J. Mater. Sci. Technol. ›› 2022, Vol. 131: 1-13.DOI: 10.1016/j.jmst.2022.05.017
• Research Article • Next Articles
Hao-Xuan Liua, Hai-Le Yana,*(
), Nan Jiaa, Shuai Tangb, Daoyong Congc, Bo Yanga, Zongbin Lia, Yudong Zhangd, Claude Eslingd, Xiang Zhaoa,*(), LiangZuo a
Received:2022-01-14
Revised:2022-04-14
Accepted:2022-05-05
Published:2022-06-08
Online:2022-06-08
Contact:
Hai-Le Yan,Xiang Zhao
About author:zhaox@mail.neu.edu.cn (X. Zhao)Hao-Xuan Liu, Hai-Le Yan, Nan Jia, Shuai Tang, Daoyong Cong, Bo Yang, Zongbin Li, Yudong Zhang, Claude Esling, Xiang Zhao, LiangZuo . Machine-learning-assisted discovery of empirical rule for inherent brittleness of full Heusler alloys[J]. J. Mater. Sci. Technol., 2022, 131: 1-13.
Fig. 1. (a) Scatter plot of shear modulus (G) versus bulk modulus (B) of the X2YZ-type full Heusler alloys. Relations of (b) B, (c) G, and (d) the Pugh's ratio k versus cohesive energy (Ec) and lattice volume (V). The color of the scatter represents the lattice volume (V).
Fig. 2. Workflow of the present work.
Fig. 3. Elemetal abundance map for the X, Y and Z elements of X2YZ Heusler alloys in the collected dataset. X and Y spread all over the transition metal elements, and Z covers all main-group elements of III and IV in the elemental periodic table.
| Element properties | Abbr. | Simple substance properties | Abbr. |
|---|---|---|---|
| Atomic number | N | Atomic radius | AR |
| Row | R | Covalent radius | CR |
| Atomic weight | AW | Ionic radius | IR |
| Mendeleev number | MN | Density | D |
| Column | C | Melting temperature | MT |
| Number of s valence electrons | Vs | Boiling temperature | BT |
| Number of p valence electrons | Vp | Heat capacity | HC |
| Number of d valence electrons | Vd | Heat fusion | HF |
| Number of f valence electrons | Vf | Bulk modulus | B |
| Number of total valence electrons | V | Shear modulus | G |
| Number of unfilled s states | Us | Magnetic moment | M |
| Number of unfilled p states | Up | Volume | V |
| Number of unfilled d states | Ud | Band gap energy | Gap |
| Number of unfilled f states | Uf | First ionization energy | IE |
| Number of total unfilled states | U | Space group number | SG |
| Electronegativity | En | Electron work function | EWF |
Table 1. Elemental and simple-substance properties and their abbreviations (Abbr.) for featurization.
| Element properties | Abbr. | Simple substance properties | Abbr. |
|---|---|---|---|
| Atomic number | N | Atomic radius | AR |
| Row | R | Covalent radius | CR |
| Atomic weight | AW | Ionic radius | IR |
| Mendeleev number | MN | Density | D |
| Column | C | Melting temperature | MT |
| Number of s valence electrons | Vs | Boiling temperature | BT |
| Number of p valence electrons | Vp | Heat capacity | HC |
| Number of d valence electrons | Vd | Heat fusion | HF |
| Number of f valence electrons | Vf | Bulk modulus | B |
| Number of total valence electrons | V | Shear modulus | G |
| Number of unfilled s states | Us | Magnetic moment | M |
| Number of unfilled p states | Up | Volume | V |
| Number of unfilled d states | Ud | Band gap energy | Gap |
| Number of unfilled f states | Uf | First ionization energy | IE |
| Number of total unfilled states | U | Space group number | SG |
| Electronegativity | En | Electron work function | EWF |
Fig. 4. Pearson correlation coefficient of the top 20 strong-correlated descriptors. The correlations with the positive and negative values are highlighted in green and red colors, respectively.
