Li13Ti28O56

High-Entropy Materials HEA Traditional Materials TRA

MP-ID: mp-774263 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

Li13Ti28O56

MP-ID

mp-774263

Elements

Sites

Density

3.6399

g/cm³

Volume

1,061.34

Å³

Cell a

10.3649

Cell b

10.3649

Cell c

10.3649

α Angle

99.54

β Angle

99.54

γ Angle

99.54

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
18.13	4.8929	33.2	(1,1,1)
18.16	4.8851	100.0	(2,0,-1)
35.14	2.5541	14.6	(3,2,0)
35.17	2.5519	29.1	(4,0,-1)
35.18	2.5508	14.6	(3,1,-3)
36.74	2.4464	1.8	(2,2,2)
36.80	2.4425	5.4	(4,0,-2)
42.73	2.1161	79.4	(4,2,-2)
46.73	1.9437	1.8	(4,2,1)
46.77	1.9423	2.7	(5,1,-1)
46.81	1.9408	5.4	(5,-2,-2)
56.46	1.6298	6.2	(5,3,-1)
56.49	1.6289	2.1	(2,-1,-6)
56.49	1.6289	10.5	(4,4,-3)
56.51	1.6284	7.2	(5,2,-4)
61.98	1.4972	23.5	(6,2,0)
62.06	1.4954	23.4	(6,-2,-4)
65.15	1.4319	4.4	(6,2,1)
65.19	1.4311	4.4	(7,0,0)
65.24	1.4301	4.3	(7,-1,-3)
65.25	1.4299	4.4	(6,0,-5)
73.25	1.2922	1.0	(5,4,2)
73.36	1.2905	3.0	(8,-1,-2)
73.39	1.2901	1.5	(7,-1,-5)

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Energy Properties

Formation Energy/atom

-3.25580

eV/atom

Energy/atom

-8.64730

eV/atom

Energy above Hull

0.0066

eV/atom

Uncorrected Energy

-8.2507

eV/atom

Volume/atom

10.94

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0886

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000080

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.577

Element Family

Metalloid-Nonmetal

Solute Fraction

0.423

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

0.9452

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

7.8581

J/mol·K

Ω Parameter

0.0389

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

44.935%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

1.0402

smaller = more stable mixing

VEC

3.598

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-131.772

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8603

SS Former

Phase Tendency

Traditional Material Features

ROM Blended-Feature Radar

Rating & Classification

Tier

Score

0.563

Family

O-rich Multi-Component

Matrix Element

O · 0.577

Related Tasks

Related computation task IDs (2)

