Ruddlesden-Popper phase A2BO4 oxides: Recent studies on structure, electrical, dielectric, and optical properties

In the last two decades, structure and properties of Ruddlesden–Popper phase (RP) A2BO4 oxides with K2NiF4 structure, have been widely investigated. But to the best of our knowledge, no review article is available in the literature on recent studies on these oxides. Therefore, in this article, recent studies on structure, electrical, dielectric, and optical properties of these oxides have been reviewed. Special attention is put on to highlight the effect of doping and oxygen stoichiometry on the structure and properties of these oxides. Further, important applications of these oxides have also been mentioned in this article.

In the last several years, rapid growth in solar cells and optoelectronic devices based on 3D organicinorganic halide-based perovskites is observed. But their inherent instabilities over moisture, light, and heat strongly hindered this growth. Recently 2D organic-inorganic based layered perovskites received increasing attention owing to their superior ambient stability. These 2D perovskites have demonstrated to exhibit abundant and tunable optoelectronic properties, high quantum efficiency, and large specific surface area, which hold a good prospect for a range of electronic and optical applications [46,47].
During 1980-1990, Rao and his group [48,49] carried extensive research work on structure and magnetic properties of A BO oxides. Magnetic properties of these oxides were investigated more extensively than transport properties. They published a few review articles and chapters in the book on these oxides [50]. After observation of superconductivity up to 35 K in the Ba-doped La CuO ternary compound by George Bednorz and Alex Müeller of IBM Zurich Laboratory in 1986 [51], research works on A BO oxides further intensified. However, in the last two decades, these oxides have attracted attention because of their applications based on their electrical, optical, and dielectric properties. Recently two review articles have been published in the literature on diffusion/transport of oxide ion [52,53]. To the best of our knowledge, no recent review articles on the overall development of structure, properties, and applications of A BO layered perovskites are available in the literature. Therefore, in this article structure, electrical, dielectric, and optical properties of A BO along with various applications have been reviewed. In addition, various strategies for enhancing their properties using suitable doping at Aas well as B-sites are discussed. We expect that this article will intensify research on A BO layered perovskites and finally commercialization of devices based on these oxides.

Structure and oxygen stoichiometry
The A BO compounds crystallize in two major structural forms: T-type and T′-type [54]. The schematic structure of T-type La NiO ternary oxide is shown in Fig. 2(a). For clarity, only half cell ( /2 × /2 × ) is shown. The Ni cations are located at the center of apically elongated octahedra, also known as NiO octahedra; the six Ni − O distances are: Ni − O (O(1)) × 4 = 1.947 Å a n d Ni − O (O(2)) × 2 = 2.267 Å; two long distant atoms are along the -axis. The La cation is surrounded by nine oxygen atoms, four O atoms (in the same level of La atom), four O atoms (in Ni level, above (below)), and one O atom (head-below (head-above) from La atom). These nine O atoms make a LaO polyhedra. The La atom is not located at the center of this polyhedra, but it is little shifted towards the capping O . The NiO octahedra and LaO polyhedra share faces with each other and each NiO octahedra is connected with four nearest neighboring NiO octahedra in -plane by common shared O atoms. Each NiO octahedra with eight La atoms of O level makes a LaNiO perovskite unit. Between two perovskite units, there is a LaO rocksalt layer in -plane. Therefore, the www.springer.com/journal/40145 La NiO structure can be described as an intergrowth of an alternative layer of LaNiO perovskite and LaO rocksalt along the -axis. Thus T-type A BO ternary oxides are known as A BO layered perovskite or RP-phase layered perovskite. K NiF has a similar structure. Hence, this structure is also commonly referred as K NiF structure.
In contrast to T-type structure in T′-type structure, the cationic arrangement is the same, but the anionic arrangement is different [55]. Basal oxygens, O , do not change its position but apical oxygens, O , are shifted to the face of the unit cell, between the levels of cation A, designated as O . The schematic structure of T′-type Pr CuO ternary oxide is shown in Fig. 2 Fig. 2(a), so the structure of La NiO compromises the following sequences of layers.
The subscript o and c indicate whether the cation is at the origin or center of the mesh, respectively. Similar stacking of BO and A O bilayers in T′ -type structured Pr CuO is also schematically shown in Fig. 2(b). The A BO compounds also crystalize in T * -type of structure, which is a hybrid of Tand T′ -type structure [54]. Recently several research groups have investigated the Tand T′-type structures using well known Goldschmidt tolerance factor t as a criterion. The tolerance factor is based on the analysis of perovskite supercells (also known as perovskite tolerance factor) and given as follows [57]: where, , , and are ionic radii of cation A, cation B, and oxygen, respectively. The tolerance factor " " for Ttype structure is found in the range of 0.99 ≥ ≥ 0.87 while for T′ -type structure the tolerance factor lies in the range of 0.86 > ≥ 0.83.
Under high pressure, the lower limit of for T′-type structure extends up to 0.81. The T * -type structure exists for a narrow range of tolerance factors, lies in between the of Tand T′-type structure [54].
