#### 3.1. Determination of H Diffusion by Permeation Measurement

Charging parameters: Without the promoter, which inhibits the recombination of hydrogen, there was no significant hydrogen absorption. The same effect was observed with sulphuric acids of different molarity (see

Figure 7). In contrast to the acids, the bases exhibited poor electrical conductivity. It was shown that from a molarity of 1 mmol/L NaOH and 0.1 mmol/L H

_{2}SO

_{4} the potential limit of 20 V of the galvanostat was exceeded. The solutions were mixed with 1 g/L NaCl to improve conductivity. It was found that NaCl has no influence on hydrogen absorption.

Figure 8 describes the hydrogen uptake under the influence of different pH-values. It could be observed that hydrogen absorption is not further influenced from a pH-value greater than 3. It can be assumed that additional hydrogen is produced by corrosion (metal dissolution) at pH-values less than or equal to 3. Higher values cause passivation by the formation of a barrier layer.

The current density has a considerable influence on the hydrogen absorption (see

Figure 9). A current density of 1 mA/dm

^{2} did not lead to hydrogen absorption. With higher currents a steadily increasing hydrogen absorption could be observed, but also an increased bubble formation. A strong formation of bubbles during the permeation measurements could lead to falsification of the results, as they occupy the workpiece surface and thus influence the resulting current density. The investigations were carried out with a 10 mmol/L NaOH solution (1 g/L NaCl and CH

_{4}N

_{2}S for each). Since there was no direct correlation between pH-values greater than 3 and hydrogen absorption (see

Figure 9) it was assumed that the investigated current densities were representative for all NaOH polarities up to 10

^{−4} mol/L H

_{2}SO

_{4}.

Influence of the pH-value:

Figure 10 shows the measured oxidation currents for 1–100 mmol/L NaOH and H

_{2}SO

_{4} after deduction of the corrosion current. The bases used led to almost identical curves. From a molarity of 1 mmol/L H

_{2}SO

_{4} the measured oxidation currents increased steadily. A concentration of 10 mmol/L and 100 mmol/L H

_{2}SO

_{4} caused a very steep increase of the measurement curves. The sudden increase in hydrogen absorption from a sulphuric acid molarity of 10 mmol/L could already be determined during the loading tests. During the standardization of the data, only small differences were found in the courses. The right part of

Figure 10 shows the sample after the permeation tests. The measuring surface was free of corrosion products. Only an outer corrosion ring was formed. It can be assumed that the ring was caused by contact corrosion. The ring appeared in all investigations and had no measurable influence.

Figure 11 summarizes the results of the investigations with NaOH and H

_{2}SO

_{4} of different polarities as loading solution. All electrolytes were mixed with 1 g/L CH

_{4}N

_{2}S, the alkaline ones additionally with 1 g/L NaCl. A slight increase of the diffusion rate could be observed with increasing reduction of the pH-value. The cause is assumed to be the formation of a passive layer at higher pH-values. Acid solutions, on the other hand, lead to a dissolution of the oxide layer, which is presumably diffusion-inhibiting. However, the low influence of the pH-value and the associated passivation can also be attributed to the sample thickness (≈ 1 mm). The diffusion-inhibiting effect of the passive layer is almost negligible due to the thickness ratios between substrate and oxide layer. On average, identical diffusion coefficients could be determined for both quenched and tempered steels (≈4 × 10

^{−11} m

^{2}/s at room temperature).

Influence of sample thickness: The influence of possible oxide layers or passive layers was determined. Barrier and cover layers on the metal can inhibit diffusion. The change of the material thickness with an assumed constant barrier layer should clarify the influence. An increase of the diffusion velocity from a material thickness of 1.4 mm could be observed as well as a growing discrepancy between the ferritic starting material and the martensitic hardened steel. It can be assumed that the absorption time has an influence on the measured diffusion time if the thickness is too low. The effect is further enhanced if the material to be investigated (such as the ferritic material) has a high H-diffusion rate. In martensitic microstructures with a lower diffusion rate, the influence is already significantly reduced. In addition, the influence of the pH-value becomes more pronounced (see

Figure 12).

