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Zr9TiCoRe3

High-Entropy Materials HEA

MP-ID: mp-3291594 · Space group: P6_3/mmc (#194)

Basic Information

Formula
Zr9TiCoRe3
MP-ID
mp-3291594
Elements
4
Sites
28
Density
8.9307
g/cm³
Volume
552.76
ų
Cell a
8.7071
Å
Cell b
8.7071
Å
Cell c
8.4191
Å
α Angle
90.00
°
β Angle
90.00
°
γ Angle
120.00
°
Space Group
P6_3/mmc
Point Group
6/mmm
Crystal System
Hexagonal
Bravais Lattice
Hexagonal P
Stability
Yes
Packing Fraction
0.7400

X-ray Diffraction

Diffraction Pattern
X-axis: 2θ (°); Y-axis: relative intensity; CuKa ; λ=1.5406 Å
Diffraction Peaks (Top 24)
2θd (Å)Ihkl
11.74 7.5405 45.9 (1,0,-1,0)
21.11 4.2095 21.6 (0,0,0,2)
23.60 3.7703 1.6 (2,0,-2,0)
23.60 3.7703 3.3 (2,-2,0,0)
24.21 3.6756 11.9 (1,0,-1,2)
25.89 3.4410 16.3 (2,0,-2,1)
29.52 3.0262 1.1 (2,-1,-1,2)
31.86 2.8085 9.3 (2,0,-2,2)
34.09 2.6301 21.5 (1,0,-1,3)
35.72 2.5135 27.1 (3,0,-3,0)
37.34 2.4085 78.7 (3,0,-3,1)
37.34 2.4085 39.3 (0,3,-3,1)
38.13 2.3600 100.0 (3,-1,-2,2)
40.05 2.2512 65.9 (2,0,-2,3)
41.48 2.1768 10.2 (4,-2,-2,0)
41.48 2.1768 5.1 (2,-4,2,0)
41.86 2.1581 5.5 (3,0,-3,2)
42.97 2.1048 17.6 (0,0,0,4)
44.65 2.0297 15.2 (4,-1,-3,1)
44.65 2.0297 3.0 (1,-4,3,1)
44.70 2.0273 5.0 (1,0,-1,4)
46.99 1.9336 1.0 (4,-2,-2,2)
48.28 1.8851 1.4 (4,0,-4,0)
48.63 1.8723 3.2 (3,0,-3,3)
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Energy Properties

Formation Energy/atom
-0.27048
eV/atom
Energy/atom
-27.99562
eV/atom
Energy above Hull
0.0000
eV/atom
Uncorrected Energy
-27.9956
eV/atom
Volume/atom
19.74
ų
c/a Ratio
0.9669

Electronic Properties

Metallic
Metal
Band Gap
0
eV
Direct Gap
No
CBM
N/A
eV

Magnetic Properties

Magnetic
No
Total Mag. Moment
0.1751
μB
Mag. Ordering
NM
Mag. Sites
0
Magnetization/Volume
0.000320
μB/ų

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)
Composition Info
Major / Matrix Element
Zr · 0.643
Element Family
4d-TM
Solute Fraction
0.357
Interstitial Fraction
0.000

High-Entropy Alloy Features

Composite Radar (normalized)
Element-Class Share
Mix Entropy ΔS/R
0.9911
HEA criterion (>1.0 = high entropy)
Mix Entropy ΔS
8.2403
J/mol·K
Ω Parameter
1.1893
Ω > 1.1 favors solid solution
Atomic Size Mismatch δr
7.888%
δr < 6.6% favors single-phase solid solution
Electronegativity Diff Δχ
0.2515
smaller = more stable mixing
VEC
5.000
valence electron concentration, affects phase stability
Mix Enthalpy ΔH_mix
-16.450
kJ/mol; negative = exothermic mixing
Entropy Norm
0.7150
SS Former
0
Phase Tendency
AM

Related Tasks

Related computation task IDs (1)

Citation & References

Materials Project Page
https://materialsproject.org/materials/mp-3291594
Reference Citation

The crystal structure and related material properties of Zr9TiCoRe3 were obtained from the Materials Project database (MP-ID: mp-3291594, database version v2026.04.13).

