六硼化鑭（LaB6）因具低功函數、良好熱電子發射能力與高溫穩定性，被視為霍爾推進器中空陰極之候選材料；然而，高溫下表面金屬原子蒸發會改變表面化學計量與偶極，進而影響電子發射與壽命。本研究以自旋極化 DFT+U 系統性探討由 La、Ce、Pr、Nd、Sm、Gd 組成之十種等比例四元多稀土六硼化物。十種成分共三十個表面構型完成結構與功函數計算；La 蒸發能共有二十九個有效構型，其中九種成分完成三個構型，LaPrNdGdB6 完成兩個。Bader 電荷、COHP 與 DOS 分析則以已完成後處理之原八種成分為範圍，LaPrNdGdB6 與 LaPrNdSmB6 尚未納入上述電子結構分析。十種成分之平均功函數介於 2.202–2.315 eV，與線性組合預測呈良好相關（r＝0.87，R²＝0.76），並與平均晶格常數呈強負相關（r＝−0.94，R²＝0.89）。現有平均 La 蒸發能介於 6.951–7.948 eV，其中 LaPrNdGdB6 的 7.948 eV 為兩個有效構型之暫定平均；十種成分平均為 7.545 eV，較純 LaB6 計算基準 6.436 eV 提升約 17.2%。蒸發能亦與晶格常數呈強負相關（r＝−0.91，R²＝0.83）。在原八種成分中，Bader、COHP、DOS 與 ELF 結果共同支持 B6 骨架具強共價特徵、稀土–B 作用以離子性為主，且 Sm 的電荷轉移與 Sm–B 鍵結均較弱；惟 Bader 電荷不等同形式氧化態，相關結果應視為與 Sm 混合價傾向一致，而非單獨證明。混合焓計算顯示新增 LPNG 與 LPNS 於 0 K 參考下為負值，但實際相穩定性仍需考量振動熵、短程有序與競爭相。整體而言，平均晶格大小與局域鍵結共同造成低功函數與高蒸發能之取捨，LaCePrNdB6 仍為資料完整且兼顧兩項性能之候選組成。

Rare-earth hexaborides are promising thermionic cathode materials because they combine low work functions with high-temperature stability. This study used spin-polarized density functional theory with an on-site Coulomb correction (DFT+U) to evaluate ten equiatomic quaternary multi-rare-earth hexaborides composed of La, Ce, Pr, Nd, Sm, and Gd. Thirty surface configurations were analyzed for work function. Twenty-nine valid La-vacancy calculations were available for evaporation-energy analysis: nine compositions had three configurations, whereas LaPrNdGdB6 had two. Bader charge, crystal orbital Hamilton population (COHP), and density-of-states analyses were completed for the original eight compositions only. The ten-composition mean work functions ranged from 2.202 to 2.315 eV and correlated strongly with the linear-combination estimate and average lattice constant. The available mean La evaporation energies ranged from 6.951 to 7.948 eV and averaged 7.545 eV, approximately 17.2% above the calculated LaB6 reference. Sm-containing systems tended toward lower work functions and lower La evaporation energies, whereas Gd-containing systems tended toward higher evaporation energies. Bader, COHP, DOS, and ELF results for the eight fully analyzed compositions were consistent with an ionic rare-earth–boron interaction embedded in a covalent B6 framework and with weaker Sm–B bonding. These findings identify lattice size and local bonding as coupled design variables for balancing electron emission and surface thermal stability.

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