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 GdCl3 (Materials Project id mp-23265)

        38       13       36        0        0        0  
        13       38       36        0        0        0  
        36       36       74        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       12  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 35.556 GPaEV = 46.057 GPaGV = 17.933 GPaνV = 0.28411
ReussKR = 21.491 GPaER = 30.438 GPaGR = 12.041 GPaνR = 0.26394
HillKH = 28.523 GPaEH = 38.26 GPaGH = 14.987 GPaνH = 0.27644

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10.306 GPa 12 GPa 25 GPa 28 GPa 28 GPa 114.69 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.181 GPa 58.229 GPa -17.766 TPa–1 32.149 TPa–1 6.4022 GPa 28 GPa-0.220320.88913Value
Anisotropy 3.036 4.374Anisotropy
Axis 0.7071
0.7071
0.0000
0.6826
0.0000
0.7308
0.0000
0.0000
1.0000
-0.1305
0.9914
0.0000
0.4999
0.5001
-0.7071
-0.0000
0.0000
1.0000
-1.0000
-0.0001
0.0000
0.3685
0.3686
0.8534
Axis
-0.5001
-0.4999
-0.7071
-0.5000
0.8660
-0.0000
0.0001
-1.0000
0.0000
-0.7071
0.7071
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