ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of Sr3Ti2O7 (Materials Project id mp-3349)

       265       75       84        0        0        0  
        75      265       84        0        0        0  
        84       84      246        0        0        0  
         0        0        0       75        0        0  
         0        0        0        0       75        0  
         0        0        0        0        0       91  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 140.22 GPaEV = 209.5 GPaGV = 83.733 GPaνV = 0.25099
ReussKR = 140.18 GPaER = 207.84 GPaGR = 82.943 GPaνR = 0.25289
HillKH = 140.2 GPaEH = 208.67 GPaGH = 83.338 GPaνH = 0.25194

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
75 GPa 75 GPa 91 GPa 165.25 GPa 190 GPa 420.75 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 195.93 GPa 227.24 GPa 2.33 TPa–1 2.4738 TPa–1 75 GPa 95 GPa0.195180.32073Value
Anisotropy 1.16 1.0617 1.267 1.6432Anisotropy
Axis 0.4337
0.4338
0.7898
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.9455
0.0005
0.3257
0.7557
0.0001
-0.6549
Axis
0.1736
0.9848
-0.0000
-0.7071
0.7071
0.0000
-0.0005
1.0000
-0.0000
-0.6549
0.0000
-0.7557
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane