Open access peer-reviewed chapter

Effects of Doping and Oxygen Nonstoichiometry on the Thermodynamic Properties of Some Multiferroic Ceramics

Written By

Speranta Tanasescu, Alina Botea and Adelina Ianculescu

Submitted: March 23rd, 2011 Reviewed: April 29th, 2011 Published: August 23rd, 2011

DOI: 10.5772/16392

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1. Introduction

In order to find new ways to tune, enhance and optimize the properties of novel materials designed for different applications, the thorough knowledge of their thermodynamics is essential. The determination of the thermodynamic data and the thermochemical investigation of the formation reactions are essential for evaluating the long term stability and compatibility when the compounds are used in different applications. A careful search for experimental values is very important so much the more the literature is rather scarce as concerns the quantitative thermodynamic data for many multicomponent systems exhibiting balances of competing interactions. The focus of our present work is on multiferroic ceramics, which represents a "complex materials" class presenting a combination of magnetic and electrical properties which make the studies of novel multifunctional structures a very important issue of research.

BiFeO3 (BFO) of perovskite structure it is well known for its magnetic and ferroelectric ordering temperatures (TN~640 K, TC~1100 K) being one of the most attractive single phase multiferroic materials. For this reason there have been extensive studies of the structure, magnetic and electrical properties in bulk and in thin films, as well. Nevertheless, the wide potential for magnetoelectric applications of BFO may be inhibited because some major problems. Besides the small remanent polarization, the high coercive field and the inhomogeneous magnetic spin structure, the large leakage current it is still one of the major problems limiting device applications of BFO. The high conductivity and leakage found especially at higher temperatures were firstly considered caused by the high difficulty to produce single phase of BiFeO3 (Catalan, 2009; Carvalho, 2008; Mitoseriu, 2005; Yuan, 2006). Very small impurities or parasitic phases segregated at grains at boundaries could have a doping effect and transform the dielectric into a semiconductor. Besides, as in most ferrites, the leakage current in BiFeO3 could be attributed to the spontaneous change of the oxidation state of Fe (the partially reduction of Fe3+ ions to Fe2+) causing a high number of oxygen vacancies as a result of electrical neutrality requirement, giving rise to thermal activated hoping conductivity and resulting in low electrical resistivity (Palkar, 2002; Wang, 2004). Impurities and oxygen vacancies are also important for thin films, because they are known to artificially enhance the remanent magnetization (Catalan, 2009).

Forming binary solutions with other perovskites with good dielectric properties (like BaTiO3, PbTiO3 or LnFeO3) was explored as a possible route for diminish the mentioned problems (Buscaglia, 2006; Ismailzade, 1981; Ianculescu, 2008; Kim, 2004, 2007; Kumar, 1999, 2000; Singh, 2008, 2009; Zhu 2004, Prihor Gheorghiu, 2010; Wang, 2005). The coexistence of ferroelectric and magnetic properties in Bi1-xBaxFe1-xTixO3 materials was noticed up to high temperatures (Kumar, 2000). However, in the BiFeO3-rich region, these ceramics show weak magnetoelectric (ME) coupling effect, the problem of losses being only partially solved (Kumar, 1999).

The substitution of other elements for the Bi- and/or Fe-site was shown to enhance the ferroelectric and magnetic ordering in BiFeO3. Doping with small amounts of rare earths proved to suppress the inhomogeneity of magnetic spin structure, stabilizing macroscopic magnetization of BiFeO3 (Ivanova, 2003; Jiang, 2006; Sahu, 2007). Even though there are still questions about the structural evolution with composition (Catalan, 2009), previous studies on La-substituted BiFeO3 indicate the decreasing of TC and the increasing of TN with La concentration (Chen, 2008; Sahu, 2007). On the other hand, substituting with Mn in BiFeO3-based compounds was shown to improve the leakage current density and to induce changes in the magnetic order of the system, especially in the thin films (Azuma, 2007; Singh, 2007; Sahu, 2007; Habouti, 2007, Fukumura, 2009, Takahashi, 2007; Selbach, 2009, Wang, 2010). The simultaneous influence of La and Mn substitutions on the structural and functional properties of BiFeO3 was discussed in a few papers (Bogatko, 1998; Ianculescu, 2009, Gagulin, 1997; Habouti, 2007; Kothari, 2007; Palkar, 2003; Pradhan, 2008; Zheng, 2010). Very little work was reported on the thermodynamic behaviour in the co-doped (Bi,La)(Fe,Mn)O3 solid solutions (Gagulin, 1997; Tanasescu, 2010).

Recent investigations using advanced techniques, motivated by the prospect of new applications, have uncovered rich complexities that had not previously been recognized, when the development of new multifunctional bismuth ferrite perovskites, that combine sensitive responses to electric, magnetic, and stress fields, is intended [Ederer, 2005; Ramesh, 2007; Stroppa, 2010]. These phenomena occur at the crossover from localized to itinerant electronic behaviour and from ferroelectric (FE) to antiferromagnetic (AFE) displacive transitions, and are associated with dynamic, cooperative local deformations that are invisible to conventional diffraction studies. Due to the progress in methods for experimental analyzing distribution of elements at interfaces, some information has been accumulated on the chemical stabilities and properties of micro and nanostructured multifunctional materials. However the fundamental understanding was limited to rather simple cases. Such analyses need the thermodynamic data, because the driving forces for chemical reactions and diffusion can be given properly in terms of thermodynamic properties. This constitutes a considerable field of investigation, which is starting to be explored for both basic and applicative purposes (Boyd, 2011; Selbach, 2009; Tanasescu, 2004, 2008).

The present studies are focused upon the investigation of the effect of different compositional variables on the thermochemical properties and thermodynamic stability of multiferroic ceramics. Some compounds from specific systems were selected for discussion: multiferroic lead-free ceramics based on the (1-x)BiFeO3 - xBaTiO3 (0 x0.30) solid solutions and Bi1-xLaxFe1-yMnyO3 with x = 0.1; y = 0 - 0.5 perovskite-type materials.


2. Experimental

2.1. Sample preparation

(1-x)BiFeO3 – xBaTiO3 (0 x 0.30) ceramic samples were prepared by classical solid state reaction method from high purity oxides and carbonates: Bi2O3 (Fluka), Fe2O3 (Riedel de Haen), TiO2 (Merck) and BaCO3 (Fluka), by a wet homogenization technique in isopropyl alcohol. The place of the selected compositions on the BiFeO3 – BaTiO3 tie line of the quaternary Bi2O3 – BaO – Fe2O3 –TiO2 system is also presented in Fig. 1(a).

