Phase stability and magnetic properties in fcc Fe-Cr-Mn-Ni alloys from first-principles modeling

Systematic investigation of phase stability of the magnetic fcc Fe-Cr-Mn-Ni system—promising candidate structural materials to replace conventional austenitic steels—has been performed using a combination of spin-polarized density-functional theory, cluster expansion, and Monte Carlo simulations. The developed model was able to reproduce all known ground states (GSs) in the studied system and to predict new ones with strongly negative formation enthalpy—ternary ${\mathrm{CrMnNi}}_2$ and quaternary ${\mathrm{FeCr}}_2{\mathrm{MnNi}}_4$. Investigation of phase stability was done at 0 K and finite temperatures in the whole concentration range and allowed us to observe the important role of Ni and Mn. Ni is the only element in the system that increases the order-disorder transition (ODT) temperature, which means that the fcc alloys with decreased concentration of Ni will form solid solutions at lower temperatures. Analysis of the effect of the addition of Mn to Fe-Cr-Ni alloy confirms a general trend of statistical correlation between the averaged magnitude of magnetic moments and volume per atom found from the predicted stable structures in the quaternary system and underlying subsystems. This linear magneto-volume relationship trend is, however, weaker in Fe-Cr-Mn-Ni alloys in comparison with those in the Fe-Cr-Ni system. Furthermore, Ni and Mn form the most stable GS—$\text{L}{1}_0$-MnNi, which has one of the strongest tendencies to segregate in fcc Fe-Cr-Mn-Ni alloys evidenced by the strength of Mn-Ni short-range ordering (SRO). Mn-Ni SRO significantly increases ODT temperature in the vicinity of $\text{L}{1}_0$-MnNi and to the equiatomic region. The ODT of ${\mathrm{Cr}}_{18}{\mathrm{Fe}}_{27}{\mathrm{Mn}}_{27}{\mathrm{Ni}}_{28}$ alloy is found to be $1290\pm 150$ K, which supports the experimental observation of the disordered solid solution structure in ${\mathrm{Cr}}_{18}{\mathrm{Fe}}_{27}{\mathrm{Mn}}_{27}{\mathrm{Ni}}_{28}$ alloy at higher temperatures.

Figure 1

Undecorated two-, three-, and four-body clusters with size $\omega$ and label $n$, which are used in this work.

Figure 2

(a) Enthalpy of formation, (b) volume per atom, and (c) average magnitudes of magnetic moments per atom of fcc Cr-Mn ordered and SQS structures calculated using DFT. Black solid line marks the convex hull of fcc structures. Black dashed line connects the most stable fcc structures of respective pure elements. Vegard's law estimate for magnetic and nonmagnetic fcc structures is indicated by the orange dashed line and blue dash-dotted line, respectively. The results obtained for the most stable structures and magnetic configurations for each considered alloy composition are indicated by filled markers, and the less stable structures are indicated by open markers. Values for SQS structures are indicated by filled markers with black edges.

Figure 3

(a) Enthalpy of formation, (b) average magnitudes of magnetic moments per atom, (c) volume per atom of fcc Fe-Mn structures calculated using DFT. The notation is the same as in Fig. 2. Experimental data (superscript a) are adapted from the work of Kubitz and Hayes [83].

Figure 4

Atomic structure and magnetic moments of the binary Mn-Ni GSs calculated in a conventional fcc $2\times 2\times 2$ super cell using collinear magnetism in DFT: (a) AFM $\text{L}{1}_0$-MnNi and (b) FM $\text{L}{1}_2\text{−}{\mathrm{MnNi}}_3$. The color code of the arrows shows the magnitudes of magnetic moments.

