Simultaneous Assessment of the YBa2Cu3O6+z Thermodynamics Under the Linear Error Model

Rudnyi, E. B.; Kuzmenko, V. V.; Voronin, G. F.

doi:doi:10.1063/1.556023

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Journal of Physical and Chemical Reference Data / Volume 27 / Issue 5

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J. Phys. Chem. Ref. Data 27, 855 (1998); doi:10.1063/1.556023 (34 pages)

Simultaneous Assessment of the YBa₂Cu₃O_6+z Thermodynamics Under the Linear Error Model

E. B. Rudnyi, V. V. Kuzmenko, and G. F. Voronin

Chemistry Department, Moscow State University, 119899 Moscow, Russia

(Received 22 Oct 1997)

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Abstract

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About 3000 experimental points obtained in 220 miscellaneous experiments published in 57 papers have been processed simultaneously in order to obtain the most reliable Gibbs energy of the YBa₂Cu₃O_6+z solid solution in the temperature range from 250 to 1300 K. A part of this solution is well-known as the “Hi-T_c Y123” phase. All other thermodynamic properties of the solution including the conditions for the tetragonal-orthorhombic phase transition and the miscibility gap at lower temperatures, are derived from the assessed Gibbs energy. The linear error model introduced recently by one of the authors has been employed for the simultaneous assessment. The results obtained are compared with those of the conventional weighted least squares method and the benefit of the new approach is discussed. Another problem in simultaneous assessment that is also considered is visualizing the quality of the fit. New types of graphs (partly based on the linear error model) that facilitate visualizing the quality of the fit are presented. (A critical review with 72 references.) © 1998 American Institute of Physics and American Chemical Society.

KEYWORDS and PACS

Keywords

yttrium compounds, barium compounds, collections of physical data, high-temperature superconductors, free energy, solid solutions, solid-state phase transformations, least squares approximations, heat of formation, specific heat, maximum likelihood estimation, chemical thermodynamics, enthalpy of formation, entropy, Gibbs energy, heat capacity, high-temperature superconductor, lattice model, maximum likelihood, mixed model, variance component, visualizing quality of the fit

PACS

01.30.Kj

Handbooks, dictionaries, tables, and data compilations
74.72.-h

Cuprate superconductors
74.25.Bt

Thermodynamic properties
64.70.K-

Solid-solid transitions
82.60.Cx

Enthalpies of combustion, reaction, and formation
65.40.-b

Thermal properties of crystalline solids
65.60.+a

Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.
65.80.-g

Thermal properties of small particles, nanocrystals, nanotubes, and other related systems
02.50.-r

Probability theory, stochastic processes, and statistics