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 TbScO3 (Materials Project id mp-31119)

       320      116      119        0        0        0  
       116      216      107        0        0        0  
       119      107      283        0        0        0  
         0        0        0       78        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0       98  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 167 GPaEV = 212.73 GPaGV = 82.6 GPaνV = 0.2877
ReussKR = 161.74 GPaER = 207.3 GPaGR = 80.577 GPaνR = 0.28638
HillKH = 164.37 GPaEH = 210.02 GPaGH = 81.588 GPaνH = 0.28705

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78 GPa 78 GPa 98 GPa 130.11 GPa 181.56 GPa 507.33 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 156.87 GPa 249.75 GPa 1.3594 TPa–1 2.9929 TPa–1 68.271 GPa 98 GPa0.170560.4045Value
Anisotropy 1.592 2.2016 1.435 2.3715Anisotropy
Axis 0.0000
1.0000
0.0000
0.8966
0.4429
-0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.4162
0.7071
0.5716
1.0000
0.0000
-0.0000
0.6185
0.7444
0.2515
1.0000
-0.0000
0.0000
Axis
-0.4162
0.7071
-0.5716
-0.0000
1.0000
0.0000
-0.7139
0.6661
-0.2161
0.0000
1.0000
-0.0001
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