Fig. 5. Results of descriptor screening for ductility of Heusler alloys. (a) Univariate screening; (b) Recursive elimination; (c) Exhaustive screening. (d) Importance of key descriptors in the random forest (RF) model.
| Step | Descriptors (Abbr.) | Descriptors (Abbr.) | ||
|---|---|---|---|---|
| Univariate screening | Ionic radius of X (IRX) | Covalent radius of X-Z (CRX-Z) | ||
| Space group number of X-Y (SGX-Y) | Number of s valence of X-Y (VsX-Y) | |||
| Mean value of unfilled d states (Udm) | Mean value of shear modulus (Gm) | |||
| Number of d valence of X-Y (VdX-Y) | Mean value of heat capacity (HCm) | |||
| Shear modulus of X (GX) | Ionization energy of X (IEX) | |||
| Electronegativity of X (EnX) | ||||
| Recursive elimination screening | Mendeleev number of X (MNx) | Number of s valence of X (VsX) | ||
| Exhaustive screening | Number of d valence of X (VdX) | Mean value of electronegativity (ENm) | ||
| Heat capacity of X (HCX) | Standard deviation of unfilled states (Usd) | |||
| Mean value of ionic radius (IRm) | Space group number of X (SGX) | |||
Table 2. Retained descriptors after the univariate screening, the recursive elimination, and the exhaustive screening.
| Step | Descriptors (Abbr.) | Descriptors (Abbr.) | ||
|---|---|---|---|---|
| Univariate screening | Ionic radius of X (IRX) | Covalent radius of X-Z (CRX-Z) | ||
| Space group number of X-Y (SGX-Y) | Number of s valence of X-Y (VsX-Y) | |||
| Mean value of unfilled d states (Udm) | Mean value of shear modulus (Gm) | |||
| Number of d valence of X-Y (VdX-Y) | Mean value of heat capacity (HCm) | |||
| Shear modulus of X (GX) | Ionization energy of X (IEX) | |||
| Electronegativity of X (EnX) | ||||
| Recursive elimination screening | Mendeleev number of X (MNx) | Number of s valence of X (VsX) | ||
| Exhaustive screening | Number of d valence of X (VdX) | Mean value of electronegativity (ENm) | ||
| Heat capacity of X (HCX) | Standard deviation of unfilled states (Usd) | |||
| Mean value of ionic radius (IRm) | Space group number of X (SGX) | |||
| Materials category | MAE | MSE | RMSE |
|---|---|---|---|
| Conventional Heusler alloys | 0.005 | 0.052 | 0.073 |
| All-d-metal Heusler alloys | 0.004 | 0.040 | 0.061 |
Table 3. Prediction performance of the trained RF model in the 10-fold cross-validation for conventional X2YZ-type and all-d-metal Heusler alloys.
| Materials category | MAE | MSE | RMSE |
|---|---|---|---|
| Conventional Heusler alloys | 0.005 | 0.052 | 0.073 |
| All-d-metal Heusler alloys | 0.004 | 0.040 | 0.061 |
Fig. 6. Comparison between kRF predicted by the trained RF model and the true value kTrue of X2YMg. The radius of the circle represents the value of ?ln(RE), where RE is the relative error [RE=(kRF ? kTrue)/(kTrue)]. The bigger the radius of circle is, the smaller the RE is.
Fig. 7. Relationships between the screened 6 descriptors and the target k. (a) The number of d valence electrons of X (VdX) and the mean value of electronegativity (Enm); (b) The heat capacity of X (HCX) and mean value of ionic radius (IRm); (c) IRm and standard deviation of unfilled states (Usd). (d) The relationships among the reciprocal of Pugh's ratio (k?1), Cauchy pressure Cp and crystal structure of X (CSX). Note that for the alloys with superior ductility, i.e., alloys with large k?1 and large Cp, the corresponding X component almost all have a face-centered cubic (FCC) crystal structure (highlighted in red). In contrast, the ductility of the alloys is relatively poor when CSX is HCP (hexagonal close-packed structure) or complex cubic CC (highlighted in blue or orange).
