关注：

1） Convex hull图的物理化学意义及其画法

2）纵坐标能量eV/atom，  atom的定义为横坐标两段的物质为名义上的"atom"，如“Sc”和“H2”, "CaH2"和"H2"均达标一个"atom"

4.Convex hull

Andreas回答：

Maybe convex hull is nonsense.

Different compounds can be stable under thesame pressure range as shown in the above figure .  The relative stability depends on the initialmixture ratio. For example:

For example, a tie line between LiH₆and LiH would show that a mixture ofthese could yield LiH₂ (but not LiH₃) at P =150GPa, providedthat the kinetic barriers are not too high.

  LiH₆ + LiH→LiH₂

  LiH₂+2 H₂→ LiH₆

【类似与相图中的杠杆定则，稳定性与分解产物有关，convex hull phasediagram】

From absolute formationenthalpy  to relative formation enthalpy,we often lift up the lower enthalpy compound (such as B) to the ZERO place.

【相比常规的relative convex hull phase diagram,可以认为上图是absolute convex hull phase diagram】

Binary Compositional Phase Diagrams

Figure 2: Calculated Fe-PPhase Diagram

Figure2 is an example of a calculated binary Fe-P phase diagram at 0K and 0 atm usingthe PDApp.

Binaryphase diagrams show the complete convex hull for the system, where the y-axis is theformation energy per atom and the x-axis is the composition (e.g., in the Fe-Pphase diagram, the x-axis is the fraction of P).

The black lines show the convex hullconstruction, which connects stable phases.Unstable phases will always appear above theconvex hull line;one measure of the thermodynamic stability of an arbitrary compound is its distance from the convex hullline, which predicts the decomposition energy of that phase into the most stable phases.

 解读：

（1）在tie-line上的都是稳定的物相，画tie-line时，下一点的选择应保证连接线是所有最近邻点连线中位置最低的(hf最低)。

（2） 在tie-line上的都是稳定的物相，在其上方的相是不稳定的，在其下方的相？？？？

【选作基准相的物质必须稳定，不会转变为相图中的其他相 ？ 但自身可发生同质异构转变！】

From Prof . Miaomao Shen

For the most stable structures ateach pressure, the enthalpy of formation per atom is calculated using the followingformula:

hf(CsF_n) = (H(CsF_n) - H(CsF)- (n -1)H(F₂)/2)/(n + 1).[28, 29]

We choose to use the enthalpy of CsF instead of Cs (see the above formula) because ofthe substantial stability of CsF throughout the studied pressure range.

Thus, changing Cs to CsF does not change theconvexity of the compounds with higher F compositions, although the absolutevalue of hf does change.[29]