin-like other cryptocurrency tend to generate bubbles and that they do not have fundamental value [29]. Moreover, bitcoin fluctuations are characterized by sudden jumps and extreme pricing, which is characteristic for immature markets [30]. Autoregressive moving average and log-periodic power law models were applied to show that the price of bitcoin depends on the Chicago Board Options Exchange Index Volatility Index, which is indicative of speculation potential [31]. Other scientists argue that fluctuations in the price of Bitcoin are positively correlated with the amount of BTC users and are determined by the shocks of unknown sources of origin. The latter have an endogenous character and are not generated by the impact of specific variables, such as indexes S&P 500, gold rate against the US dollar or (XAU) and the Shanghai stock exchange index (SSE) [32]. According to Bouoiyour et al. [33], bitcoin’s price fluctuations are best characterized by a generalized hyperbolic distribution.
\nThe variability of bitcoin against the dollar in 2015 significantly decreased compared with the preceding period. The authors also claimed that bitcoin can be characterized by excessive asymmetry and the price is prone to the negative shocks negative than positive once.
\nStatistical process control (SPC) has found its application in many scientific areas. One of the tools, which are used by the SPC, is control charts (see \nFigure 1\n). A control chart (CC) is a graphical representation of a process. It presents an average value of the quality characteristics reflected on the chart by a central line (CL). Auxiliary lines, called upper control limit (UCL) and lower control limit (LCL), are used for the presentation of deviations from the mean of the process. Control limits are usually set as three times the standard deviation (3-sigma (σ) limits). The main idea behind control charts is to monitor an underlying process. If the observations fluctuate in a natural way within set advance control limits and if they do not reveal any specific patterns, then it is said that the process is under control. If, however, the monitored process breaks the established control limits, then it is understood that the process is out of control and specific actions should be launched to return the process under control. For further details considering control charts, please refer to Ref. [34].
\nControl chart scheme.
SPC uses different types of charts, depending on the type of data used. For the continuous data, the following charts dedicated to variables are used:
\nxbar-s charts (controlling the mean and standard deviation of a process),
xbar-r chart (calculating the mean and the range of a process),
charts for moving ranges, etc.
For data based on countcharts for attributes are applied, e.g. np chart, p chart, c chart, u chart, etc.
\nFor the purpose of this research, the following control charts will be applied, namely an xbar-s chart and a CUSUM with the moving range chart.
\nXbar-s charts are used to monitor the variation and mean of the process. If the sample size (n) is not constant and is relatively large (n > 10), in such a case xbar-s charts are preferable against xbar-R chart.
\nFor the unknown parameters of the s-bar chart and the variable sample size, the central line is defined as an average standard deviation for all samples (Eq. (1))
\nwhere m is the number of samples, n\ni is the individual sample size and s\ni is an individual value of standard deviation for each sample defined as \n
The upper (Eq. (2)) and lower control limit (Eq. (3)), which define the boundaries for the (3σ)-three-sigma control limits are calculated based on the following formulae:
\nwhere c\n4 is a constant.
\nSimilarly, the control limits are determined for the xbar chart, which accompanies the s-chart. The central line is calculated as an average value of the individual averages (Eq. (4))
\nThe three-sigma control limit is determined by the upper control limit (Eq. (5)) and the lower control limit (Eq. (6)) in the form:
\nIt is assumed that the underlying process is under control if it varies between defined control limits. The breach of any of the control limits points at the process being out of control.
\nMoving range chart enables to plot the sum of ranges of the adjacent pairs of observation within the investigated period. The central line (see Eq. (7)) is calculated as an average range of k-samples and the control limits (see Eqs. (8) and (9)) are set as m-times deviation from the average process range.
\nwhere R\n\ni\n is a range in sample i, k is the number of samples, m is a multiplier chosen to establish control limits, usually set to 3 and d\n3 is a constant and \n
CUSUM control charts plot the cumulative sum of deviation from the assumed target value (see Eq. (10)).
\nwhere C\n\ni\n is a cumulative sum, \n
If the process is under control, then a cumulative sum (C\n\ni\n) follows a random walk process with mean equals 0 [35]. It is assumed that the process is out of control, if the average values drift from the target value. If the values move in the positive direction, then the upper cumulative sum is written as in Eq. (11).
\nIf, however, they move into the negative values, then the lower cumulative sum is defined as in Eq. (12). Finally, if the process exceeds the decision interval, which is contained between the positive and negative sum, then it is assumed, that the process is out of control:
\nwhere k is a target value, \n
The main goal of this research was to compare the variability of two exchange rates: bitcoin to US Dollar (BTC/USD) and Euro to US Dollar (EUR/USD). The average exchange rates for the quarterly data between 2010 and 2016 will be taken into consideration. The final result of the appliance of the xbar-s chart for BTC/USD is presented in \nFigure 2\n.
\nxbar-s chart BTC/USD 2010-2016.
It is visible that the process is out of control and the layout of the chart is strongly affected by the significant volatility exchange rate increase in 2013. In the period before, it was a long run of very low prices. After the peak in 2013, the level of the exchange rate has never reached a comparable value. Taking the above into consideration, the whole investigated period should be divided into consistent and disjoint periods, i.e. the covering time before the positive price shock, namely the year 2013 and the period after 2013. An attempt to analyse the whole period can be misleading due to the faultily estimated control lines understood as a process average and standard deviation.
\nThe first studied period was the initial phase of the development of bitcoin. Within that time, the exchange rate has changed significantly, starting from 0.08 USD for 1 BTC, reaching 13.51 USD for 1 BTC at the end of 2012. The xbar-s chart (\nFigure 3\n) has generated the CL at the level of 0.62. The layout of the chart suggests that the process being out of control in the period reaching April 2011, when the average volatility was significantly under the LCL equalling to 0.31.
