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 CaAsAu (Materials Project id mp-3927)

       139       85       20        0        0        0  
        85      139       20        0        0        0  
        20       20       60        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 65.333 GPaEV = 72.58 GPaGV = 27.6 GPaνV = 0.31485
ReussKR = 47.879 GPaER = 62.527 GPaGR = 24.38 GPaνR = 0.28234
HillKH = 56.606 GPaEH = 67.621 GPaGH = 25.99 GPaνH = 0.3009

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 27 GPa 54 GPa 55.259 GPa 228.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 51.079 GPa 85.965 GPa 3.1646 TPa–1 14.557 TPa–1 20 GPa 30.751 GPa0.0892860.59194Value
Anisotropy 1.683 4.6000 1.538 6.6297Anisotropy
Axis 0.0988
0.5622
0.8211
0.7883
0.6152
-0.0000
0.5904
0.8071
-0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5291
0.4691
-0.7071
0.0000
0.0000
1.0000
0.4070
0.9134
-0.0000
Axis
-0.7660
0.6428
-0.0000
-0.5291
-0.4692
-0.7071
-1.0000
0.0000
0.0000
-0.9134
0.4070
-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