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 ScCd3 (Materials Project id mp-30494)

        91       51       36        0        0        0  
        51       91       36        0        0        0  
        36       36      122        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       20  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 61.111 GPaEV = 71.209 GPaGV = 27.267 GPaνV = 0.30579
ReussKR = 60.876 GPaER = 67.055 GPaGR = 25.469 GPaνR = 0.31642
HillKH = 60.994 GPaEH = 69.14 GPaGH = 26.368 GPaνH = 0.31107

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20 GPa 28 GPa 28 GPa 40 GPa 80.116 GPa 183.88 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.094 GPa 103.75 GPa 4.7516 TPa–1 5.8376 TPa–1 20 GPa 32.085 GPa0.146850.50235Value
Anisotropy 1.726 1.2286 1.604 3.4208Anisotropy
Axis 0.9914
0.1305
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
1.0000
-0.0002
-0.0000
-0.0529
0.7051
0.7071
0.4620
0.8869
0.0000
-0.6510
0.7591
-0.0000
Axis
0.0002
1.0000
-0.0000
-0.0529
0.7051
-0.7071
0.0000
0.0000
-1.0000
-0.7591
-0.6510
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