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 ScRu3 (Materials Project id mp-973022)

       223      172      148        0        0        0  
       172      223      148        0        0        0  
       148      148      242        0        0        0  
         0        0        0       97        0        0  
         0        0        0        0       97        0  
         0        0        0        0        0      111  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 180.44 GPaEV = 199.16 GPaGV = 75.667 GPaνV = 0.31605
ReussKR = 180.43 GPaER = 151.53 GPaGR = 55.709 GPaνR = 0.36002
HillKH = 180.43 GPaEH = 175.74 GPaGH = 65.688 GPaνH = 0.33767

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 95.654 GPa 97 GPa 97 GPa 111 GPa 541.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.368 GPa 256.43 GPa 1.8153 TPa–1 1.9119 TPa–1 25.5 GPa 111 GPa-0.154790.84958Value
Anisotropy 3.113 1.0532 4.353Anisotropy
Axis 0.0000
1.0000
0.0000
-0.5913
0.5913
0.5483
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
1.0000
-0.0000
-0.0000
0.6928
-0.0000
-0.7211
0.0000
0.7281
-0.6855
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
0.0001
-0.7211
0.0002
-0.6928
-1.0000
0.0000
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