III. RESULTS 5 Specific heat the interstitial charge. Brillouin-zone (BZ) integration was performed with the tetrahe- dron method 19 on a 270 special k -point mesh (4600 k -points in the full BZ). We carefully tested the convergence of the results presented with respect to the parameters mentioned and found them to be fully sufficient for all the presented characteristics of the SmPd$_{2}$Al$_{3}$ compound. We also analyzed the temperature evolution of the magnetic entropy. In addi- tion we included spin-orbit coupling into the calculations for the electronic structure of the valence states (delocalized Bloch states); we found only minor changes in the DOS curves and calculated crystal field parameters. The calculations first principles of the crystal field interaction were performed using the method described in ref. $^{20}$. In these calculations the electronic structure and corresponding distribution of the ground state charge density was obtained using the full-potential APW + lo method. The CF parameters originated from the aspherical part of the total single-particle DFT potential in the crystal. To eliminate self-interaction, a self-consistent procedure was first converged with the 4f electrons in the core $^{20}$, which was the open-core approximation used in this work. To diagonalize the mi- croscopic CF Hamiltonian of the hexagonal point group symmetry, we used J = 5/2, J = 7/2 and J = 9/2 multiplets and Wybourne parameterization of the CF matrix elements $^{21}$. Therefore the J -mixing and the intermediate-coupling many-particle 4f -wave functions were properly taken into account. The CF perturbation matrix had a dimension of 24 and the resulting eigenenergies and eigenfunctions were used to calculate the magnetic susceptibility as a function of temperature. We successfully prepared the SmPd$_{2}$Al$_{3}$ single crystal of high quality as confirmed by the Laue patterns. The XRPD data contained only the reflections compatible with a hexagonal structure of the PrNi$_{2}$Al$_{3}$ type(space group P6/mmm ) with lattice parameters a = 5.293 ˚ A, c = 4.064 ˚ A, which are in good agreement with published data. The proper 1:2:3 stoichiometry of the grown crystal was confirmed by EDX analysis within the accuracy of the method. No spurious phase has been located. We also carried out an area analysis and concentrations gradients were also studied. No concentration gradients have been detected. The C$_{P}$ vs. T data were collected by two series of measurements in a magnetic field