In [

21] the same effect could be observed. The authors tested the influence of a 0.5–2 mm thick sample. With increasing membrane thickness the measured permeation current density decreases. In contrast, the diffusion coefficients determined by the time-lag method were increased. The diffusion coefficient increased from 1.10 × 10

^{−11} m

^{2}/s (0.5 mm) to 3.49 × 10

^{−11} m

^{2}/s (2 mm) for pure iron. The authors held mechanical polishing responsible, which led to a change in the microstructure and, thus, to hardening [

21]. The effect explains the significant difference in the investigations carried out here. In the initial state, strain hardening is more pronounced than in the quenched and tempered state due to the lower strength. An examination was carried out by varying the processing of the sample surface on hardened 22MnB5 thin sheets.

Influence of surface condition: 22MnB5 fine bleach with different grain sizes (P800 and P80) was ground and prepared by compressed air blasting with solid Al

_{2}O

_{3} granulate (see

Figure 13). The surface with a P800 grain was produced by stepwise polishing. The surfaces were processed on the loading side as well as on the analysis side. By using an acid and a lye the pH-value should be excluded. Compressed air blasting led to the lowest diffusion velocities. It can be assumed that this process produces the highest surface hardenings. Grinding with different grain sizes, on the other hand, does not seem to have any discernible influence.

#### 3.2. Determination of H Diffusion by Thermal Desorption Analysis

Constant heating rate (temperature ramp):

Figure 14 (left) shows various desorption curves for the 22MnB5 and its coating concepts. For a more detailed description of the coating concepts, please refer to the publications [

22]. All curves were subject to the same temperature regime. It can be seen that the coatings shift the signal maxima to higher temperatures. From this it can be concluded that the zinc-based and even more so the aluminium-based coating prevents hydrogen diffusion and therefore also inhibits desorption. In the right part of

Figure 14, the temperatures of the signal maxima and the corresponding heating rates are entered according to Equation (2) and their increase is determined by a linear regression. The activation energy was determined by multiplying the increase by the negative of the universal gas constant.

The diffusion constant was then calculated, depending on the sample geometry, using the material thickness d or radius a with Equation (3). The following values result for the quenched and tempered steels 37MnB4 and 22MnB5 and their coating concepts (see

Table 5). The listed diffusion coefficients were calculated with Equation (1) at a temperature of 22 °C.

Table 5 shows the diffusion velocities of the steels 37MnB4 and 22MnB5. It becomes clear that the coatings lead to a reduction of the hydrogen transport as they act as a barrier.

Empirical test: The measurement shown in

Figure 15 (left) shows that the hydrogen effused faster than the samples could be heated. As the temperature is of crucial importance for the calculatory verification, it was averaged from the beginning to the end of the measurement at any time. (see Equation (9)).

where Ø

T is the average temperature;

T is the temperature; and

t is the time.

Following the determination of the average temperature, the measurements were compared with the desorption curves from the calculation. The calculated comparison was made with the previously determined values from the thermal desorption analysis using Equations (8) and (10). Equation (10) was derived from (8), by removing the Fourier series and convert to

t:

With both equations a satisfactory agreement with the measurement could be determined on the basis of the previously determined values. Only Equation (10) shows an error if desorption is too low (see

Figure 15, right). This can be justified by removing the Fourier series. From a desorption of approx. 50%, both calculated curves are almost identical.

By simply converting the Equation (10) from

t to

D, the diffusion velocity can be determined.

Figure 16 shows the calculated diffusion rates at different desorption rates. For comparison, the calculated diffusion coefficients from the previously determined values (T-ramps) are also entered. From a desorption of 50%, a high degree of agreement could be demonstrated. A disadvantage is that no statements can be made about the activation energy and the pre-exponential diffusion coefficient, as is also the case with permeation measurement.

