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 CrTe4Au (Materials Project id mp-12743)

        50        9       10        0       -6        0  
         9       94       14        0       16        0  
        10       14       46        0       -3        0  
         0        0        0       21        0        8  
        -6       16       -3        0       24        0  
         0        0        0        8        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 28.444 GPaEV = 57.044 GPaGV = 24.467 GPaνV = 0.16576
ReussKR = 25.889 GPaER = 48.753 GPaGR = 20.551 GPaνR = 0.18614
HillKH = 27.167 GPaEH = 52.913 GPaGH = 22.509 GPaνH = 0.17538

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14.754 GPa 17.989 GPa 31.246 GPa 37.249 GPa 56.248 GPa 102.51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 35.309 GPa 82.853 GPa 6.3753 TPa–1 17.073 TPa–1 14.754 GPa 38.132 GPa-0.123220.64073Value
Anisotropy 2.347 2.6779 2.585Anisotropy
Axis -0.7085
-0.0000
-0.7058
-0.3420
0.8889
-0.3047
0.0000
1.0000
0.0000
0.5567
0.0000
0.8307
-0.6154
0.0000
0.7882
-0.4407
0.7052
0.5554
0.0000
1.0000
-0.0000
0.0000
1.0000
0.0000
Axis
0.0000
-1.0000
0.0000
-0.6540
-0.6761
0.3394
-0.7515
0.0000
0.6597
-0.6597
0.0000
-0.7516
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