Anisotropy of the K absorption in gallium single crystals

Weber, W. M. 1962

ANISOTROPY

Physica 28 689-694

OF THE K ABSORPTION SINGLE CRYSTALS

IN GALLIUM

by W. M. WEBER NatuurkundigLaboratoriumder Rijksuniversiteit,Groningen,Nederland.

synopsis The orientation of the crystallographic axes of a thin single crystal of gallium being determined, the gallium K absorption spectrum was photographed for two different orientations of the absorber with respect to the incident X-ray beam. A more pronounced fine structure was observed when the c-axis of the single-crystal absorber and the X-ray beam were parallel. Another single crystal of gallium gave the same result.

9 1. Introduction. Kronig’sr) theory of the extended X-ray fine structure predicts a dependence of this structure upon the direction of the incident X-ray beam with respect to the crystallographic axes of a single crystal. This dependence is expected to be even more pronounced if the X-rays are polarized. Early photographs of the gallium K absorption region, taken by us with a solidified gallium foil as an absorber and using only weakly polarized X-rays, showed changes in the fine structure after successive recrystallisations. So it was suggested that the X-ray absorption is anisotropic if the gallium absorber becomes anisotropic. In order to obtain a decisive answer, two thin single-crystal plates of gallium were prepared, which could be used as absorbers. After determining the orientations of the crystallographic axes of these foils, the K absorption spectra were photographed for each of them, the X-rays again being only weakly polarized. $2. PreParation of the gallium single-crystal foils. A sheet of “melinex” polyester film was sandwiched between two solid perspex plates which could be pressed together. In the centre of the film a piece of 4mm x 12mm was cut out so as to provide space for the gallium foil to be prepared. The thickness of the melinex film amounted to 15 lo,,the desired thickness of the gallium foil. A cylindrical hole drilled through the upper perspex plate ends in the hole in the melinex film; at this entry its diameter was 0.1 mm. The system could be heated uniformly; a small hole in the perspex plates contained a thermistor for measuring the temperature (fig. 1). When the temperature was about 31°C (the melting point of gallium -

689 -

690

W.

M. WEBER

being 29.8”(I), some gallium metal (taken from the same stock as beforez) was inserted in the hole in the melinex film. When the perspex blocks werpressed together carefully, the liquid metal filled the hole and the cana completely, the excess of gallium escaping through the latter. Then thl temperature

was lowered

about

1°C below the melting

point

of gallium

whereafter the supercooled metal was contacted with a single crystal o gallium to initiate solidification. The process of solidification was perceptibll by a change in colour. The single-crystal properties of the samples were checked by taking Laue diagrams of several parts of these samples*).

ut 0

Fig.

1. Perspex

single-crystal

plates

with

1

2cm

melinex

film

used for

the preparation

foils. A 15 p melinex film with hole B; C perspex plates; hole in upper plate; E hole for thermistor.

of the

galliun

U cylinclrica

5 3. Determination of the crystallographic axes. Two gallium single-crysta: foils, 13 and 16 p thick, have been examined for the orientation of their crystallographic axes by means of X-ray diffraction*). A preliminary survey could be obtained by fixing the sample on the rocking head of a Weissenberg goniometer and making a Laue diagram on a cylindrical fila with a tube fitted with a molybdenum target and operated at 50 kV. On the developed film the main zones could be distinguished readily and a chosen zone-axis could be brought roughly parallel to the incident X-ray beam by means of the rocking head arcs and the rotation axis of the goniometer. Then the cylindrical film was replaced by a flat film perpendicular to the collimator, so that any symmetry plane through the axis could be observed readily. This procedure was repeated until the three different axes of the orthorhombic crystal, characterized as the intersection of two symmetry planes, had been brought parallel to the X-ray beam. The axes were identified by making oscillation photographs with the copper Kcc radiation from another X-ray tube and measuring the transIation periods. It was striking that the intensity distribution of the spots on the Laue *) These checks and determinations were kindly performed by Professor Mr. K. Yntema of the ,,Instituut voor Kristalfysica der Rijksuniversiteit”, diffraction photographs and interpreting them.

W. G. Perdok and Groningen, taking

ANISOTROPY

OF THE

diagram of the metrically

K ABSORPTION

IN GALLIUM

pseudo-tetragonal

SINGLE

691

CRYSTALS

c-axis showed a complete

lack

of tetragonal symmetry. In fig. 2 we indicated the orientations of the crystallographic axes with respect to the plane of the foil. The normal to the plane of the foil is taken as the Z-axis. The 13 p foil has its largest dimension (12 mm) in the direction of the X-axis, whereas the 16 p gallium foil has its largest dimension in the direction of the Y-axis. The crystallographic c-axis forms an angle 6 with the Z-axis, the C.&plane makes the angle 7 with the ZY-plane. The crystallographic ab-plane, perpendicular to the c-axis, intersects the XY-plane along line s (perpendicular to line I). The u-axis (or the b-axis) forms an angle y with line s.

perpendicuhr

to

c-a?% I

ct

X

Fig.

2.

Orientation of the crystallographic axes in the 13 and 16 p gallium single-crystal foils. Explanation in the text.

