The Effect of Ionic Substitution on the E.P. of Superconductor using Madelung Method

The effect of substitution of the ion 2 Sr instead of La +3 in the superconductor 4 2 CuO Sr La x x was studied, an increase in electrostatic potential energy E. P. (E) with increase of Sr % was noticed, and a step change in P. E. when Sr is added is noticed indicating a phase change occurrence in the crystal structure .Increase of Tc, with the increase of Sr, noticed earlier, is linked with increase of E.P. and a relation between E.P. and Tc is found 2 545 . 1 604 . 6 227 . 90 E E Tc , the increase of Tc is due the creation of holes by valance difference between La & Sr, which also leads to collapse of crystal by reduction of repulsion between Sr & Cu atoms this have the same effect as the application of pressure on the crystal, which increases Tc also. For x >0.15, Tc decreases due to the appearance of vacancies which may have screening effect of the electrostatic field. Introduction The Effect of Ionic Substitution on the E.P. of 4 2 CuO Sr La x x ... 79 After the discovery of the High Temperature Superconductors HTSC (Bednorz & Muller, 1986), these compounds have received great importance, since (Wu et al, 1987) was succeeded to synthesize the superconductor YBa2Cu3O7 (YBCO) (Tc=95 K). Thus refrigeration cost was decreased by thousand time . The newly discovered materials are CuO based ceramics that remain Superconducting near 100 K. Soon after this discovery many other Superconducting compounds with higher critical temperatures was synthesized, like Bi-Sr-Ca-Cu-O (BSCCO), and Ba-Sr-Ca-Cu-O (BSCCO) (Sharp, 1990). Higher critical temperature was recorded like that of the compound Hg-Ba-Ca-Cu-O (HBCCO) with the critical temperature 135 K (Chu, 2002). The CuO compounds are insulators. By substituting for certain atoms in the unit cell, these materials are made to behave as metals and may become superconductors. The transition temperature depend strongly on the density of states at the Fermi level, that parameter in turn is strongly affected by doping of the initial ceramics with other atoms of different valance to provide extra electrons (Or holes) which are then available for participation in Superconductivity (Chu, 2002). The practice of doping has along history in the field of semiconductors, and similar efforts applied to HTSC. A tremendous quantity of substitution have been tried to improve mechanical, magnetic or transport properties of these materials. The Fermi level is badly distorted from a simple spherical shape by the anisotropy in HTSC(Pickett,1989). Superconductivity observed in La2CuO4 system when La is partially substituted by Ba then forming the compound La2-x BaxCuO4 the value of TC reaches maximum value when x = 0.15 . Substitution by divalent ions 2 2 2 , , Cu Sr Ba M Leads to the appearance of superconductivity for 0.05 < x < 0.3 in La2-xMxCuO4-y (Takagi et al, 1989). The aim of this research is to study the effect of ionic substitution of Sr ion in the compound La2-x SrxCuO4-y on the electrostatic potential energy and its relation to the critical temperature Tc. Bassam Mahmoud Mustafa 80 Fig.1: the crystal structure of La-Sr-Cu-O, octahedral structure surrounding the Cu ion (Sharp, 1990) The crystal structure The structure of the Superconducting phase was identified as a derivative of the layered pervoskite and shown in figures 1 and 2 .Fig. shows CuO2 layers which consist of octahedrally coordinated Cu, with Cu-O length of 1.9 A in the a-b plane and 2.4A in c direction .Also the Cu atom occur at (000) and (1⁄2, 1⁄2 , 1⁄2) lattice sites in the unit cell, similar to the body centered structure. The substituted Sr Ion occupy a fraction of La ion and the difference in valance bring about a increase in the number of holes. Superconductors with hole conduction are called P-type similar to that followed in semiconductors. Since 2 3 , Sr La are large ions the compound formed have the formula A2BO4, unlike the pervoskite which has the ABO3. If however, a slice of the pervoskite structure of thickness one unit cells taken fig. 2. Thus it has a stoichiometry A2 BO4. If these units are displaced relative to one another they formed a tetragonal structure with c = 3a. Where a is the length of the cell edge of the pervoskite building bricks. In this structure the x of the copper atoms, must be in the oxidation state (3+), in order to compensate for the presence of the Sr atoms (Sharp, 1990). The Effect of Ionic Substitution on the E.P. of 4 2 CuO Sr La x x ... 81 Fig.2: derivation of the A2BO4 structure from three pervoskite units (Sharp, 1990). Theory One of the important properties of the HTSC are their ionic bonds (Wright & Butler,1990). As shown in fig.2 Cu ion are coordinated to six oxygen ions as first nearest neighbors, and 8 La ions as second nearest neighbors. First of all we try to calculate the binding energy for the pure crystal i.e. without Sr substitution. If we try to compute the electrical potential energy E.P., which as we think: is an important parameter that greatly affects charge distribution inside the crystal, especially when we try to understand the effect of doping on the properties of the superconductor, because it affect the charge balance by the introduction of the new ion, with different valances. to calculate the E.P. we use Madelung method (Torrance & Metzger, 1989) where the electrical potential energy between a reference ion and the other ions of the crystal is considered. This energy is calculated as follows (Kittel, 2005).