🚧 WEBSITE UNDER CONSTRUCTION (last update 2026-06-09)🚧
The table GHEA Phase Models (see point 2 of this page) contains the crystallographic and thermodynamic description of the phases modelled in GHEA.
Some rules and assumptions adopted for the modelling are discussed in the Introduction here below.
Rules and assumptions adopted to chose the most appropriate thermodynamic models for the GHEA phases are described in the following. Rules and abbreviations used in the Table Phase Models are also illustrated.
Thermodynamic phase models are expressed according to the Compound Energy Formalism (CEF).
Thermodynamic sublattice (SL) models of the GHEA phases are generally inspired by the crystal structure: each SL usually correspond to a single or a group of crystallographic sites (Wyckoff positions). Grouping occurs only when necessary to keep the total number of SLs lower than 3 or 4. Only similar crystallographic sites (same coordination and occupancy) can be merged in a single thermodynamic SL.
Phase names are usually selected according to the following criteria:
Prototype name followed by _TY (e.g. MOSI2_TY) is the default choice when the phase model is based on the crystal structure.
Chemical formula (e.g. FEAL2) is generally used for phases modelled with reference to the stoichiometry.
Element ordering. In all cases element symbols appearing in chemical formulas are ordered according to the Pettifor’s chemical scale reported here below
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
He Ne Ar Kr Xe Rn Fr Cs Rb K Na Li Ra Ba Sr Ca Yb Eu Y Sc Lu
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
Tm Er Ho Dy Tb Gd Sm Pm Nd Pr Ce La Lr No Md Fm Es Cf Bk Cm Am
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
Pu Np U Pa Th Ac Zr Hf Ti Nb Ta V Mo W Cr Tc Re Mn Fe Os Ru
64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
Co Ir Rh Ni Pt Pd Au Ag Cu Mg Hg Cd Zn Be Tl In Al Ga Pb Sn Ge
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103
Si B Bi Sb As P Po Te Se S C At I Br Cl N O F H
Exceptions to the mentioned rules are listed here below.
Strukturbericht symbol is used only for: A1, A2, A3, C14, C15, C36, D0_19
Greek letters are used only for: GAMMA SIGMA, MU, CHI
Latin letters followed by _PHASE are used only for: P3_PHASE, R_PHASE
FCC4 BCC2 are used for ordered phases based on A1 and A2, respectively (the number at the end of the phase name refers to the number of sublattices used in the model). 1.2 Sublattices (SLs)
Further assumptions:
Integer stoichiometric numbers (instead of mole fractions) are preferentially used to express stoichiometric ratios between SLs.
When more SLs are present, they are ordered according to the decreasing coordination of the corresponding crystallographic sites or (often equivalently) according to the position in the Pettifor’s scale or the decreasing atomic radius (e.g. (Ti, ...)1(Al, ...)2 for TIAL2 and (Mg, ...)1(Cu, ...)2 for C15, but (Ti, ...)2(Ni, ...)1 for TI2NI_TY).
List of the Table Sections
Section 1: FCC, BCC, HCP and related phases
Section 2: Unary, single SL phases
Section 3: Binary 1:X (X=1 ... 12) phases
Section 4: Binary 2:X (X=1..17) phases
Content of the Table
COLUMN 1 contains the phase name adopted in GHEA (bold), possibly other names (in parenthesis) used in literature, and crystal structure information.
COLUMN 2 contains a description of the SL model(*) adopted in GHEA and two lines describing the phase in .TDB format (they can be copy/pasted in a TDB file).
COLUMN 3 remarks and comments about the phase and the adopted model.
(*) Sublattice model, when referred to crystal structure, is reported as follows:
( [constituent] in [site], [site coordination] )[stoichiom] ( [constituent] in [site], [site coordination] )[stoichiom] ...
where [constituent] can be:
El Any element (generic) MA A-type Metal (with larger atomic radius) X Non-metallic element (generic)
M Metallic element (generic) MB B-type Metal (with smaller atomic radius) XI Interstitial non-metallic element
VA Vacancy
and [site] is the Wyckoff symbol of a crystallographic site (e.g.: (M in 4a, CN12)1 (XI,VA in 4b, CN6)1)
Pearson symbol
Prototype
Space Group
COLUMN 2
Sublattice model (*)
TDB declarations:
PHASE ...
CONSTITUENTS ...
COLUMN 3
Remarks
cF4
Cu
Fm-3m
(M in 4a, CN12)1 (XI,VA in 4b, CN6)1
PHASE A1 %M 2 1 1 !
CONST A1 : M : XI,VA : !
Magnetic contribution
Second SL corresponds to octahedral interstitial sites
Disordered contribution to the ordered FCC4 phase
cF8
NaCl
Fm-3m
(M in 4a, CN12)1 (C in 4b, CN6)1
PHASE MC %M 2 1 1 !
