Physica B 180 & 181 (1992) 828-830 North-Holland Al I

Elastic diffuse neutron scattering in dilute interstitial solid solutions

P. Barb&is, B. Beuneu and C.H. de Novion Laboratoire des Solides Irradk, CEAICEREM-Ecole Polytechnique, 91 128 Palaiseau Cedex, France

NiC Cl “, and NbO,, o2 single crystals have been studied in a quenched state, with polarized neutrons for NiC,, uI. A non-linear model was used to obtain the large static displacements (and magnetic perturbations for Ni-C) on four atomic shells around an interstitial. No short-range order between interstitials could be observed.

1. Introduction

Interstitial metalloid atoms induce important modifi- cations of mechanical, electrical and magnetic prop- erties of metals. We know that atomic displacements in the interstitials neighbourhood are very large, but few experimental studies of local atomic arrangements are available.

Two interstitial solid solutions have been studied by elastic neutron diffuse scattering: a face-centered cubic (FCC) Ni-C(1 at%) sample and a body-centered cubic (BCC) Nb-O(2 at%) sample. Polarized neutron technique was used for the ferromagnetic Ni-based

sample, to determine also the magnetic disturbance induced by the atoms, and because of the high inco- herent cross-section of nickel (eliminated by taking the difference between the intensities obtained with neu- tron spins up and down).

2. Experimental

The FCC Ni-C(1 at%) single-crystal was grown from the Ni(C) alloy by the Bridgman method by Mr. Perrier de la Bathie (CNRS-Grenoble, France).

The BCC NbO, single-crystal (with c = 2.3 ? 0.2% from the lattice parameter increase) has been pre- pared from a Nb single-crystal of nominal purity 99.999% (Goodfellow Metals Ltd-Cambridge). This sample was oxidized at 1050°C in a dynamic pressure of 2 x 10e4 Torr of oxygen for 30 h, homogenized at 1450°C in a 5 x lo-’ Torr vacuum for 60 h, and then quenched from 1050°C.

Measurements have been made in the (1 i 0) re- ciprocal plane on two-axis spectrometers of Laboratoire L&on Brillouin’ (CEN-Saclay, France).

NbO, 02 was measured at room temperature on the G4-4 spectrometer with time-of-flight analysis (A = 2.56 A). Data were corrected for background and calibrated with a vanadium standard. NiC, 0, was mea- sured at 15 K on the G6-1 spectrometer with a polar-

‘Laboratoire commun CEA-CNRS.

ized neutron beam (A = 4.732A). Data were calib- rated by the incoherent scattering of nickel.

3. Model

Because of the very large distortions around the impurities, the attempts to use the classical linear developments of the scattering intensity as a function of these displacements were unsuccessful for the two samples.

With the following assumptions: _ the defects are located on the octahedral sites, _ they are isolated (not interacting) so that the diffuse

intensity is I = N,J, where N, is the number of defects and I, the intensity due to one interstitial,

- the distortions around the defects keep the sym- metry of the site

- only three or four atomic shells around the defect are perturbed,

_ in the Ni-C case, the magnetic moment on the carbon is zero (from hyperfine field measurements

[II)> formulae can be derived for the diffuse intensity [2,5]. The intensity is a non-linear function of the positions of the atoms in the first shells around the defect and of the magnetic moment on these atoms (in the Ni-C case). These parameters are obtained from a non-

linear least-squares fit.

4. Results

Ni-C: the intensities have been measured in the domain 11q11 < 1.2 x 27rla of the (1 70) reciprocal plane. A local maximum is observed in the (1 1 1) direction and a minimum in the (1 10) direction.