Fig. 8. Results of consecutive descriptor screenings for the X2YZ-type alloys with CSX = FCC. (a) Univariate screening; (b) Recursive elimination; (c) Exhaustive screening. (d) Comparison of the importance of the selected 4 key descriptors.
| Step | Descriptors (Abbr.) | Descriptors (Abbr.) | ||
|---|---|---|---|---|
| Univariate screening | Ionic radius of X (IRX) | Mean value of bulk modulus (Bm) | ||
| Unfilled states of X (UX) | Boiling point of X (BTX) | |||
| Volume of X (VX) | Ionization energy of X (IEX) | |||
| Cohesive energy of X (EcX) | Mean value of melting temperature (MTm) | |||
| Mendeleev number of X (MNX) | Number of valences of X (VX) | |||
| Atomic weight of X (AWX) | Mean value of column (Cm) | |||
| Melting temperature of X (MTX) | Mean value of electronegativity (Enm) | |||
| Column of X (CX) | Mean value of unfilled d states (Udm) | |||
| Covalent radius of X (CRX) | Heat capacity of X (HCX) | |||
| Recursive elimination screening | Exhaustive screening | Mean value of shear modulus (Gm) | Mean value of electron work function (EWFm) | |
| Mean value of unfilled states (Um) | Mean value of heat capacity (HCm) | |||
Table 4. Selected descriptors by the univariate screening, the recursive elimination, and the exhaustive screening methods for the X2YZ-type alloys with CSX = FCC.
| Step | Descriptors (Abbr.) | Descriptors (Abbr.) | ||
|---|---|---|---|---|
| Univariate screening | Ionic radius of X (IRX) | Mean value of bulk modulus (Bm) | ||
| Unfilled states of X (UX) | Boiling point of X (BTX) | |||
| Volume of X (VX) | Ionization energy of X (IEX) | |||
| Cohesive energy of X (EcX) | Mean value of melting temperature (MTm) | |||
| Mendeleev number of X (MNX) | Number of valences of X (VX) | |||
| Atomic weight of X (AWX) | Mean value of column (Cm) | |||
| Melting temperature of X (MTX) | Mean value of electronegativity (Enm) | |||
| Column of X (CX) | Mean value of unfilled d states (Udm) | |||
| Covalent radius of X (CRX) | Heat capacity of X (HCX) | |||
| Recursive elimination screening | Exhaustive screening | Mean value of shear modulus (Gm) | Mean value of electron work function (EWFm) | |
| Mean value of unfilled states (Um) | Mean value of heat capacity (HCm) | |||
Fig. 9. Relations between the 4 selected key descriptors and the target k for the X2YZ-type alloys with the X component having an FCC structure (CSX = FCC). The color of the scatter points represents the value of k. (a) The mean value of the shear modulus (Gm) and the mean value of the electron work function (EWFm). (b) The mean value of the heat capacity (HCm) and the mean value of the unfilled states (Um).
Fig. 10. Comparison of the calculated Pugh's ratio by formula kCal= mEWFm+nGm+k0 with their true values kTrue for (a) conventional Heusler alloys (m=?0.35, n = 0.0036, k0=1.68) and (b) all-d-metal Heusler alloys (m=?0.0022, n = 0.20, k0=1.08), where the circles, triangles and pentagram represent the data in dataset, data from ab-initio calculation and experimental data from literature, respectively.
