I have just sent you my comment, but it might have got lost, so I try again:
Yes, in principle. the Electrochemical Impedance Spectroscopy can yield both the densities and the mobilities of mobile charges. The density is determined by the Debye screening length that determines the "diffusion layer interface capacitance" and the mobilty is determined from the real part of the impedance within the frequency range characteristic of the electrolyte bulk response.
The problem though is that one ends up with two unknowns (the two mobilities) and only one experimental result (the electrolyte bulk resistance). The only way to solve this is a calibration of the mobility of the ion of interest against a "known mobility" of some ion in an experiment where the ion of interest is also present. Situation gets simpler when one can neglect the influence of the "conjugate ion" (either because it is much less mobile or because its density is low) on the value of measured electrolyte bulk resistance.
They might exist other less direct methods of determining the ion transport number (independent/simultaneous determination of density and the mobility of mobile charges) apart from methods like Time Of Flight, conductivity/Hall effect etc.), but I wonder how relevant they might be in your case of solid electrolyte containing Litium. You might consult "Physical Chemistry" by P.W.Adkins (Oxford University Press 1986, page 671).
I have just sent you my comment, but it might have got lost, so I try again:
Yes, in principle. the Electrochemical Impedance Spectroscopy can yield both the densities and the mobilities of mobile charges. The density is determined by the Debye screening length that determines the "diffusion layer interface capacitance" and the mobilty is determined from the real part of the impedance within the frequency range characteristic of the electrolyte bulk response.
The problem though is that one ends up with two unknowns (the two mobilities) and only one experimental result (the electrolyte bulk resistance). The only way to solve this is a calibration of the mobility of the ion of interest against a "known mobility" of some ion in an experiment where the ion of interest is also present. Situation gets simpler when one can neglect the influence of the "conjugate ion" (either because it is much less mobile or because its density is low) on the value of measured electrolyte bulk resistance.
They might exist other less direct methods of determining the ion transport number (independent/simultaneous determination of density and the mobility of mobile charges) apart from methods like Time Of Flight, conductivity/Hall effect etc.), but I wonder how relevant they might be in your case of solid electrolyte containing Litium. You might consult "Physical Chemistry" by P.W.Adkins (Oxford University Press 1986, page 671).