SPIN DENSITY DISTRIBUTION IN PARAMAGNETIC γ-OXYGEN

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SPIN DENSITY DISTRIBUTION IN PARAMAGNETIC γ-OXYGEN

D. Cox, E. Samuelsen, K. Beckurts

To cite this version:

D. Cox, E. Samuelsen, K. Beckurts. SPIN DENSITY DISTRIBUTION IN PARAM- AGNETIC γ-OXYGEN. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-582-C1-584.

�10.1051/jphyscol:19711201�. �jpa-00214026�

JOURNAL

DE PB'ESIQUE Colloque C 1 , supplkment au no 2-3, Tome 32, Pe'vrier-Mars 1971, page C 1 - ⁵⁸²

SPIN DENSITY DISTRIBUTION IN PARAMAGNETIC %OXYGEN (*) D. E. COX, E. J. SAMUELSEN (**), and K. H. BECKURTS (***)

Brookhaven National Laboratory, Upton, New York 11973, U. S. A.

Rbum6. - La diffusion magnetique des monocristaux d'oxygtne en phase cubique y a kte BtudiQ au moyen de neutrons polarises dans un champ magnetique de 80 kOe. Les rapports de polarisation observes ont Bt6 corriges des effets d'extinction. D'une manihre geneale, ils difftrent de I'unitB de quelques pour cent. Le facteur de forme magnetique est caracteristique d'une distribution de densite de spin non sphkrique. La structure cristalline a egalement kt6 precisCe au moyen de la diffraction nuclkaire.

Abstract. - Polarized neutron measurements of the magnetic scattering from single crystals of cubic

have been made in an applied field of 80 kOe. The observed polarization ratios were corrected for extinction effects and were typically different from unity by a few per cent. The magnetic form factor shows large deviations from sphericity. Nuclear data were also obtained and the crystal structure refined.

1. Introduction. - Although spin density distri- butions have been determined for a number of transi- tion and rare earth metals and compounds by neutron diffraction techniques, no detailed studies of the com- paratively small group of materials containing unpai- red p electrons have been made. The simplest example of this type is the element oxygen, and of added inte- rest is the fact that it is molecular rather than atomic orbitals which must be considered.

A detailed neutron diffraction investigation of 0, is complicated by the fact that there are two structural transformations, which are associated with changes in the amount of molecular disorder present. At atmospheric pressure, the cubic y-phase is stable from the melting point at 54.40K down to 43.8 OK. At this point there is a transformation to the rhombohe- dral /3-phase, followed a t 23.9 OK by another to the monoclinic a-phase. These transformations are accom- panied by a discontinuous decrease in the magnetic susceptibility by a factor of about two in each case [I, 21.

Recent powder neutron diffraction measurements have established that a-0, is magnetically ordered at 4.2 OK, and that short range order is present in the p-phase a t 27 OK [3]. The magnetic structure at 4.2 OK consists of oppositely directed moments in the corner and face-centered positions of the monoclinic cell [4,5].

The present paper is a preliminary account of a detailed study of the magnetic scattering from the cubic y-form of the element by means of the polarized neutron technique. This was made feasible by the development of a split-coil superconducting magnet and dewar system capable of producing a field of about 90 kOe and of allowing the sample temperature to be held at any point between room and liquid helium temperatures [6]. A second factor was the discovery that large crystals about 1.5 cm in diameter and length could be grown very readily.

2. Crystal Structure. - The crystal structures of y-O2 and isostructural P-F, have been investigated

with X-rays quite recently by Jordan et al. [7-91.

The space group chosen is Pm 3 n, with eight mole- cules in the unit cell. The molecules are centered at the 2(a) : 0, 0, 0 and 6(d) : $, 4, ⁰ positions, which have point symmetries m3 and Z2 m respectively.

In both elements there is considerable rotational disorder, but the exact nature of this was not esta- blished. Several models were tried, but the data did not allow a clearcut choice to be made. However, the basic picture is one of spherical disorder in the 2(a) sites and an oblate spheroidal electron distribution in the 6(d) sites, as indicated in figure 1.

y - OXYGEN

FIG. I. -The crystal structure of

projected on (001) as proposed by Jordan et al. 171. Molecules at the 2(a) sites at ^0,

0,0 are depicted by shaded circles and are spherically disordered.

Molecules at 6(d) sites at

4, 0 show an oblate spheroidal electron density distribution. Small numerals denote height.

above the plane.

(*) Work performed under the auspices of the ^{U. S.} Atomic Energy Commission.

(**I Guest, now returned, from Institutt for Atomenergi, Kjeller, Norway.

(***I Guest, now returned, from Kernforschungszentrum, Karlsruhe, Germany.

Since the polarized beam technique requires an accurate knowledge of the nuclear structure factors, a neutron diffraction refinement. of the structure of

y - 0 , was carried out with unpolarized neutrons of

wavelength 1.03 A. Gaseous oxygen of better than

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711201

SPIN DENSITY DISTRIBUTION IN PARAMAGNETIC y-OXYGEN C 1 - ⁵⁸³

99.99 % purity was condensed into a cylindrical A1 sample tube 3 mm in diameter. A number of crystals were grown by melting and annealing at 46. OK, in the course of which two were studied. These were about 1 cm long and grew with their [loo] and [I101 axes respectively roughly parallel to the long axis of the sample holder. A total of 40 independent reflec- tions were measured in the two zones. Least squares refinement of the data revealed that of the various models considered in the X-ray study, model Ff [9], in which there is spherical disorder at the 2(a) sites and statistical disorder in general positions around the 6(d) sites, x, y, z (x = 0.239 6, y = 0.528 5, z = 0.082 0) with isotropic temperature factors of 8.1 A2 and 7.9 A2 respectively, gave significantly the best agree- ment (R factor = 3.7 %). In this model, the mole- cular bond length is not constrained, but the value obtained, 1.18 A, is quite close to the actual value of 1.207 A.

