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 ErZnAsO (Materials Project id mp-983603)

       182       34       41        0        0        0  
        34      182       41        0        0        0  
        41       41      114        0        0        0  
         0        0        0       18        0        0  
         0        0        0        0       18        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.889 GPaEV = 102.5 GPaGV = 39.933 GPaνV = 0.28344
ReussKR = 75.936 GPaER = 78.088 GPaGR = 29.387 GPaνR = 0.32861
HillKH = 77.412 GPaEH = 90.477 GPaGH = 34.66 GPaνH = 0.3052

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 18 GPa 43 GPa 87.78 GPa 148 GPa 242.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 56.789 GPa 165.04 GPa 3.4334 TPa–1 6.3023 TPa–1 18 GPa 74 GPa0.0723160.64411Value
Anisotropy 2.906 1.8356 4.111 8.9069Anisotropy
Axis 0.4873
0.4872
0.7247
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-0.8259
0.0000
0.5639
0.7776
0.0002
0.6288
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
-0.0000
-0.0000
-1.0000
-0.0000
0.6288
0.0003
-0.7776
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