The effect of mixed valency (MV) is considered as the result of competition of metallic, covalent, and ionic bonds. Amplitudes #xi#_n of state probabilities of rare-earth (RE) ions with different numbers (n) of covalent electrons are in-troduced as expansion coefficients of the wave functions on many-electron operator spinors (MEOS). The entropy of fluctuations of chemical bonds (FCB) and strong dependence of covalent-bonds' energies r on the lattice parameter determine the phase diagrams of RE metals and compounds. Cal-culated spectra of FCB and band electrons as well as their correlators depend functionally on #xi#_n temperature (T), and pressure (P). Variational method is used for the thermodynamic potentials #PHI#(#xi#_n) The small value #xi#~2_3 0.1 is de-termined for the metallic (M) phase of Sm_(1-x)Gd_xS. This value is equivalent to MV of Sm ions and correlates with Gd critical concentration (x< 0.15) on the P-T-line of semiconductor (s/c)->M transition. The theory interprets the de-crease ( 20 times) of charge-carriers' mobility at s/c->M transition in SmS. Calculated phase P-T-x-diagrams are agreed with experiment.
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