\nxbar-s chart BTC/USD 2010-2012.
This is justified, as within that time, the price was significantly lower than in other periods. Small changes in prices had almost no effect on volatility. The numbers for May and June have breached the UCL, which equals to 0.93. This peak was connected with strong price jumps, up to 18.50 USD for BTC. The other periods were relatively stable.
\nA permanent breach of control limits on both sides of CL may be observed, but the deviations are not essential. It is worth to mention that between the years 2010–2012, the graph may imply a pattern. The observed standard deviations tend to move in the same direction almost every 4 months. The extension to the bitcoin volatility analysis gives the MR chart (\nFigure 4\n) and CUSUM chart for the standard deviation (\nFigure 5\n). At the beginning of the investigated process, the exchange rate volatility was dropping constantly. Commencing in April 2011 it is starting to grow, in par with the price increase. After a strong peak in price, which has also a solid and positive effect on price volatility, the bitcoin faced a volatility decrease at the end of 2011, after which the process started to normalize. This phase lasted until the next shock at the end of 2012, where the volatility has started to grow again.
\nMR chart BTC/USD 2010-2012.
CUSUM BTC/USD 2010-2012.
In 2013, the BTC/USD sudden price jump was observed, which has affected the average price volatility strongly. Throughout the year 2013, the exchange rate was developing steadily (see \nFigure 6\n). The jump took place between October and November. In this period, exchange rate has risen from 155 to 870. The average price volatility for the year 2013 equals to 51.87. If only the first 10 months of the year were considered, then the CL would be at the level of 12.65.
\nxbar-s chart BTC/USD 2013.
Moreover, the MR chart (\nFigure 7\n) shows that within the period between January and October 2013 ranges have fluctuated at the zero line until the exchange rate jumps, which caused an increase of almost 150, thereby, the whole process is said to be significantly out of balance.
\nMR chart BTC/USD 2013.
Bitcoin development during the period (2014–2016) was more stable compared to the previous years. The value for the central line in s-chart (\nFigure 8\n) has declined to 28.4 compared with the year 2013. At the beginning and at the end of the investigated period the price fluctuations were observed. In January 2014, the exchange rate has reached the level of 649, which was the continuation of the price increase from the year 2013 and in 2016, when the price reached again the limit of 687 US Dollars for a Bitcoin.
\nxbar-s chart BTC/USD 2014-2016.
The s-chart has produced warning signals concerning a high volatility between February and May 2014 and for June 2016 by breaching the UCL (45.25), as well as signals for low volatility between March and September 2015 by breaching the LCL (11.53). This downturn shift in price was also reflected by the CUSUM chart (\nFigure 9\n).
\nCUSUM chart BTC/USD 2014-2016.
These have caused a shift in a process, which was followed by the constant movement with the decreasing tendency of deviations from the process mean until the end of the considered period.
\nThe USD/EUR exchange rate volatility seems to be more stable within whole investigated period (see \nFigure 10\n) compared to the results for BTC/USD (\nFigure 2\n). The CL generated by the s-chart was at the level of 0.012. The volatility during the years 2010 and 2011 passes the UCL. Global financial crisis has impacted EUR/USD exchange rates strongly. After the crisis hit Greece in 2009 it has moved on and inadvertently affected other European countries, e.g. Spain and Italy. This was the most significant and long-lasting process disruption signalled by the control chart. The other breaches, which appeared in 2014 and at the beginning of 2015, are very close to the LCL (= 0.0052) and UCL (= 0.02). The deviation from CL seems to be not substantial, especially considering the process standard deviation at the level of 0.002.
\nxbar-s chart EUR/USD 2010-2016.
This development was also reflected by the CUSUM chart (\nFigure 11\n), where mainly the above average values for the standard deviation were signalled in the year 2010 and the beginning of the year 2011. The rest of the process despite the visible downturn trend remained between the UCL (0.029) and LCL (−0.029).
\nCUSUM chart EUR/USD 2010-2016.
The central line, which reflects the average standard deviation for the entire process equals 0.1272. If the time after 2013 was considered, then the average standard deviation would be equal to 0.1040, hence both results were at a comparable level.
\nThe EUR/USD exchange rate volatility starting from June 2010 was in the downward trend, which ended in December 2014. The s-chart has produced warning signals for points beyond the control limits, which were set at a level of 0.02027 for the UCL and 0.00516 for the LCL, respectively. The first signals were produced for the period between August 2010 and October 2011. Strong fluctuations in this time were caused by weak economic data mainly from the United States. It is worth to mention that this was the period short after the economic crisis, when most of the world economies were unstable.
\nBitcoin, a virtual currency, seems to be a promising alternative to a traditional means of payment. According to a survey published by the IMF, bitcoin has many advantages like low transition costs. It offers the possibility to make transactions with countries with weak financial infrastructure and might contribute to transferring developed technologies and solutions to undeveloped countries. At this point, it is worth mentioning that the idea on which the bitcoin is based has a huge potential in many areas, such as banking, accounting, data gathering and transfer, etc. At the same time, it is not without flaws. Reports and surveys concerning bitcoin mention money laundering issues, low recognisability and lack of stability.
\nIn this chapter, an attempt was made to compare the exchange rate volatility between EUR/USD and BTC/USD. The analysis has shown that the EUR/USD exchange rate volatility is much more stable compared to the BTC/USD exchange rate. In the entire investigated period, the average exchange rate volatility was at the level of 0.013. The first period after the world crisis, when the international economy was unstable and USA has published economic reports below market expectations, the exchange rate volatility has recorded an increase and charts have produced warning signals for the process being out-of-control. In the remaining period, the exchange rate volatility development did not behave in an unpredictable pattern. The downward trend is visible, but no significant shocks were observed. The lack of sudden fluctuations characterises mature economies.