aaabynqd aaabzjre

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-774263

Reference Citation

The crystal structure and related material properties of Li13Ti28O56 were obtained from the Materials Project database (MP-ID: mp-774263, 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_Li13Ti28O56
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.36488264
_cell_length_b   10.36488264
_cell_length_c   10.36488284
_cell_angle_alpha   99.53996137
_cell_angle_beta   99.53996137
_cell_angle_gamma   99.53996257
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Li13Ti28O56
_chemical_formula_sum   'Li13 Ti28 O56'
_cell_volume   1061.33706863
_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
  Li  Li0  1  0.87524200  0.30275700  0.01769800  1.0
  Li  Li1  1  0.12502100  0.55362200  0.26783200  1.0
  Li  Li2  1  0.55362200  0.26783200  0.12502100  1.0
  Li  Li3  1  0.01769800  0.87524200  0.30275700  1.0
  Li  Li4  1  0.58928400  0.16051400  0.44632600  1.0
  Li  Li5  1  0.44632600  0.58928400  0.16051400  1.0
  Li  Li6  1  0.69652600  0.83941400  0.41074000  1.0
  Li  Li7  1  0.83941400  0.41074000  0.69652600  1.0
  Li  Li8  1  0.26783200  0.12502100  0.55362200  1.0
  Li  Li9  1  0.30275700  0.01769800  0.87524200  1.0
  Li  Li10  1  0.73283000  0.73283000  0.73283000  1.0
  Li  Li11  1  0.16051400  0.44632600  0.58928400  1.0
  Li  Li12  1  0.41074000  0.69652600  0.83941400  1.0
  Ti  Ti13  1  0.92955000  0.64494500  0.99957000  1.0
  Ti  Ti14  1  0.64316700  0.49991600  0.92926300  1.0
  Ti  Ti15  1  0.07156300  0.21303300  0.28368200  1.0
  Ti  Ti16  1  0.78643100  0.07041700  0.21229100  1.0
  Ti  Ti17  1  0.78538500  0.57118600  0.21373100  1.0
  Ti  Ti18  1  0.71567400  0.78744900  0.07085500  1.0
  Ti  Ti19  1  0.64494500  0.99957000  0.92955000  1.0
  Ti  Ti20  1  0.21303300  0.28368200  0.07156300  1.0
  Ti  Ti21  1  0.28368200  0.07156300  0.21303300  1.0
  Ti  Ti22  1  0.85731900  0.35681200  0.35752500  1.0
  Ti  Ti23  1  0.14330700  0.50001700  0.92841300  1.0
  Ti  Ti24  1  0.92841300  0.14330700  0.50001700  1.0
  Ti  Ti25  1  0.21229100  0.78643100  0.07041700  1.0
  Ti  Ti26  1  0.50001700  0.92841300  0.14330700  1.0
  Ti  Ti27  1  0.07041700  0.21229100  0.78643100  1.0
  Ti  Ti28  1  0.78744900  0.07085500  0.71567400  1.0
  Ti  Ti29  1  0.92926300  0.64316700  0.49991600  1.0
  Ti  Ti30  1  0.35688000  0.35688000  0.35688000  1.0
  Ti  Ti31  1  0.64302200  0.50009600  0.42858400  1.0
  Ti  Ti32  1  0.35752500  0.85731900  0.35681200  1.0
  Ti  Ti33  1  0.42858400  0.64302200  0.50009600  1.0
  Ti  Ti34  1  0.50009600  0.42858400  0.64302200  1.0
  Ti  Ti35  1  0.57118600  0.21373100  0.78538500  1.0
  Ti  Ti36  1  0.99957000  0.92955000  0.64494500  1.0
  Ti  Ti37  1  0.07085500  0.71567400  0.78744900  1.0
  Ti  Ti38  1  0.49991600  0.92926300  0.64316700  1.0
  Ti  Ti39  1  0.35681200  0.35752500  0.85731900  1.0
  Ti  Ti40  1  0.21373100  0.78538500  0.57118600  1.0
  O  O41  1  0.05188500  0.32340900  0.95861800  1.0
  O  O42  1  0.12308600  0.12308600  0.12308600  1.0
  O  O43  1  0.10557600  0.61221000  0.09129100  1.0
  O  O44  1  0.53392100  0.32694400  0.94815300  1.0
  O  O45  1  0.04277500  0.80107400  0.96220900  1.0
  O  O46  1  0.61221000  0.09129100  0.10557600  1.0
  O  O47  1  0.81572300  0.48027300  0.03745000  1.0
  O  O48  1  0.89435600  0.24470200  0.19483800  1.0
  O  O49  1  0.95861800  0.05188500  0.32340900  1.0
  O  O50  1  0.76621700  0.18041500  0.38743100  1.0
  O  O51  1  0.88025300  0.73728200  0.16615800  1.0
  O  O52  1  0.45183500  0.02298700  0.30888800  1.0
  O  O53  1  0.62327500  0.60870400  0.10166900  1.0
  O  O54  1  0.02298700  0.30888800  0.45183500  1.0
  O  O55  1  0.30888800  0.45183500  0.02298700  1.0
  O  O56  1  0.69107400  0.40534600  0.26252600  1.0
  O  O57  1  0.54769000  0.83368100  0.97666200  1.0
  O  O58  1  0.09129100  0.10557600  0.61221000  1.0
  O  O59  1  0.94815300  0.53392100  0.32694400  1.0
  O  O60  1  0.80107400  0.96220900  0.04277500  1.0
  O  O61  1  0.37740100  0.24872200  0.18422300  1.0
  O  O62  1  0.75552900  0.66245900  0.39116200  1.0
  O  O63  1  0.96220900  0.04277500  0.80107400  1.0
  O  O64  1  0.24872200  0.18422300  0.37740100  1.0
  O  O65  1  0.81971900  0.46991100  0.51966500  1.0
  O  O66  1  0.89822000  0.23438800  0.67662100  1.0
  O  O67  1  0.18422300  0.37740100  0.24872200  1.0
  O  O68  1  0.67662100  0.89822000  0.23438800  1.0
  O  O69  1  0.60870400  0.10166900  0.62327500  1.0
  O  O70  1  0.03745000  0.81572300  0.48027300  1.0
  O  O71  1  0.46608100  0.53023700  0.33758500  1.0
  O  O72  1  0.38743100  0.76621700  0.18041500  1.0
  O  O73  1  0.32340900  0.95861800  0.05188500  1.0
  O  O74  1  0.10166900  0.62327500  0.60870400  1.0
  O  O75  1  0.53023700  0.33758500  0.46608100  1.0
  O  O76  1  0.73728200  0.16615800  0.88025300  1.0
  O  O77  1  0.90884300  0.75148000  0.67274600  1.0
  O  O78  1  0.19483800  0.89435600  0.24470200  1.0
  O  O79  1  0.33758500  0.46608100  0.53023700  1.0
  O  O80  1  0.48027300  0.03745000  0.81572300  1.0
  O  O81  1  0.59469500  0.59469500  0.59469500  1.0
  O  O82  1  0.51966500  0.81971900  0.46991100  1.0
  O  O83  1  0.40534600  0.26252600  0.69107400  1.0
  O  O84  1  0.26252600  0.69107400  0.40534600  1.0
  O  O85  1  0.83368100  0.97666200  0.54769000  1.0
  O  O86  1  0.97666200  0.54769000  0.83368100  1.0
  O  O87  1  0.66245900  0.39116200  0.75552900  1.0
  O  O88  1  0.39116200  0.75552900  0.66245900  1.0
  O  O89  1  0.46991100  0.51966500  0.81971900  1.0
  O  O90  1  0.32694400  0.94815300  0.53392100  1.0
  O  O91  1  0.67274600  0.90884300  0.75148000  1.0
  O  O92  1  0.18041500  0.38743100  0.76621700  1.0
  O  O93  1  0.24470200  0.19483800  0.89435600  1.0
  O  O94  1  0.75148000  0.67274600  0.90884300  1.0
  O  O95  1  0.16615800  0.88025300  0.73728200  1.0
  O  O96  1  0.23438800  0.67662100  0.89822000  1.0

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