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 Dy2Ge2O7 (Materials Project id mp-768241)

       223       98      101        0       -8        0  
        98      159       83        0       33        0  
       101       83      165        0       -1        0  
         0        0        0       51        0       21  
        -8       33       -1        0       71        0  
         0        0        0       21        0       55  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.44 GPaEV = 139.25 GPaGV = 53.067 GPaνV = 0.312
ReussKR = 116.06 GPaER = 117.29 GPaGR = 44.044 GPaνR = 0.33156
HillKH = 119.75 GPaEH = 128.32 GPaGH = 48.555 GPaνH = 0.3214

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31.905 GPa 44.235 GPa 74.095 GPa 86.536 GPa 111.65 GPa 375.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 79.879 GPa 203.56 GPa 0.70574 TPa–1 4.3472 TPa–1 29.224 GPa 80.681 GPa0.0619180.72288Value
Anisotropy 2.548 6.1597 2.761 11.6748Anisotropy
Axis 0.3357
0.8649
-0.3732
-0.8110
0.0000
0.5851
-0.9381
0.0000
-0.3464
0.0000
1.0000
0.0000
0.4741
0.7071
0.5246
-0.1975
0.5158
0.8336
0.0000
1.0000
0.0000
0.7527
-0.0002
0.6584
Axis
-0.4741
0.7071
-0.5246
-0.8880
-0.4543
0.0706
-0.7048
0.0000
0.7094
0.0002
1.0000
0.0001
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