Disentangling Structural Confusion through Machine Learning: Structure Prediction and Polymorphism of Equiatomic Ternary Phases ABC

A method to predict
the crystal structure of equiatomic ternary
compositions based only on the constituent elements was developed
using cluster resolution feature selection (CR-FS) and support vector
machine (SVM) classification. The supervised machine-learning model
was first trained with 1037 individual compounds that adopt the most
populated ternary 1:1:1 structure types (TiNiSi-, ZrNiAl-, PbFCl-,
LiGaGe-, YPtAs-, UGeTe-, and LaPtSi-type) and then validated using
an additional 519 compounds. The CR-FS algorithm improves class discrimination
and indicates that 113 variables including size, electronegativity,
number of valence electrons, and position on the periodic table (group
number) influence the structure preference. The final model prediction
sensitivity, specificity, and accuracy were 97.3%, 93.9%, and 96.9%,
respectively, establishing that this method is capable of reliably
predicting the crystal structure given only its composition. The power
of CR-FS and SVM classification is further demonstrated by segregating
the crystal structure of polymorphs, specifically to examine polymorphism
in TiNiSi- and ZrNiAl-type structures. Analyzing 19 compositions that
are experimentally reported in both structure types, this machine-learning
model correctly identifies, with high confidence (>0.7), the low-temperature
polymorph from its high-temperature form. Interestingly, machine learning
also reveals that certain compositions cannot be clearly differentiated
and lie in a “confused” region (0.3–0.7 confidence),
suggesting that both polymorphs may be observed in a single sample
at certain experimental conditions. The ensuing synthesis and characterization
of TiFeP adopting both TiNiSi- and ZrNiAl-type structures in a single
sample, even after long annealing times (3 months), validate the occurrence
of the region of structural uncertainty predicted by machine learning.

一种仅基于组成元素预测等原子三元合金晶体结构的方法得以开发，该方法采用了簇分辨率特征选择（CR-FS）与支持向量机（SVM）分类。该监督式机器学习模型首先使用1037个独立化合物进行训练，这些化合物采纳了最为丰富的三元1:1:1结构类型（包括TiNiSi-、ZrNiAl-、PbFCl-、LiGaGe-、YPtAs-、UGeTe-和LaPtSi型），随后使用额外的519个化合物进行验证。CR-FS算法提升了分类的辨识度，并指出包括尺寸、电负性、价电子数以及周期表位置（族数）在内的113个变量会影响结构偏好。最终模型的预测灵敏度、特异性和准确率分别为97.3%、93.9%和96.9%，证实了该方法能够在仅给出其组成的情况下可靠地预测晶体结构。CR-FS算法与SVM分类的强大能力进一步得到体现，特别是在分离多晶型结构，尤其是针对TiNiSi-和ZrNiAl型结构的同质多晶现象的考察中。分析19种在两种结构类型中均有实验报道的化合物，该机器学习模型以高置信度（>0.7）正确识别了低温多晶型，从其高温形式中区分出来。有趣的是，机器学习还揭示了某些组成难以清晰区分，并位于一个“模糊”区域（0.3–0.7置信度），表明在特定的实验条件下，两种多晶型可能出现在单个样品中。采用TiNiSi-和ZrNiAl型结构在单个样品中进行TiFeP的合成与表征，即使在长时间的退火时间（3个月）后，也验证了机器学习预测的结构不确定性区域的存在。