Most of the A BO layered perovskites crystallize either in orthorhombic structure or in tetragonal structure. The tolerance factor for tetragonal and orthorhombic structure lies in the range of 0.99 ≥ ≥ 0.88 and 0.88 ≥ ≥ 0.865, respectively [56]. The A BO layered perovskites can be further subdivided in two groups, one of which consists rare earth element (RE = La, Nd, Pr, etc.) as cation "A" and the other of which consists alkali earth element (AE = Ca, Sr, Ba) as cation "A". The layered perovskites consisting RE as cation "A", consist transition metal(s) (M = Ni, Cu, Co, etc.) in divalent state as cation "B" and the other group which consist AE as cation "A", consists of transition element(s) or post-transition element(s) ( M′ = Mn, Sn, Ti, etc. ) in the tetravalent state, as cation "B". These two groups of layered perovskites are named as RE MO , and AE M′O in this article, respectively. In recent years another group of A BO layered perovskites or doped A BO layered perovskites are also studied, which consist of both rare earth and alkaline earth elements in the form of cation "A" and cation "A′" in equal or unequal stoichiometries. The general structural formula for this group of compounds is sometimes written as "A A′ BO ". Majority of RE MO , crystallize in orthorhombic structure with space group , 4 / , , etc. while AE M′O crystallize in tetragonal structure with space group 4/ , 4/ , etc. There are also some exceptions as well, marked as "*" in Table 1, which do not follow this general categorization.
The other RE MO , with similar interlayer stresses as in La NiO , the systematic canting of MO octahedra are also there, to relieve interlayer stresses in their structure [56]. These distortions in the structure produced by the systematic canting of MO octahedra lead to the change in , 4 / , , and symmetries of the orthorhombic structure. The two nearest neighbor corner shared MO octahedra generally cant symmetrically in opposite directions about the fixed rotation axis, as shown in Fig. 3. The azimuthal orientation of rotation axes for neighboring planes of MO octahedra differ by 0° in , 90° in 4 / , and between 0° to 90° in . These octahedra canting symmetries are also characterized by long-range ordering. When either distortion is present or correlation length of canting is short, then the structure is best described by the symmetry. The symmetry is also used in assigning an average structure of the material, with uncharacterized incommensurate structure or presence of weak supercell having a dimension larger than √2 × √2 × [61].
Majority of A BO layered perovskites which crystallized in orthorhombic structure transform into the less ordered orthorhombic structure of space group above the room temperature and into a tetragonal structure at moderately high temperature. These structural transformations are referred by abbreviated name as LTO (Low-Temperature Orthorhombic), LTLO (Low-Temperature Less Orthorhombic), and HTT (High-Temperature Tetragonal) for general nomenclature [61]. At high temperature (above room temperature) above-mentioned stresses between the interlayers relaxed due to the thermal expansion of the unit cell and the MO octahedra aligned in tetragonal symmetry groups ( 4/ 4/ ). The alignment of MO octahedra disturb the periodic symmetry and produces structural transformations, initially in LTLO above the room temperature and finally in HTT at high moderately temperature. Stoichiometry of oxygen in the structure is also responsible for the structural transformation. But temperature-dependent structural transitions mentioned above are independent of oxygen stoichiometry due to the thermal expansion of unit cell [58,[60][61][62][63].
The A BO layered perovskites are generally synthesized via solid-state reaction method. During high-temperature synthesis processes ( > 1000 ℃ ), excess oxygens may accommodate in the structure at the interstitial sites and/or oxygen vacancies are created in the structure. These excess oxygens in the structure are accommodated in the form of doubly ionized oxide ions, O . In this article, Kröger-Vink notation has been followed to represent charge species and defects. In Kröger-Vink notation, the positively charged species are marked as "•" in superscript. Similarly, the negatively charged species are marked as " ′ " in superscript. When an oxide ion, O accommodates the interstitial sites, two excess holes, h • are created in the structure. Similarly, when an oxygen vacancy, V •• is created two excess electrons, e′ are created in the structure. Generation of these defects are represented by Eqs. (2) and (3) [64].
These excess holes may recombine with electrons or with divalent transition metal ions according to Eqs. (4) and (5), respectively; In RE MO , RE O bilayer is electropositive and MO layer is electronegative. Excess oxide ions mostly accommodate in the RE O bilayer interstitials and holes generally go in the MO layer due to their electropositive and electronegative nature, respectively. By this mechanism, excess oxide ions in the structure facilitate in neutralizing the electronic polarity of layers. It is also repoted that in RE MO oxides, excess oxide ions at interstitial sites minimize the electronic polarity between the RE O and MO intergrown layers [65,66]. There are also reports on RE MO , in which the creation of oxygen vacancies at basal oxygen sites, i.e., in MO layers is discussed [67]. The electronic polarity of intergrown RE O and MO layers, inhibits the creation of oxygen vacancy in RE O bilayer [66]. Location of oxygen vacancy and interstitial oxygen is schematically shown in Fig. 4 [66]. The oxygen stoichiometry of RE MO depends on the number of excess oxide ions at interstitial sites and number of oxygen vacancies in the structure. The interstitial oxide ions O , in RE O bilayers play crucial role in reducing the stresses produced by the above-mentioned mismatch On the accommodation of oxygen at interstitial sites, the electrostatic repulsion between O and neighboring apical oxygen O of RE O bilayer increases the lattice parameters " " and " " which facilitates to release of compressive and tensile stresses present in MO layer and RE O bilayer, respectively. It is also known that ionic radii of transition metal ions in lower oxidation state are smaller than their higher oxidation state. Hence, oxidation of transition metal ions reduces the effective interionic distances of M − O . Due to these two processes taking place simultaneously majority of RE MO oxides exhibit a structural transformation with increasing concentration of interstitial oxide ions [60,68,69]. For example, the hyper-stoichiometric (oxygen excess) La NiO ( 0.10 < < 0.15 ) transforms from orthorhombic to tetragonal phase [70]. The A BO layered perovskites also exhibit a structural transformation on becoming hypo-stoichiometric (oxygen deficient). For example, when Sr MnO becomes hypo-stoichiometric, i.e., Sr MnO . , transforms from tetragonal to monoclinic phase [71,72].
