Ba-based ion interference with Eu in coal and coal combustion products during quadrupole-based inductively coupled plasma mass spectrometry procedures is problematic. Thus, this paper proposes machine-learning-based prediction models for determination of the threshold value of Ba interference with Eu, which can be used to predict such interference in coal. The models are trained for Eu, Ba, Ba/Eu, and Ba interference with Eu. Under different user-defined parameters, different prediction models based on the corresponding model tree can be applied to Ba interference with Eu. We experimentally show the effectiveness of these different prediction models and find that, when the Ba/Eu value is less than 2950, the Ba-Eu interference prediction model is y = −0.18419411 + 0.00050737 × x, 0 < x < 2950. Further, when the Ba/Eu value is between 2950 and 189,523, the Ba-Eu interference prediction model of y = 0.293982186 + 0.00000181729975 × x, 2950 < x < 189, 523 yields the best result. Based on the optimal model, a threshold value of 363 is proposed; i.e., when the Ba/Eu value is less than 363, Ba interference with Eu can be neglected during Eu data interpretation. Comparison of this threshold value with a value proposed in earlier works reveals that the proposed prediction model better determines the threshold value for Ba interference with Eu.Minerals 2019, 9, 259 2 of 17 (INAA) [19][20][21], laser-ablation inductively-coupled plasma mass spectroscopy (La-ICP-MS) [22], sector-field inductively-coupled plasma mass spectroscopy ICP-MS [23], laser-induced break-down spectrometry [24][25][26], and quadrupole-based ICP-MS (ICP-Q-MS) [4,27]. Among these techniques, ICP-Q-MS has mostly been used for determination of REY concentrations in coal and CCPs. This is because of this method's ability to rapidly, precisely, and accurately measure REY content at very low detection limits in liquid and solid samples, with relatively simple spectra and a wide linearity range [14,[27][28][29]. However, in some cases, Eu concentrations in coal and CCPs cannot be accurately measured by the ICP-Q-MS. This difficulty is attributed to overlapping ion interference (such as those from M + , MO + , and/or MOH + ions) with Eu, which affects interpretation of the ICP-Q-MS spectra [30][31][32][33][34][35]. Because Ba concentrations in coal and CCPs are generally much higher than those of Eu [4,36], the most significant types of interference encountered for Eu in coal and CCPs are due to 135 Ba 16 O, 134 Ba 16 OH, 137 Ba 16 O, and/or 136 Ba 16 OH interfering with 151 Eu and/or 153 Eu. For example, the ratio of Ba vs. Eu for world coals is as high as~882 (with an average concentration of 150 µg/g Ba and 0.47 µg/g Eu) [36]. Therefore, as noted by Dai et al. [4], Eu content values in coal and CCPs determined via ICP-Q-MS should be treated with great caution. Recently, Yan et al. [27] described a reliable analytical method to avoid Ba-based ion interference with Eu in coal, CCPs, and sedimentary rocks during ICP-Q-MS procedures, which was based on AG50W-X8...