Figure 5

(a) Enthalpy of formation, (b) average magnitudes of magnetic moments per atom, (c) volume per atom of fcc Mn-Ni structures calculated using DFT. The notation is the same as in Fig. 2. Black dash-dotted line connects the true GSs, which are FM fcc Ni and AFM $\alpha$-Mn. Experimental data are as follows: ${}^{\mathrm{a}}\text{from}$ Ref. [96], ${}^{\mathrm{b}}\text{from}$ Ref. [91], ${}^{\mathrm{c}}\text{from}$ Ref. [95], ${}^{\mathrm{d}}\text{from}$ Ref. [90], ${}^{\mathrm{e}}\text{from}$ Ref. [92], ${}^{\mathrm{f}}\text{from}$ Ref. [98], ${}^{\mathrm{g}}\text{from}$ Ref. [94], ${}^{\mathrm{h}}\text{from}$ Ref. [93], ${}^{\mathrm{i}}\text{from}$ Ref. [87], ${}^{\mathrm{j}}\text{from}$ Ref. [88], ${}^{\mathrm{k}}\text{from}$ Ref. [89].

Figure 6

Interpolated DFT results for the most stable structures and magnetic configurations for Fe-Cr-Mn alloys on fcc lattice: (a) enthalpy of mixing; (b) enthalpy of formation; (c) average magnitudes of magnetic moments; and (d) volume per atom. Green dashed lines separate the regions with different predominant magnetic configuration, which are indicated in (c). Gray dash-dotted line indicates the concentrations where $\mathrm{VEC}=7$; the region below the line has lower VEC and the region above it has higher VEC; VEC for pure Fe is 8.

Figure 7

Interpolated DFT results for the most stable structures and magnetic configurations for Cr-Mn-Ni alloys on fcc lattice: (a) enthalpy of mixing; (b) enthalpy of formation; (c) average magnitudes of magnetic moments; and (d) volume per atom. Green dashed lines separate the regions with different predominant magnetic configuration, which are indicated in (c). Filled circles represent GSs. Gray dashed line indicates the concentrations where $\mathrm{VEC}=8$ and gray dash-dotted line, where $\mathrm{VEC}=7$. The region on the right side has lower VEC and the region on the left side has higher VEC. VEC for pure Cr is 6 and for pure Ni is 10.

Figure 8

Interpolated DFT results for the most stable structures and magnetic configurations for Fe-Mn-Ni alloys on fcc lattice: (a) enthalpy of mixing, (b) enthalpy of formation, (c) average magnitudes of magnetic moments, and (d) volume per atom. Green dashed lines separate the regions with different predominant magnetic configuration, which are indicated in (c). Filled circles represent GSs. Experimental data are adapted from the following: ${}^{\mathrm{a}}\text{Menshikov}$ et al. [110] (the line that separate the regions of FM and AFM stability) and ${}^{\mathrm{b}}\text{Ettwig}$ and Pepperhoff [112] (line of FM-AFM magnetic phase transition with the change of Ni concentration). Gray dashed line indicates the concentrations where $\mathrm{VEC}=8$; the region above the line has lower VEC and the region below it has higher VEC. VEC for pure Mn is 7 and for pure Ni is 10.

Figure 9

The most stable structures for each considered composition calculated using DFT for Fe-Cr-Mn-Ni quaternary alloys and the underlying ternary and binary alloys on fcc lattice: (a) enthalpy of mixing from CE; (b) enthalpy of mixing from DFT; (c) enthalpy of formation from DFT; (d) average magnitudes of magnetic moments; and, (e) volume per atom.

Figure 10

Atomic structure of the predicted quaternary GS ${\mathrm{FeCr}}_2{\mathrm{MnNi}}_4$ in a conventional fcc unit cell.

Figure 11

Theoretical magnetic phase diagram of quaternary fcc Fe-Cr-Mn-Ni alloys based on the results of DFT calculations.

Figure 12

Magneto-volume relation for (a) binary; (b) ternary and (c) quaternary alloys based on DFT calculations for structures with VEC $>7$. Filled circles represent the most stable structures for each composition; solid lines represent the line fitting for the most stable structures.

