The stopping power Δ E and the energy-loss resolution δ E / Δ E of Single-Crystal CVD-Diamond Detectors (SC-DDs) measured with relativistic Heavy Ions (HIs) are interpreted as global quality parameters, characterizing simultaneously crystal texture and carrier-trapping concentrations, as well as the charge-transport properties of intrinsic diamond samples. HI spectra are presented, where spectral lines are obtained similar to the predictions of the Lindhard and Sørensen (LS) theory [J. Lindhard, A.H. Sørensen, Phys. Rev. A 53 (1996) 2443]. The spectroscopic results indicate an almost defect free material, and spatial homogeneity of all parameters relevant to the detector signal (i.e., mass density, dielectric constant, drift mobility and velocity of the charge carriers). Measured and simulated transient current signals generated by relativistic 132Xe ions are discussed according to theories [A. Many, G. Rakavy, Phys. Rev., 126 (1962) 1980; G. Juška, M. Viliunas, O. Klíma, E. Šípek, J. Kočka, Phil. Mag. B 69 (1994) 277; G. Juška, M. Viliunas, K. Arlauskas, J. Kočka, Phys. Rev. B 51 (1994) 16 668] of space-charge limited current (SCLC) transients. The evidence of the spectroscopic results is confirmed by the current-mode studies, and thus indirectly, the potential of the characterization method as well.