Hf9Re3RuW

High-Entropy Materials HEA

MP-ID: mp-3294928 · Space group: P6_3/mmc (#194)

Materials Project API

Basic Information

Formula

Hf9Re3RuW

MP-ID

mp-3294928

Elements

Sites

Density

14.9329

g/cm³

Volume

544.87

Å³

Cell a

8.6242

Cell b

8.6242

Cell c

8.4590

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

Stability

Yes

Packing Fraction

0.7405

X-ray Diffraction

Diffraction Pattern

Target / Radiation

X-axis: 2θ (°); Y-axis: relative intensity; Cu Kα ; λ=1.5418 Å

Diffraction Peaks (Top 24)

2θ	d (Å)	I	hkl
11.85	7.4688	16.0	(1,0,-1,0)
21.00	4.2295	1.4	(0,0,0,2)
26.08	3.4163	1.7	(2,0,-2,1)
31.70	2.8229	3.5	(3,-1,-2,0)
31.70	2.8229	7.0	(2,1,-3,0)
31.97	2.7994	13.5	(2,0,-2,2)
33.46	2.6778	1.6	(3,-1,-2,1)
33.98	2.6379	20.1	(1,0,-1,3)
36.08	2.4896	14.3	(3,0,-3,0)
37.66	2.3883	46.5	(3,0,-3,1)
37.66	2.3883	23.2	(0,3,-3,1)
38.34	2.3480	100.0	(3,-1,-2,2)
40.07	2.2503	46.9	(2,0,-2,3)
41.90	2.1561	7.6	(4,-2,-2,0)
41.90	2.1561	15.2	(2,2,-4,0)
42.12	2.1455	1.7	(3,0,-3,2)
42.76	2.1148	15.3	(0,0,0,4)
44.53	2.0348	2.0	(1,0,-1,4)
45.06	2.0120	6.1	(4,-1,-3,1)
47.32	1.9209	1.3	(4,-2,-2,2)
47.32	1.9209	2.6	(2,2,-4,2)
48.80	1.8663	2.1	(3,0,-3,3)
49.54	1.8402	2.5	(2,0,-2,4)
53.66	1.7082	1.3	(4,0,-4,2)

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Energy Properties

Formation Energy/atom

-0.34400

eV/atom

Energy/atom

-46.08592

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-46.0859

eV/atom

Volume/atom

19.46

Å³

c/a Ratio

0.9808

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

1.5557

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.002860

μB/Å³

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

0.7424

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

7.070%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.3783

smaller = more stable mixing

VEC

5.071

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-31.106

kJ/mol; negative = exothermic mixing

Entropy Norm

0.7150

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfmea

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3294928

Reference Citation

The crystal structure and related material properties of Hf9Re3RuW were obtained from the Materials Project database (MP-ID: mp-3294928, 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

3D Crystal Structure Rendering

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Raw CIF Data

# generated using pymatgen
data_Hf9Re3RuW
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.62422177
_cell_length_b   8.62422106
_cell_length_c   8.45900402
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   120.00000272
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Hf9Re3RuW
_chemical_formula_sum   'Hf18 Re6 Ru2 W2'
_cell_volume   544.86592208
_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  0.19818824  0.80181176  0.44530152  1.0
  Hf  Hf1  1  0.19818824  0.39637549  0.44530152  1.0
  Hf  Hf2  1  0.60362451  0.80181176  0.44530152  1.0
  Hf  Hf3  1  0.80181176  0.19818824  0.55469848  1.0
  Hf  Hf4  1  0.80181176  0.60362451  0.55469848  1.0
  Hf  Hf5  1  0.39637549  0.19818824  0.55469848  1.0
  Hf  Hf6  1  0.80181176  0.19818824  0.94530152  1.0
  Hf  Hf7  1  0.80181176  0.60362451  0.94530152  1.0
  Hf  Hf8  1  0.39637549  0.19818824  0.94530152  1.0
  Hf  Hf9  1  0.19818824  0.80181176  0.05469848  1.0
  Hf  Hf10  1  0.19818824  0.39637549  0.05469848  1.0
  Hf  Hf11  1  0.60362451  0.80181176  0.05469848  1.0
  Hf  Hf12  1  0.54202518  0.45797482  0.25000000  1.0
  Hf  Hf13  1  0.54202518  0.08405035  0.25000000  1.0
  Hf  Hf14  1  0.91594965  0.45797482  0.25000000  1.0
  Hf  Hf15  1  0.45797482  0.54202518  0.75000000  1.0
  Hf  Hf16  1  0.45797482  0.91594965  0.75000000  1.0
  Hf  Hf17  1  0.08405035  0.54202518  0.75000000  1.0
  Re  Re18  1  0.88830738  0.11169262  0.25000000  1.0
  Re  Re19  1  0.88830738  0.77661376  0.25000000  1.0
  Re  Re20  1  0.22338624  0.11169262  0.25000000  1.0
  Re  Re21  1  0.11169262  0.88830738  0.75000000  1.0
  Re  Re22  1  0.11169262  0.22338624  0.75000000  1.0
  Re  Re23  1  0.77661376  0.88830738  0.75000000  1.0
  Ru  Ru24  1  0.33333300  0.66666700  0.25000000  1.0
  Ru  Ru25  1  0.66666700  0.33333300  0.75000000  1.0
  W  W26  1  0.00000000  0.00000000  0.50000000  1.0
  W  W27  1  0.00000000  0.00000000  0.00000000  1.0

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