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 PrCo2 (Materials Project id mp-2085)

       140      108      108        6        5       -5  
       108      140      108        5        6       -5  
       108      108      140        5        5       -6  
         6        5        5       22        0        0  
         5        6        5        0       22        0  
        -5       -5       -6        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 118.67 GPaEV = 55.732 GPaGV = 19.6 GPaνV = 0.42173
ReussKR = 114.79 GPaER = 54.01 GPaGR = 18.996 GPaνR = 0.42158
HillKH = 116.73 GPaEH = 54.871 GPaGH = 19.298 GPaνH = 0.42165

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21.235 GPa 21.901 GPa 21.901 GPa 32.099 GPa 32.099 GPa 356.76 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.791 GPa 63.634 GPa 1.8479 TPa–1 5.0158 TPa–1 15.918 GPa 22.082 GPa0.289320.59222Value
Anisotropy 1.39 2.7143 1.387 2.0469Anisotropy
Axis -0.0160
-0.0160
0.9997
-0.5893
0.5527
0.5893
0.7071
0.0000
0.7071
0.5774
0.5773
-0.5774
0.0000
0.7071
0.7071
0.7071
0.0000
0.7071
0.7005
0.7004
-0.1371
-0.7071
0.0000
-0.7071
Axis
-0.1155
0.7024
-0.7024
0.0817
0.9933
-0.0817
-0.7071
0.7071
0.0000
0.0689
-0.9952
-0.0690
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