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Ti4Cr3(PO4)6

High-Entropy Materials HEA

MP-ID: mp-555289 · Space group: P-1 (#2)

Basic Information

Formula
Ti4Cr3(PO4)6
MP-ID
mp-555289
Elements
4
Sites
37
Density
3.4558
g/cm³
Volume
440.76
ų
Cell a
6.4565
Å
Cell b
8.1586
Å
Cell c
9.5514
Å
α Angle
106.09
°
β Angle
105.80
°
γ Angle
102.71
°
Space Group
P-1
Point Group
-1
Crystal System
Triclinic
Bravais Lattice
Triclinic P
Stability
No
Packing Fraction
0.5240

X-ray Diffraction

Diffraction Pattern
X-axis: 2θ (°); Y-axis: relative intensity; CuKa ; λ=1.5406 Å
Diffraction Peaks (Top 24)
2θd (Å)Ihkl
11.91 7.4280 22.1 (0,1,0)
12.66 6.9937 14.5 (0,1,-1)
14.92 5.9374 1.6 (1,0,-1)
15.05 5.8867 17.3 (1,0,0)
15.94 5.5587 2.7 (1,-1,0)
18.43 4.8144 21.3 (1,-1,-1)
19.60 4.5284 19.0 (1,-1,1)
19.82 4.4794 4.4 (1,1,-1)
19.84 4.4745 7.6 (0,1,-2)
20.71 4.2889 4.7 (0,0,2)
20.84 4.2618 1.1 (1,0,-2)
21.12 4.2059 2.5 (1,0,1)
22.06 4.0292 5.1 (1,1,0)
22.41 3.9669 2.2 (0,2,-1)
22.72 3.9145 4.0 (1,1,-2)
23.90 3.7237 2.9 (1,-2,0)
23.96 3.7140 9.2 (0,2,0)
24.75 3.5979 2.1 (1,-2,1)
25.47 3.4968 1.5 (0,2,-2)
27.10 3.2906 21.4 (1,-1,2)
27.50 3.2439 1.5 (0,1,2)
28.30 3.1538 8.2 (1,1,1)
28.34 3.1488 33.5 (2,0,-1)
28.37 3.1464 1.5 (2,-1,-1)
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Energy Properties

Formation Energy/atom
-2.79203
eV/atom
Energy/atom
-8.51595
eV/atom
Energy above Hull
0.0482
eV/atom
Uncorrected Energy
-7.9083
eV/atom
Volume/atom
11.91
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
15.9990
μB
Mag. Ordering
FM
Mag. Sites
7
Magnetization/Volume
0.036300
μB/ų

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)
Composition Info
Major / Matrix Element
O · 0.649
Element Family
Metalloid-Nonmetal
Solute Fraction
0.351
Interstitial Fraction
0.162

High-Entropy Alloy Features

Composite Radar (normalized)
Element-Class Share
Mix Entropy ΔS/R
1.0200
HEA criterion (>1.0 = high entropy)
Mix Entropy ΔS
8.4801
J/mol·K
Ω Parameter
0.0678
Ω > 1.1 favors solid solution
Atomic Size Mismatch δr
39.367%
δr < 6.6% favors single-phase solid solution
Electronegativity Diff Δχ
0.7716
smaller = more stable mixing
VEC
4.324
valence electron concentration, affects phase stability
Mix Enthalpy ΔH_mix
-59.276
kJ/mol; negative = exothermic mixing
Entropy Norm
0.7358
SS Former
0
Phase Tendency
AM

Related Tasks

Related computation task IDs (2)

Citation & References

Materials Project Page
https://materialsproject.org/materials/mp-555289
Reference Citation

The crystal structure and related material properties of Ti4Cr3(PO4)6 were obtained from the Materials Project database (MP-ID: mp-555289, 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_Ti4Cr3(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.45645900
_cell_length_b   8.15859370
_cell_length_c   9.55136584
_cell_angle_alpha   106.08724056
_cell_angle_beta   105.79867679
_cell_angle_gamma   102.71123872
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ti4Cr3(PO4)6
_chemical_formula_sum   'Ti4 Cr3 P6 O24'
_cell_volume   440.76483479
_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
  Ti  Ti0  1  0.03058500  0.19955700  0.01804500  1.0
  Ti  Ti1  1  0.39383900  0.95716000  0.60402500  1.0
  Ti  Ti2  1  0.96941500  0.80044300  0.98195500  1.0
  Ti  Ti3  1  0.60616100  0.04284000  0.39597500  1.0
  Cr  Cr4  1  0.27105300  0.30366300  0.77882600  1.0
  Cr  Cr5  1  0.72894700  0.69633700  0.22117400  1.0
  Cr  Cr6  1  0.00000000  0.50000000  0.50000000  1.0
  P  P7  1  0.41266900  0.74368100  0.87009500  1.0
  P  P8  1  0.78294000  0.35700700  0.73874600  1.0
  P  P9  1  0.90805900  0.89803800  0.66170200  1.0
  P  P10  1  0.09194100  0.10196200  0.33829800  1.0
  P  P11  1  0.21706000  0.64299300  0.26125400  1.0
  P  P12  1  0.58733100  0.25631900  0.12990500  1.0
  O  O13  1  0.30049100  0.54599100  0.75828500  1.0
  O  O14  1  0.26027100  0.79839500  0.96281200  1.0
  O  O15  1  0.18418500  0.44531900  0.18604700  1.0
  O  O16  1  0.12491600  0.29681300  0.42036100  1.0
  O  O17  1  0.35239000  0.22792400  0.00882600  1.0
  O  O18  1  0.07543200  0.05469100  0.16362200  1.0
  O  O19  1  0.97847600  0.30298700  0.83465700  1.0
  O  O20  1  0.29746200  0.04584000  0.41844600  1.0
  O  O21  1  0.64761000  0.77207600  0.99117400  1.0
  O  O22  1  0.70253800  0.95416000  0.58155400  1.0
  O  O23  1  0.21533300  0.69236000  0.43222300  1.0
  O  O24  1  0.69950900  0.45400900  0.24171500  1.0
  O  O25  1  0.02152400  0.69701300  0.16534300  1.0
  O  O26  1  0.44143000  0.85862300  0.76826500  1.0
  O  O27  1  0.92456800  0.94530900  0.83637800  1.0
  O  O28  1  0.78466700  0.30764000  0.56777700  1.0
  O  O29  1  0.81581500  0.55468100  0.81395300  1.0
  O  O30  1  0.12579000  0.02370200  0.65972700  1.0
  O  O31  1  0.54856400  0.23861000  0.73004100  1.0
  O  O32  1  0.87421000  0.97629800  0.34027300  1.0
  O  O33  1  0.87508400  0.70318700  0.57963900  1.0
  O  O34  1  0.73972900  0.20160500  0.03718800  1.0
  O  O35  1  0.45143600  0.76139000  0.26995900  1.0
  O  O36  1  0.55857000  0.14137700  0.23173500  1.0
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