5. Measurement results and individual discussion of diffusion coeffi-
5.2. Results of overall system diffusion coefficient measurements
Pd diffusioncoefficient/m2 s−1
noPd E1 D1 C2 C1 B2 B1 A5
A3 sample
A2 A1 10−17 10−18 10−19 10−20 10−16
PLD
Figure 5.5.: Diffusion coefficients measured in this work sorted after sample. The PLD samples are marked by a grey box. Black squares are measured byin situ XRD measure-ments, blue triangles are measured by gas volumetry measurements and red circles are measured by resistance measurements.
Three methods were used to measure diffusion coefficients: X-ray diffraction (see chapter 3.5 and equation 3.20), gas volumetry (see chapter 3.2 and equation 3.10) and resistance measurement (see chapter 3.3 and equation 3.17). These methods give the overall system diffusion coefficient of the sampleDXRD/G/Rove (the superscript gives the measurement method). This is most likely a combination of the grain diffusion coefficient DV and the grain boundary diffusion coefficient DGB, but the single components cannot be distinguished by the methods utilized in this work. Table B.3 in the appendix B.2.2 gives the results for the different samples measured. The same information is shown in figure 5.5. Diffusion coefficients measured byin situXRD are plotted in black, values measured by a resistance measurement are plotted in red and the gas volumetry measurements are plotted in blue. The PLD samples are marked by a gray background. The black dashed line gives the average diffusion coefficient of all diffusion coefficients measured: Dove = 6.9+140−6.5·10−18m2s−1. The gray solid lines mark are the variance. The average was calculated from the logarithm of the
diffusion coefficients, because diffusion coefficients are expected to be log-normal distributed. Figure 5.5 shows that the measured diffusion coefficients for a single sample fit together well, independent of the method. This is even more valid if only a single loading step is taken into account6. Because of this, in the following the average diffusion coefficient of each loading step is discussed.
diffusioncoefficient/m2 s−1
10−17 10−18 10−19 10−20 10−16
103 104 105 106 teval /s
10 100 1000
λ
a) b)
Figure 5.6.: Comparison of the diffusion coefficient with (a) the time range of the evalu-ation teval and (b) λ. The PLD samples are marked as blue diamonds. Samples where no resistance measurement was available to measure the diffusion length are marked as open circles. The average and variance of all diffusion coefficients is marked by a dashed black line and gray solid lines respectively.
Figure 5.6 a) compares the diffusion coefficients evaluated by gas volumetry and resistance measurements with the evaluated time teval. Both methods are based on the diffusion from a well-stirred fluid of limited volume using the first term approximation as discussed in chapter 3.2.3 and 3.3.3 (equation 3.10 and 3.17). The first term is an appropriate approximation for long measuring times. Therefore, for short times a change in the measured diffusion coefficients can occur as the approximation becomes invalid. This is not found for the measurements in this work.
Figure 5.6 b) compares the diffusion coefficients with λ (compare equation 3.5).
Again, no trend is found. As discussed in chapter 3.2.2, the first term approximation is appropriate forλ >0.4. This is fulfilled for all samples. Therefore, no dependency of the diffusion coefficient on λ is expected. In both parts of figure 5.6 the blue diamonds mark the PLD samples. While one shows a very low diffusion coefficient the other falls within the variance of all samples.
Open circles mark samples that were measured without a resistance measurement (this includes both samples of batch IBS-C and sample IBS-A5). This means that
6Only for sample IBS-D1 and IBS-E1 more than one loading step were measured.
no diffusion length was measured at the same time. To evaluate the diffusion length for these samples the hydrogen concentration cH in the sample was calculated by equation 3.2. Assuming a maximum concentration of cH =2 and a linear hydride front growing through the magnesium film, the volume fractionφcM gH2 of the MgH2
can be estimated:
φcM gH2 ≈cH/2
For some samples this value can be compared with the volume fraction φRM gH2 as calculated from the resistance values (see figure B.5 a) in appendix B.2.2). It was found that φM gH2, as calculated via the concentration cH is smaller than when calculated via the resistance R. This is important to remember as the resistance already underestimates the hydride volume fraction φM gH2 (see chapter 3.3.2).
Figure 5.7: Comparison
As discussed in chapter 2.2.4 grain size can influence the diffusion coefficient in poly-crystals because it changes the amount of influence the volume and grain boundary diffusion coefficients have on the system diffusion. Therefore, figure 5.7 presents the diffusion coefficient as a function of the grain size of the sample. The in-plane grain size of the as-prepared samples was applied for anytime a sample was measured for the first time (see table 4.2 and chapter 4.1). If the sample was loaded a second time the grain size of the loaded and unloaded sample was applied (see table 4.2 and chapter 4.3). This size was measured after all loading experiments were finished.
Therefore, it is implied that the grain structure changes during the first loading but not significantly afterwards. This is assumed because of the results shown in chapter 4. No dependence on the grain size can be found. The PLD samples may be, on average, slower than the IBS samples but this is not a clear dependence.
Two possible dependencies of the diffusion coefficient on experimental parameters were found in this work. The first is shown in figure 5.8. The diffusion coefficients are shown as function of the hydrogen loading pressurepH. A possible increase for
increasing hydrogen pressure is found and indicated by a red dotted line. It will be discussed in chapter 6.3. Figure 5.9 shows the other possible dependence. The diffusion coefficient is plotted as function of the iron content of the samples. A linear fit shows the increase of D with increasing iron content. The diffusion coefficients are plotted linearly to clarify the linear dependence. As before, the black dashed line still shows the average diffusion coefficient and the gray solid lines the variance.
diffusioncoefficient/m2 s−1
10−17 10−18 10−19 10−20 10−16
0 200 400 600 800
hydrogen pressure /hPa
Figure 5.8.:Comparison of the diffusion coefficient with the hydrogen loading pressurepH. The PLD samples are marked as blue diamonds. Samples where no resistance measurement was available to measure the diffusion length are marked as open circles. The average and variance of all diffusion coefficients is marked by a dashed black line and grey solid lines respectively. The red dashed line is a guide-of-eye for a possible correlation between pH
andD.
15
diffusioncoefficient
10
5
0
0 2 4 6 8 10 12 14 16
iron content /at%
/(10−17 m2 s−1 )
Figure 5.9.:Comparison of the diffusion coefficientDwith the iron content of the sample.
The PLD samples are marked as blue diamonds. Samples where no resistance measurement was available to measure the diffusion length are marked as open circles. The average and variance of all diffusion coefficients is marked by a dashed black line and gray solid lines respectively. The red fitting function shows the linear dependence betweenDand the iron