3. Polarized Beam Measurements. - A number of crystals were grown in a cylindrical A1 holder about 1.5 cm in diameter as described above. In most cases, this procedure yielded one large crystal in the 314 wide region between the coils accessible to neutrons, although a second smaller specimen was also obtained occasionally. No particular orientation appeared to be favored. Unfortunately, a large crystal never grew with its [loo] or [I101 axis close enough to the vertical for reflections in these zones to be measured. One drawback was the fact that the dewar assembly could not be tilted more than 50 for mechanical reasons.

In all, data were collected from nine different crystals.

Measurements were made at 46% in a field of about 80 kOe with a beam of wavelength 1.18 A

from a C O ~ . , ~ F ~ , ~ ~ , monochromator having a pola- rizing efficiency of about 98 %. Polarization ratios were measured for 27 independent reflections, inclu- ding 18 of the first 19. Since it was quite clear from the outset that severe extinction effects were usually present, integrated intensities were measured for the majority of reflections in order to allow for subsequent corrections. In a number of cases either the same reflections from several crystals or equivalent reflec- tions from the same crystal were measured.

For each crystal, least squares refinement of the data was carried out with an extinction correction of the type proposed by Zachariasen [lo]. Quite large

corrections were required for the strong reflections ; for example, values of the observed and corrected polarization ratio for (210) were 1.037 and 1.064 respectively in one typical case. ,Mean values of y, the ratio of the magnetic to nuclear structure factor derived from the corrected polarization ratios are listed in Table I, together with the standard errors.

The internal self-consistency of the data is very good on the whole, as exemplified by the figures for the (210) and (422) reflections given in Table 11.

Fourier sections of the spin density distribution obtained from the data in Table I show clearly an approximately spherical distribution around the 2(a) sites, but a more ellipsoidal distribution around the 6(d) sites. Large deviations from sphericity are also evident from the values of y listed in Table I. Form factor calculations for various models are currently in progress [ l l ] and will be described in a separate publication.

Acknowledgment. - We wish to acknowledge help- ful discussions with F. Leoni and M. Blume, and expe- rimental assistance from F. Langdon.

Observed values of y, the ratio of the magnetic (FM) to the nuclear structure factor (FN) for thejirst 15 peaks of y-0,. Values of FN are in units of 10-l2 cm per unit cell and are calculated for the model described in text.

hkl -

110 200 210 21 1 220 310 222 320 321 400 410 41 1 330 420 421

sin 011 0.104

0.147 0.165 0.181 0.209 0.233 0.255 0.266 0.276 0.295 0.304 0.313 0.313 0.330 0.338

Values of the extinction-corrected polarization ratio (R) measured for several (210) and (422) re$ections from y-0,. Equivalent reflections from the same crystal are listed where measured. Figures in parentheses are standard deviations from counting statistics referred to the least significant digits.

Reflection Crystal

I I1 I11 IV v VII

- - - - - - ^-

210 1.064 (5) 1.064 (10) 1.070 (3) 1.068 (5) - -

1.069 (4)

422 - 1.028 (3) - 1.030 (2) 1.030 (8) 1.032 (5)

1.029 (2) 1.023 (4)

C 1 - 584 D. E. COX, E. 5. SAMUELSEN AND K. H. BECKURTS

References

[I] BOROVIC-ROMANOV (A. S.), ORLOVA (M. P.), and [6] LANGDON (F. T.), to be published.

S ~ E L K ~ V (1P- G-1, Dokl. Akad. Nauk SSSR, [7] JORDAN (T. H.), STREIB (W. E.), SMITH (H. W.), and 1954, 99, 699. LIPSCOMB (W. N.), Acta Cryst., 1964, 17, 177.

[2] KANDA (E.), HASEDA (T.), and OTSUBO (A.), Physica,

1954, 20, 131 ; Sci. Rept. Res. Inst. Tohoku 181 SMITH (H. W.), Ph. D. Thesis, Haward University,

Univ., 1955, 7 , 1. 1966.

[3] COLLINS (M. F.), Proc. Phys. Soc., 1966, 89, 415. [91

(T- H.1, STREIB OI(T. and L J ~ C ~ M B w. ^N.),

[4] ALIKHANOV (R. A.), Zh ETF Pis. Red., 1967, 5,430 ; J. Chem. Phys., 1964, 41, 760.

Engl. Transl. : JETP Lett. 1967, 5 , 349. [lo] ZACHARIASEN (W. H.), Acta Cryst., 1967, 23, 558.

151 BARRETT (C. S.1, MEYER (L.1, and WA~~ERMAN (J.1; [Ill LEONI (F.), private communication.

J. Chem. phys., 1967,47, 592.

Imprime en France.

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NOC. P. P. A. P. 267.41.

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