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Hf9TiRe3Au

High-Entropy Materials HEA

MP-ID: mp-3297349 · Space group: P6_3/mmc (#194)

Basic Information

Formula
Hf9TiRe3Au
MP-ID
mp-3297349
Elements
4
Sites
28
Density
14.3570
g/cm³
Volume
557.45
ų
Cell a
8.7503
Å
Cell b
8.7503
Å
Cell c
8.4068
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
11.68 7.5780 1.4 (1,0,-1,0)
15.74 5.6287 2.3 (1,0,-1,1)
20.30 4.3752 1.7 (2,-1,-1,0)
21.14 4.2034 6.9 (0,0,0,2)
23.48 3.7890 7.8 (2,0,-2,0)
25.79 3.4544 7.0 (2,0,-2,1)
29.47 3.0312 9.6 (2,-1,-1,2)
31.23 2.8642 1.6 (3,-2,-1,0)
31.80 2.8144 25.6 (2,0,-2,2)
33.04 2.7112 9.0 (3,-1,-2,1)
34.11 2.6283 15.1 (1,0,-1,3)
35.54 2.5260 6.3 (3,0,-3,0)
35.54 2.5260 12.6 (3,-3,0,0)
37.17 2.4192 82.3 (3,0,-3,1)
38.02 2.3670 100.0 (3,-1,-2,2)
40.02 2.2530 70.1 (2,0,-2,3)
41.27 2.1876 35.0 (4,-2,-2,0)
43.04 2.1017 19.4 (0,0,0,4)
44.43 2.0390 2.3 (4,-1,-3,1)
44.43 2.0390 11.4 (4,-3,-1,1)
45.27 2.0030 1.9 (3,-1,-2,3)
46.82 1.9405 2.0 (4,-2,-2,2)
48.02 1.8945 2.9 (4,0,-4,0)
48.52 1.8762 4.7 (3,0,-3,3)
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Energy Properties

Formation Energy/atom
-0.36962
eV/atom
Energy/atom
-45.16371
eV/atom
Energy above Hull
0.0000
eV/atom
Uncorrected Energy
-45.1637
eV/atom
Volume/atom
19.91
ų
c/a Ratio
0.9607

Electronic Properties

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

Magnetic Properties

Magnetic
No
Total Mag. Moment
0.0005
μB
Mag. Ordering
NM
Mag. Sites
0
Magnetization/Volume
0.000000
μB/ų

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)
Composition Info
Major / Matrix Element
Hf · 0.643
Element Family
5d-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
0.6319
Ω > 1.1 favors solid solution
Atomic Size Mismatch δr
6.085%
δr < 6.6% favors single-phase solid solution
Electronegativity Diff Δχ
0.3690
smaller = more stable mixing
VEC
5.143
valence electron concentration, affects phase stability
Mix Enthalpy ΔH_mix
-33.725
kJ/mol; negative = exothermic mixing
Entropy Norm
0.7150
SS Former
0
Phase Tendency
IM

Related Tasks

Related computation task IDs (1)

Citation & References

Materials Project Page
https://materialsproject.org/materials/mp-3297349
Reference Citation

The crystal structure and related material properties of Hf9TiRe3Au were obtained from the Materials Project database (MP-ID: mp-3297349, 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_Hf9TiRe3Au
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.75032903
_cell_length_b   8.75032838
_cell_length_c   8.40676552
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99999872
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Hf9TiRe3Au
_chemical_formula_sum   'Hf18 Ti2 Re6 Au2'
_cell_volume   557.45306444
_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
  Hf  Hf0  1  0.19305296  0.80694704  0.44845741  1.0
  Hf  Hf1  1  0.19305296  0.38610492  0.44845741  1.0
  Hf  Hf2  1  0.61389508  0.80694704  0.44845741  1.0
  Hf  Hf3  1  0.80694704  0.19305296  0.55154259  1.0
  Hf  Hf4  1  0.80694704  0.61389508  0.55154259  1.0
  Hf  Hf5  1  0.38610492  0.19305296  0.55154259  1.0
  Hf  Hf6  1  0.80694704  0.19305296  0.94845741  1.0
  Hf  Hf7  1  0.80694704  0.61389508  0.94845741  1.0
  Hf  Hf8  1  0.38610492  0.19305296  0.94845741  1.0
  Hf  Hf9  1  0.19305296  0.80694704  0.05154259  1.0
  Hf  Hf10  1  0.19305296  0.38610492  0.05154259  1.0
  Hf  Hf11  1  0.61389508  0.80694704  0.05154259  1.0
  Hf  Hf12  1  0.54246333  0.45753667  0.25000000  1.0
  Hf  Hf13  1  0.54246333  0.08492866  0.25000000  1.0
  Hf  Hf14  1  0.91507134  0.45753667  0.25000000  1.0
  Hf  Hf15  1  0.45753667  0.54246333  0.75000000  1.0
  Hf  Hf16  1  0.45753667  0.91507134  0.75000000  1.0
  Hf  Hf17  1  0.08492866  0.54246333  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
  Re  Re20  1  0.88634916  0.11365084  0.25000000  1.0
  Re  Re21  1  0.88634916  0.77269833  0.25000000  1.0
  Re  Re22  1  0.22730167  0.11365084  0.25000000  1.0
  Re  Re23  1  0.11365084  0.88634916  0.75000000  1.0
  Re  Re24  1  0.11365084  0.22730167  0.75000000  1.0
  Re  Re25  1  0.77269833  0.88634916  0.75000000  1.0
  Au  Au26  1  0.33333300  0.66666700  0.25000000  1.0
  Au  Au27  1  0.66666700  0.33333300  0.75000000  1.0
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