**3. Crystal structure and synthesis of cuprate**

The two typical structural types of Ln2CuO4 double oxides are assigned by T (or O) and T′ [16]. The indicative T′ means that the symmetry of the structure is tetragonal while the prefix O designates that the symmetry is orthorhombic. A third structural type exists and is designated by T\* for certain oxides of the general formula Ln2–y-xLn′yMxCuO4 (where Ln and Ln′ are lanthanides and M an alkali or alkaline earth such as Ba or Sr) [20–22]. The rare-earth ionic radius of the Ln2CuO4 oxides (Ln = lanthanides) is an essential criterion that imposes the type of structure adopted. All Ln2CuO4 compounds stabilize in the T′-type structure at room temperature, except for Ln=La which adopts the T-type structure. This difference is due to the enormous size of the La3+ ion which prevents the stabilization of the T′ structure. However, the small ionic radii of the other lanthanides favor the crystallization of the T′ phase, the common prototype for this phase of which is the compound Nd2CuO4 [23].

## **3.1 T-type structure (La2MO4 system with M = Cu, Ni, and Co)**

The T-type structure relates to the La2MO4 system where M = Cu, Ni, and Co. At elevated temperatures, the La2MO4-type compounds correspond to the K2NiF4-type structure of tetragonal symmetry with the space group I4/mmm [24–26]. The structure is described by the stacking, along the c-axis, of sheets of the MO2 type separated from each other by double layers of the NaCl type or, by the stacking of the layers of octahedron MO6 of the perovskite-type which are translated relative to each other by (½, ½, and ½) and separated by La-O sheets of the NaCl type [27] (**Figure 2**).

The coordination of the lanthanum atom is equal to 9 or 4 + 4 + 1 oxygen ions with different bond lengths. The shortest bond (strong bond) is between the apical oxygen

#### **Figure 2.**

*Unit cell of the T-type structure: (a) HTT quadratic phase (Space Group: I4/mmm) (ICSD 41643), (b) LTO Low-temperature orthorhombic phase (Space Group: Bmab) (ICSD50265).*

and the rare-earth atom (Ln–O)+ . The transition metal is in coordination 4 (four) with respect to the equatorial oxygen and 2 with respect to the apical oxygen. The lengths of Map bonds vary according to the type of transition metal M [28]. Indeed, the Co–Oap and Ni–Oap bonds are equivalent, while the length of the Cu–Oap bond is lengthened on the c-axis by the Jahn Teller effect [29] due to the volume state of the Cu2+. It is equal to 13.15 Å for La2CuO4 while it is between 12.55 Å and 12.70 Å for La2CoO4 [30] and La2NiO4 [31]. The octahedra MO6 is perfectly aligned with the c–axis; in case, HTT (high-temperature tetragonal) is ideal. At room temperature, the phases of the three systems: La2CoO4, La2NiO4, and La2NiO4, have an orthorhombic structure of the Bmab type called "low temperature orthorhombic" (LTO).

#### **3.2 T′-type structure**

The structure of the T′ type derives from that of the T type which results from a displacement of the apical oxygen atoms in the tetrahedral sites formed by the lanthanide ions, from where the layers of the NaCl type are replaced by layers of the fluorite type. The coordination number of Cu becomes 4 (square plane coordination) and that of Ln is 8 instead of 9 [32, 33]. This structural transformation leads exclusively to a change in the coordination of the oxide; thus, the cation M is in square plane coordination, and the LnO2 layers are of the fluorine type and no longer of the NaCl type. Therefore, the crystal structure of the T' phase can be described as an entanglement of fluorite (Ln/O2/Ln) blocks with infinite shell blocks CuO2. However, the space group remains the same for the 2 structures. The structures of Nd2CuO4 [12] and Pr2CuO4 [34] are shown in **Figure 3**.

**Figure 3.** *Structure of the typical quadratic phase T' (ICSD 261660).*

*The Cuprate Ln2CuO4 (Ln: Rare Earth): Synthesis, Crystallography, and Applications DOI: http://dx.doi.org/10.5772/intechopen.109193*


#### **Table 1.**

*Atomic positions of the T and T' structures with the space group I4/mmm.*

The atomic positions of the two structures T and T' are presented in **Table 1**. The values of the atomic coordinates have been obtained from the crystallographic information file (CIF) obtained from the ICSD database.

