Nuclear Instruments and Methods in Physics Research A234 (1985) 495-497 495 North-Holland, Amsterdam

D E T E R M I N A T I O N O F T H E C O H E R E N T S C A T I ' E R I N G L E N G T H O F C A R B O N U S I N G N E U T R O N INTERFEROMETRY

Andreas K. F R E U N D a), Ulrich K I S C H K O ,.a), Ulrich B O N S E b) and Thomas W R O B L E W S K I a.b)

a) Institut Max yon Laue-Paul I..angevin, BP 156, F-38042 Grenoble C~dex, France b) lnstitut fftr Physik, Universiti~t Dortmund, Postfach 50 0500, D-4600 Dortmund 50, Fed. Rep. Germany

Received 9 August 1984

Highly oriented pyrolytic graphite samples were used for determining the coherent scattering length of the bound carbon atom by means of neutron interferometry. The value of 6.647 + 0.005 fm agrees well with results obtained by various other techniques.

1. Introduction

Neutron interferometry [1] is the most direct method amongst the various techniques permitting a precise measurement of coherent scattering lengths [2]. One condition for the applicability of this method is sample homogeneity. If density fluctuations exist in the sample, for instance produced by dislocations or precipitates of impurities, phase incoherence occurs which may strongly affect and even completely destroy the interference pat- tern. This happened when trying to determine the coherent scattering length, b c, of carbon using polycrys- talline graphite samples [3]. The same type of samples had been studied earlier in transmission experiments [4,5]. Despite the density fluctuations of about 0.5% rather accurate values for be were reported [4]. These values and the most precise experimental result ob- tained by means of a gravity refractometer [6] are given in table 1. The latter technique used various liquids containing carbon, hydrogen and chlorine and derived b~ for these elements from the measured scattering lengths of the liquids. Besides these experiments on the natural isotopic composition, the coherent scattering lengths of t2C and 13C were determined separately using the Christiansen filter technique and a mixture of crystalline powder and a liquid [7].

In principle, neutron interferometry yields compara- ble accuracy as already demonstrated for other elements [1]. The aim of the present investigation was to de- termine b c of carbon using samples of well known defect structure and to complete results obtained by other methods studying different forms and compositions of the sample. Phase incoherence can be substantially re-

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duced using highly oriented pryolytic graphite (HOPG) which is a pseudocrystalline form of carbon [8]. This material is already well known as a highly efficient neutron monochromator [8,9] and can be obtained in several qualities.

2. Sample characterization

The HOPG material supplied by Union Carbide Inc., Parma, Ohio, is classified according to the ap- parent mosaic spread, ~8, measured with neutrons. We have controlled the mosaic spread of 6 top quality (ZYA grade) monochromators, 4 medium (ZYB) and 6 low grade (ZYD) samples using a double-crystal dif- fractometer [10] and neutrons with a wavelength of 2.4 ,~. The results agreed with the specifications quoted by the manufacturer, namely 0.4 + 0.1 °, 0.8 + 0.2 ° and 1.2 + 0.2 °, respectively. However, the true mosaic spread, % which is an intrinsic crystal property and always smaller than fl, has to be measured under nearly extinc- tion-free conditions, and this was done by means of -f-ray diffractometry [11-13]. The mean values of ,/were 0.30 ° for ZYA, 0.43 ° for ZYB and 0.62 ° for ZYD grade material. Both absolute reflectivities for neutrons and details of ,/-ray rocking curves showed that five of the fourteen samples were inhomogeneous with respect to their defect distribution.

Three samples were chosen for the interferometric study: sample A was top grade material, sample D was homogeneous like sample A but of lower quality, and sample B was intermediate in quality but inhomoge- neous. The layer spacing, d, of these samples was de- termined using Cu K a X-rays and a modified version of Bond's method [14] where the angle between two sym- metrical crystal positions with respect to the well-col-

496

Table 1 Coherent scattering length

A.K. Freund et al. / Coherent scattering length of carbon

for the bound carbon atom after ref. [2] and the result of the present work.

Year Method Sample Result (fm)

1947 transmission powder 6.7 1951 Bragg diffraction powder 6.4 + 0.2 1967 gravity refractometer liquid 6.648 +0.004 1971 gravity refractometer liquid 6.648 ±0.003 1971 transmission [4] powder 6.648 +0.005 1971 transmission [5] powder 6.648 ±0.004 1975 gravity refractometer [6] liquid 6.6484 ± 0.0013 present interferometry HOPG 6.647 ± 0.005

limated X-ray beam was measured. These experiments and the interferometric studies were both performed at a temperature of 22°C. The results of the ~,-ray and X-ray experiments are given in table 2. They show that there is no measurable increase in the layer spacing with mosaic spread ~, for samples A and B while a factor of 2 in "t corresponds to a change of 0.0015 + 0.0002 ,A in d. The ideal d-spacing at 20°C for samples without disorder is between 3.353 and 3.354 ,~ [8]. From a relation given in ref. [15]

d = 3,353 + 0.425 A~2(A ) (1)

we can calculate the mean-square displacement A22 of adjacent layers parallel to the layer planes. The results are A22 = 2.3 X 10 -3 for samples A and B (mean value) and 5.8 × 10 -3 for sample D, respectively, after correc- tion for thermal expansion taking A d / d = 2.5 X 10-5/°C. Similar values for this mean-square displace- ment have been observed in neutron backscattering experiments [16].

Because the lattice disorder expands the layers mainly in the direction of the c axis while the lattice parameter a is practically not affected, it is possible to determine the density, p, of the samples:

p d = 2 A c / A a 2 sin 60 °, (2)

where A c is the atomic weight of carbon and A is Avogadro's number. Values of 12.011 for A c and of 2.4619 A for a have been used for calculating the densities given in table 2. They agree with results from

macroscopic density measurements on top grade HOPG [17].