The oxygen stoichiometry in structure can also be tailored by substitutions at A and B sites. There are three kinds of substitutions (isovalent, donor, and acceptor) having been done in A BO layered perovskites. Further, in the case of isovalent substitution, substituted ion may have smaller or larger ionic radius than the host ion. Isovalent substitution of smaller ionic radii helps in increasing the void space of interstitial sites, thus, supporting accommodation of higher concentration of excess oxygen in the structure. The substitution of larger ionic radii has vice versa effect. The isovalent substitution also helps in increasing or reducing the above-mentioned stresses of intergrown layers, due to increment or decrement in interionic distances, respectively. For example, on substitution of Ni in La Cu Ni O oxygen content increases with the increasing content of Ni. The size of octahedra with Ni gets reduced due to the smaller ionic radius of Ni ( = 0.69 Å) as compared to Cu ( = 0.73 Å). Thus, void space in La O bilayer is increased and facilitates easier accommodation of O [68].
The donor substitutions are generally done in AE M′O by substituting RE ions at the AE site. The RE substitution creates excess electrons in the structure according to Eq. (6). These excess electrons may reduce M cation to M , according to Eq. (7). On account of this, the RE AE O rocksalt bilayer becomes electropositive and M′ M′ O becomes electronegative, which helps in accommodating more O in RE AE O rocksalt bilayers. For example, La Sr MnO , (0.25 ≤ ≤ 0.6) consist of excess oxygen in the structure as compared to Sr MnO [39]. Excess electrons created due to RE substitution do not only reduces M′ cations, but also some of them may recombine with excess holes (according to Eq. (4)) created by interstitial oxide ions (according to Eq. (2)). If these two processes of reduction of M cation and recombination of electron and hole occurring simultaneously (may make ≠ ), the concentration of reduced ′ ion can be different from twice of concentration of RE substituent.
The acceptor substitutions in RE MO have been made by replacing RE ions with AE ions. Acceptor dopants normally create excess holes in the structure according to Eq. (8). These excess holes recombine with neutral oxygen vacancies and help them stabilizing as V •• , according to Eq. (9). Another possibility is that these excess holes recombine with divalent (M ) ions to form trivalent ions (M ) as given by Eq. (10). The study of Nd Sr NiO ceramics confirms this hypothesis. This solid solution is an oxygen-deficient material and the content of oxygen decreases with increasing Sr content [73]. La Sr CuO was studied by Kanai et al. [74] as a function of Sr content, oxygen partial pressure, and temperature. This study shows that it is an oxygen deficient material for www.springer.com/journal/40145 > 0.5 in −6 < log( (O )/atm) < 0 partial pressure range at 900 ℃. The variation of oxygen content with oxygen partial pressure is shown in Fig. 5. Similar to Nd Sr NiO , La Sr CuO also becomes more oxygen deficient with increasing Sr content.

Electrical properties
In the beginning of twenty-first century A BO ± layered perovskites renewed their interest after the investigation of oxygen transport properties of La NiO ± at high temperature [75][76][77]. Electrical properties of A BO ± layered perovskites at low temperature were extensively studied after the discovery of superconductivity in La CuO ± . But in recent years, more attention has been focused on the study of high-temperature electronic and oxide ion transport properties of A BO ± layered perovskites. In this context, La NiO ± is widely studied for their phase stability, oxygen stoichiometry and high-temperature transport properties, and a comparative study with La CuO ± is established. La NiO ± shows a semiconductor to metal-like transition at 350 ℃ and have electrical conductivity 100 Ω · cm at transition temperature which is lower than electrical conductivity of mixed electronic-ionic conducting perovskite oxides [78]. However, oxide ion conductivity of La NiO ± in the intermediate temperature range is higher than that of mixed electronic-ionic conducting perovskite oxides. Skinner and Kilner [79] have shown that oxide ion conductivity is higher in La NiO than conductivity of La . Sr . Co . Fe . O (LSCF), but, one order lower than the best perovskite oxide ion conductor La . Sr . CoO (LSC) perovskite. Most of the undoped A BO layered perovskites are poor oxide ion conductor due to less oxygen vacancies and interstitial oxide ions [80]. As discussed in Section 2, on partial substitution the oxygen stoichiometry tunes, i.e., material either becomes hypo-stoichiometric or hyper-stoichiometric [39,81]. Oxygen vacancies in the structure provide necessary pathways for oxide ion migration via hopping through the vacant sites [82]. Generally, on acceptor substitution A BO layered perovskites becomes hypo-stoichiometric. But, sometimes even after substituting acceptor ions structure is hyper-stoichiometric. This is because of excess number of interstitial oxide ions than the oxygen vacancies in structure. The interstitial oxide ions also migrate in the structure and contribute to the oxide ion conductivity. Some of acceptor substituted hyper-stoichiometric structures show high mixed ionic and electronic conductivity [79]. The substitution of acceptor cations at A-site also promotes the oxidation of B-cation, according to Eq. (10). Partial oxidation of B-cation enhances the electrical conductivity. Electron bounded with unoxidized B-cation hops to neighboring oxidized B-cation. During this hopping process, the unoxidized B-cation oxidizes and oxidized B-cation reduces and becomes unoxidized. Similarly, hole bounded with oxidized B -cation hops to neighboring unoxidized B-cation, and during this hopping process, the oxidized B-cation reduces and unoxidized B-cation oxidizes. Sometimes these hopping processes, also produce a lattice distortion on local level at reducing and oxidizing B-cation sites, due to Jahn-Teller (JT) effect [39,83,84]. Thus, the hopping of electron/hole between the reduced and unreduced B-cation is different from the conduction of electron in metals and conduction of electron/hole in semiconductors. In some materials, local lattice distortion and electron/hole make a bound pair with each other (known as polaron), and conduction of these bound pair is known as polaronic conduction [19,85,86]. Further, when two polarons get closer and bound with each other to minimize their energy by sharing distortion with each other is known as bound bipolaron. Strongly bounded bipolarons are small in size and have integer spin, and thus, have bosonic properties. Formation of bipolarons without sharing distortion with each other is possible by Bose-Einstein condensation mechanism. This might be a possible mechanism for high-temperature superconductivity. The theme of this article makes this discussion out of the scope of this article.