\nBTC/USD exchange rate volatility is developing in a completely different way. \nFigure 2\n shows three establishing phases of this virtual currency; the first one before 2013, when the price level and the overall recognition were nearly zero. The average volatility was equal to 0.6. This value was affected by the price increase from June 2011. In the year 2013, another strong price jump was visible, when the exchange rate has risen from 155 to 870. The third period under consideration was also susceptible to price shocks, namely at the beginning of 2014 and in June of 2016. This unexpected price increase has strongly affected the average exchange rate volatility of BTC/USD. What is positive, the declining tendency in volatility can observe.
\nIn 2013, the average process volatility including outliers caused by price jumps was equal to 51.8, between 2014 and 2016 it has decreased to 28.4. The xbar-s chart and MR-chart for BTC/USD have showed that except for the above-mentioned price fluctuations the process was most of the time under control. It is worth noting at this point that the range between the upper and lower control limits for the bitcoin is broad, which was caused by the extreme price movements. Because of this lack of stability, it is difficult to model bitcoin behaviour. As such, an attempt to forecast its future behaviour based on its past values would be impossible.
\nThe lack of BTC/USD exchange rate predictability and its excessive volatility causes that at least at this stage of development bitcoin cannot threaten the traditional and regarded as stable, currencies such as USD or EUR. It is also associated with a small recognisability and is still limited to a number of places where it can be exchanged or traded. The bitcoin’s founder Satoshi Nakamoto said that he is not sure if the bitcoin in this form will survive, but he is convinced that virtual currencies will exist in the future, in this form or in a different one, due to the increasing loss of confidence and trust among the business partners [36].
\nOver the years, piezoelectric materials have been heavily investigated for ultrasonic device applications. Of the many piezoelectric materials, Pb(Zr1−xTix)O3 (PZT)-based materials are more attractive for these applications, such as piezoelectric actuators, ultrasonic motors, and piezoelectric transformers [1, 2, 3, 4, 5, 6, 7, 8, 9]. As Pb(Mn1/3Nb2/3)O3 (PMnN), Pb(Zn1/3Nb2/3)O3 (PZN) have been found to be promising ferroelectric ceramics with good piezoelectric characteristics, high Curie temperature, they meet well with the requirements of ultrasonic transducer applications [6, 7, 8]. They are ferroelectric materials that have characteristics such as: high dielectric constant, the temperature at the phase transition point between the ferroelectric and paraelectric phase is broad (the diffuse phase transition), and a strong frequency dependency of the dielectric properties [6, 10, 11, 12]. The PZT-PZMnN ceramics, as one of PZT-Pb(B′, B″)O3 solid solutions, received more attention due to their high piezoelectric properties [6, 10, 11, 12, 13, 14]. So far, the sintering temperature of PZT-based ceramics is usually too high, approximately 1200°C [9]. To improve the sinterability and properties of lead piezoelectric ceramics, on the basis of the conventional solid phase sintering method, various advanced manufacturing techniques have been applied to the fabrication of lead ceramics such as the two-stage calcination method [15], high energy mill [16] and liquid phase sintering [9, 15, 17, 18, 19, 20], hot isostatic pressing, hot pressing, microwave sintering, and spark plasma sintering [17] has been used effectively. Among them, the liquid phase sintering is a simple and effective method of improving the properties of PZT-based ceramics, which is currently attracting the interests of many scientists [15, 16]. By using various additives, such as NiO, B2O3, Bi2O3, Li2CO3, BiFeO3, ZnO, CuO, and Bi2O3, many researchers have successfully decreased the sintering temperature of PZT-based ceramics [5, 6, 13, 14, 18, 19, 20, 21, 22, 23]. We also attempted decreasing sintering temperatures from 1150 to 930°C, which significantly improved the electrical properties of the ceramics. In these ceramics, Li2CO3 is considered as a liquid-phase sintering aid [5, 21, 24]. The addition of Li2CO3 improved the sinterability of the Bi0.5(Na0.8K0.2)0.5TiO3 ceramic samples and caused an increase in the density and grain size at a sintering temperature of 1100°C [19]. With increasing Li2CO3 content, the phase structure of the ceramics changed from rhombohedral to tetragonal, indicating that it is close to the morphotropic phase boundary (MPB) of this system.
In this chapter, in order to develop the composition ceramics for high-intensity ultrasound applications, xPb(ZryTi(1−y))O3-(0.925-x)Pb(Zn1/3Nb2/3)O3-0.075Pb(Mn1/3Nb2/3)O3 (PZT-PZN-PMnN) ceramics were fabricated by the B-site oxide mixing technique. The aim of the chapter was, first, to carry out a phase formation, piezoelectric, ferroelectric, and dielectric characteristics in a solid solution of PZT-PZN-PMnN. The compositions synthesized in this study were x = 0.65, 0.70, 0.75, 0.80, 0.85, and 0.90 in the ternary system, xPb(Zr0.47Ti0.53)O3-(0.925 − x)Pb(Zn1/3Nb2/3)O3-0.075Pb(Mn1/3Nb2/3)O3. Then detailed systematic structural analysis and the study of physical properties were carried out for x = 0.8 compositions by varying the value of y in the Zr/Ti ratio. This will help to better determine how variations in the phase content affect local atomic arrangements and hence the electrical properties; and, second, to study the effect of ZnO nanoparticles on the sintering behavior and electrical properties of 0.8Pb(Zr0.48Ti0.52)O3-0.125Pb(Zn1/3Nb2/3)O3-0.075Pb(Mn1/3Nb2/3)O3 piezoelectric materials; the application, fabrication of ultrasonic transducers are reported and discussed.
