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 ThB2C (Materials Project id mp-2997)

       402       62       95       -0        0        0  
        62      402       95        0        0        0  
        95       95      329        0        0        0  
        -0        0        0       93        0        0  
         0        0        0        0       93       -0  
         0        0        0        0       -0      170  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181.89 GPaEV = 314.83 GPaGV = 129.93 GPaνV = 0.21152
ReussKR = 181.41 GPaER = 296.65 GPaGR = 120.84 GPaνR = 0.22746
HillKH = 181.65 GPaEH = 305.8 GPaGH = 125.39 GPaνH = 0.21943

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
93 GPa 93 GPa 170 GPa 246.15 GPa 340 GPa 546.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 255.45 GPa 371.38 GPa 1.7384 TPa–1 2.0356 TPa–1 93 GPa 170 GPa0.0922890.39206Value
Anisotropy 1.454 1.1709 1.828 4.2482Anisotropy
Axis 0.5720
0.2345
0.7860
0.2588
0.9659
0.0000
0.3793
0.9253
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.4028
0.9153
0.0000
-0.7489
0.6626
-0.0000
0.7275
0.2162
0.6512
Axis
1.0000
0.0001
-0.0000
-0.9153
-0.4028
-0.0000
-0.6626
-0.7489
-0.0000
0.6242
0.1855
-0.7589
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