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 PrCo2B2C (Materials Project id mp-12985)

       280      146      122        0        0        0  
       146      280      122        0        0        0  
       122      122      246        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0      137  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 176.22 GPaEV = 188.09 GPaGV = 71.133 GPaνV = 0.32211
ReussKR = 174.48 GPaER = 156.46 GPaGR = 57.926 GPaνR = 0.35055
HillKH = 175.35 GPaEH = 172.44 GPaGH = 64.53 GPaνH = 0.33611

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40 GPa 40 GPa 134 GPa 137 GPa 141.4 GPa 530.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 121.93 GPa 288.67 GPa 1.6527 TPa–1 2.4258 TPa–1 40 GPa 137 GPa0.0535270.63233Value
Anisotropy 2.367 1.4677 3.425 11.8133Anisotropy
Axis 0.6969
0.0000
0.7172
0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
-0.0003
-0.0000
-0.7071
0.7071
-0.0000
0.5706
0.5705
0.5908
Axis
-0.7660
0.6428
-0.0000
0.0003
1.0000
0.0000
-0.7071
-0.7071
-0.0000
0.4176
0.4178
-0.8068
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