The mixtures were granulated using a 4 % PVA (polyvinyl alcohol) solution as binder agent, shaped by uniaxial pressing at 160 MPa into pellets of 20 mm diameter and ~3 mm thickness. The presintering thermal treatment was carried out in air, at 923 K, with 2 hours plateau. The samples were slowly cooled, then ground, pressed again into pellets of 10 mm diameter and 1- 2 mm thickness and sintered in air, with a heating rate of 278 K/min, for 1 hour at 973 and 1073 K, respectively (Ianculescu, 2000; Prihor, 2009; Prihor Gheorghiu, 2010).

Bi0.9La0.1Fe1−xMnxO3 (0 ≤ x ≤ 0.5) ceramics have been prepared by the same route, in the same conditions and starting from the same raw materials (Ianculescu, 2009). The place of the investigated compositions in the quaternary Bi2O3 – La2O3 – Fe2O3 – Mn2O3 system is presented in Fig. 1(b).

Figure 1.

Place of the investigated compositions: (a) Bi1-xBaxFe1-xTixO3 in the quaternary Bi2O3 – BaO – Fe2O3 –TiO2 system; (b) Bi0.9La0.1Fe1-xMnxO3 in the quaternary Bi2O3 – La2O3 – Fe2O3 – Mn2O3 system

2.2. Sample characterization

In both Bi1-xBaxFe1-xTixO3 and Bi0.9La0.1Fe1−xMnxO3 systems, the phase composition and crystal structure of the ceramics resulted after sintering were checked with a SHIMADZU XRD 6000 diffractometer with Ni-filtered CuK radiation ( = 1.5418 Å), 273.02 K scan step and 1 s/step counting time. To estimate the structural characteristics (unit cell parameter and rhombohedral angle) the same step increment but with a counting time of 10 s/step, for 2θranged between 293–393 K was used. Parameters to define the position, magnitude and shape of the individual peaks are obtained using the pattern fitting and profile analysis of the original X-ray 5.0 program. The lattice constants calculation is based on the Least Squares Procedure (LSP) using the linear multiple regressions for several XRD lines, depending on the unit cell symmetry.

A HITACHI S2600N scanning electron microscope SEM coupled with EDX was used to analyze the ceramics microstructure.

The solid-oxide electrolyte galvanic cells method was employed to obtain the thermodynamic properties of the samples. As shown in previous papers (Tanasescu, 1998, 2003, 2009) the thermodynamic stability limits of the ABO3-δ perovskite-type oxides are conveniently situated within the range of oxygen chemical potentials that can be measured using galvanic cells containing 12.84 wt.% yttria stabilized zirconia solid electrolyte and an iron-wüstite reference electrode. The design of the apparatus, as well as the theoretical and experimental considerations related to the applied method, was previously described (Tanasescu, 1998, 2011).

The measurements were performed in two principal different ways:

Under the open circuit conditions, keeping constant all the intensive parameters, when the electromotive force (EMF) measurements give information about the change in the Gibbs free energy for the virtual cell reaction. The EMF measurements were performed in vacuum at a residual gas pressure of 10-7 atm. The free energy change of the cell is given by the expression:

ΔGcell=μO2μO2(ref)= 4FEE1

where Eis the steady state EMF of the cell in volts;μO2, μO2(ref)are respectively, the oxygen chemical potentials of the sample and the reference electrode and Fis the Faraday constant (F=96.508 kJ/V equiv.).

By using the experimental values of the electromotive force of the cell and knowing the free energy change of the reference electrode (Charette, 1968; Kelley 1960, 1961), the values of the relative partial molar free energy of the solution of oxygen in the perovskite phase and hence the pressures of oxygen in equilibrium with the solid can be calculated:


The relative partial molar enthalpies and entropies were obtained according to the known relationships (Tanasescu, 1998, 2011):


The overall uncertainty due to the temperature and potential measurement (taking into account the overall uncertainty of a single measurement and also the quoted accuracy of the voltmeter) was ±1.5 mV. This was equivalent to ±0.579 kJ mol-1 for the free energy change of the cell. Considering the uncertainty of ±0.523 kJ mol-1 in the thermodynamic data for the iron-wüstite reference (Charette, 1968; Kelley 1960, 1961), the overall data accuracy was estimated to be ±1.6 kJ mol-1. For the enthalpies the errors were ±0.45 kJ mol-1 and for the entropies ±1.1 J mol-1 K-1. Errors due to the data taken from the literature are not included in these values because of the unavailability of reliable standard deviations.

By using a coulometric titration technique coupled with EMF measurements (Tanasescu, 2011), method which proved to be especially useful in the study of the compounds with properties highly sensitive to deviations from stoichiometry. The obtained results allow us to evidence the influence of the oxygen stoichiometry change on the thermodynamic properties. The titrations were performed in situat 1073 K by using a Bi-PAD Tacussel Potentiostat. A constant current (I) is passed through the cell for a predetermined time (t). Because the transference number of the oxygen ions in the electrolyte is unity, the time integral of the current is a precise measure of the change in the oxygen content (Tanasescu, 1998; 2011). According to Faraday's law, the mass change |Δm|(g) of the sample is related to the transferred charge Q(A sec) by:

|Δm|= 8.291·105QE5

As one can see, a charge of 1 10-5 A sec, which is easily measurable corresponds to a weight change of only 8x 10-10 g. This makes it possible to achieve extremely high compositional resolution, and very small stoichiometric widths in both deficient and excess oxygen domains can be investigated. Thus, the effect of the oxygen stoichiometry can be correlated with the influence of the A- and B-site dopants.

After the desired amount of electricity was passed through the cell, the current circuit was opened, every time waiting till the equilibrium values were recorded (about three hours). Practically, we considered that EMF had reached its equilibrium value when three subsequent readings at 30 min intervals varied by less than 0.5 mV. After the sample reached equilibrium, for every newly obtained composition, the temperature was changed under open-circuit condition, and the equilibrium EMFs for different temperatures between 1073 and 1273 K were recorded.