CONST MC : M : C,VA : !
This is the A1 phase with interstitial C in the second SL
All the interaction parameters are the same as A1 of the corresponding M
cP4 tP4
AuCu3 AuCu
Fm-3m P4/mmm
(M in 1a, CN12).25 (M in 1d, CN12).25 (M in 1f, CN12).25 (M in 1g, CN12).25 (XI,VA in 4b, CN6)1
PHASE FCC4:F %GM 5 0.25 0.25 0.25 0.25 1 !
CONST FCC4:F : M : M : M : M : XI,VA : !
4-SL ordered FCC phase
Magnetic contribution
Fifth SL for octahedral interstitial sites
Disordered contribution from A1
cI2
W
Im-3m
(M in 2a, CN8+6)1 (XI in 6b, CN6)3
PHASE A2 %AN 2 1 3 !
CONST A2 : M,VA : XI,VA : !
Magnetic contribution
Second SL corresponds to octahedral interstitial sites
Disordered contribution to the ordered BCC2 phase
VA are also included in the metal SL
cP2
CsCl
Pm-3m
(M in 1a, CN8+6).5 (M in 1b, CN8+6).5 (XI in 3d, CN6)3
PHASE BCC2 %AN 3 0.5 0.5 3 !
CONST BCC2 : M,VA : M,VA : XI,VA : !
2-SL ordered BCC phase
Magnetic contribution
Third SL corresponds to octahedral interstitial sites
Disordered contribution from A2
VA are also included in the metal SL
hP2
Mg
P63/mmc
(M in 2c, CN12)1 (XI in 1/2 of 2d, CN6).5
PHASE A3 %M 2 1 0.5 !
CONST A3 : M : XI,VA : !
Magnetic contribution
Second SL for 1/2 of octahedral interstitial sites
--
--
--
Model not related to crystal structure
PHASE ALPHA_B % 1 1.0 !
CONST ALPHA_B : B : !
---
hR36
beta-B
R-3m
Model not related to crystal structure
PHASE BETA_B % 1 1.0 !
CONST BETA_B : B : !
---
cF8
C-diam.
Fd-3m
Model not related to crystal structure
PHASE DIAMOND % 1 1.0 !
CONST DIAMOND : C,SI : !
---
hP4
C-graph.
P63/mmc
Model not related to crystal structure
PHASE GRAPHITE % 1 1.0 !
CONST GRAPHITE : B,C : !
---
oC8
CrB
Cmcm
(MA in 4c, CN7)1 (MorX in 4c', CN9)1
PHASE WC_TY % 2 1 1 !
CONST WC_TY : MO,W : C : !
Typical compositions: CrB NiB YCo YAl HfAl HfNi ITl
Related to FEB_TY
hP12
MoC.67
P63/mmc
Model based on stoichiometry
(MA)1 (C)1
PHASE ETA_MOC % 2 1 1 !
CONST ETA_MOC : MO,W : C,VA : !
Typical compositions: WC, MoC
oP8
FeB
Pnma
(M in 4c, CN7)1 (M or X in 4c', CN9)1
PHASE WC_TY % 2 1 1 !
CONST WC_TY : MO,W : C : !
Typical compositions: FeB CoB YNi TiSi
Related to CRB_TY
cP8
FeSi
P213
(M,Si in 4a, CN7)1 (Si,M in 4a', CN7)1
PHASE FESI_TY % 2 1 1 !
CONST FESI_TY : M,SI : M,SI : !
Typical compositions: CoSi CrSi FeSi
oP56
MoNi
P212121
(MA in 3*4a)12 (MA,MB in 5*4a)20
(MB in 6*4a)24
PHASE MONI_TY % 3 12 20 24 !
CONST MONI_TY : MA : MA,MB : MB : !
14 occupied Wyckoff positions: all of them are 4a with different coordinates.
hP2
WC
P-6m2
Model based on stoichiometry
(MA)1 (C)1
PHASE WC_TY % 2 1 1 !
CONST WC_TY : MO,W : C : !
Typical compositions: WC, MoC
hP12
MgZn2
P63/mmc
(MA,MB in 4f, CN16)1
(MB,MA in 2a+6h, CN12)2
PHASE C14 % 2 1 2 !
CONST C14 : MA,MB : MB,MA : !
TCP Laves phase
cF24
MgCu2
Fd-3m
(MA,MB in 8a, CN16)1
(MB,MA in 16d, CN12)2
PHASE C15 % 2 1 2 !
CONST C15 : MA,MB : MB,MA : !
TCP Laves phase
hP24
MgNi2
P63/mmc
(MA,MB in 4e+4f, CN16)1
(MB,MA in 4f'+6g+6h, CN12)2
PHASE C36 % 2 1 2 !
CONST C36 : MA,MB : MB,MA : !
