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 BaCoO2 (Materials Project id mp-19086)

       117       61       59        3        0        0  
        61      117       59       -3        0        0  
        59       59      117        0        0        0  
         3       -3        0       34        0        0  
         0        0        0        0       34        3  
         0        0        0        0        3       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 78.778 GPaEV = 81.433 GPaGV = 30.667 GPaνV = 0.32772
ReussKR = 78.773 GPaER = 80.323 GPaGR = 30.195 GPaνR = 0.33005
HillKH = 78.775 GPaEH = 80.879 GPaGH = 30.431 GPaνH = 0.32888

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26.757 GPa 33.21 GPa 35.243 GPa 56.79 GPa 58.662 GPa 236.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.292 GPa 91.197 GPa 4.1835 TPa–1 4.3278 TPa–1 26.757 GPa 35.243 GPa0.234880.42254Value
Anisotropy 1.244 1.0345 1.317 1.7990Anisotropy
Axis -0.0000
0.9688
0.2480
0.6632
0.3829
0.6431
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.8001
0.4620
0.3827
0.3314
0.1913
-0.9239
0.0001
0.6144
0.7890
-0.0000
0.6719
0.7407
Axis
-0.5000
-0.8660
-0.0000
-0.5000
0.8660
0.0000
-0.0001
0.7890
-0.6144
-1.0000
-0.0000
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