## 1 Introduction  
Coal is a complex natural material with a diverse chemical structure, containing both organic and inorganic components. It includes all naturally occurring elements and over 200 minerals, each hosting one or more of these elements [1, 2]. Major inorganic elements in coal exceed 0.1% by weight (e.g., Al, Si, Ti, Fe, and Ca), whereas trace elements (e.g., As, V, Cu, Zn, Pb, rare earth elements, and U) are typically present in concentrations below 0.1%, ranging from 1 ppb to several hundred ppm [2]. Understanding the occurrence of these elements is crucial as it provides insights into peat formation, coal diagenesis, and basin development. Practically, this knowledge affects coal mining, preparation, combustion, and utilization by helping to avoid technological issues (abrasion, corrosion, fouling, and slagging) and is crucial for evaluating environmental pollution control, health impacts, and its applications as an industrial raw material in cement manufacturing, wastewater treatment, and valuable element recovery [2, 3, 4, 5, 6]. Various analytical techniques, such as ICP-MS/AES, AAS, NAA, and DPASV, are employed to characterize coal combustion ash, each offering distinct advantages like low detection limits, high sensitivity, and wide dynamic ranges. Among these, X-ray fluorescence (XRF) techniques are particularly effective for simultaneous multi-elementanalysis [4]. XRF techniques offer several benefits, including reduced sample preparation time, lower costs, and the avoidance of hazardous chemicals. In recent years, X-ray fluorescence has emerged as a powerful method for analyzing environmental samples, including coal ash. XRF instrumentation is advantageous due to its lower capital cost compared to Neutron Activation Analysis (NAA), faster analysis times relative to ICP-AES, and widespread availability [4]. In contrast, ICP-AES requires time-consuming dissolution procedures, which can lead to the loss of volatile elements such as As, Pb, Se, Sb, and Zn [7; 8; 9]. XRF is an effective method for rapid routine analysis of major and minor elements, offering a significant advantage due to its potentially wide application in industry settings for quick assessments [10]. The application of XRF for analyzing the chemical composition of coal and coal ash has been widely adopted in industrial, economic, and environmental studies across several countries, including Russia (28 studies), Australia (17), China (15), the USA (11), India (11), Mongolia (5), Portugal (5), the UK (4), Turkey (4), Spain (4), Austria (2), Canada (2), Kazakhstan (2), Poland (2), and others. Publications span various years: before 2000--6; 2001-2005--12; 2006-2010--11; 2011-2015--19; 2016-2020--31; and 2021-2023--13. More than half of the articles are concentrated in 8 journals, while the remainder are spread across approximately 30 other publications [11]. The major advantages of XRF analysis are as follows: (i) its versatility and wide availability as a common laboratory instrument; (ii) modern instruments often feature full automation for up to 50 samples; (iii) easy sample preparation, typically involving only pulverization and pelletization; and (iv) a broad concentration range from over 1 ppm to 100 wt%, with detection limits of 0.04 wt% for Al, 0.05 wt% for Si, 100 ppm for minor elements, and 20 ppm for trace elements [12; 13]. XRF, in particular, is recognized as highly effective for analyzing high-temperature ash (HTA) to determine both major and trace elements [13; 14; 15]. HTA of coals is generally preferred for elemental analysis over fly ash or bottom ash derived from power plants, as HTA offers a more complete recovery of elements, particularly for coal and its ashes [16]. Recent studies on the inorganic geochemical characteristics of coal deposits in Kazakhstan, specifically in the Shubarkol coal deposit and Karagandy coal basin focusing on the k7 coal seam, highlight the potential for industrial extraction of rare metals from coal and coal waste, emphasizing coal's value as a source of critical elements [17; 18; 19].