Perovskite-Based Materials for Energy Applications

The role of energy in modern society is fundamental. Constraints due to the emissions of air pollutants from the excessive use of fossil fuels have increased dramatically in the last years. Over the years various devices and systems have been developed to transform energy from forms supplied by nature to forms that can be used by people. Another issue is to absorb energy generated at one time and to discharge it to supply power at a later time, what is called energy storage. This is also a matter to focus when it comes to searching for solutions of energy problems. Perovskites are promising key materials for energy applications, and in this chapter is a literature review summarizing the reported progress in energy applications of perovskite-type ceramic materials. To understand the fundamental nature of structure – property relationships, defect chemistry plays an important role. This paper, a mini-review, briefly describes from available literature and summarizes accordingly. It is focused on perovskite crystal structures, perovskite materials for solid oxide fuel cells, perovskite electrocatalyst and photocatalysts, and perovskite transport features.


Introduction
There is going to be huge demand for energy. The growing population and the growing of industrialization will increase the demand for energy. The world needs more energy to allow global living standards to continue to improve.
Currently most of our energy comes from fossil fuels, which originated from deep within the Earth's crust. This had disastrous effects on the planet because the burning of coal, oil, and gas has been linked to the rising levels of greenhouse gases on the Earth's atmosphere, generating climate change. The global energy landscape requires improvements. There is a slow going on transition to a more sustainable energy system. Not only to meet the need of rising energy demand but also in terms of policy, reducing carbon emission energy systems is the biggest challenges of our time.
Along with these challenges come opportunities-and that is what makes this a really exciting time for material science with respect to efficient and cost-effective energy conversion and energy storage. The process of changing energy from one form to another is energy conversion, and energy storage is the capture of energy produced at one time for use at a later time.
This work aims to provide an overview, based on available literature, of perovskite materials for energy applications and will focus especially on solid oxide fuel cells for efficient power generation from fuels and electrocatalysts for oxygen reduction reaction, oxygen evolution reaction, as well as on the defect chemistry in general of such materials. A large number of articles related on this topic have been published in the past decades. Unfortunately, it is not possible to cover all the aspects and references in the literature.
Due to their properties, the perovskite materials are of considerable technological importance covering a very broad range of practical applications. Notable is the discovery in the 1940s of the ferroelectric properties of barium titanate (BaTiO 3 ) used in electronics for capacitors and transducers [1]. In the mid-1980s, the first high-temperature superconductor was discovered, lanthanum barium copper oxide and, in 1987 Nobel Prize in physics, was awarded for this discovery [2]. As of 2012, perovskites have been identified as possible inexpensive base materials for highefficiency commercial photovoltaics, and perovskites also have optoelectronic properties such as strong light absorption and facilitated charge transport [3]. Some of perovskites' typical properties are ferromagnetism [4], piezoelectricity [5,6], electrical conductivity [7,8], superconductivity [9,10], ion conductivity [11,12], magnetism [13,14], catalytic properties [15,16], electrode materials [17,18], and optical [19,20].
This work will describe their defect chemistry which plays an important role in energy applications where the transport properties are the main players. Their defect chemistry is responsible for properties like ionic conductivity [21], mixed conductivity [22], proton conductivity [23], and catalytic conductivity [24] which make perovskite being used for solid oxide fuel cells (SOFC), electrolyte, SOFC electrode, and catalyst.

