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 Ca2SiO4 (Materials Project id mp-4481)

       147       62       64        0        0        0  
        62      123       59        0        0        0  
        64       59      177        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0       45  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.778 GPaEV = 125.59 GPaGV = 49.467 GPaνV = 0.26942
ReussKR = 88.794 GPaER = 121.46 GPaGR = 47.744 GPaνR = 0.27202
HillKH = 89.786 GPaEH = 123.53 GPaGH = 48.605 GPaνH = 0.2707

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
45 GPa 56 GPa 59 GPa 71.353 GPa 100.47 GPa 275.18 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 89.981 GPa 142.87 GPa 2.6959 TPa–1 5.0794 TPa–1 36.123 GPa 59 GPa0.134830.41733Value
Anisotropy 1.588 1.8842 1.633 3.0953Anisotropy
Axis 0.0000
1.0000
0.0000
-0.4502
0.2429
0.8593
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
0.0000
0.7470
0.6649
-0.7923
0.0000
0.6101
Axis
-0.7071
0.7071
0.0000
-1.0000
0.0000
0.0000
-0.0001
-0.6649
0.7470
-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