**1. Introduction**

Einstein [1] developed the first model approach regarding the atoms in a crystalline solid as independent harmonic oscillators vibrating at the same frequency by assuming the density of state as a delta function. Debye [2–4] modeled the vibrations in a solid as normal modes of a continuous elastic body, which corroborates well for long-wavelength vibrations that do not depend on the detailed atomic character of the solid and do conform better with experimental scatters at lower temperatures. The density of state modeled by Debye failed for many materials, which present a gap in the density of state [5, 6]. The Debye model does not consider rotational, electronic, and magnetic contributions [7–11]. Ferreira et al. [12, 13] considering Gibbs–Thomson coefficients for equilibrium and nonequilibrium nucleation conditions, and the assumption that when cleaved, certain crystals exhibit surface stress that gives rise to small but detectable strains in the interior of the crystal, i.e., microscopic considerations that predict the presence of surface stress whenever a new surface is created [14], derived a model for pure

elements and compounds, regarding the critical radius expressed in terms of the temperature drop employing the correlation between the solid–liquid surface tension and the bulk melting entropy by unit volume, given in terms of the Gibbs– Thomson coefficient [15, 16]. Consequently, based on the nucleation of solid–liquid or solid–solid phases, the total number of atoms in the volume and a correspondent density of *n* atoms limited by nucleation conditions were proposed to calculate the density of state. Ferreira et al.'s model consists of the phonic, electronic, rotations contributions and predicts magnetic anomalies, such as phase transition temperatures.

In this paper, model predictions of the molar heat capacity of transitional elements from absolute zero to the melting point are compared with the Thermo-Calc Software simulations and experimental data.
