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 NaNO3 (Materials Project id mp-4531)

        58       20       18        8        0        0  
        20       58       18       -8        0        0  
        18       18       32        0        0        0  
         8       -8        0       13        0        0  
         0        0        0        0       13        8  
         0        0        0        0        8       19  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.889 GPaEV = 38.651 GPaGV = 15.133 GPaνV = 0.27701
ReussKR = 26.4 GPaER = 29.606 GPaGR = 11.273 GPaνR = 0.31309
HillKH = 27.644 GPaEH = 34.17 GPaGH = 13.203 GPaνH = 0.29399

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.456 GPa 8.6403 GPa 20.693 GPa 24.544 GPa 42.36 GPa 89.307 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 20.244 GPa 57.282 GPa 7.5758 TPa–1 22.727 TPa–1 7.456 GPa 24.544 GPa-0.0585010.77049Value
Anisotropy 2.83 3.0000 3.292Anisotropy
Axis 0.6546
0.3779
-0.6547
-0.8082
0.4666
0.3593
0.9655
0.2604
0.0000
0.0000
0.0000
1.0000
-0.4933
0.2848
0.8219
-0.5000
0.8660
-0.0001
0.0000
0.7502
-0.6612
0.5000
0.8660
-0.0000
Axis
-0.5000
-0.8660
0.0000
-0.7118
-0.4109
0.5696
-1.0000
0.0000
0.0000
-0.6033
0.3484
-0.7174
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