Third-order elastic constants of the high temperature superconductor Bi2Sr2CaCu2O8 (original) (raw)
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Third-order elastic constants of the high-temperature superconductor
Superconductor Science and …, 1998
The complete set of third-order elastic constants of the high-temperature superconductor La 1.8 Sr 0.2 CuO 4 is calculated by taking into account the interactions between nine nearest-neighbour atoms in the lattice. Finite deformation theory is used to obtain the strain energy density φ of a tetragonal 2-1-4-type single crystal of the high-temperature superconductor La 1.8 Sr 0.2 CuO 4 . This is compared with the strain-dependent lattice energy in continuum model approximation. The second-order derivative of the potential function is obtained from the measured C 11 . The third-order derivative is evaluated from the Mie-Grüneisen interatomic potential. The second-order elastic constants of La 1.8 Sr 0.2 CuO 4 are calculated and compared with the available measured values. The third-order elastic constants of La 1.8 Sr 0.2 CuO 4 are negative and their absolute magnitudes are one order higher than those of the second-order elastic constants.
Journal of Solid State Chemistry, 1996
4-10). Best results are obtained for stoichiometric starting The anisotropy of low-temperature thermal expansion of the ratios 2 : 2 : 1 : 2. The Bi-2 : 2 : 1 : 2 phase of bismuth cuprates high-temperature superconductor Bi 2 Sr 2 CaCu 2 O 8 (Bi-2 : 2 : 1 : 2) has the ideal composition Bi 2 Sr 2 CaCu 2 O 8 and has a T c of is analyzed theoretically. The generalized Grü neisen parameabout 90 K (11). The structure of Bi 2 Sr 2 CaCu 2 O 8 is pseudoters (GPs) of elastic waves propagating in different directions tetragonal (I4/mmm) (12). The lattice parameters a of Bi-2 : 2 : 1 : 2 are calculated using the measured values of (ϭ5.4091 Å ), b (ϭ5.4209 Å ), and c (ϭ30.8445 Å ) can be second order elastic constants and first order pressure derivaapproximated by an orthorhombic cell (a Ȃ b) with the tives of second order elastic constants. For this, we have used copper oxide layers in the ab plane (13). Hence the symmethe measured values of the second order elastic constants of try of the Bi-2 : 2 : 1 : 2 is, however, no greater than pseudo-G. A. Saunders et al. The 12 third order elastic constants of orthorhombic. Bi 2 O 2 layers consist of two parallel planar the Bi-2 : 2 : 1 : 2 system are calculated from the expressions of BiO sheets. The bonds between the bismuth oxide layers effective second order elastic constants. All the third order in the structure are weak and hence the crystallites of these elastic constants are negative except C 155 and C 112 . Some values of generalized Grü neisen parameters are negative. The general-compounds have been shown to cleave readily between ized GPs ␥Љ j are all positive except ␥Љ 2 (؊0.048) at ؍ 85؇. The these layers . The present objective is to study the Brugger gammas are calculated and the low-temperature limits thermal expansion and the Grü neisen parameters of Biof the Grü neisen gamma are determined using the procedure 2 : 2 : 1 : 2. We have calculated the generalized isothermal of Menon and Ramji Rao. ␥ Ϫ L has the value of 4.4 for the Bi-Grü neisen parameters ͲЈ j and ͲЉ j for the acoustic modes. 2 : 2 : 1 : 2 system. The low-temperature limit of the Grü neisen For this, the third order elastic constants of Bi 2 Sr 2 CaCu 2 O 8 gamma is positive. Therefore, we expect volume expansion to are obtained from second order elastic constants and first be positive down to absolute zero for the Bi-2 : 2 : 1 : 2 system. order pressure derivatives of second order elastic con-
Effect of elastic stress on the resistivity and Tc of (Bi, Pb)2Sr2Can−1CunOx
Physica C: Superconductivity, 1991
We have measured the effect of elastic uniaxial stress a in the a direction on the superconducting transition temperature Tc of (Bi, Pb)2Sr2CaICu20~ (2212) and (Bi, Pb)zSr2Ca2Cu3Ox (2223). We find dT/doll =-10_+2 K/GPa for 2212 and-6_+ 2K/ GPa for the 2223 compound. Combining these results with those of others on d Tc/dP we find that dTc/do'33 = + 18 K/GPa. An estimate of the elastic constants of these compounds from the work of others together with these results implies that the change in Tc with a fractional change in the c-axis spacing is probably positive, although the uncertainties in the elastic constants make this estimate subject to a large uncertainty. The resistance changes by less than 1 part in 12 000 for strains up to 0.5%, implying that din p/dtrt L =-76>(10-3 GPa-1.
Elastic anisotropy and lattice instability in Bi2Sr2Ca1Cu2O8 single crystal
Physics Letters A, 1989
The veh~cityand attenuation versus temperatureof ultrasonic longitudinal waves propagating along two directions in the a-b plane at 10 to the a and b axes were measured for a Bi2Sr2Ca1Cu2O8 single crystal. The anisotropic elasticity in the a-b plane is manifeste4. One direction shows obvious softening around 250 K, the other reveals only monotonic stiffening from room temperature d~wn to T~. Attenuation peaks at 95, 150, and 250 K are attributed to a phase-like transition offirst order.