There are various factors on which oxide ion conductivity in these oxides depends. Some of them are oxygen stoichiometry, temperature, oxygen partial pressure, mobility, etc. The dependence of oxide ion conductivity ( ) on temperature is represented by the Arrhenius relationship, given as follows [87]: ( 1 1 ) where and is a pre-exponential factor and activation energy of oxide ion migration, respectively. In Table 1, the values of activation energy and highest value of electrical conductivity (measured experimentally) along with their references are listed. In these studies migration of oxide ions have been emphasized. For example, in La Sr CuO the activation energy of oxygen diffusion decreases with increasing concentration of Sr upto ≤ 0.7 , and after that increases for 0.7 < ≤ 2.0. The increase in the value of activation energy is explained in terms of immobilization of oxygen vacancy due to cluster formation of defects with Cu or ordering of oxygen sublattices [88]. Bochkov et al. [89] studied on La Co Cu O solid solution and suggested that increasing Co at Cu increases the oxygen content and decreases the electronic conductivity. Oxygen permeation flux also increases with increasing Co concentration for 0.02 ≤ ≤ 10, and after that decreases with further increase in Co concentration, indicates the participation of interstitial oxide ions in oxide ion conduction. The dependence of oxide ion conduction on membrane thickness emphasized the role of surface exchange rates. Oxide ion diffusion is expected to occur via the interstitial oxygen migration mechanism. But, the oxygen permeability studies in La Ni . Fe . O and La Ni . Fe . Cu . O by Kharton et al. [90] demonstrated that both interstitial migration and vacancy diffusion mechanisms are contributing in total ionic conductivity.
It is noted that both oxygen hyper-stoichiometric (A BO ) and hypo-stoichiometric (A BO ) oxides consist oxygen vacancies, V •• and oxide ions, O as defects. Consequently, in these materials oxide ion conductivity is mediated by both oxygen vacancies and interstitial oxide ions. Therefore, the diffusion coefficient of oxygen is given as [91]: where and are diffusion coefficient of oxygen vacancy and interstitial oxide ion, respectively. Whereas, V •• and O represent concentration of oxygen vacancy and interstitial oxide ion, respectively. The oxygen diffusion in these materials is anisotropic in nature. Molecular dynamics (MD) studies of oxide ion conduction in La . Sr . CuO .
and LaSrCuO . showed that the mobility of oxygen species in La(Sr) O bilayers and CuO is significantly different and later being more favored for oxide ion conduction [92,93]. Opila et al. [88] have reported the anisotropic nature of oxygen diffusion in -plane (basal plane) and along -axis in La Sr CuO . Atomistic computer simulation of oxide ion conduction mechanisms in tetragonal La NiO was done by Cleave et al. In this study, a number of vacancy pathways within the ab-plane and along the c-axis were considered. Interstitial migration of oxide ion according to interstitial migration mechanism was also considered. This study showed that the activation energy for oxide ion migration via vacancies is lower than the activation energy for migration of oxide ions via interstitial sites. In vacancy mechanism the activation energy for oxide ion migration within the -plane among equatorial sites is 0.55 eV and via apical sites is only 0.35 eV. And, if an oxide ion moves from equatorial site to a vacant site at apical site it has to overcome an energy barrier of 0.77 eV. Whereas, in interstitial migration mechanism oxide ion has to overcome an energy barrier of 0.86 eV for their migration in -plane [82]. Chroneos et al. [94] investigated the conduction pathways of interstitial oxide ions and vacancies in stoichiometric tetragonal La NiO by MD simulation method. This study also shows that the vacancy migration mechanism in -plane is a most favorable mechanism of the oxide ion conduction with the migration activation energy of 0.51 eV in a temperature range of 500 − 800 ℃. Oxygen stoichiometry does not affect activation energy very significantly. Experimental studies on polycrystalline La NiO by Sayers et al. [95] predicted that the activation energy for oxygen migration is 0.54 eV. This is consistent with the most recent MD studies by Chroneos et al. [94]. increased the interest of researchers towards investigation of dielectric properties of RP phase oxides including A BO oxides [114][115][116][117]. Although, in recent years La NiO has been widely investigated for its mixed ionic and electronic conducting (MIECs) properties useful for SOFCs. But dielectric properties of doped and undoped La NiO oxides have also been investigated due to their very large (giant/colossal) value of the dielectric constant in the wide range of temperature and frequency. Due to high value of dielectric constant these oxides have immense potential for their applications in modern microelectronics and for the development of capacitor-based energy storage devices [118].
