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Cr21(WC3)2

High-Entropy Materials HEA Traditional Materials TRA

MP-ID: mp-641575 · Space group: Fm-3m (#225)

Basic Information

Formula
Cr21(WC3)2
MP-ID
mp-641575
Elements
3
Sites
29
Density
8.5741
g/cm³
Volume
296.63
ų
Cell a
7.4860
Å
Cell b
7.4860
Å
Cell c
7.4860
Å
α Angle
60.00
°
β Angle
60.00
°
γ Angle
60.00
°
Space Group
Fm-3m
Point Group
m-3m
Crystal System
Cubic
Bravais Lattice
Cubic F
Stability
Yes
Packing Fraction
0.7400

X-ray Diffraction

Diffraction Pattern
X-axis: 2θ (°); Y-axis: relative intensity; CuKa ; λ=1.5406 Å
Diffraction Peaks (Top 24)
2θd (Å)Ihkl
16.75 5.2934 85.6 (1,1,0)
16.75 5.2934 85.6 (0,1,1)
16.75 5.2934 85.6 (1,0,1)
23.77 3.7430 34.7 (2,1,1)
23.77 3.7430 34.7 (1,1,2)
23.77 3.7430 34.7 (1,2,1)
23.77 3.7430 34.7 (1,0,-1)
23.77 3.7429 34.7 (1,-1,0)
23.77 3.7429 34.7 (0,1,-1)
29.22 3.0562 13.6 (2,2,2)
29.22 3.0561 13.6 (2,0,0)
29.22 3.0561 13.6 (0,0,2)
29.22 3.0561 13.6 (0,2,0)
33.87 2.6467 2.0 (2,2,0)
33.87 2.6467 2.0 (0,2,2)
33.87 2.6467 2.0 (2,0,2)
38.01 2.3673 49.9 (3,2,1)
38.01 2.3673 49.9 (3,1,2)
38.01 2.3673 49.9 (1,2,3)
38.01 2.3673 49.9 (2,1,3)
38.01 2.3673 49.9 (2,3,1)
38.01 2.3673 49.9 (1,3,2)
38.01 2.3673 49.9 (2,1,-1)
38.01 2.3673 49.9 (1,-1,-2)
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Energy Properties

Formation Energy/atom
-0.08437
eV/atom
Energy/atom
-9.87803
eV/atom
Energy above Hull
0.0000
eV/atom
Uncorrected Energy
-16.4109
eV/atom
Volume/atom
10.23
ų
c/a Ratio
-

Electronic Properties

Metallic
Metal
Band Gap
0
eV
Direct Gap
No
CBM
N/A
eV

Magnetic Properties

Magnetic
Yes
Total Mag. Moment
0.1395
μB
Mag. Ordering
FiM
Mag. Sites
13
Magnetization/Volume
0.000470
μB/ų

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)
Composition Info
Major / Matrix Element
Cr · 0.724
Element Family
3d-TM
Solute Fraction
0.276
Interstitial Fraction
0.207

High-Entropy Alloy Features

Composite Radar (normalized)
Element-Class Share
Mix Entropy ΔS/R
0.7441
HEA criterion (>1.0 = high entropy)
Mix Entropy ΔS
6.1867
J/mol·K
Ω Parameter
0.4055
Ω > 1.1 favors solid solution
Atomic Size Mismatch δr
17.957%
δr < 6.6% favors single-phase solid solution
Electronegativity Diff Δχ
0.3790
smaller = more stable mixing
VEC
5.586
valence electron concentration, affects phase stability
Mix Enthalpy ΔH_mix
-40.038
kJ/mol; negative = exothermic mixing
Entropy Norm
0.6773
SS Former
0
Phase Tendency
AM

Traditional Material Features

ROM Blended-Feature Radar
Rating & Classification
Tier
A
Score
0.880
Family
Interstitial Alloy
Matrix Element
Cr · 0.724

Related Tasks

Related computation task IDs (2)

Citation & References

Materials Project Page
https://materialsproject.org/materials/mp-641575
Reference Citation

The crystal structure and related material properties of Cr21(WC3)2 were obtained from the Materials Project database (MP-ID: mp-641575, 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

