Ti2V3Cr(PO4)6

High-Entropy Materials HEA

MP-ID: mp-759931 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

Ti2V3Cr(PO4)6

MP-ID

mp-759931

Elements

Sites

Density

3.2520

g/cm³

Volume

444.44

Å³

Cell a

8.4429

Cell b

8.4429

Cell c

8.4429

α Angle

61.98

β Angle

61.98

γ Angle

61.98

Space Group

Point Group

Crystal System

Trigonal

Bravais Lattice

Stability

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
14.63	6.0543	1.2	(1,1,0)
20.43	4.3474	58.5	(1,0,-1)
21.06	4.2177	9.4	(2,1,1)
24.31	3.6610	100.0	(2,1,0)
25.22	3.5313	13.9	(2,0,0)
29.51	3.0272	7.9	(2,2,0)
31.75	2.8186	16.2	(2,0,-1)
32.67	2.7410	3.8	(2,1,-1)
33.50	2.6754	47.8	(3,2,1)
35.77	2.5100	30.9	(2,-1,-1)
36.16	2.4842	5.2	(3,1,0)
38.59	2.3329	2.1	(3,2,0)
42.89	2.1088	8.1	(4,2,2)
43.73	2.0702	1.6	(3,-1,1)
44.92	2.0181	2.5	(4,1,1)
45.17	2.0072	3.8	(4,3,2)
47.95	1.8974	26.7	(4,3,1)
49.02	1.8584	5.5	(4,1,0)
49.22	1.8511	2.0	(2,2,-2)
49.82	1.8305	19.2	(4,2,0)
53.21	1.7213	1.9	(3,0,-2)
53.83	1.7031	1.9	(3,1,-2)
54.03	1.6971	2.5	(4,4,4)
54.05	1.6966	1.2	(4,0,3)

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Energy Properties

Formation Energy/atom

-2.72533

eV/atom

Energy/atom

-8.39032

eV/atom

Energy above Hull

0.0768

eV/atom

Uncorrected Energy

-7.7351

eV/atom

Volume/atom

12.35

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

9.0239

μB

Mag. Ordering

FiM

Mag. Sites

Magnetization/Volume

0.020300

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.667

Element Family

Metalloid-Nonmetal

Solute Fraction

0.333

Interstitial Fraction

0.167

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0361

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.6144

J/mol·K

Ω Parameter

0.1177

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

38.376%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7467

smaller = more stable mixing

VEC

4.306

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-32.188

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6438

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabyzcf aaadzsqh

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-759931

Reference Citation

The crystal structure and related material properties of Ti2V3Cr(PO4)6 were obtained from the Materials Project database (MP-ID: mp-759931, 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_Ti2V3Cr(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.44284859
_cell_length_b   8.44284859
_cell_length_c   8.44284892
_cell_angle_alpha   61.98404630
_cell_angle_beta   61.98404630
_cell_angle_gamma   61.98404787
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ti2V3Cr(PO4)6
_chemical_formula_sum   'Ti2 V3 Cr1 P6 O24'
_cell_volume   444.43883023
_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  0.00243400  0.00243400  0.00243400  1.0
  Ti  Ti1  1  0.50066900  0.50066900  0.50066900  1.0
  V  V2  1  0.35741500  0.35741500  0.35741500  1.0
  V  V3  1  0.14158600  0.14158600  0.14158600  1.0
  V  V4  1  0.64107700  0.64107700  0.64107700  1.0
  Cr  Cr5  1  0.85805700  0.85805700  0.85805700  1.0
  P  P6  1  0.74887700  0.04377000  0.45847400  1.0
  P  P7  1  0.04377000  0.45847400  0.74887700  1.0
  P  P8  1  0.45847400  0.74887700  0.04377000  1.0
  P  P9  1  0.54561300  0.24760000  0.95526400  1.0
  P  P10  1  0.95526400  0.54561300  0.24760000  1.0
  P  P11  1  0.24760000  0.95526400  0.54561300  1.0
  O  O12  1  0.89223000  0.49622300  0.67678500  1.0
  O  O13  1  0.49622300  0.67678500  0.89223000  1.0
  O  O14  1  0.67678500  0.89223000  0.49622300  1.0
  O  O15  1  0.90168200  0.06074000  0.25290400  1.0
  O  O16  1  0.82077100  0.00682900  0.61005800  1.0
  O  O17  1  0.59761900  0.24962500  0.43847700  1.0
  O  O18  1  0.06074000  0.25290400  0.90168200  1.0
  O  O19  1  0.24962500  0.43847700  0.59761900  1.0
  O  O20  1  0.39238900  0.17737100  0.99436400  1.0
  O  O21  1  0.43847700  0.59761900  0.24962500  1.0
  O  O22  1  0.75048600  0.09478700  0.93823400  1.0
  O  O23  1  0.99436400  0.39238900  0.17737100  1.0
  O  O24  1  0.00682900  0.61005800  0.82077100  1.0
  O  O25  1  0.25290400  0.90168200  0.06074000  1.0
  O  O26  1  0.56331700  0.39983700  0.74976100  1.0
  O  O27  1  0.61005800  0.82077100  0.00682900  1.0
  O  O28  1  0.74976100  0.56331700  0.39983700  1.0
  O  O29  1  0.93823400  0.75048600  0.09478700  1.0
  O  O30  1  0.39983700  0.74976100  0.56331700  1.0
  O  O31  1  0.17737100  0.99436400  0.39238900  1.0
  O  O32  1  0.09478700  0.93823400  0.75048600  1.0
  O  O33  1  0.32111500  0.10643100  0.50714200  1.0
  O  O34  1  0.50714300  0.32111500  0.10643100  1.0
  O  O35  1  0.10643100  0.50714300  0.32111500  1.0

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