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 ErCu (Materials Project id mp-1955)

       126       56       56        0        0        0  
        56      126       56        0        0        0  
        56       56      126        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 79.333 GPaEV = 99.64 GPaGV = 38.6 GPaνV = 0.29067
ReussKR = 79.333 GPaER = 99.126 GPaGR = 38.369 GPaνR = 0.29175
HillKH = 79.333 GPaEH = 99.383 GPaGH = 38.484 GPaνH = 0.29121

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 41 GPa 41 GPa 70 GPa 70 GPa 238 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 91.538 GPa 104.92 GPa 4.2017 TPa–1 4.2017 TPa–1 35 GPa 41 GPa0.234440.34025Value
Anisotropy 1.146 1.0000 1.171 1.4513Anisotropy
Axis 0.0000
1.0000
0.0000
-0.5774
0.5774
-0.5773
0.9914
0.0000
0.1305
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
0.7071
-0.0006
-0.7071
0.0003
1.0000
0.0004
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