K4Ge2Au7

High-Entropy Materials HEA Traditional Materials TRA

MP-ID: mp-9201 · Space group: R-3m (#166)

Materials Project API

Basic Information

Formula

K4Ge2Au7

MP-ID

mp-9201

Elements

Sites

Density

8.1297

g/cm³

Volume

343.24

Å³

Cell a

10.0644

Cell b

10.0644

Cell c

10.0644

α Angle

37.78

β Angle

37.78

γ Angle

37.78

Space Group

R-3m

Point Group

-3m

Crystal System

Trigonal

Bravais Lattice

Stability

Yes

Packing Fraction

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
9.47	9.3348	8.1	(1,1,1)
16.02	5.5319	8.1	(1,0,0)
16.02	5.5319	16.1	(0,1,0)
16.94	5.2340	100.0	(1,1,0)
19.01	4.6674	51.0	(2,2,2)
20.21	4.3935	2.9	(2,1,1)
27.37	3.2580	2.3	(1,0,-1)
27.37	3.2580	1.2	(0,1,-1)
30.04	2.9747	16.7	(3,3,2)
32.37	2.7659	14.1	(2,0,0)
32.37	2.7659	28.2	(0,2,0)
33.54	2.6715	6.4	(3,2,1)
33.54	2.6715	32.0	(3,1,2)
34.27	2.6170	57.5	(2,2,0)
34.27	2.6170	28.7	(2,0,2)
35.80	2.5085	7.4	(4,3,3)
35.80	2.5085	3.7	(3,4,3)
38.58	2.3337	17.6	(4,4,4)
38.81	2.3206	8.1	(4,4,3)
39.07	2.3058	3.0	(3,3,1)
39.07	2.3058	1.5	(3,1,3)
40.07	2.2502	5.1	(4,3,2)
40.07	2.2502	5.1	(3,4,2)
41.09	2.1968	10.2	(4,2,2)

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Energy Properties

Formation Energy/atom

-0.34330

eV/atom

Energy/atom

-3.16551

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-31.6076

eV/atom

Volume/atom

26.40

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

0.0000

μB

Mag. Ordering

Unknown

Mag. Sites

Magnetization/Volume

0.000000

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Au · 0.538

Element Family

5d-TM

Solute Fraction

0.462

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

0.9840

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.1807

J/mol·K

Ω Parameter

1.9296

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

22.865%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7619

smaller = more stable mixing

VEC

6.846

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-4.281

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8956

SS Former

Phase Tendency

Traditional Material Features

ROM Blended-Feature Radar

Rating & Classification

Tier

Score

0.653

Family

Au-rich Multi-Component

Matrix Element

Au · 0.538

Related Tasks

Related computation task IDs (5)

aaadnffp aaadqzle aaaemvfg aaaeuelm aaafsfyk

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-9201

Reference Citation

The crystal structure and related material properties of K4Ge2Au7 were obtained from the Materials Project database (MP-ID: mp-9201, 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

Loading 3D structure…

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Raw CIF Data

# generated using pymatgen
data_K4Ge2Au7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.06435023
_cell_length_b   10.06434921
_cell_length_c   10.06434940
_cell_angle_alpha   37.77582692
_cell_angle_beta   37.77583645
_cell_angle_gamma   37.77582811
_symmetry_Int_Tables_number   1
_chemical_formula_structural   K4Ge2Au7
_chemical_formula_sum   'K4 Ge2 Au7'
_cell_volume   343.24159949
_cell_formula_units_Z   1
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
  K  K0  1  0.68259270  0.68259270  0.68259270  1.0
  K  K1  1  0.31740730  0.31740730  0.31740730  1.0
  K  K2  1  0.81040856  0.81040856  0.81040856  1.0
  K  K3  1  0.18959144  0.18959144  0.18959144  1.0
  Ge  Ge4  1  0.54501570  0.54501570  0.54501570  1.0
  Ge  Ge5  1  0.45498430  0.45498430  0.45498430  1.0
  Au  Au6  1  0.00000000  -0.00000000  -0.00000000  1.0
  Au  Au7  1  0.22317919  0.22317919  0.79467937  1.0
  Au  Au8  1  0.22317919  0.79467937  0.22317919  1.0
  Au  Au9  1  0.79467937  0.22317919  0.22317919  1.0
  Au  Au10  1  0.20532063  0.77682081  0.77682081  1.0
  Au  Au11  1  0.77682081  0.77682081  0.20532063  1.0
  Au  Au12  1  0.77682081  0.20532063  0.77682081  1.0

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