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 ScAg (Materials Project id mp-11237)

       108       69       69        0        0        0  
        69      108       69        0        0        0  
        69       69      108        0        0        0  
         0        0        0       45        0        0  
         0        0        0        0       45        0  
         0        0        0        0        0       45  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 82 GPaEV = 91.462 GPaGV = 34.8 GPaνV = 0.3141
ReussKR = 82 GPaER = 79.132 GPaGR = 29.545 GPaνR = 0.33916
HillKH = 82 GPaEH = 85.355 GPaGH = 32.173 GPaνH = 0.32651

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 39 GPa 45 GPa 45 GPa 45 GPa 246 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 54.203 GPa 114.12 GPa 4.065 TPa–1 4.065 TPa–1 19.5 GPa 45 GPa-0.00652370.64306Value
Anisotropy 2.105 1.0000 2.308Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.4830
0.8365
0.2588
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
-0.0000
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