Four phases are observed in superconducting Bi-Ca-Sr-Cu-O samples. The superconducting phase, with onset temperature near 120 K, is a 15.4-Å-layered compound with composition near ${\mathrm{Bi}}_2$ ${\mathrm{Ca}}_1$ ${\mathrm{Sr}}_2$ ${\mathrm{O}}_9$ and an A-centered orthorhombic unit subcell 5.41×5.44×30.78 A${̊}^3$. X-ray diffraction and electron microscopy data are consistent with a structure of alternating perovskite and ${\mathrm{Bi}}_2$ ${\mathrm{O}}_2$ layers. High-resolution transmission electron microscopy images reveal a b-axis superstructure of 27.2 Å, numerous (001) stacking faults, and other defects.

The relationship between linear elasticity theory of solids and their equations of state (EoS) is reviewed, along with the commonly-used types of isothermal EoS, thermal expansion models, and P-V-T EoS. A new console program, EosFit7c, is presented. It performs EoS calculations and fitting for both volume and linear isothermal data, isobaric data and P-T data. Linear data is handled by cubing the quantities and treating them as volumes in all EoS formulations. Least-squares fitting of EoS to data incorporates the option to weight the fit with the measurement uncertainties in P, V and T simultaneously. The EosFit7c program is built with a new library of subroutines for EoS calculations and manipulation, written in Fortran. The library has been incorporated as a module, cfml_eos, in the publicly-available CrysFML library. The module handles Murnaghan, Tait, Birch-Murnaghan, Vinet, and Natural Strain EoS. For P-V-T calculations any of these isothermal EoS can be combined with a variety of published thermal expansion models, including a model of thermal pressure. The entire library has been revalidated against other software and against an ab-initio re-derivation of the EoS, which identified a number of small errors in published formulae for some EoS.

Diffraction experiments at high pressures provide measurement of the variation of the unit-cell parameters of the sample with pressure and thereby the variation of its volume (or equivalently its density) with pressure, and sometimes temperature. This last is known as the ‘Equation of State’ (EoS) of the material. It is the aim of this chapter to present a detailed guide to the methods by which the parameters of EoS can be obtained from experimental compression data, and the diagnostic tools by which the quality of the results can be assessed. The chapter concludes with a presentation of a method by which the uncertainties in EoS parameters can be predicted from the uncertainties in the measurements of pressure and temperature, thus allowing high-pressure diffraction experiments to be designed in advance to yield the required precision in results. The variation of the volume of a solid with pressure is characterised by the bulk modulus, defined as K = − V ∂ P /∂ V . Measured equations of state are usually parameterized in terms of the values of the bulk modulus and its pressure derivatives, K′ = −∂ K /∂ P and K″ = −∂2 K /∂ P 2, evaluated at zero pressure. These zero-pressure (or, almost equivalent, the room-pressure values) are normally denoted by a subscript “0,” thus: K = − V (∂ P /∂ V ) P =0, K ′ = −(∂ K /∂ P ) P =0, and K ″ = −(∂2 K /∂ P 2) P =0. However, throughout this chapter a number of notational conventions are followed for ease of presentation. Unless specifically stated, the symbols K′ and K ″ (without subscript) refer to the zero-pressure values at ambient temperature, all references to bulk modulus, K …

Two superconducting phases, ${\mathrm{Tl}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10+\mathrm{\delta }}$ (2223) and ${\mathrm{Tl}}_2$ ${\mathrm{Ca}}_1$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_2$ ${)}_{8+\mathrm{\delta }}$ (2122), both with onset ${\mathrm{T}}_{\mathrm{c}}$ near 120 K and zero resistivity at 100 K, have been isolated from samples in the Tl-Ca-Ba-Cu-O system. The new 2223 superconductor has a 5.40×5.40×36.25-A${\mathrm{̊}}^3$ pseudotetragonal unit cell. The 2122 superconductor, which appears to be structurally related to ${\mathrm{Bi}}_2$ ${\mathrm{CaSr}}_2$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$, has a 5.44×5.44×29.55-A${\mathrm{̊}}^3$ pseudotetragonal subcell. The 2223 phase is probably related to 2122 by the addition of extra calcium and copper layers.