Till date the origin of colossal dielectric constant (CDC) is highly debated. Many authors, as Lunkenheimer et al., Sinclair et al., and Cohen et al. assigned the origin of CDC to extrinsic effects, i.e., to Maxwell-Wagner (MW) interfacial polarization at sample-electrode/grain-grain boundary interfaces [114,[119][120][121]. Interfacial polarization or space charge polarization occurs when conducting charge carriers traveling within the grains get pile up at grain-grain boundary interfaces due to insulating nature of grain boundaries. However, some authors claim that intrinsic effect, i.e., small polaronic hopping and hence charge ordering is responsible for the colossal dielectric constant (CDC) [122][123][124]. There is also another group of authors, who believe that both intrinsic as well as extrinsic effects are responsible for CDC in different range of temperature and frequencies [17,[124][125][126]. Dielectric properties of La NiO oxide have been further modified by substituting different alkaline earth metals (Ca, Sr, and Ba) at La site. Chouket et al. [124] studied LaSrNiO , and reported dielectric relaxation phenomenon. They attributed dielectric relaxation phenomenon to small polaronic hopping process due to closeness of activation energies of relaxation time and bulk electrical conduction. However, a large difference in activation energies of bulk and grain boundaries electrical conduction confirmed the existence of the MW effect in the ceramic. In another studies on Mn-substituted LaSrNi Mn O nickelates, they have reported two dielectric relaxation processes in two different temperature ranges [125]. The relaxation process occurring between 200 and 300 K was attributed to MW polarization due to conducting (grain) and insulating (grain boundary) regions. A weaker relaxation process below 150 K was ascribed to charge ordering. Equivalence in activation energies of low temperature and high frequency dielectric relaxation time and bulk electrical conductivity calculated according to small polaronic model confirms the role of adiabatic small polaronic hopping process in dielectric relaxation. Song . have studied dielectric properties of La . Ba . NiO ceramics prepared by spark plasma sintering (SPS) process. In this oxide also two dielectric relaxation processes were observed. The lower temperature relaxation process was credited to the charge ordering and high temperature one to the Maxwell-Wagner polarization. Although the dielectric loss of La . Ba . NiO is lower than that of some Sr substituted nickelate ceramics, but still it is not suitable for the practical applications due to high dielectric loss [127]. Shi et al. [128] have reported colossal dielectric properties in La Ca NiO . Among all the samples, at 1 MHz La . Ca . NiO has the highest value of dielectric constant ( = 5103) whereas La . Ca . NiO has the lowest loss. Doping of Ca effectively increases the and reduces the dielectric loss. Fan et al. [21] tried to explain the dielectric loss from the relationship of two polar-phonon modes and structure. According to their theory, dielectric loss is influenced by  [129]. They reported that this sample retains its colossal dielectric constant well into the technically required gigahertz frequency range. The dielectric properties of La / Sr / NiO are superior to other colossal dielectric materials, including most investigated CaCu Ti O (CCTO). Wang et al. [126] studied dielectric properties of the A / Sr / Ni Al O (A = La, Nd; = 0.2, 0.3) solid solution. They ascribed giant dielectric response of composition with = 0.3 to the adiabatic small polaronic hopping process, because the value of activation energy of dielectric relaxation and bulk electrical conduction is very close. However, in the composition with = 0.2, both dielectric relaxations were observed, attributed to adiabatic small polaronic hopping process and MW effect. In all the above-mentioned studies on dielectric properties of undoped, doped, and co-doped La NiO oxides, low temperature (< 150 K) dielectric relaxation process is attributed to small polaronic hopping mechanism based on the closeness of activation energy values of bulk conductivity and dielectric relaxation. Similarly, high temperature ( > 150 K ) dielectric relaxation process is ascribed to Maxwell-Wagner polarization based on the closeness of activation energy values of grain boundaries conduction and high-temperature dielectric relaxation.
The contribution of oxygen vacancy in the giant dielectric constant of Sm . Sr . NiO has been studied by Liu et al. [130]. The giant dielectric response in as-sintered Sm . Sr . NiO ceramic is directly linked to the small polaronic hopping process, while in the annealed sample it is linked to oxygen vacancy concentrations. Annealing in a nitrogen gas atmosphere increases the oxygen vacancies in Sm . Sr . NiO , and consequently, the dielectric constant at low temperature is decreased and increased at high temperature. However, the dielectric loss is increased in the overall temperature range. Dielectric studies in oxygen hyper-stoichiometric Nd NiO ceramic by Liu et al. [19] confirmed the similar mechanism of dielectric relaxation. In hyper-stoichiometric ceramics, excess holes are generated in the structure according to Eq. (2), as mentioned in Section 2. As the content of excess oxygen decreases the concentration of excess holes also decreases and hence the activation energy of dielectric relaxation at low temperature increases. These studies reveal that the dielectric properties of A BO strongly depends on oxygen stoichiometry.
Jia et al. [16] studied the effect of polaronic concentration on dielectric properties of Mn-substituted Sm . Sr . NiO ceramics. They have reported that the dielectric loss decreases with increasing content of Mn ions at Ni sites. At low temperature, on increasing content of Mn ions at Ni sites polaron concentration decreases and its size increases leading to increase in the value of dielectric constant and decrease in the dielectric loss. The change in the microstructure of La . Sr . Ni Ga O ceramic as a function of concentration of Ga has been carried out. The substitution of Ga in La . Sr . Ni Ga O ( = 0, 0.1, 0.3) has remarkably influenced the microstructure and increased the value of total resistance [131]. Due to increase in the value of resistance of La . Sr . Ni Ga O , its dielectric constant has increased and loss has decreased significantly.
