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Magnetic neutron scattering at small momentum transfer caused by spin fluctuations in molten iron
Volume 61A, number 1
PHYSICS LETTERS
4 April 1977
MAGNETIC NEUTRON SCATTERING AT SMALL MOMENTUM TRANSFER CAUSED BY SPIN FLUCTUATIONS IN MOLTEN IRON M. WEBER and S. STEEB Max-Planck-Institu t fur Metallforschung, Stuttgart, Germany
and W. KNOLL Inst itut Laue Langevin, Grenoble, France Received 11 February 1977 Molten iron exhibits strong scattering of neutrons at small momentum transfer, which is caused by spin fluctuations. At 1600°Cthe corresponding correlation length amounts to 2.7 A.
The existence of large scale fluctuations in magnetization which occur in the vicinity of the Curie point in solid Fe has been the subject of numerous neutron scattering studies (a short review is given in [1]). These fluctuations give rise to intense scattering at small momentum transfer q which can be described in the so called hydrodynamic region by Van Hove’s theory of magnetic critical scattering [2] . Evidence for the persistence of short range fluctuations within the liquid phase of iron has been established by the measurements to be reported here. The experiment was performed on the D4 two-axis diffractometer located near the hot source of the Grenoble high-flux reactor, using neutrons of wavelength X = 0.7 A [3]. Although not especially designed for neutron scattering studies at small momentum transfer, this instrument provides reliable data down to qmin 0.2 A~.This minimum momentum transfer turns out to be sufficient for the study of short range fluctuations, as was shown by investigations on concentration fluctuations in binary liquid metal mixtures [4, 5] . The samples (purity 99.95%) were sealed in polycrystalline A12O3 tubes (inner diameter 0.7 cm, wall thickness 0.05 cm) and heated up to 1600°C.The measured intensity was fully corrected for scattering and absorption from the container and the heater as well as for self absorption, multiple and incoherent scattering contributions. Absolute differential scattering cross sections were obtained by calibration with a vanadium standard. 78
looc o n
‘~—~ ~
800 °~
sample i sample 2
—
experiment
---
nuciearplus pamrnagnec
- -
scatterIng (ca/c.) 7/~1’scattering
600
400
200
~0
0.4
0.8
1.2
06 2.0 q Fig. 1. Molten iron at 1600°C.Differential scattering cross section as a function of momentum transfer.
Fig. 1 shows the result of two independent measthe full curve is drawn through the experimental points and represents the sum of the coherent nuclear and the magnetic differential scattering
urements where
cross sections per atom. The coherent nuclear scattering cross section can be calculated from the Ashcroft and Lekner hard-sphere structure factors using a hardsphere diameter of 2.25 A and a packing fraction of 0.45 according to [6] The nuclear scattering cross section thus obtained is plotted as dash-dotted line in fig. I. For negligible interaction between spins the mag.
Volume 61A, number 1
PHYSICS LETTERS
netic scattering contribution reduces to the paramagnetic scattering cross section which was calculated according to [7] from the
(
do
\
=
mag.
(‘ye2
)2
2S(S+1) F(q)12
mec2
r~(q2+ K?) (1)
4 April 1977
¶
°samplel nsample2 3
2
0
00
01
02
0.3
0.4
0.5
U~
Fig. 2. Molten iron at 1600°C.Inverse magnetic scattered intensity versus q2.
