PrGeAu

High-Entropy Materials HEA Traditional Materials TRA

MP-ID: mp-1019094 · Space group: P6_3mc (#186)

Materials Project API

Basic Information

Formula

PrGeAu

MP-ID

mp-1019094

Elements

Sites

Density

9.8287

g/cm³

Volume

138.71

Å³

Cell a

4.4632

Cell b

4.4681

Cell c

8.0288

α Angle

90.00

β Angle

90.00

γ Angle

119.96

Space Group

P6_3mc

Point Group

6mm

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
22.14	4.0144	12.6	(0,0,0,2)
25.55	3.4868	13.9	(0,1,-1,1)
25.57	3.4837	13.8	(1,0,-1,1)
25.57	3.4837	13.8	(1,-1,0,1)
32.12	2.7865	50.0	(0,1,-1,2)
32.14	2.7849	100.0	(1,0,-1,2)
40.37	2.2341	30.8	(1,1,-2,0)
40.37	2.2341	30.8	(1,-2,1,0)
40.42	2.2316	30.7	(2,-1,-1,0)
41.00	2.2014	6.1	(0,1,-1,3)
41.01	2.2006	6.1	(1,0,-1,3)
41.01	2.2006	6.1	(1,-1,0,3)
45.17	2.0072	19.4	(0,0,0,4)
46.52	1.9521	7.5	(1,1,-2,2)
46.56	1.9505	3.8	(2,-1,-1,2)
48.37	1.8816	2.6	(0,2,-2,1)
48.43	1.8796	2.6	(2,0,-2,1)
48.43	1.8796	2.6	(2,-2,0,1)
52.49	1.7434	12.6	(0,2,-2,2)
52.54	1.7419	12.5	(2,0,-2,2)
52.54	1.7419	12.5	(2,-2,0,2)
58.89	1.5683	2.2	(0,2,-2,3)
58.93	1.5672	2.2	(2,0,-2,3)
58.93	1.5672	2.2	(2,-2,0,3)

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Energy Properties

Formation Energy/atom

-0.82184

eV/atom

Energy/atom

-5.05263

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-32.2199

eV/atom

Volume/atom

23.12

Å³

c/a Ratio

1.7989

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

Pr · 0.333

Element Family

Lanthanide

Solute Fraction

0.667

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0986

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.1339

J/mol·K

Ω Parameter

1.9916

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

16.545%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.5815

smaller = more stable mixing

VEC

6.000

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-5.742

kJ/mol; negative = exothermic mixing

Entropy Norm

1.0000

SS Former

Phase Tendency

Traditional Material Features

ROM Blended-Feature Radar

Rating & Classification

Tier

Score

0.430

Family

Pr-rich Multi-Component

Matrix Element

Pr · 0.333

Related Tasks

Related computation task IDs (5)

aaadmwkj aaadsvxc aaaembry aaaeqyug aaafxgxd

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-1019094

Reference Citation

The crystal structure and related material properties of PrGeAu were obtained from the Materials Project database (MP-ID: mp-1019094, 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_PrGeAu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.46319477
_cell_length_b   4.46812770
_cell_length_c   8.02874921
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.96347096
_symmetry_Int_Tables_number   1
_chemical_formula_structural   PrGeAu
_chemical_formula_sum   'Pr2 Ge2 Au2'
_cell_volume   138.71061025
_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
  Pr  Pr0  1  0.00010337  0.00020675  0.75070957  1.0
  Pr  Pr1  1  -0.00010337  -0.00020675  0.25070957  1.0
  Ge  Ge2  1  0.66655924  0.33311848  0.97399493  1.0
  Ge  Ge3  1  0.33344076  0.66688152  0.47399493  1.0
  Au  Au4  1  0.66664207  0.33328514  0.51529550  1.0
  Au  Au5  1  0.33335793  0.66671486  0.01529550  1.0

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