Er10Si4Bi3Pb

High-Entropy Materials HEA

MP-ID: mp-3292618 · Space group: C2 (#5)

Materials Project API

Basic Information

Formula

Er10Si4Bi3Pb

MP-ID

mp-3292618

Elements

Sites

Density

9.3310

g/cm³

Volume

466.09

Å³

Cell a

8.5135

Cell b

8.5135

Cell c

7.8587

α Angle

89.92

β Angle

89.92

γ Angle

125.09

Space Group

Point Group

Crystal System

Monoclinic

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
11.71	7.5545	11.8	(1,-1,0)
16.98	5.2205	15.9	(1,0,1)
17.03	5.2057	17.8	(1,0,-1)
22.63	3.9293	20.8	(0,0,2)
22.65	3.9254	20.6	(1,1,0)
23.55	3.7773	16.8	(2,-2,0)
25.33	3.5162	49.2	(1,1,1)
25.40	3.5072	47.0	(1,1,-1)
25.55	3.4860	18.6	(1,-1,2)
25.57	3.4832	18.7	(2,0,0)
26.00	3.4267	41.3	(1,0,2)
26.07	3.4183	44.7	(1,0,-2)
31.01	2.8842	39.2	(2,-1,2)
31.06	2.8793	41.3	(2,-1,-2)
32.18	2.7815	63.6	(1,1,2)
32.29	2.7726	65.4	(1,1,-2)
32.89	2.7231	50.0	(2,-2,2)
32.89	2.7231	50.0	(2,-2,-2)
32.91	2.7218	99.9	(3,-1,0)
33.76	2.6554	52.5	(3,-2,1)
33.76	2.6554	52.5	(2,-3,-1)
33.78	2.6534	100.0	(3,-2,-1)
34.36	2.6102	6.8	(2,0,2)
34.46	2.6029	7.2	(2,0,-2)

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Energy Properties

Formation Energy/atom

-0.87122

eV/atom

Energy/atom

-34.54575

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-34.5458

eV/atom

Volume/atom

25.89

Å³

c/a Ratio

0.9231

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0473

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000100

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Er · 0.556

Element Family

Lanthanide

Solute Fraction

0.444

Interstitial Fraction

0.222

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.1200

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.3116

J/mol·K

Ω Parameter

90.5573

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

14.670%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.3879

smaller = more stable mixing

VEC

8.611

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-0.154

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8079

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfite

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3292618

Reference Citation

The crystal structure and related material properties of Er10Si4Bi3Pb were obtained from the Materials Project database (MP-ID: mp-3292618, 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_Er10Si4Bi3Pb
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.51350516
_cell_length_b   8.51350497
_cell_length_c   7.85871684
_cell_angle_alpha   89.91512780
_cell_angle_beta   89.91512387
_cell_angle_gamma   125.08648093
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Er10Si4Bi3Pb
_chemical_formula_sum   'Er10 Si4 Bi3 Pb1'
_cell_volume   466.09128578
_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
  Er  Er0  1  0.03974167  0.28341113  0.33418328  1.0
  Er  Er1  1  0.95801864  0.71379513  0.66409450  1.0
  Er  Er2  1  0.46271843  0.21556712  0.83944775  1.0
  Er  Er3  1  0.78443288  0.53728157  0.16055225  1.0
  Er  Er4  1  0.54289561  0.78783284  0.16101360  1.0
  Er  Er5  1  0.21216716  0.45710439  0.83898640  1.0
  Er  Er6  1  0.71658887  0.96025833  0.66581672  1.0
  Er  Er7  1  0.28620487  0.04198136  0.33590550  1.0
  Er  Er8  1  0.99736645  0.00263355  0.00000000  1.0
  Er  Er9  1  0.50007190  0.49992810  0.50000000  1.0
  Si  Si10  1  0.36365018  0.36356370  0.13653151  1.0
  Si  Si11  1  0.63643630  0.63634982  0.86346849  1.0
  Si  Si12  1  0.13886327  0.13746882  0.63641355  1.0
  Si  Si13  1  0.86253118  0.86113673  0.36358645  1.0
  Bi  Bi14  1  0.20581816  0.79418284  0.00000000  1.0
  Bi  Bi15  1  0.70645076  0.29354924  0.50000000  1.0
  Bi  Bi16  1  0.29348487  0.70651513  0.50000000  1.0
  Pb  Pb17  1  0.79256081  0.20743919  1.00000000  1.0

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