3. Interferometer experiments

The three HOPG samples were studied on the inter- ferometer of the Institut Laue-Langevin, Grenoble. De- tails of the interferometer and the experimental method are described elsewhere [18,19]. Only 8 h measuring time was needed for obtaining a statistical error smaller than the systematic errors. Interferograms with and without the sample (A) are shown in fig. 1. The results for be and for the contrast are given in table 2. Three measurements on sample D gave a reproducibility of the b c values better than + 0.0002 fm or a relative error of 3 × 10 -5 due to statistics.

The systematic errors were mainly due to the limited accuracy of the values for the wavelength of 1.8389(6) ,A and for the sample thickness. The corresponding rela- tive errors were 3 x 10 -4 and 5 × 10 -4, respectively. The errors in Ac and in p and also the correction for the impurity content of the samples were much smaller than the errors given above. The weighted mean of all results for the three samples and the errors given above lead to a value of 6.647 + 0.005 fm for the coherent scattering length of the bound atom. This value agrees with the results reported in ref. [2] and its accuracy is compara- ble to that obtained by other methods except the gravity refractometer [6]. The fact that the contrast for the

Table 2 Experimental results for the three graphite samples.

Sample A B C

Thickness (#m) 1746 + 1 1387 + 1 y (degree) 0.29 + 0.01 0.38 + 0.01 d (,/k) at 22°C 3.35418 + 0.00005 3.35414 + 0.00010 p (g/cm 3) at 22°C 2.2655 +0.0001 2.2656 +0.0001 Contrast (%) 19.8 4.4 b c (fm) 6.647 6.650

2018 + 1 0.77 +0.02 3.35563 + 0.00010 2.2645 + 0.0001

21.4 6.647

A.K. Freund et al. / Coherent scattering length of carbon 497

4.0

34

8 2.8

C

8 22

x

1.6 -I

a I

I !

t .8 -0.3 0.2 0.7 A t (ram)

1,2

Fig. 1. Pair of interferograms in the H-beam obtained by shifting the sample alternatively in and out of the beam. (a) without sample. (b) HOPG sample (A) in the beam. The phase difference of nearly ~r due to the sample is deafly visible. At is the difference between the two neutron path lengths in the interferometer [1].

samples A and D was the same whereas a much smaller contrast was observed for sample B indicated that phase incoherence was produced by an inhomogeneous defect distribution while uniform lattice disorder had not ob- servable effect, at least for the quality of the material studied. As expected the result for b c is independent of the contrast and hence of the amount and distribution of defects. On the other hand, the samples must be carefully characterized with respect to density. Assum- ing the same density for samples B and D would have introduced a systematical error of 0.003 fm in b c.

4. Conclusion

The availability of carbon in the form of HOPG permitted to determine the coherent scattering length of the carbon atom by means of neutron interferometry. The experimental error was similar to that of other techniques and mainly limited by the accuracy of sam- ple thickness and neutron wavelength. While the latter,

with present techniques, can be determined to better than 4 × 10 -5 [1], the definition of sample thickness is much harder to improve. The value be = 6.647 + 0.005 fm agrees well with results from other work. It was shown once more that sample homogeneity is important for taking full advantage of interferometry as a rapid, accurate and rather simple technique for the determina- tion of neutron scattering lengths.

This work was supported by the Bundesminister fi~r Forschung und Technologie, Bonn (03-B56A01-9) which is gratefully acknowledged.

References

[1] W. Bauspiess, U. Bonse and H. Rauch, Nucl. Instr. and Meth. 157 (1978) 495.

[2] L. Koester and H. Rauch, Summary of Neutron Scattering Lengths, Report 2517/RB, IAEA, Vienna (1981); L. Koester, in: Neutron Interferometry, eds., U. Bonse and H. Rauch (Clarendon Press, Oxford, 1979) p. 195.

[3] W. Bauspiess, private communication. [4] W. Dilg and H. Vonach, Z. Naturforschung 26a (1971)

442. [5] T.L. Houk, Phys. Rev. C3 (1971) 1886. [6] L Koester and W. Nistler, Z. Phys. A272 (1975) 189. [7] L. Koester, K. Knopf and W. Waschkowski, Z. Phys.

A292 (1979) 95. [8] A.W. Moore, Chemistry and Physics of Carbon, vol. 2

(Dekker, New York, 1973) pp. 162-187. [9] A. Freund and B. Forsyth, Treatise Mater. Sci. Technol.

15 (1979) 471. [10] A. Boeuf, G. Gobert and F. Rustichelli, Nucl. Instr. and

Meth. 124 (1975) 533. [11] J. Schneider, J. Appl. Cryst. 7 (1974) 541. [12] J. Schneider, J. Appl. Cryst. 7 (1974) 547. [13] A. Hamwi, P. Touzain, L. Bonnetain, A. Boeuf, A. Freund

and C. Riekel, Mater. Sci. Eng. 57 (1983) 161. [14] W.L. Bond, Acta Cryst. 13 (1960) 814. [15] W. Ruland, Chemistry and Physics of Carbon, vol. 4

(Dekker, New York, 1968) p. 1. [16] A. Heidemann, unpublished. [17] A.W. Moore, A.R. Ubbelohde and D.A. Young, Proc.

Roy. Soc. (London) A280 (1964) 153. [18] W. Bauspiess, in: Neutron Interferometry, eds., U. Bonse

and H. Rauch, (Clarendon Press, Oxford, 1979) p. 76. [19] U. Bonse and U. Kischko, Z. Phys. A305 (1982) 171.