Differential scanning calorimetric measurements were performed with a SETSYS Evolution Setaramdifferential scanning calorimeter (Marinescu, in press; Tanasescu, 2009). For data processing and analyses the Calisto–AKTS software was used. The DSC experiments were done on ceramic samples under the powder form, at a heating rate 10°C/min. and by using Ar with purity > 99.995% as carrier gas. For measurements and corrections identical conditions were set (Marinescu, in press). The critical temperatures corresponding to the ferro-para phase transitions, the corresponding enthalpies of transformations as well as heat capacities were obtained according to the procedure previously described (Marinescu, in press; Tanasescu, 2009).


3. Results and discussion

3.1. BiFeO3-BaTiO3 system

3.1.1. Phase composition and crystalline structure

The room temperature XRD patterns (Fig. 2(a)) show perovskite single-phase, in the limit of XRD accuracy for all the investigated compositions after pre-sintering at 923 K/2 h followed by sintering at 1073 K/1 h and slow cooling. For all investigated ceramics, perovskite structure of rhombohedral R3c symmetry was identified, with a gradual attenuation of the rhombohedral distortion with the increase of BaTiO3 content. This tendency to a gradual change towards a cubic symmetry with the BaTiO3 addition is proved by the cancellation of the splitting of the XRD (110), (111), (120), (121), (220), (030) maxima specific to pure BiFeO3 (2 ≈ 31.5°, 39 °, 51°, 57°, 66°, 70°, 75°), as observed in the detailed representation from Fig. 2(b). The evolution of the structural parameters provides an additional evidence for the influence of BaTiO3 admixture in suppressing rhombohedral distortion (Fig. 3). Besides, the expansion of the lattice parameters induced by an increasing barium titanate content in (1−x)BiFeO3 – xBaTiO3 system was also pointed out (Prihor, 2009).

Figure 2.

a) Room temperature X-ray diffraction patterns of the (1−x)BiFeO3 – xBaTiO3 ceramics pre-sintered at 923 K/2 h, sintered at 1073 K/1 h and slow cooled; (b) detailed XRD pattern showing the cancellation of splitting for (1 1 1), (1 2 0) and (1 2 1) peaks, when increasing x.

Figure 3.

Evolution of the structural parameters versus BaTiO3 content.

3.1.2. Microstructure

Surface SEM investigations were performed on both presintered and sintered samples. The SEM image of BiFeO3 ceramic obtained after presintering at 923 K shows that the microstructure consists of intergranular pores and of grains of various size (the average grain size was estimated to be ~ 20 μm), with not well defined grain boundaries, indicating an incipient sintering stage (Fig. 4(a)). The SEM images of samples with x = 0.15 and x = 0.30 (Figs. 4(b) and Figs. 4(c) ) indicate that barium titanate addition influences drastically the microstructure. Thus, one can observe that BaTiO3 used as additive has an inhibiting effect on the grain growth process and, consequently, a relative homogeneous microstructure, with a higher amount of intergranular porosity and grains of ~ one order of magnitude smaller than those ones of non-modified sample, were formed in both cases analyzed here.

Figure 4.

Surface SEM images of (1-x)BiFeO3 – xBaTiO3 ceramics obtained after presintering at 923 K/2 hours: (a) x = 0, (b) x = 0.15 and (c) x = 0.30

BiFeO3 pellet sintered at 1073 K/1h exhibits a heterogeneous microstructure with bimodal grain size distribution, consisting from large grains with equivalent average size of ~ 25 m and small grains of 3 - 4 m (Fig. 5(a)). The micrograph of the ceramic sample with x = 0.15 (Fig. 5(b)) shows that the dramatic influence of the BaTiO3 on the microstructural features is maintained also after sintering. Thus, a significant grain size decrease was observed for sample with x = 0.15. Further increase of BaTiO3 content to x = 0.30 (Fig. 5(c)) seems not to determine a further drop in the average grain size. Consequently, in both cases a rather monomodal grain size distribution and relative homogenous microstructures, consisting of finer (submicron) grains were observed (Ianculescu, 2008; Prihor, 2009). Irrespective of BaTiO3 content, the amount of intergranular porosity is significantly reduced in comparison with the samples resulted after only one-step thermal treatment. This indicates that sintering strongly contributes to densification of the Bi1-xBaxFe1-xTixO3 ceramics.

Figure 5.

Surface SEM images of (1-x)BiFeO3 – xBaTiO3 ceramics obtained after presintering at 923 K/2 hours and sintering at 1073 K/1 hour: (a) x = 0, (b) x = 0.15 and (c) x = 0.30

3.1.3. Thermodynamic properties of Bi1-xBaxFe1-xTixO3

Of particular interest for us is to evidence how the appropriate substitutions could influence the stability of the Bi1-xBaxFe1-xTixO3 perovskite phases and then to correlate this effect with the charge compensation mechanism and the change in the oxygen nonstoichiometry of the samples.

In a previous work (Tanasescu, 2009), differential scanning calorimetric experiments were performed in the temperature range of 773-1173 K in order to evidence the ferro-para phase transitions by a non-electrical method. Particular attention is devoted to the high temperature thermodynamic data of these compounds for which the literature is rather scarce. Both the temperature and composition dependences of the specific heat capacity of the samples were determined and the variation of the Curie temperature with the composition was investigated. The effect of the BaTiO3 addition to BiFeO3 was seen as the decrease of the Curie transition temperature and of the corresponding enthalpy of transformation and heat capacity values (Tanasescu, 2009) (Fig. 6). A sharp decline in the TC was pointed out for BiFeO3 rich compositions (Fig. 6). In fact, the Cp of the rhombohedral phase (x = 0) is obviously larger than that of the Bi1-xBaxFe1-xTixO3 perovskite phases, whereas the Cp of each phase shows a weak composition dependence below the peak temperature. In particular, the value of Cp for x = 0.3 was found to be fairly low, which we did not show in the figure. The decreasing of the ferroelectric – paraelectric transition temperature with the increase of the BaTiO3 amount in the composition of the solid solutions with x = 0 0.15 indicated by the DSC measurements is in agreement with the dielectric data reported by Buscaglia et al (Buscaglia, 2006).

Some reasons for this behaviour could be taken into account. First of all, these results confirm our observations that the solid solution system BiFeO3 – BaTiO3 undergoes structural transformations with increasing content of BaTiO3. The decrease of the ferroelectric-paraelectric transition temperature Tc observed for the solid solution (1-x)BiFeO3xBaTiO3 may be ascribed to the decrease in unit cell volume caused by the BaTiO3 addition. Addition of Ba2+ having empty p orbitals, reduces polarization of core electrons and also the structural distorsion. The low value obtained for Cp at x = 0.3 is in accordance with the previous result indicating that ferroelectricity disappears in samples above x ~ 0.3 (Kumar, 2000).