BibTeX
@article{Horton2025,
  author  = {Horton, Matthew K. and Huck, Patrick and Yang, Ruo Xi and Munro, Jason M. and Dwaraknath, Shyam and Ganose, Alex M. and Kingsbury, Ryan S. and Wen, Mingjian and Shen, Jimmy X. and Mathis, Tyler S. and Kaplan, Aaron D. and Berket, Karlo and Riebesell, Janosh and George, Janine and Rosen, Andrew S. and Spotte-Smith, Evan W. C. and McDermott, Matthew J. and Cohen, Orion A. and Dunn, Alex and Kuner, Matthew C. and Rignanese, Gian-Marco and Petretto, Guido and Waroquiers, David and Griffin, Sinead M. and Neaton, Jeffrey B. and Chrzan, Daryl C. and Asta, Mark and Hautier, Geoffroy and Cholia, Shreyas and Ceder, Gerbrand and Ong, Shyue Ping and Jain, Anubhav and Persson, Kristin A.},
  title   = {Accelerated data-driven materials science with the Materials Project},
  journal = {Nature Materials},
  year    = {2025},
  volume  = {24},
  number  = {10},
  pages   = {1522--1532},
  month   = {oct},
  doi     = {10.1038/s41563-025-02272-0},
  issn    = {1476-4660},
  url     = {https://doi.org/10.1038/s41563-025-02272-0},
  abstract = {The Materials Project was launched formally in 2011 to drive materials discovery forwards through high-throughput computation and open data. More than a decade later, the Materials Project has become an indispensable tool used by more than 600,000 materials researchers around the world. This Perspective describes how the Materials Project, as a data platform and a software ecosystem, has helped to shape research in data-driven materials science. We cover how sustainable software and computational methods have accelerated materials design while becoming more open source and collaborative in nature. Next, we present cases where the Materials Project was used to understand and discover functional materials. We then describe our efforts to meet the needs of an expanding user base, through technical infrastructure updates ranging from data architecture and cloud resources to interactive web applications. Finally, we discuss opportunities to better aid the research community, with the vision that more accessible and easy-to-understand materials data will result in democratized materials knowledge and an increasingly collaborative community.}
}

3D Crystal Structure Rendering

Loading 3D structure…

Style: Ball & Stick
Raw CIF Data
# generated using pymatgen
data_Cr21(WC3)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.48602488
_cell_length_b   7.48596866
_cell_length_c   7.48598519
_cell_angle_alpha   59.99875090
_cell_angle_beta   59.99902684
_cell_angle_gamma   59.99890216
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Cr21(WC3)2
_chemical_formula_sum   'Cr21 W2 C6'
_cell_volume   296.63496346
_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
  Cr  Cr0  1  0.00000528  0.00001316  0.00000382  1.0
  Cr  Cr1  1  0.61541278  0.61539849  0.15377910  1.0
  Cr  Cr2  1  0.61540966  0.15377480  0.61540993  1.0
  Cr  Cr3  1  0.15377681  0.61538876  0.61540014  1.0
  Cr  Cr4  1  0.61543830  0.61538423  0.61540554  1.0
  Cr  Cr5  1  0.38460053  0.38456097  0.84623620  1.0
  Cr  Cr6  1  0.38459563  0.84624750  0.38456716  1.0
  Cr  Cr7  1  0.84623814  0.38458166  0.38458774  1.0
  Cr  Cr8  1  0.38459569  0.38457737  0.38458255  1.0
  Cr  Cr9  1  0.00001273  0.00000280  0.33946027  1.0
  Cr  Cr10  1  0.66051587  -0.00000333  0.33947764  1.0
  Cr  Cr11  1  -0.00000661  0.66052002  0.33948656  1.0
  Cr  Cr12  1  0.66052653  0.33948444  -0.00001313  1.0
  Cr  Cr13  1  0.00000155  0.33946452  0.00000212  1.0
  Cr  Cr14  1  -0.00000708  0.33948302  0.66051802  1.0
  Cr  Cr15  1  0.33947945  0.66053678  0.00000396  1.0
  Cr  Cr16  1  0.33947060  0.00001040  0.66052962  1.0
  Cr  Cr17  1  0.33946869  -0.00000628  0.00000520  1.0
  Cr  Cr18  1  -0.00000188  0.00002130  0.66052134  1.0
  Cr  Cr19  1  -0.00001333  0.66052699  0.00002205  1.0
  Cr  Cr20  1  0.66050658  0.00000663  0.00000908  1.0
  W  W21  1  0.74998992  0.74998461  0.75001151  1.0
  W  W22  1  0.24997539  0.25001861  0.25000582  1.0
  C  C23  1  0.72482727  0.72483390  0.27517591  1.0
  C  C24  1  0.27516788  0.72483859  0.27516409  1.0
  C  C25  1  0.72484054  0.27516617  0.27515580  1.0
  C  C26  1  0.27516476  0.27516355  0.72483282  1.0
  C  C27  1  0.72483335  0.27517816  0.72482981  1.0
  C  C28  1  0.27517499  0.72484118  0.72482936  1.0
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