Perovskites and related structures
The perovskite structure is adopted by many compounds residing on the generic formula ABX 3 , the same type of crystal structure as calcium titanium oxide (CaTiO 3 ), constituting the family of perovskite compounds. We owe the discovery of perovskite to Gustav Rose, a German mineralogist who performed the studies in the Ural Mountains in Russia back in 1893. During that time, he identified perovskite, a naturally occurring oxide species, with the chemical formula CaTiO 3 and named it after Russian mineralogist Count Lev Alekseyevich von Perovski [25].
The ideal perovskite-type structure is cubic with space group Pm3m [26]. The positive charge B-type cations are occupying the centers of corner-shared octahedra of negative charge X-type anions such as oxygen halides, sulfides, or nitrides, and positive charge A-type cations are filling the resulting interstices. We restrict this  study to the oxide perovskites. In Figure 1a, alternative ways to view the perovskite structure are displayed: the cubic perovskite unit cell. Figure 1b emphasizes the octahedral coordination of the small cation. Green spheres represent A cations, blue spheres represent B cations, and red spheres represent oxygen anions forming an octahedron. Most perovskites are distorted and do not have the ideal undistorted cubic structure. Few perovskite compounds actually form the ideal cubic structure. The mineral perovskite itself, calcium titanate CaTiO 3 , is an orthorhombic distortion of the basic structure; strontium titanate SrTiO 3 is often used as the prototype.
The equation determined by Goldschmidt correlates geometrically crystal structures in terms of the ionic packing using the Goldschmidt's tolerance factor t [27]. Favorable for cubic perovskite structure is the tolerance factor having values between 0.8 and 1; otherwise the ideal cubic structure is a distorted structure. Empirical mathematical expression involving the unit cell length ratio, here r A , r B , and r O , is the ionic radii for A, B, and O, respectively; t is given as Cations with large ionic radius are occupying A sites, and cations with smaller ionic radius are occupying B sites. A and O form cubic closest packing, and B is in the octahedral voids in the packing. In an ideal structure, where the atoms are simply bonding to one another, the B-O distance is equal to a/2, whereas the A-O distance is equal to (a/√2) where a = length of unit cell.
The orthorhombic (Figure 2) and tetragonal (Figure 3) phases are the most common non-cubic variants [26] with octahedral distortions and translational A site offsets. As previously mentioned, green spheres represent A cations, blue spheres represent B cations, and red spheres represent oxygen anions.
Perovskites allow chemical tailoring because of the wide range of ions and valences which they can accommodate. By suitable formulation many valuable properties can be tailored. One interesting quality of perovskites is that they can accommodate more than one element for both A-and B sites constituting complex perovskites. These can be represented as (A 1 1 Substitutional aliovalent cations residing on the host cation sites generate oxygen vacancies. Furthermore for the B site, the element of transition metal can be in different oxidation states A(B' x B" y )O 3 , where x + y = 1. Aliovalent substitutions require a charge compensation mechanism because the ionic compound must be neutral. Therefore, either ion vacancies are created or one of the metals is partially or fully reduced or oxidized.
Another interesting and useful to deal with is the complex set of phase relationships. These are useful in such materials because they are sensitive to external conditions, including temperature, pressure, strain, and composition [28].
The perovskite structure also lends itself to the building of superstructures as seen in Figure 4. The Ruddlesden-Popper phases are a series of structures consisting of sequences of max 3 n; perovskite blocks are separated by a rock-salt structure block. The first member of the Ruddlesden-Popper series is A 2 BO 4 or ABO 3 -AO which is isostructural with potassium tetrafluoridenickelate (II) K 2 NiF 4 , the prototype structure.
A second family of superstructures are the Aurivillius phases ( Figure 5) [29]. This is represented by the general formula (Bi 2 O 2 )(A nÀ1 B n O 3n+1 ), where A is a large monovalent, divalent, or trivalent 12-coordinate cation and B is a small trivalent, pentavalent, or hexavalent metallic 6-coordinate cation. Basically, their structure is built by alternating layers of [Bi 2 O 2 ] 2 + and perovskite blocks (A n-1 B n O3 n+1 ) 2 that contain a layer of octahedral B sites.
Various synthesis methods have been developed for the preparation of perovskite materials while managing efficiently the environmentally friendly processing in conjunction with phase structure tailored to the needed properties. Small changes in the crystal will have a large impact on functional properties, crystallinity, and stability. Among these techniques, dry ways like solid-state reaction mechanochemical processing or wet routes like sol-gel and microwave methods are widely used.