Lead-based mixed B-site cation perovskites of (B′, B″)O3-type exhibit diffuse phase transition (DPT) behaviors of broad dielectric constant spectra in contrast to the sharp phase transitions of Pb(Zr,Ti)O3 and PbTiO3 [25]. The complex perovskite compounds are difficult to synthesize by conventional solid-state reaction method owing to the formation of pyrochlore phases and reduction of desirable properties, such as the electromechanical coupling factor and dielectric constant, which originate from the perovskite structure [25]. The B-site oxide mixing technique (BO) [26, 27] (formation of a B-site precursor of (B′, B″)O2-type, followed by a reaction with PbO) has been applied to several complex perovskite compositions and the results are quite successful [22, 28, 29]. In the conventional method (MO), oxide powders of PbO, ZrO2, TiO2, ZnO, MnO2, and Nb2O5 were weighed and milled for 8 h. To identify the temperature for calcining PZT-PZN-PMnN, we investigated the data of thermal gravimetric (TG) and thermal analysis (DTA) of PZT-PZN-PMnN powder (Figure 1). As per the above results, the TG curve exhibits a linear decrease in the total mass of the studied powder. However, the DTA curve shows an endothermic peak from 739 to 840°C, corresponding to the ion evaporation. To ensure the phase creation in the sample, the mixture powder was calcined at temperatures a little higher than 850°C after being milled for 8 h and pressed into pellets [30]. Afterward, the calcined PZT-PZN-PMnN pellets were continued to be milled for 16 h and pressed into disk 12 mm in diameter and 1.5 mm in thick under 100 Tan/cm2.
TG/DTA curves for the powder mixture compositions.
In the B-site oxide mixing technique, in order to identify the temperature for calcining of (Zn,Mn)Nb2(Zr,Ti)O6 (BO), we investigated the data for thermal gravimetric (TG) and thermal analysis (DTA) of (Zn,Mn)Nb2(Zr,Ti)O6 powders, as shown in Figure 2. As per results, the TG curve of the mixture powder shows that the total mass of the studied powder decreases linearly. However, the DTA curve shows the endothermic peak at 978°C, corresponding to the temperature of powder evaporation. In order to ensure that the temperature is at least above 978°C for each powder grain, the mixture powder was calcined at little higher temperature of 1100°C [6, 11, 21, 22] after the powders of BO and PbO were weighed and milled for 8 h.
TG and DTA curves of (Zn,Mn)Nb2(Zr,Ti)O6 power at 10°C/min heating rate.
The powders were calcined at a temperature of 850°C for 2 h, producing the PZT-PZN-PMnN compound. The samples were sintered at 950°C for 2 h. Figure 3 shows the X-ray diffraction (XRD) patterns of the PZT-PZN-PMnN ceramics prepared by different methods. From X-ray diagrams, we can see that the BO sample has only pure perovskite phase with rhombohedral structure, and this was determined by the (200) diffraction peak observed near 44° with no splitting. As seen in Figure 4, the BO sample was almost fully dense, and the average grain size of the sample was large. However, in the MO sample, besides the perovskite phase with rhombohedral structure (Figure 3), there is a small pyrochlore phase. This is in good accordance with the microstructure (Figure 4). It is said that formation of the pyrochlore phase may be due to the steric and electrostatic interaction between the high polarization of the Pb2+ cation and the B-sites cation (Zn+2, Nb+5) [24, 27, 31].
X-ray diffraction diagram of the BO and MO samples.
Microstructures of BO and MO samples.
The crystalline structure of the sintered ceramics was analyzed by X-ray diffraction (XRD) analysis at room temperature. The surface morphology was examined using field emission scanning electron microscopy (SEM), X-ray energy dispersive spectra (EDS) was measured using a Hitachi S-3400N scanning electron microscope with an EDS system Thermo Noran, and the densities of the ceramic samples were measured by the Archimedes method from the ceramic samples weighed in air, in water and the density of water. The grain size is determined from SEM micrographs by a linear intercept method. The dielectric properties of ceramics (relative dielectric constant and dielectric loss) were measured with a HIOKI 3532 impedance analyzer. The electromechanical coupling factors kp, kt and piezoelectric constant (d31) were determined by the resonance method according to the IEEE Standard 61 using an impedance analyzer Agilent 4196B and RLC HIOKI 3532 [32, 33]. The ferroelectric properties were measured by applying the Sawyer-Tower method [34].
Lead-zinc niobate Pb(Zn1/3Nb2/3)O3 (PZN) materials were first synthesized in the 1960s [35, 36]. It is one of the well-known relaxor perovskite ferroelectrics exhibiting a diffused phase transition with a phase transition temperature around 140°C (Tm) [6, 12]. However, pure perovskite lead-zinc niobate ceramics are relatively difficult to prepare by conventional solid-state reaction method [37]. The addition of other perovskite materials such as PbTiO3, BaTiO3, and PbZr0.47Ti0.53O3 (PZT) is necessary to stabilize the perovskite structure for PZN ceramics [12, 25, 38, 39]. The B-site ions in the PZT perovskite structure (Zr4+, Ti4+) might have been partially substituted by the B-site ions of the relaxor-type PZN structure (Zn2+, Nb5+), which allowed the PZT-PZN solid-solution system to retain the perovskite structure and the high sinterability of lead-based relaxor ceramics [12, 25, 38, 39]. Based on the preparation of pyrochlore-free Pb(Ni1/3Nb2/3)O3 (PNN), Vittayakorn et al. [40] studied the effects of PZT contents on the dielectric and ferroelectric properties of 0.5PNN-(0.5 − x)PZN-xPZT ceramics. The results showed that the dielectric constant (εr), the remanent polarization (Pr), and Curie temperature (Tc) increase with the increase in PZT content. With the combination of the preeminent properties between PZT, PZN, and PMnN, the PZT-PZN solid-solution systems hope to achieve the prominent properties of normal ferroelectric PZT and relaxor ferroelectric PZN and PMnN, which could exhibit better piezoelectric and dielectric properties simultaneously. In this section, in order to improve electrical properties, we have prepared xPZT-(0.925 − x)PZN-0.075PMnN ceramics with the content of PZT from 0.65 to 0.90. The xPb(ZryTi(1−y)O3-(0.925 − x)Pb(Zn1/3Nb2/3)O3–0.075Pb(Mn1/3Nb2/3)O3 ceramic samples have been fabricated by the B-site oxide mixing technique as described in Section 2.
