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 CrH (Materials Project id mp-24669)

       284      134      132        0        0        0  
       134      284      132        0        0        0  
       132      132      298        0        0        0  
         0        0        0       74        0        0  
         0        0        0        0       74        0  
         0        0        0        0        0       75  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 184.67 GPaEV = 200.03 GPaGV = 75.8 GPaνV = 0.31947
ReussKR = 184.6 GPaER = 199.81 GPaGR = 75.707 GPaνR = 0.3196
HillKH = 184.63 GPaEH = 199.92 GPaGH = 75.754 GPaνH = 0.31954

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
74 GPa 74 GPa 75 GPa 150 GPa 161.92 GPa 554.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 196.59 GPa 214.63 GPa 1.7165 TPa–1 1.8503 TPa–1 74 GPa 79.391 GPa0.294610.33741Value
Anisotropy 1.092 1.0779 1.073 1.1453Anisotropy
Axis -0.6132
0.5537
0.5634
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.6088
0.7934
0.0000
-0.0000
-0.0000
1.0000
0.5644
0.4260
0.7071
0.2742
0.9617
-0.0000
0.6380
0.0001
-0.7701
Axis
-0.7648
0.6443
0.0000
0.5646
0.4258
-0.7071
0.0002
-0.0001
-1.0000
-0.7701
-0.0001
-0.6380
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