Perovskite defect chemistry
In crystalline state an array of atoms is regularly repeated in three dimensions. This construction leads to a perfect crystalline solid with all atoms present and located in their ideal positions. However, a zero entropy is needed for the perfect crystalline state to exist. Above absolute zero temperature is a probability that defects from ideality will exist. All real materials contain defects. These defects, in terms of dimensionality, can be vacancies and interstitials which are point defects, dislocations which are line defects, and grain boundaries which are plane defects.
Point defects cause an increase of the configurational entropy contribution to the free energy at nonzero temperatures and will therefore always be present.
The formation of a point defect can be considered as a chemical reaction. At constant temperature, T, and pressure, p, the reaction is carried on in the direction that lowers the Gibbs free energy as follows: where H is the enthalpy, U is the internal energy, S is the entropy, and V is the volume. The enthalpy H is defined as The change in free energy for the formation of n independent defects can be written as follows: In the above equation, the configurational entropy Δ f S c is the part of the entropy change associated with randomly distributing n defect in the material. For a single defect, the formation free energy Δ f G is independent of the number of defects and can be written as follows: The point defects are a nonstoichiometric perturbation of the ideal lattice having or not electrically charge. Materials can also be prepared in such a way as to increase the number of defects.
There are two main categories for point defects: intrinsic defects and extrinsic defects. The intrinsic defects are internal to the crystal. The extrinsic defects are created when an impurity atom or ion is inserted into the lattice. The main categories of intrinsic defects are Schottky disorder and Frenkel disorder.
The Schottky disordering mechanism presumes that atoms leave their sites in the crystal bulk and rebuild the crystal lattice on the surface. As a result, the vacancies are formed in both cation and anion sublattices. According to the Frenkel mechanism, an atom moves from its regular site to the nearest interstitial position; hence, two types of defect are formed in the crystal, namely, the vacancy and the interstitial atom.
A vacancy is formed if an atom is not present on the site that it should occupy in a perfect crystal. By removing one atom from the chemical formula of perovskite, a set of vacancies called Schottky defect is created, which is the removal of an oxygen atom. Oxygen ion has a charged of À2. The defect left behind after removal, a charge of +2, for an oxygen atom will be V Ö in Kröger-Vink notation. The following equation is written for the creation of oxygen vacancy, Schottky disorder: V indicates a vacancy, the subscript O indicates the oxygen host site, and superscript denoted by two dots is the defect charge of +2.
An interstitial is an ion situated on any site that would be unoccupied in a perfect crystal. The interstitial is denoted by a subscript i, in Kröger-Vink notation. Frenkel defects deal with the displacement of the ions from its sites to interstitial sites.
When an ion is substituted with an ion of different valence, another type of point defect is created, called substitutional defect.
Defect chemistry complies with the conservation rules which indicate the charge conservation by maintaining crystal electrical neutrality overall, and the mass balance and host structure should be preserved.
The possible point defects in ABO 3 perovskite are the oxygen vacancies, A site vacancies, B vacancies, A interstitials, and B interstitials. The metal interstitial, B interstitial, defects are not energetically favored and less likely to be present.
Let us have a look at the LaCoO 3 simultaneous doping on the A site and B site, with Sr., respectively, Fe and Cr. This is a way to increase oxide ion conductivity and at the same time to retain the required thermodynamic stability of doped lanthanum cobaltite.
Substitution of Cr 3+ for Co 3+ in the LaCoO 3 results in the formation of Cr 4+ according to the reaction The charge disproportionation equation for Co site is A free electron in the conduction band and an itinerant hole in the valence band appear simultaneously.
Owing to its intrinsic zero-dimensional nature, a point defect, or any single atom, is difficult to observe experimentally, and much of the knowledge about point defects is inferred by implicit methods.

Perovskites transport properties
The key important factors for the ionic transport of perovskite materials are their defect chemistry and crystal structure. Point defects, mainly ionic defects, have major impact on transport properties like ionic diffusion and ionic conductivity. These properties are the most important in technical applications mentioned in this chapter, dealing with movement of ions within crystal.
Vacancies, interstitials, and substitutional defects can all be charged. The linear response that relates the current density to the applied field is the conductivity. This proportionality constant can be expressed as follows: where E is the applied electric field in V*cm À1 , I i is the current density for species i in A*cm À2 , and σ i is the conductivity σ i in 1*Ω À1 *cm À1 .
The charge may be transported by electrons or holes, by ions, or by both. There are also solids that exhibit simultaneously significant levels of both ionic and electronic transport and are referred to as mixed conductors, MIECs. While ionic conduction is mainly related to crystal structure, electronic conduction is determined by the electronic bandgap.
The conductivity is proportional to the concentration of charge carriers noted c i carriers/Volume; the charge they carry is z i e (C/charge), where e is the unit electronic charge, mobility noted μi, which is their ability to move in an electric field.
Having z i unit charges on the carrier is described for their mobility to move in an electric field by their mobility μ i ; the conductivity is described by the relations (11) where c i is the concentration of charge carriers per volume and z i e the charge they carry in C per charge.
In response to a concentration gradient, the system attempts to return to a homogenous equilibrium state by eliminating the gradient. The Fick's first law describes the unidirectional diffusion: (12) where dc i = dx is the concentration gradient of species i, J i is its flux in particles*cm À2 *s À1 , and D i is the diffusion constant in particles*cm À4 .

