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 ScPd (Materials Project id mp-2781)

       156       93       93        0        0        0  
        93      156       93        0        0        0  
        93       93      156        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       44  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114 GPaEV = 105.02 GPaGV = 39 GPaνV = 0.34646
ReussKR = 114 GPaER = 102.53 GPaGR = 37.973 GPaνR = 0.3501
HillKH = 114 GPaEH = 103.78 GPaGH = 38.486 GPaνH = 0.34827

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
44 GPa 44 GPa 44 GPa 63 GPa 63 GPa 342 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 86.53 GPa 116.95 GPa 2.924 TPa–1 2.924 TPa–1 31.5 GPa 44 GPa0.221640.46402Value
Anisotropy 1.352 1.0000 1.397 2.0936Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.2053
0.7663
0.6088
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.7071
0.0002
-0.7071
0.0000
-1.0000
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