Figure 6.

Variation of the Curie transition temperatureTC and of the heat capacityCp with composition. Inset: Variation ofTC and enthalpy of transformation for BiFeO3 rich compositions (x=0; 0.05; 0.1) (Tanasescu, 2009)

At the same time, the diffused phase transitions for compositions with x > 0.15 could be explained in terms of a large number of A and B sites occupied by two different, randomly distributed cationic specimens in the perovskite ABO3 lattice. Previous reports on the substituted lanthanum manganites indicate that the mismatch at the A site creates strain on grain boundaries which affect the physical properties of an ABO3 perovskite (Maignan, 2000). Besides, the role of charge ordering in explaining the magnetotransport properties of the variable valence transition metals perovskite was emphasized (Jonker, 1953). Investigating the influence of the dopants and of the oxygen nonstoichiometry on spin dynamics and thermodynamic properties of the magnetoresistive perovskites, Tanasescu et al (Tanasescu, 2008, 2009) pointed out that the remarkable behaviour of the substituted samples could be explained not only qualitatively by the structural changes upon doping, but also by the fact that the magneto-transport properties are extremely sensitive to the chemical defects in oxygen sites.

Though the effects of significant changes in the overall concentration of defects is not fully known in the present system of materials, extension of the results obtained on substituted manganites, may give some way for the correlation of the electrical, magnetic and thermodynamic properties with the defect structure. The partial replacement of Bi3+ with Ba2+ cations acting as acceptor centers could generate supplementary oxygen vacancies as compensating defects, whereas the Ti4+ solute on Fe3+ sites could induce cationic vacancies or polaronic defects by Fe3+ → Fe2+ transitions. The presence of the defects and the change of the Fe2+/ Fe3+ ratio is in turn a function not only of the composition but equally importantly of the thermal history of the phase. Consequently, an understanding of the high temperature defect chemistry of phases is vital, if an understanding of the low temperature electronic and magnetic properties is to be achieved. To further evaluate these considerations, and in order to discriminate against the above contributions, experimental insight into the effects of defect types and concentrations on phase transitions and thermodynamic data could give a valuable help.

For discussion was chosen the compound Bi0.90Ba0.10Fe0.90Ti0.10O3 for which strong magnetoelectric coupling of intrinsic multiferroic origin was reported (Singh, 2008). The results obtained in the present study by using EMF and solid state state coulometric titration techniques are shown in the following.

Figure 7.

Temperature dependence of EMF for Bi0.90Ba0.10Fe0.90Ti0.10O3

The recorded EMF values obtained under the open circuit condition in the temperature range 923-1273 K are presented in Fig. 7. The thermodynamic data represented by the relative partial molar free energies, enthalpies and entropies of the oxygen dissolution in the perovskite phase, as well as the equilibrium partial pressures of oxygen have been calculated and the results are depicted in Figs. 8-11. A complex behavior which is dependent on the temperature range it was noticed, suggesting a change of the predominant defects concentration for the substituted compound.

As one can see in Fig. 7, at low temperatures, between 923 and ~1000 K, EMF has practically the same value E=0.475 V. Then, Fig. 7 distinctly shows a break in the EMF vs. temperature relation at about 1003 K, indicating a sudden change in the thermodynamic parameters. A strong increase of the partial molar free energy and of the partial pressure of oxygen was observed until 1050 K (Figs. 8 and 9) which can be due to structural transformation related to the charge compensation of the material system. Then, on a temperature interval of about 40 K the increasing of the energies values is smaller. After ~ 1090 K a new change of the slope in the ΔG¯O2and logpO2variation is registered on a temperature interval of about 130 degrees, followed again, after 1223 K, by a sudden change of the thermodynamic data, the higher ΔG¯O2value being obtained at about 1260 K.

Figure 8.

Variation ofΔG¯O2with temperature - linear fit in the selected temperature ranges: 943-1003 K, 1003-1053 K, 1053-1093 K and 1093-1223 K

Figure 9.

The plot oflogpO2vs. 1/Tfor the selected temperatures ranges

The break point at about 1003 K is mainly due to first order phase transition in Bi0.90Ba0.10Fe0.90Ti0.10O3 associated with the ferroelectric to the paraelectric transition TC. The 10% BaTiO3 substitution reduces the ferroelectric transition temperature of BiFeO3 with about 100K. This transition is also evident from calorimetric measurements (Tanasescu, 2009). The less abrupt first order transition at 1050 K is qualitatively in concordance with the transition to thepolymorph which was previously identified in the literature for BiFeO3 at 1198-1203K (Arnold, 2010; Palai, 2008; Selbach, 2009).

In Fig. 10 we represented the partial molar free energies of oxygen dissolution obtained in this study for both Bi0.90Ba0.10Fe0.90Ti0.10O3 and BiFeO3 at temperatures lower than their specific ferroelectric transition temperatures. We would like to specify that in the case of BiFeO3, the EMF measurements were performed at temperatures not higher than 1073 K due to the instability of BiFeO3 at higher temperatures. As one can see in Fig. 10, at 923 K, the partial molar free energies of oxygen dissolution in BiFeO3 and Bi0.90Ba0.10Fe0.90Ti0.10O3 samples are near each other. With increasing temperature, the highest ΔG¯O2values were obtained for BiFeO3, suggesting an increased oxygen vacancies concentration in this compound. The result could be explained by the fact that at low temperatures the conduction is purely intrinsic and the anionic vacancies created are masked by impurity conduction. As the temperature increases, conduction becomes more extrinsic (Warren, 1996), and conduction due to the oxygen vacancies surface. This fact is also evident from the density measurements (Kumar, 2000), as well as electron paramagnetic resonance studies on perovskites (Warren, 2006). The increased concentration of oxygen vacancies in BiFeO3 is consistent with the large leakage current reported for BiFeO3 (Gu, 2010; Qi, 2005; Palkar, 2002; Wang, 2004). The electrical characteristics (Qi, 2005) indicated that the main conduction mechanism for pure BFO was space charge limited, and associated with free carriers trapped by oxygen vacancies. The coexistence of Fe3+ and Fe2+ causes electron hopping between Fe3+ and Fe2+ ions, oxygen vacancies acting as a bridge between them, which increases the leakage current. According to the defect chemistry theory, doping BiFeO3 with aliovalent ions should change the oxidation state of iron and the concentration of oxygen vacancies. Qi and coworkers (Qi, 2005) have suggested as possible mechanisms to achieve the charge compensation in the 4+ cation-doped material: filling of oxygen vacancies, decrease of cation valence by formation of Fe2+, and creation of cation vacancies. Based on our results, the doping with Ti4+ is expected to eliminate oxygen vacancies causing the decreasing of ΔG¯O2and logpO2values.