Figure 5 shows XRD patterns of the PZT-PZN-PMnN ceramics at various contents of PZT. As observed, all ceramics have pure perovskite phase with dominantly tetragonal structure. The lattice parameters (a, c) of the samples have been evacuated from the (002) and (200) peaks of diffraction patterns, which are shown in the inset of Figure 5. When PZT content increases, the tetragonality c/a ratio increases. According to the PbZrO3-PbTiO3 phase diagram, Pb(Zr0.47Ti0.53)O3 is the tetragonal phase (space group P4mm) near the morphotropic phase boundary region at room temperature (RT) [41, 42]. While Pb(Mn1/3Nb2/3)O3 is a cubic structure and the PZN composition was determined to be the rhombohedral (space group R3m) [36, 38]. Therefore, with increasing the molar fraction of PZT, the crystal symmetry of the PZT-PZN-PMnN should change due to the tetragonal distortions of PZT [6, 25, 40]. In order to determine what chemical composition of the PZT-PZN-PMnN ceramic changes during sintering, the EDS analysis is performed and is shown in Figure 6. The presence of lithium (Li) is not plotted here because its atomic number is low and the mass percentage is too small [43]. Table 1 also showed the comparison in the mass of Pb, Zr, Ti, Nb, Zn, and Mn elements between before and after sintering of the PZT-PZN-PMnN ceramics. It is quite clear that the chemical composition of the synthesized ceramic obtained by EDS analysis can roughly accord with the general formula of the material without Pb. The reason could be explained by the evaporation of PbO during sintering [6, 25, 31]. Therefore, it is necessary to add excess 5 wt% PbO to compensate for lead loss during sintering.
XRD patterns of PZT-PZN-PMnN ceramics at various contents of PZT.
EDS spectrum of 0.8PZT-0.125PZN-0.075PMnN ceramics.
Elements | The mass percentage of elements from the precursors | Mass percentage of elements from the synthesized ceramic |
---|---|---|
Pb | 64.4 | 57 |
Zr | 10.72 | 10.24 |
Ti | 6.10 | 4.97 |
Nb | 3.79 | 3.06 |
Zn | 0.83 | 0.59 |
Mn | 0.42 | 0.43 |
The chemical composition of the PZT-PZN-PMnN ceramics.
Figure 7 shows microstructures of the PZT-PZN-PMnN ceramics at various contents of PZT. The average grain size of these samples is increased with the increase of PZT content in Table 2. On the other hand, the average grain size is reduced when x increases above 0.8. These results are obviously consistent with the change in the density of PZT content of PZT-PZN-PMnN ceramics, as shown in Table 2.
Surface morphologies observed by the SEM of PZT-PZN-PMnN ceramics at various contents of PZT.
Samples | M65 | M70 | M75 | M80 | M85 | M90 |
---|---|---|---|---|---|---|
Average grain size (μm) | 0.56 ± 0.02 | 0.66 ± 0.02 | 0.90 ± 0.02 | 1.04 ± 0.01 | 0.85 ± 0.02 | 0.83 ± 0.03 |
The average density of ceramics (g/cm3) | 7.77 ± 0.02 | 7.78 ± 0.01 | 7.80 ± 0.01 | 7.81 ± 0.01 | 7.72 ± 0.01 | 7.69 ± 0.02 |
The average grain size of PZT-PZN-PMnN ceramics.
Table 2 shows the density of the PZT-PZN-PMnN ceramics as a function of the PZT content. With the increase of PZT content up to 0.8, the mass density of PZT-PZN-PMnN ceramics increases. It achieves a maximum value (ρ = 7.81 g/cm3, 96% of the theoretical density in which the theoretical density of ceramic is calculated using Eq. (1):
where n = number of atoms associated with each unit cell in ABO3, A = atomic weight, VC = volume of the unit cell in ABO3, and NA = Avogadro’s number.
This is explained by the content of PZT was added to the ceramic system is less than 0.8 mol, a large number of pores were present, indicating insufficient densification of the sample (Figure 7: some SEM for M70, M90 are missing and M75 is not good). As the PZT content increases, the ceramics became denser, and the sample was almost fully dense at a PZT content of 0.8 mol.
The PZT content dependence of the dielectric constant (εr), dielectric loss (tan δ), and mass density (ρ) of the PZT-PZN-PMnN ceramics at 1 kHz and RT is illustrated in Figure 8. It can be seen that dielectric properties are strongly influenced by the composition of the ceramics. When the content of PZT increases from 0.65 to 0.8 mol, values of εr increase and reach to the maximum of 1230 at 0.8 mol of PZT. Then, these rapidly decrease with increasing x, while tan δ decreases with increasing PZT content. The minimum tan δ of 0.005 is obtained at x = 0.8 and then increased. It could be explained by the combination of a large and homogeneous grain size and the highest densification for the composition of 0.8PZT-0.125PZN-0.075PMnN ceramic [22].