The studies of La . Sr . Ni Ga O also highlighted the effect of sample electrode interface polarization on the dielectric properties. The effect of DC bias on non-ohmic sample-electrode contact and grain boundary responses were studied in Mg substituted La . Sr . Ni Mg O ceramics by Meeporn et al. [43]. For undoped La . Sr . NiO , capacitance " " decreases with increasing DC bias voltage and follows the Mott-Schottky law which confirmed the effect of sample electrode interface on the dielectric properties. However, for Mg substituted La . Sr . Ni Mg O the decrease in " " values with increasing DC bias voltage does not follow the Mott-Schottky law, indicating negligible contribution of sample electrode interface polarization. This decrease in capacitance " " is attributed to significant increase in the resistance of grain boundaries on Mg substitution.
The dielectric properties of manganite A BO oxides were also studied. In Sr Mn . Ti . O only one high temperature (above 453 K ) dielectric relaxation is present, which is attributed to the MW polarization. The low-temperature dielectric relaxation generally originated from adiabatic small polaronic hopping process is absent in Sr Mn . Ti . O . It was observed that in Sr Mn . Ti . O both titanium and manganese ions are in "4+" oxidation state that is why the concentration of oxygen vacancies and polarons in the unit cell are almost zero [132]. It is important to notice here that the dielectric constant of Sr Mn . Ti . O is not as high as of doped and co-doped La NiO . This is because degree of polyhedral distortions in Sr Mn . Ti . O is much less as compared with doped/co-doped La NiO . Further, it is observed that when all the "B" cation are in the same oxidation state, the distortion in the polyhedra is minimum and charge ordering is absent. This results in lowering dielectric www.springer.com/journal/40145 constant values. The effect of charge ordering has been studied in Pr doped Ca Pr MnO . Undoped Ca MnO does not show charge-order, and the measured intrinsic dielectric constant is only 14. The Pr doping induces charge-order in the system causing noteworthy increase in the value of dielectric constant, (~220) for Ca . Pr . MnO [133].

2 Microwave dielectric materials
There is also another group of A BO layered perovskites, which have been studied for low-loss microwave dielectric applications. The general formula for these ceramics is MLnBO (M = Ca, Sr, Ba; Ln = Y, La, Nd, Sm; B = Al, Ga, (Mg . Ti . ), (Zn . Ti . )) [134]. Among these oxides, CaLaAlO and SrYAlO are not stable. This is because, for these two oxides the difference between tolerance factor " " of layered perovskite and its perovskite unit (i.e., LaAlO in CaLaAlO , and YAlO in SrYAlO ) is greater than 4.3%. Stability of CaLaAlO has been improved by substituting Sr at Ca, in Ca Sr LaAlO stability is reported for composition with > 0.9 [135]. In the crystal structure of MLnBO , large distortion in (M, Ln)O polyhedra and BO octahedra are observed in the crystal structure. These distortions originate due to a large difference in the ionic radii of M and Ln cations, also leading to an interlayer size mismatch. Between these interlayers static electric polarization may also be present due to "2+" oxidation state of cation M and "3+" oxidation state of cation Ln (discussed in detail in Section 2) [21,134,136,137].
There are several studies in which improvement in × ( = = and = frequency) has been achieved by reducing interlayer static electric polarization [21,136,138,139]. The solid solution of SrLaAlO , SrNdAlO , SrSmAlO , CaNdAlO with Sr TiO /Ca TiO (i.e., Sr La Al Ti O , Sr Nd Al Ti O , Sr Sm Al Ti O , Ca Nd Al Ti O , respectively) have been extensively studied by several research groups and improvement in × were reported by co-substitution of Sr(Ca)/Ti cations. Co-substitution reduces the interlayer polarization and results in improving × value. Co-substitution also decreases the tolerance factor " " and subsequently interlayer stress increases. Sometimes a new phase MTiO also appears. These two effects: decrement in tolerance factor " " and appearance of the new phase, bring a negative impact on × improvement [24,[136][137][138][139][140]. Although MLnAlO ceramics have high × values (~ 90000 GHz) and further improvement in × values is also observed in solid solution with Sr TiO /Ca TiO . But, relatively low dielectric constant ( ~ 20) and higher temperature coefficient of the resonant frequency (~− 30 ppm/℃) limit their practical applications. The improvement in was expected by replacing Al with suitable trivalent cation having ionic polarizability higher than 0.78 Å of Al cation. However, only Ga is found to be a suitable cation with ionic polarizability of 1.50 Å , by considering the stability of A BO layered perovskite structure and electrically insulator (an essential requirement for microwave dielectric ceramics). than Al and Ga . In addition, also becomes positive (29 ppm/℃ for SrLa(Mg . Ti . )O and 38 ppm/℃ for SrLa(Zn . Ti . )O ) with increase in dielectric constant [134]. Although, for these ceramics, the dielectric constant is high but higher value limits its practical application in commercial microwave devices, such as dielectric resonators and filters [141]. Recently, Sr TiO and Sr CeO were also studied for low loss microwave dielectric applications by Liu  [20,142]. High values of , × , and of Sr TiO , make it suitable for wireless passive temperature sensors application [141]. Properties of the solid solution of these two oxides have been also studied by Dai et al. For Sr Ce . Ti . O ( = 20.7, × = 115550 GHz ) very small value of (= −1.8 ppm/℃) was reported [20]. The microwave dielectric properties of some recently studied A BO oxides with respective references are listed in Table 2. A systematic improvement in low-loss microwave dielectric properties is obvious from Table 2.