Figure 10.

Variation ofΔG¯O2with temperature - linear fit in the temperature range 943-1003 K for Bi0.90Ba0.10Fe0.90Ti0.10O3 (BFO-BTO) and 923-1073 K for BiFeO3 (BFO)

Further clarification could be achieved by determining ΔH¯O2and ΔS¯O2values in particular temperature ranges in which the partial molar free energies are linear functions of temperature. Comparing the values obtained for Bi0.90Ba0.10Fe0.90Ti0.10O3 in the temperature interval of 943-1003 K with the corresponding enthalpies and entropies values of BiFeO3 in the 923-1073 K range (Fig. 11) one can observe that for the substituted compound, ΔH¯O2and ΔS¯O2values strongly increase (with ~450 kJ mol-1 and ~480 J mol-1 K-1 respectively). This finding can be explained by the relative redox stability of the B-site ions which seems to modify both the mobility and the concentration of the oxygen vacancies. It is interesting to note that increasing temperature, after the first transition point, the enthalpies and entropies values strongly decrease (with ~ 468 kJ mol-1 and ~1.4 kJ mol-1 K-1 respectively) up to more negative values. The negative values obtained for the relative partial entropies of oxygen dissolution at high temperature are indicative for a metal vacancy mechanism. Above 1053 K both the enthalpy and entropy increase again with increasing the temperature. The thermal reduction for transition metals tends to be easier with Ba doping. These may explain the reason for the different behaviors at higher temperature zone. Besides, oxygen vacancy order also show contribution to the observed phenomena, the increasing of the enthalpy and entropy values being an indication that the oxygen vacancies distribute randomly on the oxygen sublattice.

Figure 11.

Formula:Eqn022andΔH¯O2as a function of BaTiO3 content (x) at temperatures lower than ferroelectric transition temperatures.

In order to further evaluate the previous results, the influence of the oxygen stoichiometry change on the thermodynamic properties has to be examined. The variation of the thermodynamic data of oxygen deficient Bi0.90Ba0.10Fe0.90Ti0.10O3-δ samples was analyzed at the relative stoichiometry change Δδ = 0.01. In Figures 12 (a) and (b), two sets of data obtained before and after the isothermal titration experiments are plotted. Higher ΔS¯O2and ΔG¯O2values are obtained after titration at all temperatures until 1223 K; above 1223 K, the values after titration are lower than the corresponding values before titration.

Figure 12.

Variation of (a)logpO2and (b)ΔG¯O2with temperature and oxygen stoichiometry change for Bi0.90Ba0.10Fe0.90Ti0.10O3

Regarding the changes of logpO2and ΔH¯O2corresponding to the temperature range of 1093-1223 K (Fig. 13), one can observe that for Bi0.90Ba0.10Fe0.90Ti0.10O3, both the variations of enthalpy and entropy decrease with the stoichiometry change suggesting the increase in the binding energy of oxygen and the change of order in the oxygen sublattice of the perovskite-type structure. The values of the relative partial entropies of oxygen dissolution are negative and this is indicative for a metal vacancy mechanism (Töfield, 1974). Due to the large decrease inΔS¯O2, it is considered that the oxygen vacancies would not randomly distribute on all of the oxygen sites but they would be distributed to some particular oxygen sites. It is also possible that the vacancy distribution is related to some crystallographic distortions or ordering of metal sites.

Figure 13.

Formula:Eqn031andΔS¯O2as a function of the oxygen stoichiometry change (Δδ = 0.01)

Presently, however, further details and measurements of the energy and entropy of oxygen incorporation into BiFeO3-based materials at different values of nonstoichiometry are necessary in order to make clear the vacancy distribution with the stoiochiometry change.

3.2. Bi1-xLaxFe1-yMnyO3 (x=0.1; y=0-0.5)

3.2.1. Phase composition and crystalline structure

The room temperature X-ray diffraction pattern obtained for the presintered sample corresponding to the mixture 1 (Bi0.9La0.1FeO3) shows a single phase composition, consisting of the well-crystallized perovskite phase (Fig. 14(a)). A small Mn addition (x 0.1) does not change the phase composition. The increase of the manganese amount to x = 0.2 determines the segregation of a small amount of Bi36Fe2O57 secondary phase identified at the detection limit. For x 0.4 also small quantities of Bi2Fe4O9 was detected as secondary phase, indicating the beginning of a decomposition process (Fig 14(a)).

From the structural point of view the XRD data pointed out that all the samples exhibit hexagonal R3c symmetry, similar to the structure of the paternal non-modified BiFeO3 compound. Similar to Bi1-xBaxFe1-xTixO3 solid solutions, the increase of the manganese content does not determine the change of spatial group. However, certain distortions clearly emphasized by the cancellation of the splitting of some characteristic XRD peaks take place. Thus, Fig. 14(b) shows the evolution of the profile and position of the neighbouring (006) and (202) peaks specific to the Bi0.9La0.1O3 composition when Mn is added in the system. One can observe that an amount of only 10% Mn replacing Fe3+ in the perovskite structure is enough to eliminate the (006) peak in the characteristic XRD pattern. A shift of the position of the main diffraction peaks toward higher 2 values was also pointed out (for exampe the (002) peak shifts from 2 = 39.5 ° for Bi0.9La0.1FeO3 to 2 = 39.82° for Bi0.9La0.1Fe0.5Mn0.5O3).

The increase of the manganese concentration determines the decrease of both a and c lattice parameters (Fig. 15(a)) and therefore a gradual contraction of the unit cell volume (Fig. 15(b)). This evolution suggests that most of the manganese ions are more probably incorporated on the B site of the perovskite network as Mn4+, causing the decrease of the network parameters because of the smaller ionic radius of Mn4+ (0.60 Å), comparing with that one corresponding to Fe3+ (0.64 Å). These results are in agreement with those ones reported by Palkar et al (Palkar, 2003).

