Hf3Ge3Mo2C

High-Entropy Materials HEA

MP-ID: mp-3292628 · Space group: P6_3/mcm (#193)

Materials Project API

Basic Information

Formula

Hf3Ge3Mo2C

MP-ID

mp-3292628

Elements

Sites

Density

11.4189

g/cm³

Volume

278.42

Å³

Cell a

7.7457

Cell b

7.7457

Cell c

5.3585

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P6_3/mcm

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
13.20	6.7080	29.3	(1,0,-1,0)
13.20	6.7080	14.6	(1,-1,0,0)
22.96	3.8729	1.1	(2,-1,-1,0)
26.58	3.3540	8.9	(2,0,-2,0)
26.58	3.3540	8.9	(0,2,-2,0)
26.58	3.3540	8.9	(2,-2,0,0)
28.44	3.1389	27.4	(1,1,-2,1)
28.44	3.1389	54.9	(2,-1,-1,1)
33.45	2.6792	100.0	(0,0,0,2)
35.40	2.5354	28.0	(2,1,-3,0)
35.40	2.5354	28.0	(1,2,-3,0)
35.40	2.5354	28.0	(3,-1,-2,0)
35.40	2.5354	28.0	(1,-3,2,0)
35.40	2.5354	28.0	(3,-2,-1,0)
35.40	2.5354	28.0	(2,-3,1,0)
36.10	2.4881	32.9	(1,0,-1,2)
36.10	2.4881	32.9	(0,1,-1,2)
36.10	2.4881	32.9	(1,-1,0,2)
39.31	2.2918	99.0	(2,1,-3,1)
39.31	2.2918	99.0	(1,2,-3,1)
39.31	2.2918	99.0	(3,-1,-2,1)
39.31	2.2918	99.0	(1,-3,2,1)
39.31	2.2918	99.0	(3,-2,-1,1)
39.31	2.2918	99.0	(2,-3,1,1)

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Energy Properties

Formation Energy/atom

-0.69686

eV/atom

Energy/atom

-27.27035

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-27.2704

eV/atom

Volume/atom

15.47

Å³

c/a Ratio

0.6918

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0078

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000030

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Hf · 0.333

Element Family

5d-TM

Solute Fraction

0.667

Interstitial Fraction

0.111

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.3108

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

10.8979

J/mol·K

Ω Parameter

0.6487

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

18.293%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.4300

smaller = more stable mixing

VEC

4.444

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-38.767

kJ/mol; negative = exothermic mixing

Entropy Norm

0.9455

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfito

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3292628

Reference Citation

The crystal structure and related material properties of Hf3Ge3Mo2C were obtained from the Materials Project database (MP-ID: mp-3292628, 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_Hf3Ge3Mo2C
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.74572261
_cell_length_b   7.74572054
_cell_length_c   5.35845844
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99979644
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Hf3Ge3Mo2C
_chemical_formula_sum   'Hf6 Ge6 Mo4 C2'
_cell_volume   278.41661738
_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  0.76476041  0.00000013  0.75000000  1.0
  Hf  Hf1  1  0.76476067  0.76476059  0.25000000  1.0
  Hf  Hf2  1  0.99999989  0.23523972  0.25000000  1.0
  Hf  Hf3  1  0.00000011  0.76476028  0.75000000  1.0
  Hf  Hf4  1  0.23523933  0.23523941  0.75000000  1.0
  Hf  Hf5  1  0.23523959  0.99999987  0.25000000  1.0
  Ge  Ge6  1  0.40717795  0.99999984  0.75000000  1.0
  Ge  Ge7  1  0.40717799  0.40717797  0.25000000  1.0
  Ge  Ge8  1  0.00000024  0.59282212  0.25000000  1.0
  Ge  Ge9  1  0.99999976  0.40717788  0.75000000  1.0
  Ge  Ge10  1  0.59282201  0.59282203  0.75000000  1.0
  Ge  Ge11  1  0.59282205  0.00000016  0.25000000  1.0
  Mo  Mo12  1  0.66666686  0.33333336  0.00000000  1.0
  Mo  Mo13  1  0.33333314  0.66666664  0.50000000  1.0
  Mo  Mo14  1  0.66666686  0.33333336  0.50000000  1.0
  Mo  Mo15  1  0.33333314  0.66666664  1.00000000  1.0
  C  C16  1  0.00000000  0.00000000  0.50000000  1.0
  C  C17  1  0.00000000  0.00000000  0.00000000  1.0

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