In the 13 p. gallium foil 6 = 26”, 7 = 0” and y = 82”. In the 16 p foil we have 6 = 16”, q = 13” and y = 39”. 3 4. Spectrographic equipment. The absorption spectra of the 13 p gallium foil were taken with the same X-ray tube and spectrograph as described befores), whereas the spectra of the 16 p foil are obtained using a sealed-off Philips tube, type 25295/32, fitted with a molybdenum target. To the X-ray tube a d.c. voltage of 20 kV was supplied (ripple 6%). Filament current as well as high voltage were stabilized within 1oh against slow fluctuations. In both tubes the line focus itself served as a slit, the apparent width being 0.1 mm in both cases. At a distance of 35 mm from the focus a 0.8 mm wide slit Iimited the beam aperture. The absorber was placed close behind this slit.

692

W. M. WEBER

The dispersion amounted to 2.56 XII/mm film between 1150 and 1200 XU. The spectrograph could be adjusted by means of a NaI(T1) scintillation counter with a 0.1 mm wide slit. The photographic material was Ilford Ilfex film, doubly coated. In order to reduce the effect of scattering, all photographs were taken with a 10 lo aluminium foil in front of the film. 9 5. Photographs and results. Before photographing the I< absorption region for each of the gallium single-crystal foils, the homogeneity and reproducibility of the continuous radiation were accurately checked. The absorption spectra were taken at two different orientations of the absorber with respect to the incident X-ray beam. Either the beam traversed the foil in the direction of the c-axis, or the beam passed the foil in a direction making the angle 6 with the Z-axis and the angle 26 with the c-axis. In the latter case the beam was parallel with the direction I in fig. 2, in the former case the beam was parallel with the direction II (direction of c-axis). In both cases the traversed foil thickness was the same (inversely proportional to cos 6), so that for a given foil the photographed spectra I and II were directly comparable. a) For the photographs a1 and aI1, taken with the 13 p foil (7 = O”) as an absorber, the X-axis (direction of largest dimension) was parallel with the (vertical) line focus of the X-ray tube (the X-axis pointing upwards) and the X-ray beam directed in the positive I and II direction. In both cases the tube current was 18 mA and the time of exposure 15.5 hours. GALLIUM K edge

a

f LOO

Fig. 3. Microphotometric crystal

records

1 300

1 200

of the gallium

I 100

, 0 ev

K edge, taken

with

the

13~ single-

foil. Curve I : angle between X-ray beam and normal to plane of foil 25”, angle between beam and c-axis 50”. Curve II : X-ray beam and c-axis parallel.

Microphotometric records, indicated as a1 and aI1, are shown in fig. 3. It is evident that in the region between 80 and 300 eV from the edge the fine

ANISOTROPY

OF THE

K ABSORPTION

IN GALLIUM

SINGLE

CRYSTALS

693

structure is more pronounced in case II (c-axis parallel to incident beam) than in case I. At a distance of 184 eV from the edge the lead Lai emission line (2 = 1172.7 XU) appears ; this is caused by the presence of some metallic lead in the X-ray tube. In order to check the reproducibility, simultaneous photographs were taken with an additional aluminium absorber 116 p thick, placed as a horizontal strip in front of the film and covering one third of the total height. This aluminium foil reduces the intensities in our wavelength region by a factor of about two. Comparison of the microphotometric records with a1 and a11 showed that the reproducibility was perfect. Another pair of gallium K spectra, taken with the X-axis of the absorption foil perpendicular to the line focus (the Y-axis pointing downwards), was again identical with the pair a1 and aI1. GALLIUM K edge

b

r

I

500

400

300

200

I

100

I

0 ev

Fig. 4. Microphotometric records of the gallium K edge, taken with the 16~ singlecrystal foil. Curve I : angle between X-ray beam and normal to plane of foil 16’, angle between beam and c-axis 32”. Curve II : X-ray beam and c-axis parallel.

b) The two photographs b1 and bI1 have been taken with the 16 p gallium foil and another X-ray tube. The foil was placed so that the Y-axis (direction of largest dimension) and the line focus of the X-ray tube were situated in one plane, the Y-axis pointing downwards. The tube current was 27 mA and the exposure time 16 hours; we have taken the blackening on the film somewhat greater in these two photographs. Microphotometric records are shown in fig. 4. It is evident that in bI1 (c-axis parallel to incident beam) the fine structure is more pronounced, in accordance with the results for the 13 lo,gallium foil.

694

ANISOTROPY

OF THE

K ABSORPTION

IN GALLIUM

SINGLE

CRYSTALS

Acknowledgements. The author is much indebted to Professor H. Brinkman for his interest in the work and for the excellent experimental facilities offered in his laboratory. This investigation forms part of the research program of the “Stichting voor Fundamenteel

Onderzoek

der Materie

supported by the “Nederlandse Onderzoek (Z.W.O.)“.

Organisatie

(F.O.M.)“,

Received 17-4-62

1) Kronig, 2) Weber,

R., Z. Phys. 70 (1931) 317; 75 (1932) 191, 468. W. M. and Brinkman,

which is financially

voor Zuiver Wetenschappelijk

H., Physica 2.5 (1959) 633.