TCP Laves phase
aP18
Fe5(Fe.5Al.5)3Al10
P1
Model based on stoichiometry
PHASE FEAL2 % 2 1 2 !
CONST FEAL2 : Fe,M1 : Al,M2 : !
Reported as:
Fe6Al12: 18*1a sites (5 occupied by Fe, 10 occupied by Al, 3 occupied by 2/3 Al + 1/3 Fe) [AtomWorks]
Fe7Al12: 1*1a + 9*2i sites (1a+3*2i occupied by Fe, 6*2i occupied by Al) [MaterialsProject]
oI16
MoPt2
Immm
Model not related to crystal structure
PHASE MOPT2_TY % 2 1 2 !
CONST MOPT2_TY : M : M : !
Typical compositions:CrNi2 MoNi2
tI6
MoSi2
I4/mmm
(MA in 2a, CN10)1
(Si,MB in 4e, CN10)2
PHASE MOSI2_TY % 2 1 2 !
CONST MOSI2_TY : MA : Si,MB : !
Structure related to BCC, formed by 3 BCC cells along the z axis, slightly compressed along z.
m**
-
-
Model based on experimental composition
PHASE COAL3 % 2 0.255 0.745 !
CONST COAL3 : MB : Al : !
Crystal structure not completely known, possibly related to the Fe4Al13 type structure
mP16
NbPt3
P21/m
(MA in 2*2e, CN12)1 (MB in 2*2e+2*4f, CN12)3
PHASE NBPT3_TY % 2 1 3 !
CONST NBPT3_TY : MA : MB : !
Structure related to TiCu3.
tI12
Al2Cu
I4/mmc
(M in 8h, CN4)2 (M in 4a, CN10)1
PHASE AL2CU_TY % 2 2 1 !
CONST AL2CU_TY : M : M : !
Al2Cu (according to tradition) instead of CuAl2 (according to decreasing coordination)
hP5
Ni2Al3
P-3m1
(MB in 2d, CN8)2 (Al in 1a+2d, CN5-6)3
PHASE NI2AL3_TY % 3 3 2 1 !
CONST NI2AL3_TY : MB : Al : MB,Va : !
Model (AL)3 (AL,NI)2 (NI,VA)1 introduced by Ansara considering crystal defects more than crystal structure. According to crystal structure should be: (MB in 2d, CN8)2 (Al in 1a+2d, CN5-6)3
hP28
Co2Al5
P63/mmc
(MB in 2c+6h, CN9-10)2 (Al in 2a+6h'+12k, CN3-4)5
PHASE CO2AL5_TY % 2 2 5 !
CONST CO2AL5_TY : MB : Al : !
Occup 98% in 6h, 94.6% in 2c
mP22
Co2Al9
P21/c
(MB in 4e, CN9)2 (Al in (2a+4e'+4e", CN12)+
(4e"'+4e"", CN15) )9
PHASE CO2AL9_TY % 2 2 9 !
CONST CO2AL9_TY : MB : Al : !
Model based on crystal structure should bel: (CN15,4e3+4e4, Al)4 (CN12, 2a+4e1+4e2, Al)5 (CN9, 4e, Co)2
cP8
Cr3Si
Pm-3n
(MA in 6c, CN14)3 (Si,M in 2a, CN12)1
PHASE CR3SI_TY % 2 3 1 !
CONST CR3SI_TY : MA : Si,M : !
cI112
Ni3Ga4
Ia-3d
(MB in 48g, CN14)3 (Al in 16a+48f, CN5-6)4
PHASE NI3AL4 % 2 3 4 !
CONST NI3AL4 : MB : Al : !
hR21
Al4C3
R-3m
(Al in 6c'+6c", CN4)4 (C in 3a+6c"', CN5-6)3
PHASE AL4C3_TY % 2 4 3 !
CONST AL4C3_TY : M : C : !
aP15
Mn4Al11
P-1
(Cr in 2*2i, CN10)4 (Al in 1a+5*2i, CN8-12)11
PHASE CR4AL11 % 2 4 11 !
CONST CR4AL11 : MA : Al : !
mC104
V7Al45
C2/m
(Cr in 2a+4i+8j, CN12)7 (Al in 2d+8*4i+7*8j, CN11-13)45
PHASE CR7AL45 % 2 7 45 !
CONST CR7AL45 : MA : Al : !
Model based on crystal structure should bel: (16 Al sites)45 (2d+4i+8j)7
🚧 Work in 🚧 progress 🚧
tP30
CrFe
P42/mnm
(M in 4f, CN15)2 (M in 8i'+8j, CN14)8
(M in 8i'+8j, CN12)5
PHASE SIGMA % 3 2 8 5 !
CONST SIGMA3 : M : M : M : !
First SLs generally preferred by AM, last SLs generally preferred by BM.
A possible reference stoichiometry is AM2BM.
SIGMA is usually stabilised by 6.5<VEC<7.