Studies on Transition Temperature of the Superconducting Materials Related to Elastic Constants
Bangladesh Journal of Scientific and Industrial Research, 2007
For a face-centered-cubic structure crystal the parameters like atomic mass M, atomic number Z, lattice spacing are the important factors in the determination of a many body Hamiltonian H. Instead of using fcc lattice spacing we can also utilize atomic volume Ω. Using the superconducting transition temperature expressed as Tc = Tc(M)(Z,Ω), a well defined region in superconducting elements is possible. Tc may also be related to BCS theory through Debye temperature. This Debye temperature is related to elastic constants C11, C12 and C44, atomic weight and atomic volume. Also Tc for five fcc transitions metals is linear in the Cauchy deviation C* = (C12 - C44)/( C12 + C44), such linearity is also seen in bcc transition elements. Finally via elastic constants mass density and atomic volume, a correlation between C* and the Debye Ω temperature has been established for the five fcc transition elements. This correlation indirectly sets up a relation between transition temperature and elast...
Elastic properties of superconducting and non-superconducting DyBaSrCu3O7−δ
Physics Letters A, 2001
Ultrasonic longitudinal and shear wave velocities were measured for superconducting and non-superconducting DyBaSr Cu 3 O 7−δ (Dy-1113) at 10 MHz between 80 and 270 K. The superconducting sample exhibits a step-like elastic anomaly between 190 and 230 K. No elastic anomaly was observed in the non-superconducting Dy-1113. The anomaly observed in the superconducting sample is attributed to structural phase transition caused by oxygen orderings.
The relationship between the porosity and elastic moduli of the Bi-Pb-2212 high-T c superconductor
Superconductor Science and Technology, 1995
A series of Bi-Pb-2212 high-T, superconductors, having different porosities has been prepared by the solid-state reaction method. After the usual characterization of the samples by XRD, AC susceptibility, SEM, bulk-density and porosity studies, longitudinal (6) and shear (Vs) wave velocity measurements have also been undertaken by the pulse-transmission technique. Using the experimental values of V; and V,, the Young's moduli (E) of all the samples have been calculated and are later corrected to zero porosity by employing a number of theoretical equations. The corrected moduli are compared with the literature value. which itself has been arrived at by averaging the available single-crystalline stiffness constants. It is concluded from the results that among all the formulae, Mackenzie's equation and that proposed by the authors of the present investigation are in closest agreement with the literature value.
Anisotropy of the superconducting properties of Bi2Sr2CaCu2O8
Solid State Communications, 1988
We report magnetoresistance measurements up to 20 teslas on the superconducting hightemperature compound Bi2Sr2CaCu208. The upper critical field is very anisotropic ; Hc2///I-Ic2± = 20. (HI/for H H c-axis and H.L for H//(a,b) plane). This value is twice larger than in YBa2Cu307, it demonstrates the stronger 2-D character of Bi2Sr2CaCu208.
Structure optimization effects on the electronic and vibrational properties of Bi2Sr2CaCu2O8
Physical Review B, 2004
We present detailed first-principles calculations for the normal state electronic properties of the high T C superconductor Bi 2 Sr 2 CaCu 2 O 8 , by means of the linearized augmented plane wave (LAPW) method within the framework of density functional theory (DFT). As a first step, the body centered tetragonal (BCT) cell has been adopted, and optimized regarding its volume, c/a ratio and internal atomic positions by total energy and force minimizations. The full optimization of the BCT cell leads to small but visible changes in the topology of the Fermi surface, rounding the shape of CuO 2 barrels, and causing both the BiO bands, responsible for the pockets near thē M 2D symmetry point, to dip below the Fermi level. We have then studied the influence of the distortions in the BiO plane observed in nature by means of a √ 2 × √ 2 orthorhombic cell (AD-ORTH) with Bbmb space group. Contrary to what has been observed for the Bi-2201 compound, we find that for Bi-2212 the distortion does not sensibly shift the BiO bands which retain their metallic character. As a severe test for the considered structures we present Raman-active phonon frequencies (q = 0) and eigenvectors calculated within the frozen-phonon approximation. Focussing on the totally symmetric A g modes, we observe that for a reliable attribution of the peaks observed in Raman experiments, both c-and a-axis vibrations must be taken into account, the latter being activated by the in-plane orthorhombic distortion.
Sains Malaysiana, 2018
The effects of mixed-valence Mn substitution at the Cu site on the superconducting and elastic properties of La 1.85-1.5x Sr 0.15+1.5x Cu 1-x Mn x O 4 (x = 0, 0.02 and 0.04) were studied. The samples were characterized by X-ray diffraction (XRD) method, temperature-dependent resistance measurements, scanning electron microscopy (SEM) and sound velocity measurements at room temperature. An elastic softening and a decrease in the critical temperature T c was observed as Mn was substituted for Cu. The Debye temperature θ D for x = 0 and 0.02 void free samples were calculated to be 459 K and 430 K, respectively. Internal lattice strain which is related to lattice parameter ratio a/c did not correlate with T c. The electron-phonon coupling estimated using the conventional Bardeen-Cooper-Schrieffer (BCS) theory was λ = 0.367 (x = 0) and 0.368 (x = 0.02). The electron-phonon coupling in two-dimensional van Hove scenario was calculated to be λ vH = 0.0148 (x = 0) and 0.0149 (x = 0.02). These results were compared with other cuprates and related superconductors. The comparison showed that other than electron-phonon coupling, the elastic moduli might play an important role in the mechanism of superconductivity in these materials.