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 Ba(GeRh)2 (Materials Project id mp-10698)

       136       75       51        0        0        0  
        75      136       51        0        0        0  
        51       51       65        0        0        0  
         0        0        0       43        0        0  
         0        0        0        0       43        0  
         0        0        0        0        0       64  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.778 GPaEV = 103.69 GPaGV = 40.667 GPaνV = 0.27491
ReussKR = 62.139 GPaER = 85.296 GPaGR = 33.549 GPaνR = 0.27122
HillKH = 69.458 GPaEH = 94.495 GPaGH = 37.108 GPaνH = 0.27326

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35.379 GPa 43 GPa 43 GPa 61 GPa 64 GPa 240.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.346 GPa 133 GPa 1.6445 TPa–1 12.804 TPa–1 20.499 GPa 64 GPa-0.032640.77562Value
Anisotropy 3.296 7.7857 3.122Anisotropy
Axis 0.0000
0.0000
1.0000
0.6715
0.6715
0.3135
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0002
0.0001
0.7127
0.0001
-0.7015
-0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.0002
1.0000
-0.0000
-0.7015
-0.0001
-0.7127
0.0002
0.0003
-1.0000
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