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ToleranceFactorVariance of Ionic Radii e.g. in Y1-xMxBa2Cu3O6+y, we have {$R_a=(1-x)R_Y + x R_M$} with variance {$\sigma^2=(1-x)(R_y-RA)^2+x(R_M-R_A)^2$} which is also given by {$\sigma^2=(1-x)R_Y^2+xR_M^2-R_A^2$} Calculations with M=Eu/Ca. Different onic radii are reported for different coordinations, but their differences are constant. E.g. for Y the ionic radii are 104 and 115.9 pm in 6-fold and 8-fold coordination, respectively, while Ca raddi are 114 and 126 pm, respectively. Therefore the Ca-Y difference is 9.9-10 pm in both coordinations. The same is true for Eu, for wich 108.7 (6-fold) and 120.6 (8-fold) pm are reported. The Eu-Y radii difference is therefore 4.7 pm in both instances. Summarizing {$\frac {(\Delta R)_{Y-Eu}} { (\Delta R)_{Y-Ca}} = 0.47 $} hence, at the same concentration {$x$}, one must have {$\frac {\sigma^2_{Eu}}{\sigma^2_{Cu}}= 0.47^2=0.22 $} |