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 KMgAs (Materials Project id mp-1019089)

        63       13       20        0        0        0  
        13       63       20        0        0        0  
        20       20       50        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 31.333 GPaEV = 48.243 GPaGV = 19.4 GPaνV = 0.24339
ReussKR = 31.25 GPaER = 46.488 GPaGR = 18.564 GPaνR = 0.25207
HillKH = 31.292 GPaEH = 47.368 GPaGH = 18.982 GPaνH = 0.24771

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 24 GPa 31.871 GPa 50 GPa 94.129 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 39.474 GPa 54.545 GPa 10 TPa–1 12 TPa–1 16 GPa 25 GPa0.0909090.36691Value
Anisotropy 1.382 1.2000 1.562 4.0360Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
1.0000
-0.0001
-0.0000
0.9321
-0.0002
-0.3622
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
0.0001
1.0000
0.0000
-0.3622
-0.0002
-0.9321
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