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 PrSb (Materials Project id mp-1785)

       134       16       16        0        0        0  
        16      134       16        0        0        0  
        16       16      134        0        0        0  
         0        0        0       20        0        0  
         0        0        0        0       20        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 55.333 GPaEV = 87.94 GPaGV = 35.6 GPaνV = 0.23512
ReussKR = 55.333 GPaER = 70.087 GPaGR = 27.189 GPaνR = 0.28889
HillKH = 55.333 GPaEH = 79.204 GPaGH = 31.394 GPaνH = 0.26143

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 20 GPa 20 GPa 118 GPa 118 GPa 166 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.548 GPa 130.59 GPa 6.0241 TPa–1 6.0241 TPa–1 20 GPa 59 GPa0.0513070.57031Value
Anisotropy 2.439 1.0000 2.95 11.1156Anisotropy
Axis -0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
-0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
0.7071
-0.0005
-0.7071
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