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 ZrTe (Materials Project id mp-1539)

       129       56       76        0        0        0  
        56      129       76        0        0        0  
        76       76      185        0        0        0  
         0        0        0       99        0        0  
         0        0        0        0       99        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.444 GPaEV = 153.84 GPaGV = 62.467 GPaνV = 0.23136
ReussKR = 90.331 GPaER = 125.96 GPaGR = 49.685 GPaνR = 0.26759
HillKH = 92.888 GPaEH = 140.05 GPaGH = 56.076 GPaνH = 0.24872

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 73 GPa 77.52 GPa 99 GPa 99 GPa 292.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 90.71 GPa 181.85 GPa 1.4555 TPa–1 4.8075 TPa–1 36 GPa 99 GPa-0.105570.5728Value
Anisotropy 2.005 3.3030 2.75Anisotropy
Axis -0.7071
0.7071
0.0000
0.6417
-0.0000
-0.7670
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
0.4957
0.4956
0.7132
-0.4372
0.4372
0.7859
Axis
0.0002
1.0000
0.0000
0.7660
0.6428
-0.0000
-0.5043
-0.5043
0.7010
-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