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 CaSi2 (Materials Project id mp-8372)

       137       55       31      -20        0        0  
        55      137       31       20        0        0  
        31       31       69        0        0        0  
       -20       20        0       40        0        0  
         0        0        0        0       40      -20  
         0        0        0        0      -20       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.111 GPaEV = 97.828 GPaGV = 39.267 GPaνV = 0.24568
ReussKR = 54.981 GPaER = 76.954 GPaGR = 30.375 GPaνR = 0.26672
HillKH = 59.546 GPaEH = 87.422 GPaGH = 34.821 GPaνH = 0.25531

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
20.494 GPa 25.772 GPa 54.974 GPa 60.506 GPa 96.228 GPa 206.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 55.324 GPa 142.69 GPa 3.3551 TPa–1 11.478 TPa–1 20.494 GPa 60.506 GPa-0.026690.72617Value
Anisotropy 2.579 3.4211 2.952Anisotropy
Axis -0.6746
0.3895
0.6271
0.7881
0.4550
-0.4146
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
-0.0000
0.6982
0.7159
0.6200
0.3580
0.6982
-0.0000
0.6220
0.7831
-0.5000
0.8660
0.0000
Axis
-1.0000
0.0001
-0.0001
-0.5000
0.8660
0.0000
-1.0000
0.0000
-0.0000
-0.6907
-0.3988
-0.6032
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