Figure 13

Enthalpy of mixing and free energy of mixing from Monte Carlo simulations, as well as $-T{S}_{\mathrm{mix}}^{\mathrm{conf}}$ and free energies of mixing calculated using Thermodynamic Integration method and cluster expansion methods for the equiatomic Fe-Cr-Mn-Ni alloys.

Figure 14

Contribution of [(a)–(c)] $-T{S}_{\mathrm{mix}}^{\mathrm{conf}}$ and [(d)–(f)] $H_{\mathrm{mix}}$ to [(g)–(i)] $F_{\mathrm{mix}}$ in the whole concentration range at 300 K, 1000 K and 2000 K. $S^{\mathrm{conf}}$ is taken from the cluster $\omega =2,n=1$. Two-dimensional slice of $F_{\mathrm{mix}}$ [(j)–(l)], where Cr and Fe concentrations are equal.

Figure 15

Order-disorder transition temperatures as a function of each element concentration. Each data point represents different pseudobinary alloy, in which the concentration of a chosen element is equal to that on $x$ axis and the relative concentration of other elements is equiatomic.

Figure 16

(a) Order-disorder transition temperatures for the whole concentration range of Fe-Cr-Mn-Ni alloys; (b) a percentage of AFM $\text{L}{1}_0$-MnNi precipitate at 300 K in the whole concentration range, as well as [(c) and (d)] respective 2D slices where Cr and Fe concentrations are equal.

Figure 17

Formation enthalpy obtained from the MC simulations and the SRO parameters in the first coordination shell for the ${\mathrm{FeCr}}_2{\mathrm{MnNi}}_4$ intermetallic phase [(a) and (b)], ${\mathrm{Cr}}_{18}{\mathrm{Fe}}_{27}{\mathrm{Mn}}_{27}{\mathrm{Ni}}_{28}$ [9] [(c) and (d)] and the equiatomic composition [(e) and (f)]. The representative structures of each alloy generated in MC simulations at 300 K and 1100 K are shown inside the figures.

Figure 18

Calculated equations of state for known and hypothetical crystal structures and magnetic configurations of Mn.

Figure 19

Magneto-volume relation (a) for all calculated Mn structures at equilibrium volume and (b) for four sites in AFM $\alpha$-Mn.

Figure 20

(a) Enthalpy of formation, (b) average magnitudes of magnetic moments per atom, (c) volume per atom of fcc Cr-Fe structures calculated using DFT. The notation is the same as in Fig. 2.

Figure 21

Enthalpy of formation, volume per atom and magnetic moments per atom for stable states calculated using DFT for Fe-Ni alloys on fcc lattice. The notation is the same as in Fig. 2. Black dash-dotted line connects the true GSs, which are FM bcc Fe and FM fcc Ni. Experimental data: ${}^{\mathrm{a}}\text{Reck}$ et al. [121], ${}^{\mathrm{b}}\text{Shull}$ et al. [93], ${}^{\mathrm{c}}\text{Cochrane}$ et al. [142], ${}^{\mathrm{d}}\text{Nakai}$ et al. [143], ${}^{\mathrm{e}}\text{Menshikov}$ et al. [144], ${}^{\mathrm{f}}\text{Wakelin}$ et al. [122], ${}^{\mathrm{g}}\text{Owen}$ et al. [120], ${}^{\mathrm{h}}\text{Bhatia}$ et al. [123], ${}^{\mathrm{i}}\text{Shiga}$ [145], ${}^{\mathrm{j}}\text{Chamberod}$ et al. [146].

Figure 22

Enthalpy of formation, volume per atom and magnetic moments per atom for stable states calculated using DFT for Cr-Ni alloys on fcc lattice. The notation is the same as in Fig. 2. Black dash-dotted line connects the true GSs, which are FM fcc Ni and AFM bcc Cr. Experimental data are taken from: ${}^{\mathrm{a}}\text{Takano}$ et al. [119], ${}^{\mathrm{b}}\text{Besnus}$ et al. [147], ${}^{\mathrm{c}}\text{Lenkkeri}$ [148], ${}^{\mathrm{d}}\text{Jung}$ [118].