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 BaEr2CoO5 (Materials Project id mp-18746)

       259       59       42        0        0       -0  
        59      218      103        0        0       -0  
        42      103      256        0        0       -0  
         0        0        0       94       -0        0  
         0        0        0       -0       41        0  
        -0       -0       -0        0        0       49  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 126.78 GPaEV = 181.76 GPaGV = 72.067 GPaνV = 0.26105
ReussKR = 126.33 GPaER = 161.12 GPaGR = 62.575 GPaνR = 0.28743
HillKH = 126.55 GPaEH = 171.55 GPaGH = 67.321 GPaνH = 0.27408

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 49 GPa 94 GPa 129.07 GPa 221.89 GPa 382.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.82 GPa 242.07 GPa 2.3492 TPa–1 2.8646 TPa–1 41 GPa 104.86 GPa0.0581150.52376Value
Anisotropy 1.987 1.2194 2.558 9.0124Anisotropy
Axis 0.6900
0.0000
0.7238
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
-1.0000
0.7071
-0.0000
-0.7071
0.0000
0.0000
1.0000
-0.7007
0.4775
0.5301
Axis
-1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.7103
-0.3969
-0.5813
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