Literature Citation

Horton, M.K., Huck, P., Yang, R.X. et al. Accelerated data-driven materials science with the Materials Project. Nat. Mater. 24, 1522–1532 (2025). https://doi.org/10.1038/s41563-025-02272-0

BibTeX
@article{Horton2025,
  author  = {Horton, Matthew K. and Huck, Patrick and Yang, Ruo Xi and Munro, Jason M. and Dwaraknath, Shyam and Ganose, Alex M. and Kingsbury, Ryan S. and Wen, Mingjian and Shen, Jimmy X. and Mathis, Tyler S. and Kaplan, Aaron D. and Berket, Karlo and Riebesell, Janosh and George, Janine and Rosen, Andrew S. and Spotte-Smith, Evan W. C. and McDermott, Matthew J. and Cohen, Orion A. and Dunn, Alex and Kuner, Matthew C. and Rignanese, Gian-Marco and Petretto, Guido and Waroquiers, David and Griffin, Sinead M. and Neaton, Jeffrey B. and Chrzan, Daryl C. and Asta, Mark and Hautier, Geoffroy and Cholia, Shreyas and Ceder, Gerbrand and Ong, Shyue Ping and Jain, Anubhav and Persson, Kristin A.},
  title   = {Accelerated data-driven materials science with the Materials Project},
  journal = {Nature Materials},
  year    = {2025},
  volume  = {24},
  number  = {10},
  pages   = {1522--1532},
  month   = {oct},
  doi     = {10.1038/s41563-025-02272-0},
  issn    = {1476-4660},
  url     = {https://doi.org/10.1038/s41563-025-02272-0},
  abstract = {The Materials Project was launched formally in 2011 to drive materials discovery forwards through high-throughput computation and open data. More than a decade later, the Materials Project has become an indispensable tool used by more than 600,000 materials researchers around the world. This Perspective describes how the Materials Project, as a data platform and a software ecosystem, has helped to shape research in data-driven materials science. We cover how sustainable software and computational methods have accelerated materials design while becoming more open source and collaborative in nature. Next, we present cases where the Materials Project was used to understand and discover functional materials. We then describe our efforts to meet the needs of an expanding user base, through technical infrastructure updates ranging from data architecture and cloud resources to interactive web applications. Finally, we discuss opportunities to better aid the research community, with the vision that more accessible and easy-to-understand materials data will result in democratized materials knowledge and an increasingly collaborative community.}
}

3D Crystal Structure Rendering

Loading 3D structure…

Style: Ball & Stick
Raw CIF Data
# generated using pymatgen
data_Zr9TiCoRe3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.70706756
_cell_length_b   8.70706621
_cell_length_c   8.41908611
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99999760
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Zr9TiCoRe3
_chemical_formula_sum   'Zr18 Ti2 Co2 Re6'
_cell_volume   552.76349592
_cell_formula_units_Z   2
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Zr  Zr0  1  0.19996662  0.80003338  0.44031073  1.0
  Zr  Zr1  1  0.19996662  0.39993325  0.44031073  1.0
  Zr  Zr2  1  0.60006675  0.80003338  0.44031073  1.0
  Zr  Zr3  1  0.80003338  0.19996662  0.55968927  1.0
  Zr  Zr4  1  0.80003338  0.60006675  0.55968927  1.0
  Zr  Zr5  1  0.39993325  0.19996662  0.55968927  1.0
  Zr  Zr6  1  0.80003338  0.19996662  0.94031073  1.0
  Zr  Zr7  1  0.80003338  0.60006675  0.94031073  1.0
  Zr  Zr8  1  0.39993325  0.19996662  0.94031073  1.0
  Zr  Zr9  1  0.19996662  0.80003338  0.05968927  1.0
  Zr  Zr10  1  0.19996662  0.39993325  0.05968927  1.0
  Zr  Zr11  1  0.60006675  0.80003338  0.05968927  1.0
  Zr  Zr12  1  0.54273743  0.45726257  0.25000000  1.0
  Zr  Zr13  1  0.54273743  0.08547485  0.25000000  1.0
  Zr  Zr14  1  0.91452515  0.45726257  0.25000000  1.0
  Zr  Zr15  1  0.45726257  0.54273743  0.75000000  1.0
  Zr  Zr16  1  0.45726257  0.91452515  0.75000000  1.0
  Zr  Zr17  1  0.08547485  0.54273743  0.75000000  1.0
  Ti  Ti18  1  0.00000000  0.00000000  0.50000000  1.0
  Ti  Ti19  1  0.00000000  0.00000000  0.00000000  1.0
  Co  Co20  1  0.33333300  0.66666700  0.25000000  1.0
  Co  Co21  1  0.66666700  0.33333300  0.75000000  1.0
  Re  Re22  1  0.88817635  0.11182365  0.25000000  1.0
  Re  Re23  1  0.88817635  0.77635271  0.25000000  1.0
  Re  Re24  1  0.22364729  0.11182365  0.25000000  1.0
  Re  Re25  1  0.11182365  0.88817635  0.75000000  1.0
  Re  Re26  1  0.11182365  0.22364729  0.75000000  1.0
  Re  Re27  1  0.77635271  0.88817635  0.75000000  1.0
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