## 1 Introduction
### DSC-Derived DPM Calculation  
As a method of predicting part and material properties, significant research has been conducted studying the viability of using differential scanning calorimetry (DSC) techniques ([PERSON] et al., 2017). DSC is a technique that involves measuring the energy required to heat or cool a known quantity of material at a given rate, and, as such, it is capable of identifying key thermal characteristics of a material, such as the melting temperature and enthalpy of melting. For polymer PBF processes, DSC is primarily used to help identify the temperature at which the part bed is to be held throughout a build to simultaneously avoid melting the entire powder bed and crystallisation-induced part warpage.  
However, DSC can also be conducted on small quantities (\(\approx\)10 mg) of parts to determine the level of sintering induced during the manufacturing process, known as the degree of particle melt (DPM), a term first coined by [PERSON] et al. (2018). DSC techniques are used to inform one about the DPM by identifying two distinct melting peaks and measuring their ratios--one corresponding to regions of powder particles which have been melted and crystallised, known as the \"processing peak\", and another corresponding to particle cores encapsulated in the part which remains unmelted, known as the \"core peak\" ([PERSON] et al., 2016; [PERSON] et al., 2016). These peaks are best represented by Figure 2, with their ratios being a direct consequence of the energy applied during printing.  
Figure 1: The HSS process selectively sinters regions where RAM has been deposited: (**A**) powder deposition stage; (**B**) printing stage; and (**C**) sintering stage (adapted from ([PERSON] et al., 2017)).  
The majority of previous research around this subject involved Nylon-12 parts produced using the LS process. Various findings show that the DPM increases with a higher amount of melted and crystallised material (MCM), formed from virgin powder [11], represented by an increased processing peak proportion. In addition, research has derived an equation to determine the DPM directly from DSC plots, as shown in Equation (1) [12].  
\[DPM=\frac{(Total\ crystallinity-Core\ crystallinity)}{(MCM\ crystallinity-Core\ crystallinity)} \tag{1}\]  
From previous research, it has been shown that the MCM crystallinity (fully melted part) and core crystallinity (original powder) are 25% and 47%, respectively, for LS Nylon-12, with full melting occurring between 24.9 and 25.8% [13]. The total crystallinity is the crystallinity of the sample and is either measured directly or using Equation (2) [12]. The direct calculation of the total crystallinity is achieved by measuring the total melt enthalpy of a sample via DSC and dividing it by the melt enthalpy of a 100% crystalline sample (209.3 J/g) [14]. The calculation of total crystallinity using Equation (2) relies on %MCM and %Core being determined from the relative sizes of the peaks observed.  
\[Total\ crystallinity=(\%MCM\times MCM\ crystallinity)+(\%Core\ crystallinity) \tag{2}\]  
The DPM has been found to be inversely proportional to the crystallinity of the sample, disagreeing with the general appreciation that strength and stiffness increase at the expense of ductility [15]. It is therefore initially surprising that previous research determined that the strength of SLS Nylon-12 increases with an increasing DPM [16]. However, it was hypothesised during this research that an increasing DPM induces improved bonding between powder particles, acting to increase the overall integrity of the part despite the decreased crystallinity. It is therefore clear that DSC-derived DPM is a viable way of determining the mechanical properties of LS Nylon-12 parts.