| Descriptors | abbreviations |
|---|---|
| Number of p valence of X | VpX |
| Number of unfilled p states of X | UpX |
| Number of unfilled f states of X | UfX |
| Band gap of X | GapX |
| Number of p valence of Y | VpY |
| Number of unfilled p states of Y | UpY |
| Number of unfilled f states of Y | UfY |
| Band gap of Y | GapY |
| Number of s valence of Z | VsZ |
| Number of f valence of Z | VfZ |
| Number of unfilled s states of Z | UsZ |
| Number of unfilled d states of Z | UdZ |
| Number of unfilled f states of Z | UfZ |
| Magnetic moment of Z | MZ |
| Mean value of unfilled f states | Ufm |
| Standard deviation of unfilled f states | Ufsd |
| Number of p valence of X-Y | VpX-Y |
| Number of unfilled p states of X-Y | UpX-Y |
| Number of unfilled f states of X-Y | UfX-Y |
| Number of unfilled f states of X-Z | UfX-Z |
| Number of unfilled f states of Y-Z | UfY-Z |
| Band gap of X-Y | GapX-Y |
Table A1. 22 descriptors whose variances are zero.
| Descriptors | abbreviations |
|---|---|
| Number of p valence of X | VpX |
| Number of unfilled p states of X | UpX |
| Number of unfilled f states of X | UfX |
| Band gap of X | GapX |
| Number of p valence of Y | VpY |
| Number of unfilled p states of Y | UpY |
| Number of unfilled f states of Y | UfY |
| Band gap of Y | GapY |
| Number of s valence of Z | VsZ |
| Number of f valence of Z | VfZ |
| Number of unfilled s states of Z | UsZ |
| Number of unfilled d states of Z | UdZ |
| Number of unfilled f states of Z | UfZ |
| Magnetic moment of Z | MZ |
| Mean value of unfilled f states | Ufm |
| Standard deviation of unfilled f states | Ufsd |
| Number of p valence of X-Y | VpX-Y |
| Number of unfilled p states of X-Y | UpX-Y |
| Number of unfilled f states of X-Y | UfX-Y |
| Number of unfilled f states of X-Z | UfX-Z |
| Number of unfilled f states of Y-Z | UfY-Z |
| Band gap of X-Y | GapX-Y |
| Formular/method | r | Formular/method | r |
|---|---|---|---|
| mEWFm+nGm+k0 | 0.77 | Gm/EWFm1/3 | 0.49 |
| mEWFm2+nGm+k0 | 0.77 | EWFm1/3/Gm1/3 | 0.49 |
| mEWFm3+nGm+k0 | 0.77 | Gm | 0.48 |
| mEWFm1/2+nGm+k0 | 0.77 | Gm3 | 0.48 |
| mEWFm1/2+nGm1/2+k0 | 0.77 | EWFm × Gm3 | 0.47 |
| mEWFm1/3+nGm+k0 | 0.77 | Gm1/2 | 0.46 |
| mEWFm+nGm1/3+k0 | 0.77 | Gm1/3 | 0.46 |
| mEWFm1/3+nGm1/3+k0 | 0.76 | EWFm/Gm | 0.46 |
