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 AgNO3 (Materials Project id mp-552185)

        57       36       28        3        0        0  
        36       57       28       -3        0        0  
        28       28       35        0        0        0  
         3       -3        0        8        0        0  
         0        0        0        0        8        3  
         0        0        0        0        3       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37 GPaEV = 24.975 GPaGV = 9 GPaνV = 0.3875
ReussKR = 33.078 GPaER = 21.989 GPaGR = 7.9141 GPaνR = 0.38921
HillKH = 35.039 GPaEH = 23.482 GPaGH = 8.4571 GPaνH = 0.38831

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5.8377 GPa 6.7379 GPa 12.162 GPa 14.918 GPa 22.262 GPa 113.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 16.471 GPa 34.111 GPa 4.1494 TPa–1 21.932 TPa–1 5.8377 GPa 12.42 GPa0.152630.71899Value
Anisotropy 2.071 5.2857 2.127 4.7106Anisotropy
Axis -0.6397
0.3766
-0.6701
0.0000
0.9398
-0.3417
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.5847
-0.8112
0.7100
0.4262
-0.5606
0.5183
0.2875
0.8054
-0.4988
0.8667
0.0062
Axis
-1.0000
0.0000
0.0000
-0.5230
0.8522
-0.0144
-0.4981
0.8670
0.0110
-0.6226
-0.3634
0.6931
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