Figure 14.

a) Room temperature X-ray diffraction patterns for Bi0.9La0.1Fe1-xMnxO3 ceramics thermally treated at 923 K for 2 hours; (b) detailed XRD pattern showing the disappearance of (0 0 6) peak

Figure 15.

Evolution of the structural parameters versus Mn content for the Bi0.9La0.1Fe1-xMnxO3 ceramics sintered at 1073 K for 1 hour: (a) lattice parameters and (b) unit cell volume

3.2.2. Microstructure

As for Bi1-xBaxFe1-xTixO3 ceramics, SEM analyses were performed firstly on the pellets surface thermally treated at 923 K/2h. The surface SEM image of the Bi0.9La0.1FeO3 sample indicates the obtaining of a non-uniform and porous microstructure, consisting from grains of variable sizes and a significant amount of intergranular porosity (fig. 16(a)). For the sample with x = 0.20, the presence of the manganese in the system induces the inhibition of the grain growth process and has a favourable effect on the densification (Fig. 16(b)).

Figure 16.

Surface SEM images of: (a) Bi0.9La0.1FeO3; (b) Bi0.9La0.1Fe0.8Mn0.2O3 and (c) Bi0.9La0.1Fe0.5Mn0.5O3 presintered at 925 K for 2 hours

The further increase of the Mn content to x = 0.50 enhances the densification, but seems to have not anymore a significant influence on the average grain size. Thus, the Bi0.9La0.1Fe0.5Mn0.5O3 ceramic shows a dense, fine-grained (average grain size of ~ 2 µm) and homogeneous microstructure with a monomodal grain size distribution (Fig. 16(c)).

The same trend of the decrease of the average grain size with the addition of both La and Mn solutes was also observed in the case of the ceramics sintered at 1073 K for 1 hour. Thereby, unlike the non-homogeneous, rather coarse-grained BiFeO3 sample (Fig. 5(a)), the average grain size in the La-modified Bi0.9La0.1FeO3 ceramic is of only ~ 4 m (Fig. 17(a)). The increase of Mn addition causes a further decrease of the average grain size to ~ 2 m and a tendency to coalescence of the small grains in larger, well-sintered blocks (Fig. 17(b) and 17(c)).

Figure 17.

Surface SEM images of: (a) Bi0.9La0.1FeO3; (b) Bi0.9La0.1Fe0.8Mn0.2O3 and (c)Bi0.9La0.1Fe0.5Mn0.5O3 ceramics sintered at 1073 K for 1 hour.

3.3.3. Thermodynamic properties of Bi1-xLaxFe1-yMnyO3 (x=0.1; y=0.2; 0.3)

Emphasizing the role of charge ordering in explaining the magnetotransport properties of the manganites, Jonker and van Santen considered that the local charge in the doped manganites is balanced by the conversion of Mn valence between Mn3+ and Mn4+ and the creation of oxygen vacancies, as well (Jonker, 1953). Investigating the influence of the dopants and of the nonstoichiometry on spin dynamics and thermodynamic properties of the magnetoresistive perovskites, Tanasescu et al (Tanasescu, 2008, 2009) demonstrated that the formation of oxygen vacancies and the change of the Mn3+/ Mn4+ ratio on the B-site play important roles to explain structural, magnetic and energetic properties of the substituted perovskite.

In BiFeO3-BiMnO3 system was already pointed out that, even though the Mn substitution does not alter the space group of BiFeO3 for x ≤ 0.3, the possible variation of the valence state of Mn manganese together the oxygen hiperstoistoichiometry as a function of temperature and oxygen pressure could affect the crystallographic properties, electrical conductivity and phase stability of BiFe1-xMnxO3+δ(Selbach, 2009). Excepting the communicated results on DSC investigation of Bi1-xLaxFe1-yMnyO3 (x=0.1; y=0-0.5) (Tanasescu, 2010), no other work related to the thermodynamic behaviour of Bi1-xLaxFe1-yMnyO3 were reported in the literature. In that study the evolution of heat of transformation and heat capacity in the temperature range of 573 – 1173 K was analyzed. The ferroelectric transition was shifted to a lower temperature for Bi0.9La0.1FeO3 comparative to BiFeO3, in agreement with literature data (Chen, 2008). However, a non-monotonous change of TC, as well as of the thermochemical parameters is registered for the La and Mn co-doped compositions, depending on the Mn concentration, comparatively with undoped BiFeO3. A sharp decline in the Tc was pointed out for x=0.3. One reason to explain this behavior is sustained by the structural results which were already pointed out in the previous section. The increase of the manganese concentration determines the decrease of both a and c lattice parameters and therefore a gradual contraction of the unit cell volume. This evolution suggests that most of the manganese ions are more probably incorporated on the B-site as Mn4+. Besides, as already was shown, in our samples the decreasing of the average grain size with the addition of both La and Mn solutes was observed in the case of presintered, as well as ceramics sintered at 1273 K (Ianculescu, 2009; Tanasescu, 2010). For finer particles where defect formation energies are likely to be reduced, the lattice defects, oxygen nonstoichiometry etc. appear to be sizable and significant changes in overall defect concentration are expected. So, an excess of Mn4+ ions and an increased oxygen nonstoichiometry are more likely. Due to the linear relationship between the Mn-O distortion and the Mn3+ content, one could expect to find in our samples a strong dependence of the energetic parameters on the Mn3+/ Mn4+ ratio and the oxygen nonstoichiometry.

In order to understand how the thermodynamic properties are related to the oxygen and manganese content in the substituted BiFeO3, the thermodynamic properties represented by the relative partial molar free energies, enthalpies and entropies of oxygen dissolution in the perovskite phase, as well as the equilibrium partial pressures of oxygen have been obtained in a large temperature range (923-1123 K) by using solid electrolyte electrochemical cells method.

The obtained results are plotted in Figures 18 - 20. At low temperatures, between 923 and ~950 K for x=0.3 and between 923 and ~1000 K for x=0.2, theΔH¯O2values are increasing with temperature (Fig. 18(a)). The same trend is accounted for the ΔS¯O2variation (Fig. 18(b)). The break points at ~963 K and ~993 K obtained for x=0.3 and x=0.2, respectively (Fig. 18 (a)) are consistent with the Tc values of ferro-para transition in substituted samples. These values are near the ferroelectric Curie temperatures reported in the literature for BiFe0.7Mn0.3O3 (926-957 K) and BiFe0.8Mn0.2O3 (~990 K) with no La addition (Selbach, 2009; Sahu, 2007). However we have to notice that at the same Mn concentration x=0.3, the Tc value is slightly higher for the sample in which lanthanum is present, comparatively with the sample without La.