Three perturbed shells have been considered around the impurity. The results are reported in table 1:

the magnetic perturbation contribution is important -( h h‘- q t e c 1 s uare value is strongly increased when this

effect is neglected as was done by Livet [3] in a similar measurement on a polycrystalline sample),

0921-4526/92/$05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved

P. Barb&s et al. I Diffuse neutron scattering by interstitials 829

Table 1 Ni-C(l%). Magnetic perturbations +(/I kl) (in pB units)

for Ni-C, static displacements 6r(h k I) (in A) and relative

ehi-square x2 for NE,, “, and NbO, o2 fits. h k 1 are given in

ai2 units (a: lattice parameter). Values followed by* are imposed during fits.

W100) 0* -0.19 s/-Q1 11) 0* -0.06 &(2 10) 0’ -0.06

SScL 0* -3.1

Sr(lO0) 0.50 0.55 6r(l 11) -0.03 -0.03 ar’(2 10) 0.05 0.05 6r’(2 10) 0.05 0.08

X 0.52 0.16

_ the global magnetic perturbation calculated from our results is in good agreement with the measured value -3pJat C [4].

-the static displacements are not sensitive to the fit conditions. The first one is very strong. Nb-0: the experimental intensity map after inelas-

tic scattering elimination is given in fig. la. The diffuse intensity is concentrated on a diffuse maximum at 413 (1 1 1) and around the Bragg peaks. A deconvolution method has been developed [5] in order to improve the accuracy of -the time-of-flight separation of low- energy inelastic scattering processes occurring near the

Bragg peaks. The diffuse maxima at (1 0 0), (1 f 0) and (10 0)

attributed by de Novion et al. [6] to short-range order between oxygen atoms are not observed here. Thus we applied the same model as in the Ni-C case, assuming that interstitials are isolated (§3). The static displacements obtained for three and four perturbed shells around the defect are given in table 2, together with those determined by Dosch et al. [7] from a neutron scattering measurement at higher 11q11 values, analyzed within a Kanzaki force model. The displace- ments are somewhat smaller but very similar to theirs, though the harmonic assumption, which is the basis of the Kanzaki model, is not clearly justified with such distortions.

Table 2 Nb-0(2%). For text see table 1.

6r(O 0 1)

Sr(1 IO)

6r’(2 10)

W(2 10) W(2 11)

W(2 1 1)

XZ

3 shells 4 shells

0.29 0.32 -0.04 -0.04

0.01 0.01

0.04 0.04 0* 0.03 0* 0.03

0.23 0.16

Dosch et al.

0.42

-0.09

0.03

0.05

0.06

0.03

2

h,

1

0

2

h3

1

0

,

-1 0 1 h, = h 2

Fig. 1. Elastic diffuse-scattering in Laue units (1 Laue = cb:) on NbO,,.,,z in the (1 10) reciprocal plane. h,, hz, h, coordi- nates are given in (2ala) units. (a) experimental, (b) calcu-

lated.

The intensity map calculated from the fit parameters of the four shells model is reported in fig. lb. The diffuse intensity far from the maxima is well repro- duced, but the limited range of the interaction (four shells) does not allow us to explain the narrow maxi- mum in $ (1 1 1) also observed by Rowe et al. [8].

5. Conclusion

Two interstitial solid solutions have been studied

(NiC0.0, and NbO 0 ,,). In both compounds, nearest neighbours are widely displaced away from the ideal site and the usual approximations are not justified. The values obtained in our model for the first displace- ments around the defect are probably more reliable than that deduced from other methods, because no assumption is made about the amplitude of these displacements.

The large magnetic perturbation induced by carbon in nickel has been determined for the first four neigh- bour shells, and is in good agreement with the total magnetization variation measured by Cadeville et al.

[41. No chemical order between atoms was evident.

830 P. Barb&is et al. I Diffuse neutron scattering by interstitials

Acknowledgements

We wish to thank Dr. M.C. Cadeville (IPCMS- Strasbourg) who gave use the Ni-C single crystal, and the staff of the G6-1 spectrometer (Laboratoire LCon Brillouin, CEN-SACLAY, France).

References

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to be published.

[3] F. Livet, Ph.D. thesis, Institut National Polytechnique de

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