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 Li2CuAs (Materials Project id mp-15686)

       139       46        8        0        0        0  
        46      139        8        0        0        0  
         8        8       80        0        0        0  
         0        0        0       25        0        0  
         0        0        0        0       25        0  
         0        0        0        0        0       47  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 53.556 GPaEV = 94.406 GPaGV = 39.133 GPaνV = 0.20621
ReussKR = 46.875 GPaER = 83.223 GPaGR = 34.558 GPaνR = 0.2041
HillKH = 50.215 GPaEH = 88.815 GPaGH = 36.846 GPaνH = 0.20522

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
25 GPa 25 GPa 47 GPa 78.795 GPa 93 GPa 186.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.858 GPa 124.29 GPa 4.9073 TPa–1 11.519 TPa–1 25 GPa 45.988 GPa0.0432430.34662Value
Anisotropy 1.887 2.3472 1.84 8.0155Anisotropy
Axis 0.6133
0.0000
0.7898
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.5000
0.7071
0.0000
0.0000
1.0000
-0.5321
0.5321
-0.6586
Axis
0.1734
0.9849
-0.0000
0.5000
0.5000
-0.7071
0.1736
0.9848
-0.0000
0.4657
-0.4657
-0.7525
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