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 CuAgS (Materials Project id mp-5014)

        93       15       56        0        0        0  
        15       44       19        0        0        0  
        56       19      115        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48 GPaEV = 48 GPaGV = 18 GPaνV = 0.33333
ReussKR = 35.51 GPaER = 36.194 GPaGR = 13.606 GPaνR = 0.33012
HillKH = 41.755 GPaEH = 42.098 GPaGH = 15.803 GPaνH = 0.33197

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 10 GPa 18 GPa 39.164 GPa 46.959 GPa 165.88 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.701 GPa 78.89 GPa 2.4945 TPa–1 19.573 TPa–1 8 GPa 23.605 GPa0.0874450.60995Value
Anisotropy 3.194 7.8463 2.951 6.9752Anisotropy
Axis -0.6647
0.7472
-0.0001
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.7071
-0.0000
-0.7071
0.0000
1.0000
-0.0000
0.5817
-0.0000
0.8134
Axis
-0.0000
1.0000
0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
0.8134
0.0000
-0.5817
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