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 CsNiF3 (Materials Project id mp-557772)

        39       17       10        0        0        0  
        17       39       10        0        0        0  
        10       10       85        0        0        0  
         0        0        0        2        0        0  
         0        0        0        0        2        0  
         0        0        0        0        0       11  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 26.333 GPaEV = 29.887 GPaGV = 11.4 GPaνV = 0.31084
ReussKR = 24.516 GPaER = 11.678 GPaGR = 4.1103 GPaνR = 0.42061
HillKH = 25.425 GPaEH = 21.118 GPaGH = 7.7551 GPaνH = 0.36156

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 2 GPa 11 GPa 22 GPa 50.245 GPa 90.755 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.3963 GPa 81.429 GPa 7.8947 TPa–1 16.447 TPa–1 2 GPa 20.528 GPa0.048990.86057Value
Anisotropy 11.01 2.0833 10.26 17.5660Anisotropy
Axis 0.7224
0.0008
0.6914
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0682
0.7038
-0.7071
-0.0845
0.5110
0.8554
0.0947
0.5965
-0.7970
Axis
1.0000
0.0000
-0.0000
-0.0681
-0.7038
-0.7071
-0.9866
-0.1631
-0.0000
-0.1249
-0.7871
-0.6040
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