**1. Introduction**

The interest in rare Earth elements observed in recent years is driven by rising application opportunities provided by new electronic technologies and nanotechnologies [1–4]. In addition to these specialized areas of the economy, rare Earth metals (REM) are still used in the metallurgical, chemical, and metal industries. Because of their physical and chemical properties, rare Earth oxides began to be used in surface engineering. Their beneficial effect of reducing secondary dendrites and volume fraction of non-metallic inclusions was noticed in the case of nickel-based [5,6] or iron-based [7] coating microstructures. Another advantage was the increased corrosion resistance and improved passivation. In their work [8], Liu et al. reported an advantageous effect of yttrium oxide Y2O3 on the modification of the nickel-based coating, indicating, however, that the range of its application is limited (from 0.4 to 0.6%).

By influencing changes in the microstructure of steel, alloys, and metallic layers, REM directly improve tribological properties, corrosion resistance, mechanical properties, and resistance to oxidation [9–11]. Rare Earth metal additions change the parameters of the structure, e.g., grain size, number and size of inclusions [12–15], and the mechanical.

**Citation:** Malinowski, P.; Kasi ´nska, J.; Rutkowski, S.; Madej, M. Exploratory Data Analysis for the Evaluation of Tribological Properties of Wear-Resistant Surface Layers Modified with Rare-Earth Metals. *Materials* **2022**, *15*, 2032. https:// doi.org/10.3390/ma15062032

Academic Editors: Qing Liu and Jiangshan Zhang

Received: 30 January 2022 Accepted: 7 March 2022 Published: 9 March 2022

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Adding La2O3, Gd2O3, Lu2O3 particles increases the hardness of surface layers [16,17]. The authors of the work [18] showed that in the case of Si3N4 ceramics, the addition of rare Earth oxides reduced the friction coefficient and wear. Silicon nitride ceramics sintered with the addition of rare Earth oxides also constitute an important class of materials for high temperature applications. In addition to high temperature strengths, they possess good thermal shock resistance, creep resistance, and high oxidation resistance [16,19–22].

A number of tests and devices can be applied to determine tribological properties of materials and obtain a broad spectrum of information [23–25]. Using only selected parameters, e.g., a friction coefficient or linear wear, and ignoring mass loss, for example, a proper description of the tested material is impossible. In addition, the results obtained are affected by the test conditions, e.g., temperature, friction pair, motion, medium—dry friction and fluid friction [26].

Data analysis or elements of artificial intelligence, therefore, are increasingly used to correctly interpret scientific results. Exploratory data analysis was introduced to support scientific processes and use statistical methods in solving real problems. Exploratory analysis allows for determining the correlation between the results, its type and strength, as well as exclude or significantly limit the influence of the human factor [27,28].

Exploratory data analysis (EDA) may be defined as the art of looking at one or more datasets in an effort to understand the underlying structure of the data contained there [29,30].

The current paper uses the methods of exploratory data analysis to show the relationships between the selected properties of the layers. The authors also wanted to demonstrate the suitability of EDA for analysing the results of tribological tests.