Isothermal determination of the diffusion variables: To determine the

E_{a} and the

D_{0}, Equation (10) can be converted into a linear equation by logarithmizing, as shown below.

D_{0} can be calculated from the point of intersection with the ordinate and

E_{a} from the slope of the function.

Similar to the temperature ramps, the logarithmic time at which a certain hydrogen desorption took place is plotted on the ordinate from several measurements as well as the reciprocal of the corresponding mean temperature on the abscissa (see

Figure 17). The graph shows different desorption steps of four isothermal measurements (150 °C, 200 °C, 250 °C, 300 °C).

The linear regressions provide the respective slope and intersections with the ordinate. Below are the calculated values for

D_{0},

E_{a} and

D at different desorption points (see

Figure 18). The values are subject to small fluctuations and

D increases with increasing desorption. On average, a value of 2.91 × 10

^{−6} m

^{2}/s could be determined for

D_{0} and 28.76 kJ/mol for

E_{a}. The averaged

D (22 °C) was 2.76 × 10

^{−11} m

^{2}/s. All values show a good agreement with those determined before. Strong deviation below 50% desorption is probably due to the removal of the Fourier series.

Iterative determination of

D by isothermal measurements: In order to improve the results, an iterative procedure was carried out. The iteration process is described in

Figure 19. With this method, several

D_{0} were given from a selected interval. On the basis of the knowledge gained so far, an area between 1 × 10

^{−6} and 5 × 10

^{−6} m

^{2}/s was defined and divided into equal sections. A starting value of 23 kJ/mol was specified for the activation energy. From the starting value of

E_{a} and each

D_{0} the mean hydrogen concentration at all times of the measurement was calculated with Equations (1) and (8). The Fourier series was determined to n = 500 and the temperature was averaged from the beginning of the measurement to the respective measured value. The absolute deviation of the calculated desorption is then determined from the analysis with the measured desorption. At the same time, the activation energy was increased by any value

i (here: 0.01 kJ/mol) and the absolute deviation from the measurement was determined exactly as before. If the calculation with the increased activation energy has a smaller deviation than that of the initial value, this deviation is increased by

i. This iteration is repeated for all pre-exponential diffusion coefficients until no further improvement occurs. The calculated desorption curves at the beginning of the iteration as well as an isothermal measurement at 200 °C are shown in the left partial image of

Figure 20.

In this way, a suitable activation energy was determined for each pre-exponential diffusion coefficient, which, however, leads to a minimal deviation from the measurement.

Figure 20-right illustrates the problem. It shows that all characteristic curves are congruent. In addition to the graph, the predefined pre-exponential diffusion coefficients are shown with the determined activation energies, which lead to the smallest absolute deviation. It becomes clear that the

E_{a} are distributed over a wide range depending on

D_{0}.

The true value was calculated by comparison with several measurements at different temperatures (150 °C, 200 °C, 250 °C, 300 °C). The fact that

E_{a} and

D_{0} must be constant at different temperatures for hydrogen diffusion in the material was exploited. For this purpose, the standard deviation of the activation energies was formed from several measurements. The pre-exponential diffusion coefficient with the activation energies showing the smallest standard deviation among each other is the true value (see

Figure 21). The figure shows a clear minimal turning point of the standard deviation. This means that the activation energy varies the least in the minimum function, whereby it can be concluded that the value pairs determined there reflect the hydrogen diffusion in the material.

Table 6 shows an extract from the iteration procedure performed, with the specified pre-exponential diffusion coefficients as well as the determined activation energies of the respective measurement series. In this case, the

D_{0} of 2.38 × 10

^{−6} m

^{2}/s had the smallest standard deviation (0.258). The corresponding

E_{a} corresponded on average to 26.67 kJ/mol. The calculated diffusion coefficient (at 22 °C) was 4.54 × 10

^{−11} m

^{2}/s.