## 1 Introduction  
The microstructure of materials has a significant influence on the macroscopic material and component behavior [1, 2]. Regarding steels, martensite is an often-desired microstructure due to its hardness. Usually, martensite is produced with an appropriate heat treatment. Martensite of the \(\alpha^{\prime}\) type has been observed to be the most common in ferrous martensite. In [3], five morphology types of \(\alpha^{\prime}\) martensite are reported: lath, butterfly, \((225)_{\gamma}\) plate type, lenticular and thin plate. These different morphologies arise depending of the chemical composition and the start temperature of martensite \(T_{\text{MS}}\). The listed martensite types occur with decreasing \(T_{\text{MS}}\) in the order mentioned above. Besides \(T_{\text{MS}}\), the strength of the parent austenite and product martensite and the critical resolved shear stress for slip and twinning, as well as the cooling rate, seem to be determining factors for the resulting morphology [4, 5, 6, 7, 8]. Otherwise, the factors are rather poorly defined [9]. This work focuses on the lath morphology. The crystallography of lath martensite has been examined in [10; 11] using Kikuchi patterns and electron backscatter diffraction (EBSD) analysis. In these works, Fe-C alloys with different carbon contents are analyzed. Typical structures consist of a three-level hierarchy [12]: martensite laths, blocks and packets. Within this hierarchy, several laths form a block, whereby the laths are martensite crystals with the same orientation (with 0-0.4% C) or two different orientations (with \(\approx 0.6\%\) C) depending on the carbon content [11]. Several blocks with the same close packet plane (CPP) form a packet. Since a prior austenite grain (PAG) has four CPPs, several packets can be formed in it. The packet and block sizes can significantly affect the mechanical properties of the considered materials [13; 14], which can be explained by grain boundary strengthening according to the Hall-Petch strengthening mechanism [15; 16]. As a consequence, there is an interest in quantifying such size effects in order to predict the structure-property relationships. The resulting martensite sizes are determined by various factors. It has been observed that packet and block sizes decrease with increasing carbon content [11]. In [17], a correlation between PAGs and the packet size as well as the block thickness was found. With a finer austenite grain structure, a finer packet and block structure is achieved. The lath size is almost insensitive to changes in the prior austenite grain sizes [14; 18]. Furthermore, higher cooling rates can lead to finer packet and block structures [19; 20; 21; 22; 23; 24]. However, no size effect with regard to the cooling rate was found in [25]. The effects of process parameters related to induction hardening on phase transformation including microstructure size effects were recently investigated in [26; 27; 28; 29; 30; 31; 32; 33; 34]. With a focus on the influence of cooling rates on martensite transformation, constant martensite start temperatures (or at least martensite start temperatures that are not systematically dependent on the cooling rate) indicate an athermal initial nucleation mechanism. Based on the review given in [8], the research group of [PERSON] [7; 35; 36; 37] conducted extensive investigations on the influence of cooling rates on the structure and phase state of iron and low-alloy carbon steels. Accordingly, a fast isothermal martensitic transformation takes place in steels with low and medium carbon contents at moderate cooling rates. At high cooling rates, an athermal mechanism of martensitic transformation was observed. Regarding steels with carbon concentrations \(\geq 0.7\) wt%, an athermal mechanism of martensitic transformation was already observed at moderate cooling rates. The absence of an influence of the cooling rate on the kinetics of martensite formation was confirmed for plain carbon Fe-0.8 wt% [38] and FeNiCoMo alloy [39].