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 Ca(AsPd)2 (Materials Project id mp-5166)

       132       47       74        0        0        0  
        47      132       74        0        0        0  
        74       74      137        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       15  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 87.889 GPaEV = 75.773 GPaGV = 27.933 GPaνV = 0.35631
ReussKR = 86.439 GPaER = 68.255 GPaGR = 24.94 GPaνR = 0.36839
HillKH = 87.164 GPaEH = 72.028 GPaGH = 26.437 GPaνH = 0.36228

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 28 GPa 28 GPa 51.262 GPa 85 GPa 264.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.053 GPa 91.492 GPa 2.2843 TPa–1 4.6423 TPa–1 15 GPa 42.5 GPa0.076380.57633Value
Anisotropy 1.987 2.0323 2.833 7.5455Anisotropy
Axis 0.7071
0.7071
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
-0.7071
0.7071
-0.0000
1.0000
-0.0002
-0.0001
0.5513
0.5512
0.6263
Axis
0.0002
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.0002
1.0000
-0.0000
-0.7071
0.7071
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