The phase-shift method and correlation constants, which are unique electrochemical impedance spectroscopy techniques for studying the linear relationship between the phase shift (90 degrees >= -phi >= 0 degrees) versus electric potential (E) behavior for the optimum intermediate frequency and the fractional surface coverage (0 <= theta <= 1) vs E behavior, are proposed and verified to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters. On a Pt-Ir [90:10 % (by weight)] alloy in 0.5 M H2SO4 aqueous solution, the Frumkin and Temkin adsorption isotherms (theta vs E), equilibrium constants [K = 3.3 . 10(-5) exp(2.5 theta) mol(-1) for the Frumkin and K = 3.3 . 10(-4) exp(-2.1 theta) mol(-1) for the Temkin adsorption isotherm], interaction parameters (g = -2.5 for the Frumkin and g = 2.1 for the Temkin adsorption isotherm), standard Gibbs energies of adsorption of overpotentially deposited (OPD) H [(25.6 >= Delta G(0)(0) >= 19.4) kJ . mol(-1) for K = 3.3 . 10(-5) exp(2.5 theta) mol(-1) and 0 <= theta <= 1 and (20.9 < Delta G(0)(0) < 24.0) kJ . mol(-1) for K = 3.3 . 10(-4) exp(-2.1 theta) mol(-1) and 0.2 < theta < 0.8], and rates of change of Delta G(0)(0) of OPD H with theta (r = -6.2 kJ.mol(-1) for g = -2.5 and r = 5.2 kJ . mol(-1) for g = 2.1) have been determined and are compared using the phase-shift method and correlation constants. For 0.2 < theta < 0.8, a lateral attractive (g < 0) or repulsive (g > 0) interaction between the adsorbed OPD H species appears. On Pt, Ir, and Pt-Ir alloys in 0.5 M H2SO4 aqueous solution, the values of K for the Frumkin adsorption isotherms of OPD H decrease with increasing mass ratio of Ir. Negative values of g for the Frumkin adsorption isotherms of OPD H on the Pt, Ir, and Pt-Ir alloys in acidic and alkaline H2O and D2O solutions are experimentally and consistently determined. The duality of the lateral attractive and repulsive interactions is a unique feature of the adsorbed OPD H species on the Pt, Ir, and Pt-Ir alloys in acidic and alkaline H2O and D2O solutions.