4.3.1. Heckel Analysis

The Heckel model provides method for transforming force and displacement signals to a more simpler linear relationship for materials undergoing the compaction process [43]. This increases the popularity of model for studying relationship between relative density and applied compaction pressure. [19,26,44]. The basis for the Heckel equation is that the densification of the bulk powder under applied compaction pressure follows first-order kinetics [44].

The "in-die" measurements do not account for elastic recovery of material, eventually affecting data interpretation and accuracy. Therefore, in the present study, densification of RIV, MAL, and RIV-MAL Co as a function of applied compaction pressure was evaluated by Heckel analysis using "out-of-die" measurement. The "out-of-die" measurement is more reliable method to study bulk deformation of a pharmaceutical material because the material is allowed to undergo elastic deformation prior to density analysis.

The linear region of the Heckel plot provides an important property of the material, that is mean yield pressure (Py). In the Heckel plots, correlation coefficients of R<sup>2</sup> > 0.98 were achieved in the case of RIV and RIV-MAL Co, while R<sup>2</sup> > 0.91 was achieved in the case of MAL. Among these solids, RIV-MAL Co showed the highest densification and the lowest Py (Figure 5). The Py of MAL (323 MPa) is very high as compared with RIV (133 MPa) and RIV-MAL Co (83 MPa). The lower mean yield pressure (Py) value obtained for RIV-MAL Co indicates its excellent plastic deformation under the applied compaction pressure. In the same way, RIV can also undergo plastic deformation at the normally utilized compaction pressure of 133 MPa. In contrast, MAL could not undergo plastic deformation at a compaction pressure as high as 323 MPa and also exhibited severe chipping and laminations at compaction pressure > 222 MPa. This behavior demonstrates poor plasticity of MAL during bulk deformation.

**Figure 5.** A plot of mean yield pressure (Py) and tensile strength at zero porosity (σ0) for RIV, MAL, and RIV-MAL Co.
