{"id":1942,"date":"2015-07-05T23:21:56","date_gmt":"2015-07-06T06:21:56","guid":{"rendered":"http:\/\/physikon.net\/?p=1942"},"modified":"2022-06-22T09:49:17","modified_gmt":"2022-06-22T16:49:17","slug":"1942","status":"publish","type":"post","link":"http:\/\/physikon.net\/?p=1942","title":{"rendered":"Superconducting Interaction Charge in Thallium-Based High-Tc<\/sub> Cuprates: Roles of cation oxidation state and electronegativity"},"content":{"rendered":"

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Superconducting Interaction Charge in Thallium-Based High-T<\/em>C<\/sub>\u00a0Cuprates: Roles of cation oxidation state and electronegativity<\/strong>, D. R. Harshman and A. T. Fiory [arXiv<\/a>]\n

Superconductivity in the Tl-based cuprates encompasses a notably broad range of measured optimal transition temperatures TC0<\/sub>, ranging from lowest in the charge-depleted Tl-1201 compounds (Tl1\u2013x<\/sub>(Ba\/Sr)1+y<\/sub>La1\u2013y<\/sub>CuO5\u2013\u03b4<\/sub>), such as Tl0.7<\/sub>LaSrCuO5<\/sub> (37 K) and TlBa1.2<\/sub>La0.8<\/sub>CuO5<\/sub> (45.4 K), to highest in the Tl-1223 compound TlBa2<\/sub>Ca2<\/sub>Cu3<\/sub>O9\u00b1\u03b4<\/sub> (133.5 K). Seven Tl-based cuprates are considered and compared using the model of superconductive pairing via electronic interactions between two physically separated charge reservoirs, where T<\/em>C0<\/sub> \u221d (\u03c3\u03b7\/A<\/em>)1\/2\u00a0<\/sup>\u03b6\u20131<\/sup> is determined by the superconducting interaction charge fraction \u03c3 the number \u03b7 of CuO2<\/sub> layers, and the basal-plane area A<\/em>, each per formula unit, and the transverse distance \u03b6 between interacting layers. Herein it is demonstrated that \u03c3 follows from the elemental electronegativity and the oxidation state of Tl, and other structurally analogous cations. The comparatively lower elemental electronegativity of Tl, in conjunction with its oxidation state, explains the higher \u03c3 and T<\/em>C0<\/sub> values in the Tl-based compounds relative to their Bi-based cuprate homologues. A derivation of \u03c3 is introduced for the optimal Tl2<\/sub>Ba2<\/sub>Ca\u03b7\u20131<\/sub>Cu\u03b7<\/sub>O2\u03b7+2<\/sub> (for \u03b7 = 1, 2, 3) compounds, which exhibit a Tl oxidation state at or near +3, obtaining the fundamental value \u03c30<\/sub> = 0.228 previously established for YBa2<\/sub>Cu3<\/sub>O6.92<\/sub>. Also reported is the marked enhancement in \u03c3 associated with Tl+1<\/sup> and analogous inner-layer cations relative to higher-valence cations. For a model proposition of \u03c3 = \u03c30<\/sub>, the fractional Tl+1<\/sup> content of the mixed-valence compound, TlBa2<\/sub>Ca2<\/sub>Cu3<\/sub>O9\u00b1\u03b4<\/sub>, is predicted to be 1\/3 at optimization, in agreement with existing data. Charge depletion is illustrated for the two Tl-1201 compounds, where \u03c3 < \u03c30<\/sub> values are determined according to substitution of Ba+2<\/sup> or Sr+2<\/sup> by La+3<\/sup>, and\/or Tl depletion. Additionally, statistical analysis of calculated and experimental transition temperatures of 48 optimal superconductors shows an absence of bias in determining \u03c3, A<\/em>, and \u03b6.<\/p>\n\n\n\n\n\t\n\t
\"nFIG1_Tl\"<\/a>
\n

Plot of Tl+1<\/sup> fraction f<\/em>+1<\/sub> versus measured TC<\/sub> for as-synthesized and annealed (Tl1\u2013x<\/sub>Cux<\/sub>)Ba2<\/sub>(Ca\/Tl)2<\/sub>Cu3<\/sub>O<\/sub>9\u00b1\u03b4<\/sub> (open and filled triangles, respectively) [47], TlBa2<\/sub>(Ca\/Tl)2<\/sub>Cu3<\/sub>O9\u2013\u03b4<\/sub> (filled squares) [45, 46], and TlBa2<\/sub>Ca2<\/sub>Cu3<\/sub>O9\u2013\u03b4<\/sub> (open diamond) [49]; the dashed line through the data represents the trend. The filled circle denotes calculated T<\/em>C0<\/sub>Calc.<\/sup> for f<\/em>+1<\/sub> = 1\/3 predicted for TlBa2<\/sub>Ca2<\/sub>Cu3<\/sub>O9\u2013\u03b4<\/sub> with measured T<\/em>C0<\/sub>Meas.<\/sup> indicated.<\/p><\/td>\n<\/tr>\n

\"nFIG2_Tl\"<\/a>
\n

Cumulative number distribution for the differences between measured T<\/em>C0<\/sub>Meas.<\/sup> and calculated T<\/em>C0<\/sub>Calc.<\/sup> for the 48 compounds listed in Table 1 and represented by symbols indicated in legend. Curve is the modeled error function distribution of fitted width 1.31(2) K, as discussed in the text.<\/p>
\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

Dale R. Harshman and Anthony T. Fiory, J. Phys. Chem. Solids 85<\/strong>,\u00a0106 (2015)<\/a>.<\/p>\n

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