Perovskites in solid oxide fuel cell
A solid oxide fuel cell, SOFC, essentially consists of two porous electrodes separated by a dense, oxide ion-conducting electrolyte. The operating principle of such a cell is illustrated in Figure 6. The oxygen supplied at the cathode or, air electrode, reacts with incoming electrons from the external circuit to form oxide ions, which migrate to the anode or, fuel electrode, through the oxide ion conducting electrolyte. At the anode side, the oxide ions combine with H 2 , CO in the fuel to form H 2 O, CO 2 , with the effect of liberating electrons. Electrons flow from the anode through the external circuit to the cathode. To keep the cell resistance low, the electrolyte is fabricated in the form of a thin film.
Due to its operating conditions there are some limitations to materials used for SOFC.
These materials should be durable without changes of the required properties. Until now, there have been several researches to develop and fabricate materials to meet requirements of SOFC. Table 1 summarizes such perovskite materials accordingly to the SOFC component.
Electrolyte may carry either oxide ion O 2À or proton H + and should have high ionic conductivity and uniform features in structure. The important properties of cathodes are high electronic conductivity and thin porous layer where the oxygen reduction reaction takes place. The anode materials must be chemically compatible with electrolyte. Thermal expansion also is a requirement to match with electrolyte thermal expansion characteristics. The thermal expansion of solids depends on their structure symmetry and may be either isotropic or anisotropic. Properties like electrical conductivity, large triple phase boundary, and high electrocatalytic activity provide a mechanism for electronic conductivity, constituting important qualities to take in account from anode materials. Among the materials developed for SOFC components, (La, Sr)MnO 3 in air shows a conductivity of 300 S/cm [40],  (La, Sr)(Co, Fe)O 3 about 330 S/cm [41], and (La, Sr)CoO 3 about 1.22-1.60 S/cm [42,43]. (Pr, Ba, Sr)(Co, Fe)O 5 is a promising cathode material with power densities about 2.2 W/cm 2 at 600°C and has potential for commercially viable SOFC technologies [44]. The choice of material combinations for the SOFC components is crucial for determining their performances.

Perovskites in catalysis
Transition metal perovskites are important catalyst materials. The catalytic activity for perovskite materials often resides with metal oxide surface sites, and efficient use of the metals and space available requires small particles, located on a mostly inert support to enhance the thermal stability of the catalyst. Direct electrochemical water splitting is considered a key process in the development of novel energy storage systems, crucial for a sustainable and environmentally friendly energy economy. Water electrolyzers can convert water into hydrogen and oxygen through an electrochemical process, allowing H 2 to be stored as an energy vector as is seen in Figure 7.
However, the overpotentials at the anode side where the oxygen evolution reaction, OER, takes place are substantial, even when highly active, precious metal catalysts are used. Therefore, the development of anode materials based on inexpensive and abundant elements, displaying both high OER activity and stability, appears to be a crucial point toward the development of new-generation hydrogenbased storage systems. The values of OER activity about four times higher than that of bulk LaCoO 3 compound which was found to be 1.87 A/g were reported for porous and nanosphere LaCoO 3 . For porous LaCoO 3 , an OER activity of 7.51 A/g was reported, and for hollow LaCoO 3 nanospheres, an OER activity of 12.58 A/g was reported. Both values are at 1.60 V [45].
The oxygen evolution reaction OER in alkaline has the net reaction: Typically in electrocatalysis the ion of interest is the B site assumed to be an active site for OER. From a crystal field theory perspective, the octahedrally coordinated B site state d will split into several levels. The states of interest for catalysis will be the antibonding e g and t 2g states since they are typically the occupied states with highest energy and their filling will roughly determine the strength of the B-O bond. The OER activities of a series of perovskites were found to form a volcano trend when plotted versus the e g orbital filling determined using X-ray absorption nearedge structure (XANES) and spin states inferred [46]. Perovskites with an e g orbital occupancy of approximately 1 were found to be the most active. Based on this principle, highly active perovskite catalysts like Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3 with a conductivity of 8.58 Â 10 À5 S/cm, LaNiO 3 which has 2.39 S/cm, and LaCoO 3 can be used to rationally choose materials as candidates for promising OER catalyst [45,[47][48][49][50][51][52].