cording to eq. (2) (see ref. [1]): ~ = 3.1 [(T Tc)/Tc] 0.69, —
(2)
with ~ = nearest neighbour distance. The extrapolation of this description of the critical behaviour to the temperature of the present investigation yields icj~= 0.9 A. Thus, the result of the present measurement could be interpreted in terms of rudimentary spin fluctuations far away from the critical
where the parameters Kf1 and r 1 represent, respectively, the range and strength of the spin correlations, all figures having their usual meaning. This so called quasistatic approximation holds if q is constant over the range of w for which energy transfers ~ are important, a condition which is well fulfilled in this experiment. (Incident energy about 150 meV.) Therefore, within the limits of this approximation, the correlation length l4j’~ can be determined in plotting the reciprocal of the magnetic scattering cross section against the square of the momentum transfer. This should yield a linear relationship, as the q-dependency of the magnetic form factor F(q) is negligible in the q-region of interest. The data the above up 2 = experimental 0.5 A—2 as can be fulfill seen from fig. 2.relation The to q of 2.5 A determined from this plot was used to value calculate a further correction to the observed angular distribution taking into account the finite angular resolution of the instrument. This yields a corrected value of 2.7 Afor gj4. The correlation length of spin fluctuations near the critical temperature in solid iron can be described ac-
point. This kind of interpretation is strongly supported by recent thermodynamic considerations by Grimvall [8,9]. From the fact that iron follows Richards rule and that there is no large discontinuity in C~on fusion, he concluded that there is strong thermodynamic evidence for the existence of persistent spin fluctuations also in the liquid state with roughly the same associated entropy as in the solid state. This implies that there should be no fundamental difference in spin interactions between the solid paramagnetic and the liquid state of iron. We would like to thank the ILL, Grenoble, for allocation of beam time and technical support as well as the financial Verein Deutscher for support. Giessereifachleute, Düsseldorf,
References
[11na, J. Als-Nielsen, vol. 5a, ed. in: C. Domb Phase transitions and M.S. Green and critical (Academic phenomePress, London, 1976).
79
Volume 6lA, number 1
PFIYSICS LETTERS
[2] L. Passell, K. Blinowski, T. Brun and P. Nielsen, Phys. Rev. A 139 (1965) 1866. [3] Beam Facilities at ILL High Flux Reactor, Instrument Description, Grenoble (1975). [4] P.A. Egelstaff and G.D. Wignall, A.E.R.E. Rep. No. 5627 (1967). [5] W. Zaiss, S. Steeb and G.S. Bauer, Phys. Chem. Liq. 6 (1976) 21.
80
4 April 1977
[6] Y. Waseda and S. Tamaki, Phil. Mag. 32(1975) 273. [7] E.J. Lisher and J.B. Forsyth, Acta Cryst. A27 (1971) 545. 181 S.J. Filippov, N.B. Kazakov and L.A. Prounin, Izv. V.U.Z. Chern. Met. 9 (1966) 8. [9] G. Grimvall, Physica Scripta 13(1976) 59. [101 G. Grimvall, in: Proc. 3rd Intern. Conf. on Liquid metals, Bristol, 1976, to be published.
PHYSICS LETTERS
4 April 1977
MAGNETIC NEUTRON SCATTERING AT SMALL MOMENTUM TRANSFER CAUSED BY SPIN FLUCTUATIONS IN MOLTEN IRON M. WEBER and S. STEEB Max-Planck-Institu t fur Metallforschung, Stuttgart, Germany
and W. KNOLL Inst itut Laue Langevin, Grenoble, France Received 11 February 1977 Molten iron exhibits strong scattering of neutrons at small momentum transfer, which is caused by spin fluctuations. At 1600°Cthe corresponding correlation length amounts to 2.7 A.
The existence of large scale fluctuations in magnetization which occur in the vicinity of the Curie point in solid Fe has been the subject of numerous neutron scattering studies (a short review is given in [1]). These fluctuations give rise to intense scattering at small momentum transfer q which can be described in the so called hydrodynamic region by Van Hove’s theory of magnetic critical scattering [2] . Evidence for the persistence of short range fluctuations within the liquid phase of iron has been established by the measurements to be reported here. The experiment was performed on the D4 two-axis diffractometer located near the hot source of the Grenoble high-flux reactor, using neutrons of wavelength X = 0.7 A [3]. Although not especially designed for neutron scattering studies at small momentum transfer, this instrument provides reliable data down to qmin 0.2 A~.This minimum momentum transfer turns out to be sufficient for the study of short range fluctuations, as was shown by investigations on concentration fluctuations in binary liquid metal mixtures [4, 5] . The samples (purity 99.95%) were sealed in polycrystalline A12O3 tubes (inner diameter 0.7 cm, wall thickness 0.05 cm) and heated up to 1600°C.The measured intensity was fully corrected for scattering and absorption from the container and the heater as well as for self absorption, multiple and incoherent scattering contributions. Absolute differential scattering cross sections were obtained by calibration with a vanadium standard. 78
looc o n
‘~—~ ~
800 °~
sample i sample 2
—
experiment
---
nuciearplus pamrnagnec
- -
scatterIng (ca/c.) 7/~1’scattering
600
400
200
~0
0.4
0.8
1.2
06 2.0 q Fig. 1. Molten iron at 1600°C.Differential scattering cross section as a function of momentum transfer.
