Aim of the work
5. Methodology
5.5. Estimation of the activation energy of the oxygen transport
In the conducted TG experiments it was possible to measure time needed for the oxidation or, which is of a greater importance from a point of view of practical application, reduction time (in 5 vol.% H2 in Ar) of the samples at various temperatures (400-600 °C).
As these processes can be associated with insertion and removal of the oxygen from the bulk of the grains (through surface), comparison of the time needed for a certain change of mass of the sample at different temperatures should allow for an evaluation of oxygen transport-related parameters (theoretical approach). Using the approximation below, it can be assumed that the activation energy of the bulk diffusion of the oxygen can be evaluated.
Process of the oxygen transport can be divided into bulk diffusion and surface exchange part, and consequently, determination of the diffusion coefficient and surface exchange constant would be of interest. However, as changes of the oxygen content in the presented studies are close to one mole per mole of compound, the recorded weight change characteristics cannot be used as “relaxation profiles” for fitting of and . Also, the mechanism of the oxygen release has two-phase nature (see chapter 6.2.2 and appendix
B for more information), and as such, there is no way to conduct experiment in a way that the data could be analyzed like it is done in standard relaxation-type studies with small changes of the oxygen content.
The recorded time needed for the reduction presented in Arrhenius coordinates for ionic conduction (i.e. in versus coordinates, t – time, T – temperature) shows activated character (linear behavior), which allows to calculate for the respective material. To parameterize the process, change of 95% of total weight change and time needed to attain this value at respective temperature was chosen as characteristic, and such data will be presented further in this work (chapters 8.3.3, 9.5 and 10.6). However, for early considerations based on BaY1-xGdxMn2O5+δ series of oxides, was calculated assuming change of weight as 3 wt.% = 1875 μmolO·g-1, 2 wt.% = 1250 μmolO·g-1, 1 wt.% = 625 μmolO·g-1, and also 99% , 95% and 90% of change of the total weight change, and such results are gathered in Tabs. 5.3-5.8. Please notice that there are no results presented for BaYMn2O5+δ at 400 °C, due to a very slow rate of the reduction process.
Tab. 5.3. Time needed for 3 wt.% change of weight of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 3 wt.% = 1875 μmolO·g-1
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 49.70 13.15 5.88 3.47 2.18 0.85
BaY0.25Gd0.75Mn2O5+δ 33.08 12.25 6.48 3.65 2.48 0.72 BaY0.5Gd0.5Mn2O5+δ 44.67 18.92 8.40 3.87 2.28 0.83 BaY0.75Gd0.25Mn2O5+δ 34.37 10.55 5.12 2.92 2.00 0.78
BaYMn2O5+δ 21.75 7.10 3.82 2.53 0.85
Tab. 5.4. Time needed for 2 wt.% change of weight of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 2 wt.% = 1250 μmolO·g-1
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 13.28 4.13 2.33 1.68 1.22 0.65
BaY0.25Gd0.75Mn2O5+δ 10.25 4.87 3.27 2.13 1.57 0.53 BaY0.5Gd0.5Mn2O5+δ 13.28 6.36 3.70 2.11 1.42 0.63 BaY0.75Gd0.25Mn2O5+δ 10.72 4.67 2.68 1.80 1.33 0.59
BaYMn2O5+δ 6.40 3.12 2.05 1.56 0.58
Chapter 5. Methodology 71
Tab. 5.5. Time needed for 1 wt.% change of weight of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 1 wt.% = 625 μmolO·g-1
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 4.82 1.77 1.13 0.92 0.70 0.53
BaY0.25Gd0.75Mn2O5+δ 4.33 2.42 1.78 1.20 0.92 0.45 BaY0.5Gd0.5Mn2O5+δ 4.70 2.65 1.83 1.67 0.86 0.46 BaY0.75Gd0.25Mn2O5+δ 3.98 2.02 1.48 1.03 0.80 0.46
BaYMn2O5+δ 2.36 1.67 1.22 0.98 0.39
Tab. 5.6. Time needed for 99% change of total weight change of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 99% change of total weight change
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 60.50 22.86 9.30 5.25 3.18 0.82
BaY0.25Gd0.75Mn2O5+δ 46.43 27.20 10.58 6.03 5.38 0.66 BaY0.5Gd0.5Mn2O5+δ 72.25 42.42 19.45 6.15 3.30 0.88 BaY0.75Gd0.25Mn2O5+δ 55.80 24.08 9.68 5.15 3.40 0.79
BaYMn2O5+δ 51.50 16.20 10.98 8.20 0.72
Tab. 5.7. Time needed for 95% change of total weight change of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 95% change of total weight change
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 46.08 14.43 6.38 3.80 2.30 0.82
BaY0.25Gd0.75Mn2O5+δ 35.11 15.75 7.65 4.30 2.82 0.71 BaY0.5Gd0.5Mn2O5+δ 54.25 28.28 13.08 4.98 2.60 0.85 BaY0.75Gd0.25Mn2O5+δ 42.8 15.70 6.78 3.70 2.38 0.80
BaYMn2O5+δ 33.93 10.14 5.45 3.56 0.88
Tab. 5.8. Time needed for 90% change of total weight change of BaY1-xGdxMn2O5+δ, during reduction at respective temperatures together with activation energy of the process.
