*3.1. Measurements of the Thermal Diffusivity*

The measurements of the thermal diffusivity are performed with a Netzsch LFA 427 measurement device. The samples are cut into specimens with a side length of 10 mm ± 0.1 mm. The insulation of the steel sheets is removed with sandpaper with a 500 grit. A thin graphite layer is added on the samples for improved absorption of the laser impulse. A schematic overview as well as some images of the measurement device are depicted in Figure 4. The specimen is inserted into the sample holder. The device is closed, and the sample is purged with argon as a protective gas. A laser pulse is shot at the specimen, and the temperature rise is measured on the back side using an indium antimonide (InSb) infrared detector. An exemplary measurement signal of material M1 at 348 K is depicted in Figure 5. Different models are available for the evaluation of the thermal diffusivity. The first approach is introduced by Parker [18]. The relative maximum signal *s*max = 1 is evaluated. The half time *t*1/2 represents the time, when half *s*1/2 of the maximum signal *s*max is reached. The half time is used to calculate the thermal diffusivity *a* according to [18]:

$$a = 0.1388 \frac{d^2}{t\_{1/2}}.\tag{20}$$

**Figure 4.** Measurement setup for the thermal diffusivity.

**Figure 5.** Exemplary measurement signal of material M1 at 348 K.

Parker assumes ideal conditions, such as an instantaneous energy pulse, adiabatic boundary conditions or constant material properties during the temperature rise. Several improvements of this model are performed. The losses on the front and rear end are added by Cowan [19]. Radial losses are added by Cape–Lehman [20]. Within this study, the standard model with a horizontal baseline correction of the NETZSCH Proteus Software Version 7.1.0. is used, i.e., an improved version of the Cape–Lehman formulation. A total of five temperatures are measured for each material, ranging from room temperature up to 498 K. At each temperature, at least six measurements are used for the calculation of the average value and the variation. The coefficient of variation of the thermal diffusivity measurements *cv* is given in Table 4.


**Table 4.** Coefficient of variation *cv* for measurements of thermal diffusivity *a* in %.

The coefficient of variation is below 1.22% for all materials, except material M8. Material M8 shows a maximum coefficient of variation of 2.7%. These values indicate a good precision of the measurement. Please note that these values only consider the influence of the thermal diffusivity measurement procedure, i.e., the thickness is a constant value and not considered in Table 4. The measurement is repeated five times, and the average value is used for the measurements. For the measurement error estimation, the simplified Parker formula is used [18]. The general accuracy of the NETZSCH LFA is assumed to be ±3% for a 1 mm sample as given in the device data sheet [21]. This value is

not included in the accuracy of different thickness measurements, as one constant value is being used during LFA measurements. The thickness is measured with a similar outside micrometer as utilized in the measurement of the electric resistivity with a maximum measurement error of 0.001 mm. A value of Δ*d* = 0.01 mm is used for the error estimation to include geometrical errors. The estimated error of the resulting thermal diffusivity Δ*a* is calculated as follows:

$$
\Delta a = 0.1388 \frac{\left(d + \Delta d\right)^2}{t\_{1/2}} \cdot x\_{\text{m}} \tag{21}
$$

The value for *x*<sup>m</sup> is selected to be 1%, as for this value, the measurement error of the 1 mm sample of M1 fits to the given data sheet value for the maximum measurement error of 3%. The resulting estimated measurement errors according to Equation (3) for *x* = *a* are depicted in Table 5. A strong dependency on the thickness of the specimen is evaluated. The results of the thermal diffusivity measurement *a* are shown in Figure 6.

The thermal diffusivity *a* varies in a range from 3.1 mm2/s to 13.6 mm2/s. A significant difference between the values of the eight materials is visible. In particular, material M1 with a very low alloy content (see Table 1) and M8 with a very high alloy content stand out in the comparison. The thermal diffusivity of M1 is about 434% larger than the thermal diffusivity of M8 at 298 K. The thermal diffusivity is expected to play a significant role in the calculation of the thermal conductivity (Equation (19)) and the maximum possible dissipated heat in the application.

**Table 5.** Estimated measurement error of the thermal diffusivity measurement *x* = *a* in %.


**Figure 6.** Results of the thermal diffusivity measurements *a*(*ϑ*).