Temperature dependence of the dielectric constant and dielectric loss tan δ at 1 kHz of samples.
In order to characterize the dielectric loss of all samples, the measurement of dielectric constant dependent on temperature is carried out at 1 kHz, as shown in Figure 8. With increasing PZT content, the dielectric constant peak increases and becomes sharpened. Hence, the material properties change from relaxor ferroelectricity to normal ferroelectricity. The permittivity and the maximum temperature (Tm) of the ceramics are shown in Figure 9. It shows that the Tm increases with increasing PZT content and is in the range of 206–275°C. There is a difference between the phase transformation temperatures of PZN (Tm ~ 140°C) [36, 38, 40] and PZT (TC ~ 390°C) [25, 35], so it is significant to study the dependence of phase transition temperature of the PZT-PZN-PMnN ceramics on PZT content [40]. When the temperature is higher than Tm, the function ε(T) is out of order the Curie-Weiss law in the normal ferroelectric materials. The fact the relationship between dielectric constant (ε) and temperature (T) above Tm can be complied by the modified Curie-Weiss law for analyzing of experimental data [44] is shown as follows:
The plot of ln(1/ε – 1/εm) versus ln(T-Tm) of PZT-PZN-PMnN ceramics at 1KHz.
where C is the modified Curie–Weiss constant and γ is the diffuseness exponent, which changes from 1 to 2 for normal ferroelectrics to fully disorder relaxor ferroelectrics, respectively [44].
The slopes of the fitting curves (Figure 9) are used to determine the γ value of xPZT-(0.925 − x)PZN-0.075PMnN ceramics at 1 kHz. As can be seen in Figure 9, the γ changes from 1.70 to 1.88. Thus, it is indicated that the transitions are of a diffuse type and the ceramics are highly disordered.
To analyze the frequency dependence of Tm, it is necessary to use Vogel-Fulcher law [6, 45]:
where Tf is the freezing temperature, Ea is the activation energy for polarization fluctuation of a polar nanoregion, fo is a characteristic frequency or Debye frequency, and kB is the Boltzmann constant = 1.38 × 1023 J/K, and To = Ea/kB. Figure 10 shows the plot of ln(f) versus Tm as a function of the measured frequency of PZT-PZN-PMnN. The symbols are the experimental points, and the line is the corresponding fitting to the Vogel-Fulcher relationship as listed in Table 3.
The plot of ln(f) versus Tm as a function of the measured frequency of PZT-PZN-PMnN.
Samples | M65 | M70 | M75 | M80 | M85 | M90 |
---|---|---|---|---|---|---|
T0 (°C) | 398 | 254 | 302 | 331 | 217 | 253 |
Tf (°C) | 179 | 198 | 208 | 218 | 237 | 255 |
The value of fitting parameters to Vogel-Fulcher relationship.
The influence of Zr/Ti ratio on the structure of PZT-PZN-PMnN ceramics has been analyzed through the X-ray diffraction patterns (Figure 11). The patterns reveal a pure perovskite phase for all ceramic samples.
X-ray diffraction patterns of ceramics with different Zr/Ti ratio contents: M46 (Zr/Ti = 46/54), M47(Zr/Ti = 47/53), M48 (Zr/Ti = 48/52), M49 (Zr/Ti = 49/51), M50 (Zr/Ti = 50/50), and M51 (Zr/Ti = 51/49).
As can be seen, the tetragonality of PZT-PZN-PMnN ceramics decreased with increasing Zr/Ti ratio content through the c/a ratio decreases. According to Dixit et al. [46] and Kahoul et al. [47], the morphology of Pb(Zr,Ti)O3 ceramics is strongly dependent on the Zr and Ti content. The content of the rhombohedral phase gradually increases within decreasing the Zr content simultaneously, and the tetragonal phase gradually decreases. The morphological evolution with Zr contents in this work may be attributed to the increase of a rhombohedral phase in these ceramics [46, 47]. This may be because the large Zr+4 (0.86 Å) ions diffuse into the PZT-PZN-PMnN lattice to replace Ti4+ (0.61 Å), resulting in the increase in the lattice constant and a shift in the XRD peak position toward lower 2θ values, similar to our recent research [48].
Effects of the contents of Zr/Ti ratio on the microstructure development of the ceramics are shown in Figure 12. In general, surface ceramics with large grains and uniform microstructure were obtained in all samples, and the average grain size of samples is increased with the increasing content of Zr/Ti ratio. In conformity with the previous densification results, highly dense samples exhibited high degrees of grain close packing. However, some pores and abnormal grain boundaries were observed in Figure 12 (MZ50 and MZ51) and the average grain size is reduced.
Microstructures of samples with the different Zr/Ti ratio contents: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), and MZ51 (Zr/Ti = 51/49).
Figure 13 shows the temperature dependence of ε and tan δ of the ceramic samples measured at different frequencies (1 kHz–1 MHz). It can see that with the increase in Zr amount, the Tm temperature of ceramics decreases as indicated in Figure 14. This may explain that the Curie temperature of PbZrO3 ceramics is about 232°C [25], and it is lower than that of PbTiO3 ceramics, 490°C [49, 50]. It is due to the decrease of lattice parameters and bond lengths [46, 47].
Temperature dependence of relative dielectric constant ε and dielectric loss tan δ of samples at different frequencies: MZ46 (Zr/Ti = 46/54), MZ47 (Zr/Ti = 47/53), MZ48 (Zr/Ti = 48/52), MZ49 (Zr/Ti = 49/51), MZ50 (Zr/Ti = 50/50), and MZ51 (Zr/Ti = 51/49).
The Curie temperature Tm of PZT-PZN-PMnN ceramics with different amounts of Zr/Ti ratio.