In Fig. 19 we represented the partial molar free energies of oxygen dissolution obtained in this study for Bi0.9La0.1Fe0.8Mn0.2O3 and Bi0.9La0.1Fe0.7Mn0.3O3 samples at temperatures lower than their specific ferroelectric transition temperatures, and for comparison, the ΔG¯O2values of BiFeO3. As one can see in Fig. 19, the partial molar free energies of oxygen dissolution in the substituted samples are highest than thelogpO2values obtained for BiFeO3, suggesting the increasing oxygen vacancies concentration with doping. Determining the ΔG¯O2and ΔG¯O2values in particular temperature ranges until TC in which the partial molar free energies are linear functions of temperature (Figs. 19 and 20) one can observe that for the substituted compounds, the ΔH¯O2and ΔS¯O2values strongly increase in the doped compounds. Due to the relative redox stability of the B3+ ions (at the same A-site composition), both the mobility and the concentration of the oxygen vacancies will be modified. However it was noticed that the increase in B-site substitution from x = 0.20 to x = 0.30 at temperatures below 1000 K is followed by the decrease of ΔH¯O2and ΔS¯O2values with ~117.6 kJ mol-1 and ~126 J mol-1 K-1 respectively (Fig. 20), suggesting the increase of the binding energy of oxygen and an increase of order in the oxygen sublattice of the perovskite-type structure with the Mn concentration.

Figure 18.

Variation ofΔH¯O2(a) andΔS¯O2(b) with temperature and Mn content (x)

Figure 19.

Variation ofΔG¯O2with temperature - linear fit in the temperature ranges under the ferroelectric transition temperatures

Figure 20.

Formula:Eqn046andlogpO2as a function of Mn content (x) at temperatures lower than TC

After the ferroelectric transition temperatures and until 1043 K (for x=0.2), respectively until 1023 K (for x=0.3), a sharp decrease of theΔG¯O2values (Fig. 18(a)), together positive values of the enthalpies and entropies are revealed for both samples, indicating the decreasing of the thermodynamic driving force for oxygen vacancies formation and low ionic mobility. Taking into account the working conditions and the existing information as concerns the phase correlations of systems (Selbach, 2009, Carvalho, 2008), the dissociation reaction of the perovskite could be assumed to proceed in this temperature interval, Bi0.9La0.1Fe1-xMnxO3 being in equilibrium with other two solid phases, namely sillenite and mullite type-phases (Bi25Fe1-yMnyO39 and Bi2Fe4-zMnzO9, respectively). Increasing the temperature until 1083 K (for x=0.2) and 1073 K (for x=0.3), the equilibrium will be driven back to the perovskite formation, the ΔH¯O2values of the sample with x=0.3 keeping higher than those of the sample with x=0.2 (Fig. 18(a)). At 1083 K (for x=0.2) and 1073 K (for x=0.3), the registered ΔS¯O2values have practically the same values as for the samples before decomposition. The next phase transition registered at 1093 K for Bi0.9La0.1Fe0.7Mn0.3O3 is qualitatively in concordance with the transition to the polymorph which was previously identified in the literature for BiFeO3 at 1198-1203K (Arnold, 2010; Palai, 2008; Selbach, 2009) and for BiFe0.7Mn0.3O3 at 1145-1169 (Selbach, 2009). The temperature of transition to the γ phase corresponding to Bi0.9La0.1Fe0.8Mn0.2O3 could be higher than 1123 K; it was not registered in our present experiment because the highest temperature of these measurements was 1123 K.

The obtained results evidenced the complex behavior of the partial molar thermodynamic data in substituted samples, suggesting a change of the predominant defects concentration as a function of temperature range and Mn concentration. Increasing the manganese content, the decreasing of the ferroelectric Curie temperature and of the transition temperature from paraelectric to γ phase it is noted.

To further evaluate the previous results, the influence of the oxygen stoichiometry change on the thermodynamic properties has been investigated. The variation of the partial molar thermodynamic data of Bi0.9La0.1Fe0.8Mn0.2O3 (noted as BLFM0.2) and Bi0.9La0.1Fe0.7Mn0.3O3 (noted as BLFM0.3) was examined before and after two successive titrations by the same relative oxygen stoichiometry change of Δδ = 0.02 in the oxygen excess region (Figures 21 and 22). Thus, the effect of the oxygen stoichiometry can be correlated with the influence of the substituent.

Figure 21.

a) Variation ofΔG¯O2with temperature and oxygen stoichiometry change for Bi0.9La0.1Fe0.8Mn0.2O3+δ; (b)ΔG¯O2andΔG¯O2of Bi0.9La0.1Fe0.8Mn0.2O3+δas a function of the oxygen stoichiometry change (Δδ = 0; 0.02; 0.04)

Figure 22.

a) Variation ofΔG¯O2with temperature and oxygen stoichiometry change for Bi0.9La0.1Fe0.7Mn0.3O3+δ; (b)ΔH¯O2andΔS¯O2of Bi0.9La0.1Fe0.7Mn0.3O3+δas a function of the oxygen stoichiometry change (Δδ = 0; 0.02; 0.04)

For x=0.2 higher values of the partial molar thermodynamic data are obtained after titration (Fig. 21). It is expected that the change in ΔG¯O2with δ in this case to be essentially determined by the change in SO (config) and, therefore, the oxygen randomly distribute on the oxygen sites. Instead for x=0.3, both the variations of enthalpy and entropy decrease with the stoichiometry change (Fig. 22(b)), suggesting the increase in the binding energy of oxygen and change of order in the oxygen sublattice of the perovskite-type structure comparatively with the undoped compound. However it is interesting to note that the enthalpies obtained for x=0.3 after the first and the second titrations are near each other, suggesting a smaller dependence of the ΔH¯O2on the oxygen stoichiometry change at higher departure from stoichiometry. This result tends to agree with the assumption that metal vacancies prevail, since a value for enthalpy which is independent of nonstoichiometry is expected for randomly distributed and noninteracting metal vacancies (van Roosmalen, 1994; Tanasescu, 2005). The model based on excess oxygen compensated by cation vacancies and partial charge disproportionation of manganese ions was also proposed for other related systems, like LaMnO3+δ(van Rosmallen, 1995; Töpfer, 1997), BiMnO3+δ(Sundaresan, 2008), BiFe0.7Mn0.3O3+δ(Selbach, 2009), La0.5Bi0.5Mn0.5Fe0.5O3+δ(Kundu, 2008). However, the model could not explain the observed relationship in the entire oxygen-excess region. This statement was also discussed in the case of LaMnO3+δ(Mizusaki, 2000; Nowotny, 1999; Tanasescu 2005) and could be subject for further discussion.

