Hyperfine Interactions (2004) 158:111–115 DOI 10.1007/s10751-005-9017-3
#
Springer 2005
Ordering Effects and Hyperfine Interactions in FeYN Austenites A. N. TIMOSHEVSKII* and B. Z. YANCHITSKY Institute of Magnetism, National Academy of Science Ukraine, 36-b Verdansky St., 03142 Kiev, Ukraine; e-mail:
[email protected] Abstract. Using the high accurate ab-initio FLAPW method and the cluster expansion technique, interatomic NYN interactions for FeYN austenite were calculated. The interactions were used for calculation of temperature dependence of the short range order for Fe10N austenite. For two model structures with different nitrogen distributions, the hyperfine interactions were calculated. It was revealed, that EFG might be nonzero on nuclei even for Fe atoms that do not have nitrogen atoms at the first coordination shell. This finding has to be considered for interpretation of Mo¨ssbauer spectra of austenite FeYN.
1. Introduction Nitrogen as a doping element is widely used in creation of various steels, for example, in the high nitrogen steels. That is why a large number of investigations have been performed to clarify an influence of the nitrogen on the fcc matrix of iron. Many of the changes, caused by the nitrogen, originate from nitrogen distribution over iron matrix. A basic method for studying distribution of nitrogen is Mo¨ssbauer spectroscopy. There are a large number of investigations of the problem [1Y3]. But there is no single point of view in what concerns interpretation of the experimental data. Mainly this is because that there is no unique technique to decompose the experimental spectra into components, which are determined by the short range order in the austenite. A majority of investigators interpret the spectra within framework of a model which includes only three components. These components comes from three kinds of the iron atoms, the first kind corresponds to iron atom that does not have a nitrogen atom at the first coordination shell, the second and third kinds correspond to the case when one and two nitrogen atoms are located at the first shell. For complete understanding of how the quadrupole splittings on iron nuclei are formed, investigations of the short range order and the electronic structure of FeYN system are needed. Now, many of similar problems are studying using high accurate ab initio methods. For FeYN systems only a minor number of such
* Author for correspondence.
112
A. N. TIMOSHEVSKII AND B. Z. YANCHITSKY
N
Fe1,0,4
Fe0,4,0
N
Fe1,0,4
Fe0,4,0
Fe2,0,0
Fe0,0,8
Structure B Structure A Figure 1. The model structures of the stoichiometry Fe8N.
investigations have been performed [4, 5]. In the present paper, an influence of the nitrogen distribution in austenite FeYN on formation of quadrupole splittings on the iron nuclei is investigated. 2. Results and discussion For detailed investigation of dependence of different nitrogen distributions on quadrupole splittings on the iron nuclei in austenite FeYN we used a high accurate FLAPW method [6]. For two model structures with different nitrogen distributions we calculated electronic structure and hyperfine interactions. Since most of investigators believe that in FeYN system exists energetically favourable called as Fbell-like_, configuration NYFeYN [7] (iron atoms in this configuration will be denoted as Fe2), we chose two model structures in that way so the second structure contains Fe2 atom, but the first one does not. These structures can be seen in the Figure 1. Technical details of this ab initio calculation are shown in [8]. It should be stressed, that for both structures the optimization of geometry was performed; such optimization includes variations of the parameters of the unit cell and atomic positions within unit cell to achieve minimum of the total energy. On the base of the performed calculations, we investigated an influence of nitrogen atoms on two structural phases in fcc iron (low spin LS and high spin HS). Details of this investigation are discussed in [8]. Our calculations revealed that the total energy of the structure (B) is less than the total energy of the structure (A), thus confirming that formation of bell-like configurations is energetically favourable. EFG on the iron nuclei was calculated using ab initio basis and electron density by means of the method developed in [9]. The results are presented in Table I. The first structure (A) contains two kinds of iron atoms: Fe0,4,0 (four
113
ORDERING EFFECTS AND HYPERFINE INTERACTIONS IN FeYN AUSTENITES
Table I. Quadrupole splittings (mm/s) in FeYN. Structure
Fe1,0,4
Fe2,0,0
Fe0,4,0
0.00a 0.27 Y Y Exper Y Y Y Y a Quadrupole splitting is zero because the point group of this atom is Td 43m . Theory
Fe8N (A) No 225 Fm3m Fe8N (B) No 123 P4/mmm Fe4N (model) [4] Fe4N (nitride) [4] Fe4N [10] Fe10.2N [3] Fe10.2N [1] Fe11N [2]
Y 0.17 0.32 0.50 0.50 0.40 0.72 0.75
0.18 0.28 0.03 Y Y 0.25 0.39 0.39
Fe0,0,8 Y 0.48 Y Y Y Y Y Y
Table II. The interatomic interactions (eV) by the least square fit method. N
5 6
Interatomic interactions w0
w11
w12
w22
w32
w 24
w52
w62
w13
j34634.7004 j34634.6996
j1490.8849 j1490.9087
0.127 0.129
j0.041 j0.034
0.027 0.028
0.018 0.022
0.032 0.031
Y j0.007
j0.014 j0.014
N is a number of pair potentials used in the fit.