| mEWFm2+nGm2+k0 | 0.76 | EWFm × Gm2 | 0.46 |
| mEWFm+nGm2+k0 | 0.75 | EWFm1/3 × Gm | 0.46 |
| mEWFm3+nGm3+k0 | 0.73 | EWFm1/2 × Gm | 0.45 |
| mEWFm+nGm3+k0 | 0.72 | EWFm2 × Gm2 | 0.44 |
| Gm/EWFm3 | 0.64 | EWFm3 × Gm3 | 0.44 |
| Gm1/3/EWFm | 0.63 | EWFm × Gm | 0.43 |
| EWFm/Gm1/3 | 0.61 | EWFm1/2/Gm | 0.43 |
| Gm/EWFm2 | 0.58 | EWFm1/3/Gm | 0.42 |
| EWFm3/Gm | 0.58 | EWFm2/Gm2 | 0.41 |
| Gm1/2/EWFm | 0.57 | EWFm1/2 × Gm1/2 | 0.41 |
| EWFm/Gm1/2 | 0.55 | EWFm1/3 × Gm1/3 | 0.41 |
| Gm/EWFm | 0.53 | EWFm2 × Gm | 0.39 |
| Gm2/EWFm2 | 0.53 | EWFm/Gm2 | 0.38 |
| EWFm2/Gm | 0.53 | EWFm × Gm1/2 | 0.37 |
| Gm3/EWFm3 | 0.53 | EWFm3/Gm3 | 0.36 |
| Gm1/2/EWFm1/2 | 0.52 | EWFm3 × Gm | 0.35 |
| Gm2/EWFm | 0.51 | EWFm/Gm3 | 0.32 |
| mEWFm+nGm1/2 | 0.51 | EWFm × Gm1/3 | 0.32 |
| Gm1/3/EWFm1/3 | 0.51 | EWFm | 0.22 |
| Gm/EWFm1/2 | 0.5 | EWFm2 | 0.22 |
| Gm3/EWFm | 0.5 | EWFm1/2 | 0.22 |
| Gm2 | 0.49 | EWFm3 | 0.22 |
| EWFm1/2/Gm1/2 | 0.49 | EWFm1/3 | 0.22 |
Table A2. The Pearson correlation r between values of 64 hypothetical formulas with Pugh's ratio k.
| Formular/method | r | Formular/method | r |
|---|---|---|---|
| mEWFm+nGm+k0 | 0.77 | Gm/EWFm1/3 | 0.49 |
| mEWFm2+nGm+k0 | 0.77 | EWFm1/3/Gm1/3 | 0.49 |
| mEWFm3+nGm+k0 | 0.77 | Gm | 0.48 |
| mEWFm1/2+nGm+k0 | 0.77 | Gm3 | 0.48 |
| mEWFm1/2+nGm1/2+k0 | 0.77 | EWFm × Gm3 | 0.47 |
| mEWFm1/3+nGm+k0 | 0.77 | Gm1/2 | 0.46 |
| mEWFm+nGm1/3+k0 | 0.77 | Gm1/3 | 0.46 |
| mEWFm1/3+nGm1/3+k0 | 0.76 | EWFm/Gm | 0.46 |
| mEWFm2+nGm2+k0 | 0.76 | EWFm × Gm2 | 0.46 |
| mEWFm+nGm2+k0 | 0.75 | EWFm1/3 × Gm | 0.46 |
| mEWFm3+nGm3+k0 | 0.73 | EWFm1/2 × Gm | 0.45 |
| mEWFm+nGm3+k0 | 0.72 | EWFm2 × Gm2 | 0.44 |
| Gm/EWFm3 | 0.64 | EWFm3 × Gm3 | 0.44 |
| Gm1/3/EWFm | 0.63 | EWFm × Gm | 0.43 |
| EWFm/Gm1/3 | 0.61 | EWFm1/2/Gm | 0.43 |
| Gm/EWFm2 | 0.58 | EWFm1/3/Gm | 0.42 |
| EWFm3/Gm | 0.58 | EWFm2/Gm2 | 0.41 |
| Gm1/2/EWFm | 0.57 | EWFm1/2 × Gm1/2 | 0.41 |
| EWFm/Gm1/2 | 0.55 | EWFm1/3 × Gm1/3 | 0.41 |
| Gm/EWFm | 0.53 | EWFm2 × Gm | 0.39 |
| Gm2/EWFm2 | 0.53 | EWFm/Gm2 | 0.38 |
| EWFm2/Gm | 0.53 | EWFm × Gm1/2 | 0.37 |
| Gm3/EWFm3 | 0.53 | EWFm3/Gm3 | 0.36 |
| Gm1/2/EWFm1/2 | 0.52 | EWFm3 × Gm | 0.35 |
| Gm2/EWFm | 0.51 | EWFm/Gm3 | 0.32 |
| mEWFm+nGm1/2 | 0.51 | EWFm × Gm1/3 | 0.32 |
| Gm1/3/EWFm1/3 | 0.51 | EWFm | 0.22 |