Considering the partial pressure of oxygen as a key parameter for the thermodynamic characterization of the materials, we investigated the variation of ΔS¯O2with the temperature, oxygen stoichiometry and the concentration of the B-site dopant (Fig. 23). Before titration, the ΔS¯O2values of the Bi0.9La0.1Fe0.7Mn0.3O3 are higher than ΔH¯O2for Bi0.9La0.1Fe0.8Mn0.2O3, excepting the value at 1123 K which is smaller for x=0.3 comparatively with the corresponding value for x=0.2, the result being correlated with the structural phase transformation noted for the composition with x=0.3 under 1123 K.

Figure 23.

Variation oflogpO2with temperature and oxygen stoichiometry change

It is obtained that for both compounds, after titration, at the same deviation of the oxygen stoichiometry, logpO2shifted to higher values with increasing temperature. At the same temperature, the high deviation in the logpO2values with the stoichiometry change is obtained for the sample with x=0.2. Besides, at x=0.2, higher values of logpO2are obtained after the second titration, even though, increasing deviation from stoichiometry, a smaller increase of the partial pressure of oxygen was noted (Fig. 23). This could be explained by the fact that at high temperature, less excess oxygen is allowed. The sample with x=0.3 presents a smaller dependence of the logpO2on the oxygen nonstoichiometry. For small deviation from stoichiometry (Δδ=0.02), a small decrease in logpO2values is obtained, but after the second titration, the partial pressure increase again. At 1073 K, after the second titration, the same value as before titration is obtained. Increasing temperature to 1123 K, logpO2values increase again comparatively with the value before titration.

The obtained results could be correlated with some previously reported conductivity measurements. Singh et al (Singh, 2007) reported that small manganese doping in thin films of BiFeO3 improved leakage current characteristic in the high electric field region, reducing the conductivity; others authors noted the increasing of the conductivity with increasing manganese content (Chung, 2006; Selbach, 2009, 2010). If the polaron hopping mechanism is supposed for the electrical conductivity at elevated temperatures, the electronic conductivity will increase in the samples with hiperstoichiometry. According to the evolution of the partial molar thermodynamic data of the oxygen dissolution, a decrease in the oxygen ionic conductivity (together the increasing of the electronic conductivity due to the electron-hole concentration increasing) will result in the sample with increased Mn content.

Even though there are disagreements between different works regarding the nature and the symmetry of the high temperature phases in the pure and substituted BiFeO3, based on our data, we would like to point out that, in the condition of our experimental work, we may close to the stability limit of the Mn doped materials at temperatures around 1123 K. This is in accordance with theoretical consideration of the stability of ABO3 compounds based on Goldschmidt tolerance factor relationship (Goldschmidt, 1926). The evolution with temperature and oxygen stoichiometry of the thermodynamic data suggest that excess oxygen causing an increase of the tolerance factor of the system will lead to the stabilization of the cubic phase at lower temperature with increasing the departure from stoichiometry.

At this point further studies are in progress, so that correlations could be established with the observed properties at different departures of oxygen stoichiometry, in both deficit and excess region for Bi0.9La0.1Fe1-xMnxO3 materials.


4. Conclusions

Bi1-xBaxFe1-xTixO3 (0 ≤ x ≤ 0.30) and Bi0.9La0.1Fe1-xMnxO3 (0 ≤ x ≤ 0.50) ceramics were prepared by the conventional mixed oxides route, involving a two-step sintering process. Single phase perovskite compositions resulted for all the investigated ceramics, in the limit of XRD accuracy. For both cases, the presence of foreign cations replacing Bi3+ and/or Fe3+ in the perovskite lattice induces the diminishing of the rhombohedral distortion and causes significant microstructural changes, mainly revealed by the obvious decrease of the average grain size.

In order to evidence how the appropriate substitutions could influence the stability of the perovskite phases and then to correlate this effect with the charge compensation mechanism, the thermodynamic data represented by the relative partial molar free energies, enthalpies and entropies of the oxygen dissolution in the perovskite phase, as well as the equilibrium partial pressures of oxygen have been obtained by solid state electrochemical (EMF) method. The influence of the oxygen stoichiometry change on the thermodynamic properties was examined using the data obtained by a coulometric titration technique coupled with EMF measurements.

New features related to the thermodynamic stability of the multiferroic Bi1-xBaxFe1-xTixO3 and Bi0.9La0.1Fe1-xMnxO3 ceramics were evidenced, the thermodynamic behavior being explained not only by the structural changes upon doping, but also by the fact that the energetic parameters are extremely sensitive to the chemical defects in oxygen sites.

The decreasing of the ferroelectric – paraelectric transition temperature in the substituted samples was evidenced by both EMF and DSC measurements. Besides, the phase transition qualitatively corresponding to the phase transformation from paraelectric to a new high temperature phase was evidenced and the partial molar thermodynamic data describing the different phase stability domains were presented for the first time.

Bearing in mind the role of charge ordering and of the defects chemistry in explaining the electrical, magnetic and thermodynamic behavior of the doped perovskite-type oxides, it should be possible to find new routes for modifying the properties of these materials by controlling the average valence in B-site and the oxygen nonstoichiometry. Preparation method also strongly could influence the behavior of the powder in terms of non-stoichiometry, which ultimately will affect its electrical properties since they are dependent upon the presence of oxygen ion vacancies in the lattice. Besides the doping with various foreign cations, the decreasing of the grain sizes, as well as the thin film technology could be efficient methods for tuning the electrical, magnetic and thermodynamic properties of BiFeO3-based compounds to be used as multiferroic materials.



Support of the EU (ERDF) and Romanian Government that allowed for acquisition of the research infrastructure under POS-CCE O 2.2.1 project INFRANANOCHEM - Nr. 19/01.03.2009, is gratefully acknowledged. This work also benefits from the support of the PNII-IDEAS program (Project nr. 50 / 2007).


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Written By

Speranta Tanasescu, Alina Botea and Adelina Ianculescu

Submitted: March 23rd, 2011 Reviewed: April 29th, 2011 Published: August 23rd, 2011