#### **3.3 T\* type structure**

The structure of the T\* type consists of a stack of pyramids' layers (CuO5) separated either by layers (LnO) of the NaCl type, or by layers of the fluorite type (**Figure 4**). As a result, this structure is intermediate between those of the T and T′ types. The stacking sequence of the atomic planes along the c-axis is A│B│A│C│A, with A: CuO2, B: Ln–O2–Ln, and C: LnO–LnO. The Cu2+ cation is surrounded by five oxygen atoms, thus, forming a square-based pyramid while the Ln3+ cations are distributed in the coordination sites 9 and 8 in an ordered manner [22]. The structure of the T\* type phase is obtained by following a thermodynamic competition between the factors, e.g., chemical composition and pressure influencing the stability of the T and T′ phases. Due to this competition, the existence of this phase is extremely limited and coincides with the following values of the tolerance factor: 0.85 ≤ t ≤ 0.86 [31]. The existence and presence of two ions Ln3+ and Ln'3+ of varied sizes cause the crystallization of the oxide of type (Ln, Ln′)2CuO4 in the T\* type structure. This is the case where Ln is La3+ and Ln′ is less voluminous ion such as Sm3+, Eu3+ , Gd3+ , Dy3+, and Tb3+ . The domain of the T\*-type phase existence can be increased by the presence of a divalent cation with a large ionic radius such as Sr2+ which usually occupies the coordination site 9 [32]. Thus, the structure of the T\* phase can include several oxides such as (La, Ln, Sr)2CuO4 and (La, Ln′)2CuO4 (Ln = Sm, Eu, Gd, or Tb, and Ln′ = Dy, Tb, or Nd) [30]. The structure of the T\* type phase has also a quadratic symmetry, and the space group of Nd2–x–yCexSryCuO4- δ is P4/nmm [35] for example.

#### **3.4 S-Type structure**

The S-type structure [36] is a model used mainly to describe oxygen-deficient compounds such as Ln2CuO4–x (Ln = Pr, Nd, Sm, Eu, Gd) [37]. Unlike T, T', and T\*, the S phase has oxygen vacancies at the equatorial sites, half of which are occupied. The oxygen vacancies are ordered such that Cu adopts a square planar coordination as shown in **Figure 5**. The copper atoms are surrounded by 2Oap and 2Oeq instead of 4Oeq in the T' phase. This is a major difference between the two phases S and T' since the arrangement of CuO4 square planes in the S-type structure does not form 2D layers, but 1D chains which share the following corners and orientations [38, 39]. The S-type phase has orthorhombic symmetry with a space group Immm [39].

**Figure 4.** *Projection of the crystal structure of (Nd1.32Sr0.41Ce0.27)CuO3.93 (ICSD 65871) which belongs to the T\* structure type.*

## **4. Effect of doping in phase transition of cuprates**

The nature of the Cu–O bond in cuprates is strongly related to doping. Various configurations are found. For example, for the La2–xSrxCuO4 system [40, 41], the structure is of the K2NiF4 type (T phase). It contains CuO6 octahedra arranged in a planar row.

While the Nd2–xCexCuO4 [42] system exhibits a structure similar to Nd2CuO4 type (T' phase) in which the apical oxygens in the T phase structure are shifted away from the Cu atoms in order to form lines of oxygen atoms along the c-axis perpendicular to the CuO2 planes. In the Sr2CuO3 phase (S phase), the CuO3 chains, running along the a-axis of the orthorhombic structure, were isolated [43]. The T, T′, and S structures are shown in **Figure 6**. Due to the elimination of half of the oxygen atoms noticed in the CuO2 planes, the structure is transformed from the T phase to the S phase. The translation of the apical oxygens in the face positions of the lattice transforms the structure of the T phase to T' phase. The transformation between the phases T, T′, and S is observed in the Nd2CuO4 -Sr2CuO4 system [41]. Indeed, heating T-type phases such as La2CuO4, La2NiO4, and La2CoO4 under various oxygen pressures lead to the formation of oxygen-rich phases, with biphasic regions between these phases and the stoichiometric compounds La2MO4

*The Cuprate Ln2CuO4 (Ln: Rare Earth): Synthesis, Crystallography, and Applications DOI: http://dx.doi.org/10.5772/intechopen.109193*

(M: Cu, Ni, Co) [42]. In the case of La2CuO4, the obtained sample is La2CuO4.08 and La2CuO4.03 [44, 45].

The oxygen-rich phase shows superconductivity below 40 K. The reduction of Ln2CuO4 compounds (Ln: La, Pr, Nd, Sm, Eu, Gd) using hydrogen at low temperature [10] leads to the formation of new Ln2CuO4–δ compounds, with δ = 1/3 for Ln = La and δ = ½ for Ln = Pr, Nd, Sm, Eu, and Gd. For the compounds with La, Pr, and Nd, they exhibit structures similar to Sr2CuO3 [46–48].