In order to determine the piezoelectric properties of ceramics, resonant vibration spectra of the PZT-PZN-PMnN samples were measured at room temperature (Figure 15), and from these resonant spectra, the piezoelectric parameters of the samples, such as electromechanical coefficients kp, piezoelectric coefficients d31, mechanical quality coefficient Q m, and dielectric loss tan δ were determined (Figure 16). It can be observed that the kp, d31, Q m, and tan δ depend on the amount of the Zr/Ti ratio content. The piezoelectric properties of ceramics are markedly improved. The following optimized values were obtained at Zr/Ti = 48/52, kp = 0.62, d31 = 140 pC N−1, Q m = 1112, and tan δ = 0.005. This fact can be explained by the increased grain size effect and better modification of microstructure in ceramics [10, 25, 49, 50]. However, with the further increasing the Zr/Ti ratio content, the electrical properties of PZT-PZN-PMnN ceramics are reduced. The cause is due to an abnormal grain boundary, and the average grain size is also reduced, as shown in Figure 12.
The spectrum of radial resonance of MZ48 sample (at room temperature).
The values of kp, d31, Qm, and tan δ of the PZT-PZN-PMnN ceramic samples.
The P-E hysteresis loops of PZT-PZN-PMnN at room temperature are displayed in Figure 17(a), and Pr and Ec are presented in Figure 17(b). With the increase in Pr and the decrease in Ec, the ferroelectric properties of PZT-PZN-PMnN ceramics improve. With increasing of Zr/Ti ratio content, the value of Pr increases and reaches the highest value of 34.5 μC/cm2) at the Zr/Ti ratio of 48/52, and then decreases. The coercive field EC decreases slightly with the increasing of Zr/Ti ratio content and reaches the smallest value of 9.0 kV/cm at Zr/Ti ratio of 48/52.
(a) Hysteresis loops of samples and (b) Pr and Ec as a function of Zr/Ti ratios.
The effect of temperature on the ferroelectric properties of ceramics was studied by the hysteresis loops of the 0.8Pb(Zr0.48Ti0.52)O3–0.125Pb(Zn1/3Nb2/3)O3–0.075Pb(Mn1/3Nb2/3)O3 sample in the temperature range of 30–280°C (Figure 18(a)). The hysteresis loops of the ceramics exhibited excellent temperature stability due to the broad diffusive phase transition between the nonergodic and ergodic relaxor states that coexisted over a wide temperature range [51]. When the temperature increased from room temperature to 120°C, the remanent polarization and the coercive field increased (Figure 18(b)). The reason is when the temperature increases, the oxygen vacancies in the perovskite structure will move and significantly increase the conductivity of the material, which should increase the dielectric loss. However, when the temperature rises above 120°C, the remanent polarization Pr and the coercive field Ec decreased (Figure 18(b)). Generally, the size of the hysteresis loops depends on the dielectric loss of the material and the metastable macro-domain structure and the immobilizations of the domain walls [52]. Therefore, when the temperature increased, large thermal motion energy caused an increase in bipolar disorder, narrowed the hysteresis loops, and decreased the remanent polarization and the coercive field. In addition, the hysteresis loops showed that the Pr is nonzero at Tm but decays to zero at temperatures above Tm. These results are consistent with the literature [40].
(a) Hysteresis loops and (b) temperature dependence of Pr and EC of MZ48 sample at a different temperature.
In this section, in order to develop the composition ceramics for high-intensity ultrasound applications, 0.8Pb(Zr0.48Ti0.52)O3–0.125Pb(Zn1/3Nb2/3)O3–0.075Pb(Mn1/3Nb2/3)O3 + z wt% ZnO nanoparticles ceramics were fabricated by the B-site oxide mixing technique with the variations of z and then the phase formation, piezoelectric and dielectric characteristics were investigated with the variations of z. The general formula of the studied materials is 0.8Pb(Zr0.48Ti0.52)O3–0.125Pb(Zn1/3Nb2/3)O3–0.075Pb(Mn1/3Nb2/3)O3 + z wt% ZnO, where z = 0.0, 0.20, 0.25, 0.30, 0.35, 0.40, and 0.45. The obtained ZnO nanoparticles are spherical in shape, with their average diameter about 27 nm [9, 18]. On the other hand, reagent-grade oxide powders of PbO, ZnO, MnO2, Nb2O5, ZrO2, and TiO2 (purity ≥99%) were used as starting raw materials for the fabrication of the PZT-PZN-PMnN ceramics.
Figure 19 shows X-ray diffraction patterns of the PZT-PZN-PMnN ceramics at various contents of ZnO nanoparticles. All the compositions have demonstrated pure perovskite phases and no trace of the second phase. Further XRD analysis is performed in the 2θ ranges from 43 to 46°, as shown in the inset of Figure 19. It can be seen that a phase transformation from the rhombohedral structure to the tetragonal structure occurs with increasing ZnO content. The samples with z = 0.0 and 0.2 have the rhombohedral structure characterized by a peak (200)R at 2θ ≈ 44.5°. With z = 0.40 and 0.45, the ceramics exist as a tetragonal phase which is indicated by the splitting of (002)T and (200)T peaks in the 2θ range from 44 to 45° [23, 53, 54]. In the z range from 0.25 to 0.35, the ceramics coexist as rhombohedral and tetragonal phase, which is revealed by the coexistence of (002)T, (200)T, and (200)R peaks. Therefore, it could be said that the composition z from 0.25 to 0.35 is close to the morphotropic phase boundary (MPB) of this system. The phenomenon can be explained by the penetration of Zn2+ ions into the grains to substitute for B-site ions due to the similar radii of Zn2+ (0.074 nm), Ti4+ (0.0605 nm), Zr4+ (0.072 nm), and Nb5+ (0.064 nm) at the octahedral sites of the perovskite lattice, forming additional anionic vacancies. This causes a distortion in the lattice; therefore, the substitution of Zn2+ ions at Ti4+ or Zr4+ sites caused the c-axis to be lengthened and changed in lattice parameters and degree of tetragonality (c/a). These results are consistent with the literature [5, 19, 21, 48, 55].
