Fig. 4: Correlation between the predicted transition temperature and Helmholtz energy difference between β-quartz and β-cristobalite at \({T}_{{\rm{q}}-{\rm{c}}}^{\exp }\), and \({V}_{{\rm{cristobalite}}}^{\exp }\) and \({V}_{{\rm{quartz}}}^{\exp }\). | npj Computational Materials

Fig. 4: Correlation between the predicted transition temperature and Helmholtz energy difference between β-quartz and β-cristobalite at \({T}_{{\rm{q}}-{\rm{c}}}^{\exp }\), and \({V}_{{\rm{cristobalite}}}^{\exp }\) and \({V}_{{\rm{quartz}}}^{\exp }\).

From: Free-energy perturbation in the exchange-correlation space accelerated by machine learning: application to silica polymorphs

Fig. 4: Correlation between the predicted transition temperature and Helmholtz energy difference between β-quartz and β-cristobalite at 
                        $${T}_{{\rm{q}}-{\rm{c}}}^{\exp }$$
                        
                          
                            
                              T
                            
                            
                              q
                              −
                              c
                            
                            
                              exp
                            
                          
                        
                      , and 
                        $${V}_{{\rm{cristobalite}}}^{\exp }$$
                        
                          
                            
                              V
                            
                            
                              
                                c
                                r
                                i
                                s
                                t
                                o
                                b
                                a
                                l
                                i
                                t
                                e
                              
                            
                            
                              exp
                            
                          
                        
                       and 
                        $${V}_{{\rm{quartz}}}^{\exp }$$
                        
                          
                            
                              V
                            
                            
                              
                                q
                                u
                                a
                                r
                                t
                                z
                              
                            
                            
                              exp
                            
                          
                        
                      .

The filled dark green circles show explicitly computed results and the line a linear fit of them. The hollow circles mark extrapolations out of the stability regime of the phases. The light green triangles mark predictions for rung 4 and 5 functionals (labeled in italics) utilizing the fit.

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