Cation exchange is one of the most important classes of reactions controlling the soil solution composition for major ions. Modeling ion-exchange equilibria is complicated by ternary solid-phase interactions. The present study alleges that spurious ternary-interactions can be reported when dilution of the exchanging ions by other ions on the solid-phase is not accounted for in models. Ion-exchange equilibria data from the NH₄⁺–Ca²⁺–K⁺–vermiculite system is used to demonstrate that previous reports of ternary interactions in this system are an artifact of how solid-phase mole fractions are defined; what mathematicians call “compositional incoherence.” A graphical method to distinguish the effects of dilution from real chemical interactions is presented using mole fractions renormalizing in the ternary system so that they are defined the same way as they are in binary systems. Potassium was shown to not influence NH₄⁺–Ca²⁺ exchange on vermiculite when these corrections for solid-phase dilution were used.

中文翻译：

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识别离子交换平衡中三元相互作用的成分限制

阳离子交换是控制土壤溶液中主要离子组成的最重要的一类反应。三元固相相互作用使离子交换平衡建模变得复杂。本研究声称，当模型中没有考虑到交换离子被固相上的其他离子稀释时，可以报告虚假的三元相互作用。来自 NH ₄ ⁺ –Ca ²⁺ –K ^{+ 的}离子交换平衡数据– 蛭石系统用于证明该系统中三元相互作用的先前报告是如何定义固相摩尔分数的人工制品；数学家称之为“组合不连贯”。使用在三元系统中重新归一化的摩尔分数呈现了一种区分稀释效应与实际化学相互作用的图形方法，以便它们的定义方式与二元系统中的定义方式相同。当使用这些固相稀释校正时，钾被证明不会影响蛭石上的NH ₄ ⁺ –Ca ²⁺交换。