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 Cu2GeSe3 (Materials Project id mp-677105)

       104       36       35        0       -0        0  
        36      105       40        0        9        0  
        35       40      105        0       -9        0  
         0        0        0       30        0        8  
        -0        9       -9        0       22        0  
         0        0        0        8        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 59.556 GPaEV = 72.918 GPaGV = 28.133 GPaνV = 0.29594
ReussKR = 59.523 GPaER = 64.509 GPaGR = 24.447 GPaνR = 0.31937
HillKH = 59.539 GPaEH = 68.751 GPaGH = 26.29 GPaνH = 0.30755

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.321 GPa 18.514 GPa 34.679 GPa 68.32 GPa 70.436 GPa 178.73 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.32 GPa 93.335 GPa 5.4028 TPa–1 5.8937 TPa–1 16.321 GPa 37.316 GPa0.00571440.59709Value
Anisotropy 2.059 1.0909 2.286104.4885Anisotropy
Axis 0.6023
0.6904
-0.4008
0.2781
0.0000
-0.9606
0.0000
1.0000
0.0000
0.9986
0.0000
0.0537
-0.8632
-0.0000
0.5049
0.3871
0.7071
-0.5918
-0.7816
0.0000
0.6237
-0.7907
0.0001
0.6122
Axis
0.0000
-1.0000
0.0000
-0.3871
0.7071
0.5918
0.0000
-1.0000
0.0000
-0.6122
-0.0003
-0.7907
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