| Gm/EWFm1/2 | 0.5 | EWFm2 | 0.22 |
| Gm3/EWFm | 0.5 | EWFm1/2 | 0.22 |
| Gm2 | 0.49 | EWFm3 | 0.22 |
| EWFm1/2/Gm1/2 | 0.49 | EWFm1/3 | 0.22 |
| Formula | kTrue | kCal | Data type | Data sources |
|---|---|---|---|---|
| Ni51.5Fe21.5Ga27 | 0.2859 | 0.2227 | Exp. | Ref. [ |
| Cu41Mn20Al39 | 0.4318 | 0.3201 | Exp. | Ref. [ |
| Ni2MnGa | 0.2540 | 0.2604 | Exp. | Refs. [ |
| Ni49.3Mn34.2In16.5 | 0.3612 | 0.2587 | Exp. | Ref. [ |
| Ni49.3Mn34.2In16.5 | 0.2408 | 0.2587 | Exp. | Ref. [ |
| Ni2MnGa0.75B0.25 | 0.2200 | 0.2713 | DFT | This work |
| Ni2MnGa0.25B0.75 | 0.2567 | 0.2930 | DFT | This work |
| Ni2MnAl | 0.3199 | 0.2435 | DFT | This work |
| Ni2MnIn | 0.2645 | 0.2509 | DFT | This work |
| Ni2MnGe | 0.1775 | 0.2300 | DFT | This work |
| Ni2MnSn | 0.2721 | 0.2407 | DFT | This work |
| Ni2MnGa0.75Ti0.25 | 0.2559 | 0.2690 | DFT | This work |
| Ni2MnGa0.5Ti0.5 | 0.2510 | 0.2776 | DFT | This work |
| Ni2Mn0.75Ti0.25Ga | 0.3000 | 0.2669 | DFT | This work |
| Ni2Mn0.5Ti0.5Ga | 0.3317 | 0.2735 | DFT | This work |
| Ni2TiGa | 0.2985 | 0.2867 | DFT | This work |
| Ni1.75MnGaTi0.25 | 0.3432 | 0.2838 | DFT | This work |
| Ni1.5MnGaTi0.5 | 0.4191 | 0.3072 | DFT | This work |
| NiMnGaTi | 0.4752 | 0.3541 | DFT | This work |
| Ni2FeGa | 0.1733 | 0.2220 | DFT | This work |
| Pd2ZnSi | 0.1804 | 0.1291 | DFT | This work |
| Pt2HfIn | 0.1929 | 0.1763 | DFT | This work |
| Ni2MnMg | 0.2566 | 0.3011 | DFT | This work |
| Ni2MnGa0.25Cu0.75 | 0.2610 | 0.2462 | DFT | This work |
| Ni2MnCu | 0.2992 | 0.2415 | DFT | This work |
| Ni2MnGa0.75Si0.25 | 0.2662 | 0.2531 | DFT | This work |
| Ni2MnGa0.5Si0.5 | 0.2531 | 0.2458 | DFT | This work |
| Ni2MnGa0.25Si0.75 | 0.2167 | 0.2386 | DFT | This work |
| Ni2MnGa0.75In0.25 | 0.2718 | 0.2580 | DFT | This work |
| Ni2MnGa0.5In0.5 | 0.3066 | 0.2556 | DFT | This work |
| Ni2MnGa0.25In0.75 | 0.2933 | 0.2533 | DFT | This work |
| Ni2MnIn | 0.2638 | 0.2509 | DFT | This work |
| Ni2MnGa0.75Al0.25 | 0.2623 | 0.2562 | DFT | This work |
| Ni2MnGa0.5Al0.5 | 0.2752 | 0.2520 | DFT | This work |
| Ni2MnGa0.25Al0.75 | 0.3077 | 0.2477 | DFT | This work |
| Ni2MnAl | 0.3286 | 0.2435 | DFT | This work |
Table A3. Comparison of the calculated Pugh's ratio by formula kCal= mEWFm+nGm+k0 with their true values kTrue for the newly added DFT and experimental (Exp.) data.
