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An experimental determination of the Debye-Waller factor for iron by neutron diffraction

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1979 J. Phys. C: Solid State Phys. 12 L651

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J . Phys. C : Solid State Phys., Vol. 12, 1979. Printed in Great Bri tain. @ 1979

LETTER TO THE EDITOR

An experimental determination of the Debye-Waller factorfor iron by neutron diffractionS K MohanlalSchool of Physics, Madurai K amaraj University, M adurai-625 021, India

Received 30 May 1979

Abstract. An accurate powder neutron diffraction study of iron is reported. Good agreementbetween the observed and calculated structure factors was found when magnetic formfactorsof C G Shull and Y Y amada were used in the analysis of the experimental data. A least-squares refinement of the data at room temperature gave a value B,, =035 *0.04A2,whereB is a constant in the Debye-Waller factor exp[-B(sin2 @/A2].An accurate neutron diffraction measurement of an iron powder sample was carriedout at room temperature (300K). The instrument used for this purpose was the PND(powder neutron diffraction) spectrometer of John Curran Ltd, Cardif

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L652 Letter to the EditorTable 1.Reflection Bragg Nuclear Magnetich k l angle contribution contribution1 1 0 17.81" 3.686 0.5182 0 0 25.63" 3.686 0.2082 2 0 31.72" 3.686 0,0423 1 0 43.15" 3.686 0.0242 2 2 48.52" 3.686 00123 2 1 54.02" 3.686 0007

Theoretical structure factors F , were calculated from a model with only the scalefactor and the temperature factor B as refinable parameters. A least-squares refinementwas carried out comparing the calculated intensity with the observed intensity. Althoughall the seven reflections, possible within the angular range specified earlier, were measured,one reflection, namely the 211 reflection, had to be deleted in the refinement due touncertainty in the correct measurement due to the short-period reactor tripping duringthe recording of this particular peak. The refinement of the experimental data yielded avalue for the Debye-Waller factor of B,, =0.35 L 0-04A'. Good agreement betweenFo and F ,, and the estimated discrepancy index for the data

indicate the reliability of the data (see table 2).Another independent set of intensity data for the same sample were collected for aneutron wavelength of 0.82A. These measurements were carried out using a differentinstrument, a DCD spectrometer, originally used for single-crystal measurements butmodified for the present polycrystalline measurements. However, the data were foundtobeof poor quality and hence not reported.Table 2. Agreement between calculated and observed structure factors.h k l F , Fo1 1 0 16.83 16.992 0 0 8.32 8.402 2 0 869 8.383 1 0 11.42 11.532 2 2 6.3 1 6.2 13 2 1 15.18 15.53

Previous experimental values of the Debye-Waller factor for iron have been reviewedby Sirota (1969), according to which the thermal factor obtained from x-ray powdermeasurements are in the range of 0-31 to 0.36A'. In their x-ray work for the purpose ofdetermining the outer electron configuration in single crystals such as iron, Weiss andDe Marco (1958) made use of the Debye characteristic temperature OF,=430K , avalue obtained from specific heat measurements. This corresponds to B =0.33A'.The author would like to thank ProfessorK S Chandrasekaran for suggesting this workand for valuable discussions. The author is grateful to the Bhabha Atomic Research

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Letter to the Editor L653Centre, Bombay and in patricular to Dr R Chidambaram, Dr A Sequeira and DrMadhavrao for providing the facilities as well as for helpful discussions on the analysisof the experimental data. The financial assistance offered by the University GrantsCommission under the UGC National Associateship Scheme is appreciated.

ReferencesChipmanD R and Paskin A 1959 J . Appl. Phys.30 1998Shull C G and Y amada Y 1962 . Phys. Soc. J apan 17 suppl. B I11 1-6SirotaN N 1969Acta Crystall ogr. A 25 223Weiss R J andDeMarco J J 1958Rev. Mod. Phys. 30 59