Perovskites in photocatalysis
In general, an efficient photocatalyst, also called an ideal semiconductor, should include light-harvesting and redox capabilities to facilitate the desired chemical reactions, thus achieving the targeted reaction. Inorganic semiconductor materials should have adequate capability to absorb solar energy across a broad spectrum. Because of their light-harvesting property, potential photocatalysts absorb solar energy, leading to the generation of photoelectrons in the conduction band and holes in the valence band for their possible use in redox reactions.
The redox nature of a photocatalyst as an intrinsic property dictates solar energy conversion efficiency. Most semiconductors include metals/mixed metal oxides used as efficient photocatalysts with the exceptional adaptability of their properties through compositional variations; perovskites show promise for solar hydrogen production among the large number of photocatalysts being explored. As example of photocatalysts can be mentioned perovskites with formula AFeO 3 , where A: La, Pr, Ce, and perovskites with formula LaBO 3 where B: Co, Mn, Fe [53][54][55]. Under visible light LaFeO 3 with a bandgap of 2.1 eV has an oxygen evolution rate of 331.5 μmol/h*g in ethanol [56]; SrTiO 3 with a bandgap of 3.2 eV has a rate of 18.8 μmol/h*g in ethanol [57]. Perovskite materials are also frequently explored in combination with other oxides to carry out various steps of complex uphill reactions involved in water splitting reactions. In Figure 8, the schematic of the reaction processes involved in overall water splitting is shown. When the energy of incident light is larger than that of a bandgap, electrons and holes are generated in the conduction and valence bands, respectively.
The perovskites tailored through bandgap engineering approaches can harvest solar light more effectively. Such perovskites show broadband absorption over the visible to near-infrared region of the solar spectrum. Another challenge related to the charge separation between photogenerated holes and electrons has also been undertaken with perovskite compositions to achieve overall improved efficiency.

Conclusions and outlook
In the last years environment-friendly and clean energy have attracted worldwide attention due to the growing concerns about global warming and other environmental issues associated with the heavy consumption of fossil fuels. Currently, new functional materials and adaptations to existing functional materials and their use are undergoing extensive investigation and have seen a remarkable development. Perovskites drive interest in their research investigations because the promise of their excellent features to be used in important technological devices such as the solid oxide fuel cell, water electrolysis, and photocatalysts.
We described the observed remarkable feature of adjustable structure properties for perovskites, leaving room for obtaining perovskite oxides with better functional performances. The perovskite structure is viable to wide departures in compositions from the ideal formula ABO 3 . The presence of defects can change the properties of the material. When these are properly controlled, defects are the material engineer's way of tuning material properties into wanted effects.
For real world applications, there are still some challenges to tackle in order to achieve the primary goal of the energy field when perovskites with different morphologies are the target materials. Oxide perovskite materials are a competitive alternative to low-cost non-noble metal-based functional materials with high activity and stability to replace the state-of-the-art material. Approaches to prepare perovskites are usually complicated and need harsh reaction conditions like high temperatures, in most of the cases. The large-scale synthesis of perovskites is also a great challenge to researchers since most work is still limited to laboratory scale. Therefore, searching for new facile and environmentally friendly approach to synthesize perovskites is still of great importance in this field.
It can be seen from the above discussion that there are many positive outcomes in the continuous development of perovskite materials rationally engineered by defect chemistry and controlled morphologies through the preparation methods. Great efforts are dedicated for the use of in-situ characterization techniques like X-ray diffraction or microscopy, so we can explain how structural modifications, alterations in the morphology, degradation speed of perovskite happened. Moving toward commercialization it is necessary to ensure low cost and long-term stability of materials which represent a significant active research direction.