Till date, no report is found in the literature on experimental measurements to claim ferroelectric characteristics in A BO layered perovskites. Although theoretical group of researchers have suggested certain compositional and structural modifications to induce highly improper ferroelectricity (HIF) in RP oxides. On the basis of group theory, they have shown that the condensation of two distortion modes; (i) unique symmetric octahedral distortions (Fig. 6) and (ii) a combination of a single octahedral distortion with "compositional" Aor B-cation ordering (Fig. 7), can transform the centrosymmetric structure into a non-centrosymmetric structure (necessary requirement for a crystal to exhibit ferroelectricity) [143,144]. The general rule that a unique symmetric octahedral distortion for ferroelectric nature, failed to induce HIF in A BO layered perovskite as there are an even   number of " A " cations per unit cell. However, symmetrical ordering of "A" cations in (ABO )A′O layered perovskite can induce ferroelectricity [145]. The relative magnetoelectric properties corresponding to HIF is also explored in ABO and A B O . However, till date it is not explored yet in A BO layered perovskites [144]. www.springer.com/journal/40145

Optical properties
In recent years commercialization of white light-emitting diodes (WLEDs), flat-panel displays, plasma display panels (PDPs), field emission displays (FEDs), and thin-film electroluminescent devices (TFELs) could be possible due to the development of new phosphor materials with improved optical properties [29,[148][149][150]. For the development of new phosphor materials, the efforts to discover new host materials and high-performance activators are needed [29]. Traditionally sulfide and halide phosphors were extensively studied but in recent years oxide phosphors have received attention of the researchers due to their stability [29,150,151]. In A BO layered perovskite family, M SnO (M = Ca, Sr, Ba), Sr CeO , etc. have been extensively studied as host matrix for phosphor applications because of their stable crystal structure, non-toxicity, and lack of radioactive elements [29]. The incorporation of optically active lanthanide ions into these host matrices results in phosphors with photoluminescence (PL) and long-lasting phosphorescence (LLP) properties [151][152][153]. The LLP phosphors emitting in the blue and green spectral region are being used in many commercially available optical devices. However, LLP phosphors having emission in orange to red region are still out of reach for the use in optical devices. Therefore, there is need for the development of novel host materials for LLP phosphors emitting light in the orange to red wavelength range [29,153]. The properties of LLP phosphor have been modified by using a host-mixing method to change the original constituents of the lattice or introducing different co-dopant [29]. Important performance factors are bandgap, energy gap between excited states and the conduction band, and energy states corresponding to defects and their density. The luminous color of the WLED depends on the emission center used in the phosphors. The red and orange emission of phosphor mainly derives from the electron transition of the internal orbit of Sm and Eu . The Sm (electron configuration 4f ) and Eu (electron configuration 4f ) ions have incomplete 4f shell, and their outer 5s and 5p orbits shield 4f electrons against the crystal field [29,154]. Therefore, the optical spectra of Sm and Eu in the crystal lattice are fairly similar to the free ions and show good color purity. Kamimura et al. [155] reported the purple photochromism in Eu doped Sr SnO . The incorporation of Ti in alkaline earth orthostannates (M SnO ) was studied for blue photoluminescence applications. According to Yamashita et al., the excitation spectra of these orthostannates exhibited broad bands just below the fundamental absorption edges, implying that luminescence centers do not consist of the component elements in the host materials. It was suggested that the Ti containing octahedra are possible luminescence centers in these materials, as it was proposed for earlier investigated Ti-doped Mg SnO and Y Sn O [150,156].
Another phosphor which has drawn wide attention of researchers in recent years for its optical properties is Sr CeO , firstly reported by Danielson and his co-workers in 1998 [157]. It is intrinsically luminescent material and has chemically and thermal stability. Sr CeO also possesses some desirable qualities of phosphor materials such as (i) ligands-to-metal charge transfer (CT) transition of Ce at ~340 nm, (ii) efficient energy transfer that can occur from the Ce -O CT state to the trivalent rare earth in Sr CeO : RE , (iii) high efficiency for absorbing UV radiation, and (iv) the large band gap [40]. Almost all cerium-based phosphors are known due to their localized Ce excited state with luminescence arising from 4f to 5d transitions. However, in Sr CeO the cerium ion is in "4 +" oxidation state and the 4f shell is empty, the only possible transition is metal to ligand charge transfer transition originating due to the interaction of central cerium ion with neighboring oxygen ligands in CeO octahedra [158]. Figure 8(a) shows the photoluminescence excitation (PLE) spectra of Sr CeO phosphor. The excitation spectra consist of a broad spectrum in UV-region between 200 and 400 nm with a peak at 299 nm and a shoulder at 349 nm. The broadness of the excitation spectrum indicates the possibilities of using Sr CeO phosphor in UV LED chips. Two peaks in the excitation spectra of Sr CeO are associated with two different Ce − O bond-lengths. The excitation from the ground state to the excited states is attributed to the t -f (terminal) and t -f (equatorial) charge transfer states of Ce . The band t -f is spin forbidden; hence the excitation intensity associated with it is lowered than the band associated with t -f state [158]. Therefore, the higher energy band (299 nm) originates from charge transfer from apical oxygen, O to Ce and lower energy band (349 nm) originates from the charge transfer from equatorial oxygen, O to Ce . Figure 8(b) shows photo-luminescence  [158].
The improvement in the emission intensity of Sr CeO has been achieved by increasing sintering temperature as plotted in the inset of Fig. 8(b). It is mentioned that with increasing sintering temperature crystallinity improves, and hence emission intensity increases up to 1100 ℃. Above 1100 ℃ no further improvement in the crystallinity could be achieved due to high agglomeration at a higher temperature, and hence emission intensity starts decreasing. The Commission International De I-Eclairage (CIE) chromaticity coordinates of the Sr CeO phosphors sintering at different temperatures lie in the blue region.