| Formula | kTrue | kCal | Data type | Data sources |
|---|---|---|---|---|
| Ni51.5Fe21.5Ga27 | 0.2859 | 0.2227 | Exp. | Ref. [ |
| Cu41Mn20Al39 | 0.4318 | 0.3201 | Exp. | Ref. [ |
| Ni2MnGa | 0.2540 | 0.2604 | Exp. | Refs. [ |
| Ni49.3Mn34.2In16.5 | 0.3612 | 0.2587 | Exp. | Ref. [ |
| Ni49.3Mn34.2In16.5 | 0.2408 | 0.2587 | Exp. | Ref. [ |
| Ni2MnGa0.75B0.25 | 0.2200 | 0.2713 | DFT | This work |
| Ni2MnGa0.25B0.75 | 0.2567 | 0.2930 | DFT | This work |
| Ni2MnAl | 0.3199 | 0.2435 | DFT | This work |
| Ni2MnIn | 0.2645 | 0.2509 | DFT | This work |
| Ni2MnGe | 0.1775 | 0.2300 | DFT | This work |
| Ni2MnSn | 0.2721 | 0.2407 | DFT | This work |
| Ni2MnGa0.75Ti0.25 | 0.2559 | 0.2690 | DFT | This work |
| Ni2MnGa0.5Ti0.5 | 0.2510 | 0.2776 | DFT | This work |
| Ni2Mn0.75Ti0.25Ga | 0.3000 | 0.2669 | DFT | This work |
| Ni2Mn0.5Ti0.5Ga | 0.3317 | 0.2735 | DFT | This work |
| Ni2TiGa | 0.2985 | 0.2867 | DFT | This work |
| Ni1.75MnGaTi0.25 | 0.3432 | 0.2838 | DFT | This work |
| Ni1.5MnGaTi0.5 | 0.4191 | 0.3072 | DFT | This work |
| NiMnGaTi | 0.4752 | 0.3541 | DFT | This work |
| Ni2FeGa | 0.1733 | 0.2220 | DFT | This work |
| Pd2ZnSi | 0.1804 | 0.1291 | DFT | This work |
| Pt2HfIn | 0.1929 | 0.1763 | DFT | This work |
| Ni2MnMg | 0.2566 | 0.3011 | DFT | This work |
| Ni2MnGa0.25Cu0.75 | 0.2610 | 0.2462 | DFT | This work |
| Ni2MnCu | 0.2992 | 0.2415 | DFT | This work |
| Ni2MnGa0.75Si0.25 | 0.2662 | 0.2531 | DFT | This work |
| Ni2MnGa0.5Si0.5 | 0.2531 | 0.2458 | DFT | This work |
| Ni2MnGa0.25Si0.75 | 0.2167 | 0.2386 | DFT | This work |
| Ni2MnGa0.75In0.25 | 0.2718 | 0.2580 | DFT | This work |
| Ni2MnGa0.5In0.5 | 0.3066 | 0.2556 | DFT | This work |
| Ni2MnGa0.25In0.75 | 0.2933 | 0.2533 | DFT | This work |
| Ni2MnIn | 0.2638 | 0.2509 | DFT | This work |
| Ni2MnGa0.75Al0.25 | 0.2623 | 0.2562 | DFT | This work |
| Ni2MnGa0.5Al0.5 | 0.2752 | 0.2520 | DFT | This work |
| Ni2MnGa0.25Al0.75 | 0.3077 | 0.2477 | DFT | This work |
| Ni2MnAl | 0.3286 | 0.2435 | DFT | This work |
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