The improvement of tribology technology, which deals with friction, wear, and lubrication phenomena in mechanical systems, is greatly influenced by the advancement of surface analysis technology. As we strive towards realizing a carbon-neutral society, there are numerous new technological challenges that need to be addressed. To solve these challenges, it is essential to gain a more detailed understanding of the phenomena occurring at the friction interfaces and to link this knowledge to the development of friction materials and lubricants. In this context, we would like to introduce the required information for analyzing tribological surfaces, along with the expectations for the future.

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In the automotive industry, improving the sliding properties of mechanical parts such as combustion engines and transmissions is an important issue to realize highly efficient and durable vehicles for the realization of a decarbonized society. To investigate the mechanism of property development, it is essential to understand the composition and shape of surfaces, which are at the forefront of friction and wear.
In this report, we prepared oil that simulated engine degradation and investigated the correlation between the degradation status of various additives in the oil and friction properties. It was found that there is a strong correlation between the friction coefficient μ and the degradation of various additives in the oil and the amount of MoS₂ formed on the sliding surface.

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In elemental solids, the squares of the dipole matrix elements（M_tot²) were calculated from optical energy loss functions (ELFs) and compared with those of isolated atoms. It was found that these squares were significantly smaller in the elemental solid than in the corresponding atoms, and there was a notable difference in atomic number dependence between the two. Moreover, M_tot² calculated using the Bethe formula from the inelastic mean free path (IMFP) values, when compared with those directly derived from the ELF, were larger for elemental solids, except for Sc, with the difference being approximately 5%. This lecture also detailed the use of the Penn algorithm for deriving the IMFP from the measured ELF and the Lindhard dielectric function, using Mathematica for explanation. Mathematica's advantage is its facilitation of IMFP calculation using the Lindhard function, which incorporates a damping factor. However, it also has disadvantages, such as requiring an undetermined damping factor and extensive computation time. For rapid IMFP calculations, it is advisable to use the Lindhard function in the long-wavelength limit without the damping factor and to perform calculations with FORTRAN or Julia. Therefore, the lecture provided an in-depth explanation of the essential points for numerical computation using the Penn algorithm within procedural programming, as exemplified by FORTRAN.

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