Fig. 1 shows the result of two independent measthe full curve is drawn through the experimental points and represents the sum of the coherent nuclear and the magnetic differential scattering
urements where
cross sections per atom. The coherent nuclear scattering cross section can be calculated from the Ashcroft and Lekner hard-sphere structure factors using a hardsphere diameter of 2.25 A and a packing fraction of 0.45 according to [6] The nuclear scattering cross section thus obtained is plotted as dash-dotted line in fig. I. For negligible interaction between spins the mag.
Volume 61A, number 1
PHYSICS LETTERS
netic scattering contribution reduces to the paramagnetic scattering cross section which was calculated according to [7] from the
(
do
\
=
mag.
(‘ye2
)2
2S(S+1) F(q)12
mec2
r~(q2+ K?) (1)
4 April 1977
¶
°samplel nsample2 3
2
0
00
01
02
0.3
0.4
0.5
U~
Fig. 2. Molten iron at 1600°C.Inverse magnetic scattered intensity versus q2.
cording to eq. (2) (see ref. [1]): ~ = 3.1 [(T Tc)/Tc] 0.69, —
(2)
with ~ = nearest neighbour distance. The extrapolation of this description of the critical behaviour to the temperature of the present investigation yields icj~= 0.9 A. Thus, the result of the present measurement could be interpreted in terms of rudimentary spin fluctuations far away from the critical
where the parameters Kf1 and r 1 represent, respectively, the range and strength of the spin correlations, all figures having their usual meaning. This so called quasistatic approximation holds if q is constant over the range of w for which energy transfers ~ are important, a condition which is well fulfilled in this experiment. (Incident energy about 150 meV.) Therefore, within the limits of this approximation, the correlation length l4j’~ can be determined in plotting the reciprocal of the magnetic scattering cross section against the square of the momentum transfer. This should yield a linear relationship, as the q-dependency of the magnetic form factor F(q) is negligible in the q-region of interest. The data the above up 2 = experimental 0.5 A—2 as can be fulfill seen from fig. 2.relation The to q of 2.5 A determined from this plot was used to value calculate a further correction to the observed angular distribution taking into account the finite angular resolution of the instrument. This yields a corrected value of 2.7 Afor gj4. The correlation length of spin fluctuations near the critical temperature in solid iron can be described ac-
point. This kind of interpretation is strongly supported by recent thermodynamic considerations by Grimvall [8,9]. From the fact that iron follows Richards rule and that there is no large discontinuity in C~on fusion, he concluded that there is strong thermodynamic evidence for the existence of persistent spin fluctuations also in the liquid state with roughly the same associated entropy as in the solid state. This implies that there should be no fundamental difference in spin interactions between the solid paramagnetic and the liquid state of iron. We would like to thank the ILL, Grenoble, for allocation of beam time and technical support as well as the financial Verein Deutscher for support. Giessereifachleute, Düsseldorf,
References
[11na, J. Als-Nielsen, vol. 5a, ed. in: C. Domb Phase transitions and M.S. Green and critical (Academic phenomePress, London, 1976).
79
Volume 6lA, number 1
PFIYSICS LETTERS
[2] L. Passell, K. Blinowski, T. Brun and P. Nielsen, Phys. Rev. A 139 (1965) 1866. [3] Beam Facilities at ILL High Flux Reactor, Instrument Description, Grenoble (1975). [4] P.A. Egelstaff and G.D. Wignall, A.E.R.E. Rep. No. 5627 (1967). [5] W. Zaiss, S. Steeb and G.S. Bauer, Phys. Chem. Liq. 6 (1976) 21.
80
4 April 1977
[6] Y. Waseda and S. Tamaki, Phil. Mag. 32(1975) 273. [7] E.J. Lisher and J.B. Forsyth, Acta Cryst. A27 (1971) 545. 181 S.J. Filippov, N.B. Kazakov and L.A. Prounin, Izv. V.U.Z. Chern. Met. 9 (1966) 8. [9] G. Grimvall, Physica Scripta 13(1976) 59. [101 G. Grimvall, in: Proc. 3rd Intern. Conf. on Liquid metals, Bristol, 1976, to be published.