nitrogen atoms at the second coordination shell) and Fe1,0,4, these atoms at the first coordination shell have zero and one nitrogen atoms respectively. The second structure (B) has in addition Fe2,0,0 atoms (two nitrogen atoms at the first shell) and atoms Fe0,0,8 (eight atoms at the third shell). Modern interpretations believe that Fe1 atoms in structures (A) and (B) must have equal quadrupole splitting. As it follows from Table I this assumption is in contradiction with our results. In our opinion there are as least two kinds of atoms Fe1, one kind of them exists due to presence of Fe2 and the second kind has nothing common with Fe2, these kinds cannot be symmetry equivalent. As it is seen from our calculations, for structure (A) on nucleus of Fe1,0,4 the quadrupole splitting is 0.18 mm/s, whereas for structure (B) the splitting is 0.28 mm/s. A similar picture may be observed for atoms Fe0,m,n. For these atoms the quadrupole splittings are of the same order of magnitude as for atoms Fe1,0,4 and Fe2,0,0 (Table I). An important question is how many atoms of each kind does real austenite contain? To investigate the problem it is necessary to calculate temperature dependence of the short range order in FeYN system. To do this, a calculation of interatomic potentials was performed. We constructed 10 ordered structures with various distribution of nitrogen in fcc iron matrix [4]. All calculations were performed with spin polarization. Clusters corresponding to interatomic potentials are given in [4]. The values of calculated interatomic potentials are given in Table II. The symbols used have the following meaning: w(0) Y is energy of the iron atom, w(1) Y is energy of the nitrogen atom plus the energy needed to introduce the atom into iron matrix,
114
A. N. TIMOSHEVSKII AND B. Z. YANCHITSKY
0,6
c=0.10
Fraction of Fe atoms
Random Fe1
Fe0
0,5
Random Fe0
0,4
Fe1
0,3
Fe0,0
Random Fe2
0,2
Fe2
Fe1,0 Fe2
Fe0,1
0,1
Fe1,1 Fe0,2 Fe1,2
Fe0,3 0,0 0
400
800
1200
1600
2000 0
400
800
1200
1600
2000
Temperature (K) Temperature (K) Figure 2. Temperature dependence of fraction of iron atoms of different kinds for Fe10N alloy. Label Frandom_ means that nitrogen atoms dot not interact.
(2) (2) (2) (2) w1(2), w(2) 2 , w3 , w4 , w5 , w6 Y are energies of pair NYN interactions for six (3) coordination shells, w1 Y is energy of three-body NYNYN interaction. Fit by the least square method gives the maximal residual for the total energy 0.0036 eV/ atom Fe. The short range order was calculated by the Monte Carlo method for canonical ensemble. Temperature dependences of the fraction for various kinds of iron atoms for experimentally studied concentration of nitrogen 0.1 are given in Figure 2. It can be seen from the Figure 2 that the fraction of Fe0,0 atoms is nearly equal to that for Fe0,1. Atoms Fe0,0 can contribute into singlet only, but for the nuclei of Fe0,1 it is possible a formation of significant value EFG, thus adding into Mo¨ssbauer spectra a doublet. A similar situation exists for atoms Fe1,m. It is seen in Figure 2, that the numbers of atoms Fe1,0 and Fe1,1 are close, and the nuclei of this atoms might contribute significantly into the spectrum of austenite.
3. Conclusion As it follows from the presented investigation, in contradiction with existing interpretations of Mo¨ssbauer spectra, a more number of iron atoms of different kinds must be included. Even iron atoms, which do not have the nitrogen atoms at the first coordination shell, might contribute into spectra. References 1. 2. 3. 4.
Oda K., Umezu K. and Ino H., J. Phys. Condens., Matter 2 (1990), 10147. Gavriljuk V. G., Nadutov V. M. and Gladun O., Phys. Met. Metallogr. 3 (1990), 128. Foct J., Rochegude P. and Hendry, Acta Mater. 36 (1988), 501. Timoshevskii A. N., Timoshevskii V. A. and Yanchitsky B. Z., J. Phys. Condens., Matter 13 (2001), 1051.
ORDERING EFFECTS AND HYPERFINE INTERACTIONS IN FeYN AUSTENITES
5. 6. 7. 8. 9. 10.
115
Timoshevskii A. N., Yanchitsky B. Z. and Bakai A. S., Fiz. Nizk. Temp. 30 (2004), 626. Blaha P., Schwarz K. and Luitz J., (1999), ISBN 3-9501031-0-4. Gavriljuk V. G. and Berns H., High Nitrogen Steels, Springer, Berlin, 1999, p. 378. Timoshevskii A. N., Timoshevskii V. A., Yanchitsky B. Z. and Yavna V. A., Comput. Mater. Sci. 22(1Y2) (2001), 99. Blaha P., Schwarz K. and Herzig P., Phys. Rev. Lett. 54 (1985), 1192. Rochegude P. and Foct J., Phys. Status Solidi, A 98 (1986), 51.