chemical composition
time of reduction [min] at respective temperature 90% change of total weight change
[eV]
400 °C 450 °C 500 °C 550 °C 600 °C
BaGdMn2O5+δ 35.42 10.80 5.23 3.16 2.03 0.78
BaY0.25Gd0.75Mn2O5+δ 27.38 12.06 6.43 3.68 2.53 0.67 BaY0.5Gd0.5Mn2O5+δ 41.47 20.25 9.42 4.13 2.36 0.81 BaY0.75Gd0.25Mn2O5+δ 33.33 12.00 5.68 3.16 2.13 0.77
BaYMn2O5+δ 25.01 8.12 4.45 2.90 0.85
Data presented in the above tables suggest that increases (almost linearly) with the increasing value of weight change taken as the end point of the time measurement. It seems
therefore that the mechanism of the oxygen release changes as the process proceeds, which was expected taking into account two-phased nature of the process. Furthermore, the samples can be compared between each other using values of because:
Assumed different weight changes for the calculation of of the samples corresponds to the release of (in each case) a very similar amount of the oxygen from all studied samples per volume (alike density) and per weight (alike molar mass).
As microstructure of the powders is very similar with comparable grain size distribution and BET specific surface, the average diffusion distance for the oxygen to be released from grains will be comparable, and also total surface, through which the oxygen will be released will be very similar (see chapter 6.3).
However, more assumptions can be also made and justified taking into account the following information:
For most of the perovskite-type oxides the available literature data suggest that the surface exchange coefficient is at least 2-3 orders of magnitude higher than the diffusion coefficient (calculated from tracer methods or relaxation studies) [123].
See also discussion in chapter 2.3, and referenced work [60].
For powder morphology, (see chapter 6.3) the oxygen release process is highly unlikely to be limited by the surface exchange reaction only. Therefore, it is rather the bulk diffusion in the grains, which is a limiting factor.
It is also known that often does not show clearly defined temperature dependence, from which can be calculated. On the contrary, often shows activated character on temperature, with values below 1 eV being observed [123].
Structural modification during oxygen release from BaYMn2O6 through BaYMn2O5.5
to BaYMn2O5 (or reverse, oxygen uptake [7]) occurs with preservation of the structural framework (see chapter 6.2.2).
Considering above, the calculated (for times representing most of the actual weight change) can be correlated with changes of the oxygen transport in the materials as a function of temperature, and since surface exchange reaction and structural changes can
Chapter 5. Methodology 73 be neglected as not limiting, the values can be associated to the diffusion process of the oxygen in bulk of the grains, but likely, in the final step of the oxygen release process.
Since in the powdered sample the grains of different size and shape are present, no simple model can be used to evaluate behavior of the oxygen release, however, because statistically the samples are similar, averaged values can be considered. It is well known that mean square displacement of diffusing species is proportional to the diffusion coefficient and time as (23):
(23)
If conditions of the transport (as documented above) are similar, release of the oxygen from the material would directly correspond to the same mean square displacement (of the oxygen in all grains). And consequently (24):
, where (24) Therefore, temperature dependence of diffusion coefficient in Arrhenius coordinates (activation energy of ) would be the same like activation energy of reduction time. Also, considering ionic conductivity of the oxygen, and taking into account Einstein equation, it can be written that oxygen mobility is proportional to the (average or effective) diffusion coefficient at the particular temperature (25):
(25)
Electrical conductivity is known to depend on charge, concentration and mobility of the charge carriers according to the equation (26):
(26)
With constant value of and the same value of , it can be stated that the activation energy of the ionic conductivity of the mobile oxygen at the final stages of the oxygen release process would be the same as the activation energy of the reduction time. Of course, since
it corresponds to almost all of the oxygen being released from the material, and it was shown that there is no single value characterizing whole process, the above diffusion coefficient can be treated as effective one. But, anyway, the calculated activation energy on the order of 0.7-0.8 eV can be related to the activation energy of the oxygen mobility.
While this is only a very rough approximation, it seems reasonable, with values being typical for the oxygen diffusion in oxides. Please notice that the actual values of are not provided, but only the activation energy.