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 BaMg(CO3)2 (Materials Project id mp-6504)

       180       62       42        9        0        0  
        62      180       42       -9        0        0  
        42       42       87        0        0        0  
         9       -9        0       18        0        0  
         0        0        0        0       18        9  
         0        0        0        0        9       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 82.111 GPaEV = 101.16 GPaGV = 39.067 GPaνV = 0.29467
ReussKR = 70.669 GPaER = 71.881 GPaGR = 27.013 GPaνR = 0.33048
HillKH = 76.39 GPaEH = 86.63 GPaGH = 33.04 GPaνH = 0.31099

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.111 GPa 16.405 GPa 60.889 GPa 66.857 GPa 119.59 GPa 262.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.772 GPa 152.17 GPa 2.5676 TPa–1 9.0152 TPa–1 16.111 GPa 60.889 GPa-0.00290050.66621Value
Anisotropy 3.253 3.5111 3.779Anisotropy
Axis -0.5951
0.3436
-0.7265
0.8610
0.4971
0.1076
-0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.1779
0.1027
0.9787
0.0000
0.9787
0.2054
-0.0000
0.7321
-0.6812
0.6734
0.3888
0.6288
Axis
-0.5000
0.8660
0.0000
-1.0000
0.0000
-0.0000
-1.0000
-0.0000
0.0000
-0.5446
-0.3144
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