X-ray diffraction patterns of PZT-PZN-PMnN ceramics at various contents of ZnO nanoparticles [9].
Effects of the contents of ZnO nanoparticles on the microstructure development of the ceramics are shown in Figure 20. As can be described in the microstructure of ceramics, the grain size of PZT-PZN-PMnN samples is increased with the increasing content of ZnO nanoparticles. This may explain that the low melting point of ZnO nanoparticles is beneficial to generate eutectic liquid phase at low temperature, and it can act as lubrication during the sintering process, wetting solid particles and providing capillary pressure between them, thus resulting in faster grain growth of PZT-PZN-PMnN ceramics [56, 57]. However, when the ZnO concentration is large, it exceeds the solubility limit of ZnO into the ceramics, and they will be located at grain boundaries preclude the grain growth process, as shown in Figure 20(d)–(f).
Microstructures of PZT-PZN-PMnN ceramics at different contents of ZnO nanoparticles: (a) 0.20 wt%, (b) 0.25 wt%, (c) 0.3 wt%, (d) 0.35 wt%, (e) 0.40 wt%, and (f) 0.45 wt%.
Figure 21 shows evolution examples of the ferroelectric domain with the rhombohedral to tetragonal phase transformation and the grain size of the PZT-PZN-PMnN samples of about 2 μm. The SEM images of the domain structure suggest the presence of 90 and 180° domains in the tetragonal phase (Figure 21(a)), whereas the 71, 109, and 90° domains are located in the red-bordered region and primarily viewed in Figure 21(b)), and the widths of these domains were about 100 nm. Inspection of SEM images acquired at lower magnifications showed that the abundance and scale of these microtwin structures varied with location both within and between ceramic grains, with abrupt changes in the domain structure occurring at the grain boundaries [58]. One of the important contributions from our experimental works is the confirmation of the SEM images by corrosion method as a valid method for domain size assessment in bulk ceramics.
The domain structures micrographs of the PZT-PZN-PMnN ceramics; (a) 0.4 wt% ZnO; (b) 0.35 wt% ZnO [9].
This chapter presents the investigation on the fabrication and characterization of sample groups of PZT-based ceramics and the relaxor PZN-PMnN ferroelectric materials with perovskite structure. The B-site oxide mixing technique reported in this study is simple, produces large quantities, and is easy to reproduce. Experimental results showed that the electrical properties of xPb(ZryTi(1−y))O3-(0.925 − x)Pb(Zn1/3Nb2/3)O3-0.075Pb(Mn1/3Nb2/3)O3 ceramics are optimal at a Pb(ZryTi(1−y))O3 content of 0.8 mol and Zr/Ti ratio of 48/52. At these contents, the ceramics have good electrical properties: d31 = 140 pC/N, kp = 0.62, kt = 0.51, Qm = 1112, tan δ = 0.005, and Pr = 34.5 μC/cm2. Investigation of the domain structure of the two ferroelectric phases (tetragonal and rhombohedral) in the PZT-PZN-PMnN with compositions at near the MPB is described as follows: the 90 and 180° domains exist in the tetragonal phase, while 71, 109, and 90° domains are located in the rhombohedral phase. The widths of these domains were about 100 nm. The hysteresis loops of the ceramics exhibited excellent temperature stability due to the broad diffusive phase transition between the nonergodic and ergodic relaxor states that coexisted over a wide temperature range, which makes it as a promising material for high-intensity ultrasound applications.
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.02-2017.308.
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\\n\\nThe first step in obtaining funds for your Open Access publication begins with your institution or library. IntechOpen’s publishing standards align with most institutional funding programs. Our advice is to petition your institution for help in financing your Open Access publication.
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\\n\\nFor Authors who are unable to obtain funding from their institution or research funding bodies and still need help in covering publication costs, IntechOpen offers the possibility of applying for a Waiver.
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\\n\\nThe application process is open after your submitted manuscript has been accepted for publication. To apply, please fill out a Waiver Request Form and send it to your Author Service Manager. If you have an official letter from your university or institution showing that funds for your OA publication are unavailable, please attach that as well. The Waiver Request will normally be addressed within one week from the application date. All chapters that receive waivers or partial waivers will be designated as such online.
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\n\nPlease consult our Open Access Funding page to explore some of these funding opportunities and learn more about how you could finance your IntechOpen publication. Keep in mind that this list is not definitive, and while we are constantly updating and informing our Authors of new funding opportunities, we recommend that you always check with your institution first.
\n\nFor Authors who are unable to obtain funding from their institution or research funding bodies and still need help in covering publication costs, IntechOpen offers the possibility of applying for a Waiver.
\n\nOur mission is to support Authors in publishing their research and making an impact within the scientific community. Currently, 14% of Authors receive full waivers and 6% receive partial waivers.
\n\nWhile providing support and advice to all our international Authors, waiver priority will be given to those Authors who reside in countries that are classified by the World Bank as low-income economies. In this way, we can help ensure that the scientific work being carried out can make an impact within the worldwide scientific community, no matter where an Author might live.
\n\nThe application process is open after your submitted manuscript has been accepted for publication. To apply, please fill out a Waiver Request Form and send it to your Author Service Manager. If you have an official letter from your university or institution showing that funds for your OA publication are unavailable, please attach that as well. The Waiver Request will normally be addressed within one week from the application date. All chapters that receive waivers or partial waivers will be designated as such online.
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