ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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 MnCuO2 (Materials Project id mp-510589)

       355       97       78        0       -4        0  
        97      202       50        0       -1        0  
        78       50      122        0       -1        0  
         0        0        0       44        0        1  
        -4       -1       -1        0       19        0  
         0        0        0        1        0       27  

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	KV = 125.44 GPa	EV = 128.34 GPa	GV = 48.267 GPa	νV = 0.32949
Reuss	KR = 98.021 GPa	ER = 92.719 GPa	GR = 34.536 GPa	νR = 0.34235
Hill	KH = 111.73 GPa	EH = 110.55 GPa	GH = 41.401 GPa	νH = 0.3351

Eigenvalues of the stiffness matrix

λ1	λ2	λ3	λ4	λ5	λ6
18.952 GPa	26.941 GPa	44.059 GPa	92.709 GPa	156.7 GPa	429.63 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	Emin	Emax	βmin	βmax	Gmin	Gmax	νmin	νmax
Value	61.457 GPa	281.96 GPa	0.52048 TPa–1	6.6201 TPa–1	18.952 GPa	82.96 GPa	0.091644	0.72767	Value
Anisotropy	4.588		12.7193		4.377		7.9402		Anisotropy
Axis	-0.6469 0.0000 -0.7625	0.9999 0.0000 -0.0139	0.9987 -0.0000 -0.0510	0.0510 -0.0000 0.9987	0.0072 0.0000 1.0000	0.7070 0.7071 -0.0103	-0.6873 0.0000 -0.7264	-0.8504 0.0000 0.5261	Axis
					1.0000 -0.0000 -0.0072	-0.7070 0.7071 0.0104	-0.0000 -1.0000 -0.0000	-0.5261 -0.0001 -0.8504	Second axis

Spatial dependence of Young's modulus

[[355.0, 97.0, 78.0, 0.0, -4.0, 0.0], [97.0, 202.0, 50.0, 0.0, -1.0, 0.0], [78.0, 50.0, 122.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 44.0, 0.0, 1.0], [-4.0, -1.0, -1.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 27.0]] MnCuO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-510589" target="_blank">mp-510589</a>) young

Spatial dependence of linear compressibility

[[355.0, 97.0, 78.0, 0.0, -4.0, 0.0], [97.0, 202.0, 50.0, 0.0, -1.0, 0.0], [78.0, 50.0, 122.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 44.0, 0.0, 1.0], [-4.0, -1.0, -1.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 27.0]] MnCuO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-510589" target="_blank">mp-510589</a>) lc

Spatial dependence of shear modulus

[[355.0, 97.0, 78.0, 0.0, -4.0, 0.0], [97.0, 202.0, 50.0, 0.0, -1.0, 0.0], [78.0, 50.0, 122.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 44.0, 0.0, 1.0], [-4.0, -1.0, -1.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 27.0]] MnCuO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-510589" target="_blank">mp-510589</a>) shear

Spatial dependence of Poisson's ratio

[[355.0, 97.0, 78.0, 0.0, -4.0, 0.0], [97.0, 202.0, 50.0, 0.0, -1.0, 0.0], [78.0, 50.0, 122.0, 0.0, -1.0, 0.0], [0.0, 0.0, 0.0, 44.0, 0.0, 1.0], [-4.0, -1.0, -1.0, 0.0, 19.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 27.0]] MnCuO2 (Materials Project id <a href="https://www.materialsproject.org/materials/mp-510589" target="_blank">mp-510589</a>) poisson

Code version: 2020.07.26 (running on Python 3.7.2)