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 Na(Cu3O4)2 (Materials Project id mp-758835)

       165       96       96        0        0        0  
        96      165       96        0        0        0  
        96       96      165        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 119 GPaEV = 99.59 GPaGV = 36.6 GPaνV = 0.36052
ReussKR = 119 GPaER = 99.388 GPaGR = 36.518 GPaνR = 0.3608
HillKH = 119 GPaEH = 99.489 GPaGH = 36.559 GPaνH = 0.36066

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 38 GPa 38 GPa 69 GPa 69 GPa 357 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.379 GPa 103.03 GPa 2.8011 TPa–1 2.8011 TPa–1 34.5 GPa 38 GPa0.325320.39254Value
Anisotropy 1.092 1.0000 1.101 1.2066Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
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