Modeling of a microstructure and calculation a tortuosity factor for cathodic materials of LSM–YSZ

In this work changes in physico-chemical properties (oxygen interphase exchange rate and specific resistance) and microstructure parameters (TPB length and tortuosity factor) with time have been analyzed to find the quantitative relationships on the example of composite cathode material LSM-YSZ. 3D microstructure of LSM-YSZ materials has been reconstructed and tortuosity factor has been calculated on the basis of SEM image analysis using the original software.


Introduction
One of the most important areas of the global energy and energy efficiency is the development and study of the solid oxide fuel cells (SOFCs), they belong to class of chemical power sources, in which the chemical energy reagents (fuel and oxidizer) electrochemically converted into electricity.Oxygen from the air is usually in the role of oxidizer and hydrogen as fuel.SOFC retains the ability to generate electricity as long as reagents come from the outside and the results of their interaction are taken away.A signifi-cant advantage of the SOFCs is its silent operation and a lack of emissions during its operation, but there are several problems associated with the degradation of the materials that make up SOFCs.It is known that the microstructure of functional materials is a determining factor in the kinetics of the processes occurring during operation of the SOFC.The source of the information about it is the images obtained by scanning electron microscopy (SEM).To estimate the parameters of the microstructure, analysis of two-А.С. Фарленков 1, 2 , М. В. Ананьев 1, 2 1 Уральский федеральный университет, 620002, Екатеринбург, Мира, 19. Факс: (343) 375-97-78; тел.: (343) 375-44-72; E-mail: rector@urfu.ru 2 Институт высокотемпературной электрохимии УрО РАН, 620990, Екатеринбург, Академическая, 20.Факс: (343) 374-59-92; тел.: (343) 374-50-89; E-mail: Dir@ihte.uran.ru

Моделирование микроструктуры и расчет фактора извилистости для катодных материалов LSM-YSZ*
В работе на примере композиционного материала LSM-YSZ сравнивается изменение физико-химических свойств (скорости межфазного обмена кислорода и удельного сопротивления) и параметров микроструктуры (протяженности ТФГ и фактора извилистости) от времени с целью нахождения количественных взаимосвязей.Для электродных материалов LSM-YSZ проведена 3D-реконструкция микроструктуры и рассчитан фактор извилистости на основе результата анализа изображений РЭМ с использованием оригинального программного обеспечения.dimensional micrographs of sections or the surface of the material is not enough.There are a number of parameters of the microstructure, which can only be calculated from the three-dimensional model: the length of the three-phase (TFG) and interphase (FIG) boundaries; proportion of active TFG, open pores; tortuosity factor, etc.In this paper we present the main directions and results in the analy-sis of microstructure parameters on the example of the composite LSM-YSZ, and comparison of time changes in the physicochemical properties of this material (the rate of the interfacial exchange of oxygen and resistivity) and the parameters of its microstructure (TFG length and tortuosity factor) in order to find quantitative relationships.

Results and Discussion
The isotopic exchange of oxygen and microstructure of LSM-YSZ.
In this paper, tests of two symmetrical cells were carried out at T = 850 ° C, PO 2 = 10 -2 atm.First symmetrical cell was tested for 300 hours, and the other -for 1000 hours.During long-term tests by isotopic exchange of oxygen [1] the kinetics of the interaction of gas-phase oxygen with the test symmetric cells was studied.The parameters of the microstructure of the samples before and after the test was determined by the digital processing of photomicrographs of cross-sections obtained with the scanning electron microscope Tescan MIRA 3 LMU.Fig. 1 and Fig. 2 show photomicrographs of the cell structure of symmetric LSM-YSZ | YSZ | LSM-YSZ (La0,8Sr0,2MnO3-0,82ZrO2 • 0,08Y2O3) before the test.
Since the contrast between the phases of LSM and YSZ in the image is absent (Fig. 2), image analysis method was used [2], in which it was established that the distribution function of particles sizes is different, and these changes are due to coarsening of the phase LSM (Fig. 3).Conducted by 3D-reconstruction of the microstructure of the electrode symmetric cells (Fig. 4), the dependence of TFG (contact between the LSM | YSZ | O2) from time was obtained.The TFG length was defined as referred to the volume number of connections between voxels (Voxel = volume pixel) of three types, corresponding to the phases LSM, YSZ and pores [4,5].It was established that the length of TFG decreased by approximately 15% (Fig. 5), whereas the constant of interfacial oxygen exchange k decreased by about 16% after 1000 hours (Fig. 6).
Apparently, the process of interfacial oxygen exchange by TFG is sufficiently fast compared with the exchange of oxygen on individual components LSM and YSZ.As a result, a decrease in TFG lenght eventually leads to a reduction of interfacial oxygen exchange constant of the composite cathode material LSM-YSZ [7].

Conductivity and tortuosity factor of composite materials LSM-YSZ.
Tortuosity factor is statistically calculated by modeling the process of random walk of particles by Monte Carlo method.N number of stray particles is generated in the required volume.In one step of the program, each particle performs n walks with a given length L. After wandering the amount of mean-square displacements of all particles of a given ensemble is cal-
It should also be noted that the magnitude of the tortuosity factor is different from the tortuosity defined as the ratio of the average pore length to the thickness of the porous material.Unlike integral microstructure characteristics, such as porosity, the proportion of the phases and their average diameter, tortuosity factor value, depending on the environment for which it is considered to be proportional to the physico-chemical quantities.In the case of pores, tortuosity factor is proportional to the coefficient of permeability; for oxygen-ion electrolyte -the diffusion coefficient (ionic conductivity); for electronic conductor -the conductivity of the material [5].For example, the dependence of the diffusion coefficient and the mean-square of displacement from the time is described by the expression (3).
In this part of present work it is shown that the resistivity is reduced by one order of magnitute in the example of the composite material La0,6Sr0,4MnO 3 -0,9ZrO 2 • 0,1Y 2 O 3 shown that for 1000 hours at T = 800 °C, PO 2 = 10 -2 atm (fig.10).During the tests, the samples were taken after 40, 500 and 1000 hours of exposure.
On the basis of segmentation results of SEM images (Fig. 8) for the cross sections of the samples before and after testing using the developed original software, the tortuosity factors are calculated for both the porous structure and the phases of LSM and YSZ (Fig. 9).
A decrease in tortuosity factors phase LSM and YSZ was discovered; it correlates with the drop in resistivity of the test composite material (Fig. 9, 10).The monotonic dependence could not be found for the porous structure.Image analysis showed that as a result of the exposure diffusive propagation of LSM and YSZ phases occurs, which leads to the enlargement of particles at constant linear dimensions of the sample.Process of diffusion growth of YSZ phase goes faster than that of LSM, apparently due to the fact that YSZ was initially taken in the form of nanopowder (Fig. 8).Formation of more coherent phase structure comprised in the composite material is the cause of resistivity (Fig. 10).
Prolonged exposure under experimental conditions leads to improved contact between the grains of the components that make up the composite.Quantitative parameter characterizing the process of diffusive propagation of LSM and YSZ phase is the tortuosity factor.Conclusions 3D-reconstruction of the microstructure based on the analysis and SEM imaging was carried out, lengths of TFG and FIG were calculated, proportion of active TFG and open pores was found in this work.
The approach used in this study may be useful in the study of electrochemical