Rare earth element (REE) phosphates such as xenotime (YPO₄) are important hosts to the heavy (H)REE in natural systems. Xenotime is commonly associated with hydrothermal alteration and mineral replacement reactions and its composition may yield important clues about the mineralization processes from aqueous fluids in REE mineral deposits. Robust underlying thermodynamic data for the REE phosphate endmembers and aqueous species are required to simulate the stability of xenotime and the mobility of REE in natural hydrothermal fluids. In this study, the solubility of synthetic TbPO₄, HoPO₄, TmPO₄, and LuPO₄ endmembers has been measured in aqueous solutions between 100 and 250 ^∘C at saturated water vapor pressure. The solubility products (K_s0) determined in the experiments were compared to values retrieved from a combination of calorimetric data for the REE phosphates and thermodynamic properties of the aqueous REE species at elevated temperatures. The solubility of xenotime is retrograde and generally higher in the experiments than predicted by different sources of thermodynamic data. To resolve these discrepancies, the solubility data were used to optimize the thermodynamic properties of the REE phosphate endmembers and REE aqueous species. These optimizations permit retrieving a set of provisional standard Gibbs energy of formation for REE³⁺ and REEOH²⁺ at elevated temperature and were used to derive the following updated K_s0 values (uncertainty of ± 0.2 at the 95% confidence) for the reaction REEPO₄ (s) = REE³⁺ + PO₄³⁻:

稀土元素（REE）磷酸盐（例如Xenotime（YPO ₄））是自然系统中重（H）REE的重要宿主。Xenotime通常与热液蚀变和矿物替代反应有关，其组成可能为REE矿床中含水流体的矿化过程提供重要线索。需要REE磷酸盐端基和水性物质的可靠的基础热力学数据，以模拟异诺时间的稳定性和REE在天然热液中的迁移率。在这项研究中，合成TBPO的溶解度₄，HOPO ₄，TMPO ₄，和路波_4个端元已在100和250之间的水溶液测量^∘C在饱和水蒸气压力下。将在实验中确定的溶解度乘积（K _s0）与从REE磷酸盐的量热数据和REE水溶液在高温下的热力学性质的组合中获取的值进行比较。异诺时间的溶解度是逆行的，并且在实验中通常比不同热力学数据来源所预测的更高。为了解决这些差异，使用溶解度数据来优化REE磷酸盐端基和REE水溶液物种的热力学性质。这些优化允许检索REE ³⁺和REEOH ^2+的一组临时标准吉布斯形成能在高温下用于反应REEPO ₄（s）= REE ³⁺ + PO ₄ ^3-的以下更新的K _s0值（在95％置信度下，不确定度为±0.2）：