In recent years rare earth (RE ) ions such as Eu , Ho , Er , Tm , Dy , Yb etc. doped Sr CeO phosphors have attracted lots of attention from the r e s e a r c h e r s [ 1 4 8 ] . Sr CeO : Eu (Dy , Tm ) phosphors have exhibited strong red (yellow, blue) emission which makes them potential for display applications such as UV-LEDs [159]. Rare earth ions (Ho , Er , Tm , a n d Yb ) d o p e d Sr CeO phosphors have been studied for their application as lasing materials or spectral conversion materials [159]. Dy doped phosphors have shown two intense emission at 484 nm (blue) and 575 nm (yellow) useful for white light emission based optical devices. However, these emission lines (of Dy ) are very sensitive to the chemical environment surrounding the luminophore. The intensity ratios of these two emission bands are host dependent. Therefore, emission of white light can be realized by modulating the intensity of emission, i.e., by compositional modification of the host [40]. In Eu and Dy co-doped Sr CeO , the photoluminescence mechanism of energy transfer between Eu and Dy for color tunable phosphor applications has been studied by Li et al. [157]. They also studied the energy transfer between Ce -O charge-transfer state (CTS) and Eu states by theoretical calculation of the band structure. They found that the efficiency of co-doped phosphors is lowered as compared to single ion doped phosphors due to the reabsorption mechanism between the Eu and Dy co-dopants. Sr CeO : Nd nanophosphors exhibit a strong near-infrared (NIR) emission and can be used as high-efficiency laser material based on their peculiar optical properties [157].
Recent research reports have emphasized the role of co-doping of alkali metal ions (Li , Na , K ) along with rare-earth ions (RE ) in some of A BO oxides. This approach has been employed in several phosphors, like CaMO : Dy ( M = W, Mo ), Y Zr O : Dy , YBO : Eu , YPO : Eu , etc. [160][161][162][163]. The co-doping of monovalent alkali metal ions reduces the charge unbalancing problem originated by doping of trivalent rare-earth ions at divalent alkaline earth metal ions ( Ca , Sr , Br ). Co-doping of alkali metal ions ( Li , Na , K ) along with rare-earth ions ( RE ) approach has emerged as an efficient way to enhance the photoluminescence (PL) intensity and emission characteristics of A BO oxides based phosphors [40]. www.springer.com/journal/40145

Conclusions and perspective
Only those A BO compounds which crystallize in T-type structure form layered perovskite structure or K NiF structure. All the investigated A BO layered perovskites have either orthorhombic or tetragonal crystal structure. At high temperature due to the expansion in the unit cell volume of RE MO oxides, orthorhombic to tetragonal structural transformation is observed. The structural transformation in these oxides can be induced by varying oxygen stoichiometry and selecting suitable dopants. Both hypo-stoichiometric (less oxygen, A BO ) and hyper-stoichiometric (more oxygen, A BO ) can be synthesized by changing processing conditions or dopants.
Majority of A BO oxides are insulator in nature. However, hypo-/hyper-stoichiometric RE MO and AE doped RE MO have high value of conductivity due to mixed ionic-electronic conducting properties. Due to a wide range of oxygen stoichiometry and large interstitial space for oxide ion migration, the mixed ion conductivity is higher in La NiO making it useful for cathode in IT-SOFCs. Among all the investigated RE MO , Pr . Sr . Ni . Cu . O shows the highest ( 260 S · cm at 700 ℃ ) mixed ionic-electronic conductivity (MIEC). The stability of Ln NiO with commonly used electrolytes in SOFCs has been performed but more studies are needed for practical application.
Recently, some of A BO oxides having giant/ colossal dielectric constant were explored. Doped and undoped La NiO have shown very large ("giant") magnitude of the dielectric constant and thus display immense potential for their applications in modern microelectronics and for the development of capacitorbased energy storage devices. The dielectric properties of La / Sr / NiO are superior to popular high dielectric constant material CaCu Ti O (CCTO). Until now no ferroelectric characteristics have been observed experimentally in any A BO layered perovskites. Theoretical researchers have suggested certain compositional and structural modifications to induce highly improper ferroelectricity (HIF) in RP oxides. But the only compositional ordering of "A" cations found suitable in (ABO )A′O layered perovskites.
There is also another group of A BO layered perovskites which have been studied for low-loss microwave dielectric applications. Very high values of , × , and of Sr TiO , make it very suitable for wireless passive temperature sensor application. The A BO layered perovskites have also been studied for phosphor applications. M SnO ( M = Ca, Sr, Ba) and Sr CeO are extensively studied as a host matrix because of their wide optical band gap ( 3 − 5 eV ), stable crystal structure, physical and chemical stability, non-toxicity, and lack of radioactive elements. Among all the investigated A BO oxides, Sr CeO has shown self-luminescence in blue region.
In the last two decades researchers have mainly focused attention on La NiO , and studies on the properties of other oxides such as A BO ( A = Ca, Sr, Ba and B = Sn, Ti, Mn ) are very limited. Dielectric properties of Sr SnO and Sr MnO investigated by our research group are promising and need more investigations for further improvement. The understanding about the origin of high dielectric constant in La NiO is not clear and needs more experimental and theoretical research on this system. Although theoretical researchers have suggested certain compositional and structural modifications to induce HIF in RP oxides, experimentally these modifications are not employed yet.