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 CaAl4O7 (Materials Project id mp-4867)

       186       76       67        0        5        0  
        76      202       72        0        2        0  
        67       72      212        0       -1        0  
         0        0        0       51        0       15  
         5        2       -1        0       29        0  
         0        0        0       15        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114.44 GPaEV = 129.71 GPaGV = 49.467 GPaνV = 0.3111
ReussKR = 114 GPaER = 113.78 GPaGR = 42.658 GPaνR = 0.33365
HillKH = 114.22 GPaEH = 121.81 GPaGH = 46.062 GPaνH = 0.32226

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28.776 GPa 28.845 GPa 61.155 GPa 117.57 GPa 138.82 GPa 343.83 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 78.97 GPa 176.4 GPa 2.5875 TPa–1 3.4414 TPa–1 28.709 GPa 67.268 GPa0.0290330.62317Value
Anisotropy 2.234 1.3300 2.343 21.4639Anisotropy
Axis -0.6408
0.5547
0.5307
-0.0267
-0.0001
0.9996
-0.4283
0.0000
-0.9037
-0.9037
-0.0000
0.4283
-0.0416
0.0012
0.9991
-0.0224
0.7071
0.7068
0.7791
0.5790
0.2405
0.7531
0.6028
0.2635
Axis
0.9991
-0.0008
0.0416
0.0224
0.7071
-0.7067
-0.1204
0.5147
-0.8489
-0.6457
0.6005
0.4717
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