ELSEVIER Physica B 213&214 (1995) 917 921

PHYSICA[Y

Towards still better monochromators

A. Magerl

Institut Max yon Laue Paul Langevin, B.P. 156 X. F-38042 Grenoble COdex 9, France

Abstract

To date mosaic crystals are mainly in use as neutron monochromators. They are made by plastic deformation of high-quality single crystals. Although this procedure has been applied successfully in numerous cases, it may nevertheless result in an inhomogeneous or coarse microstructure, and the crystals may-not show the expected performance. Recent efforts have concentrated on the creation of structural defects which are defined on a microscopic scale. Various successful approaches e.g. by plastic deformation with locally applied forces, by either static or dynamic elastic bending, or by making alloys of appropriate compositions and thermal treatments are discussed.

1. Introduction

Monochromators are at the heart of neutron instru- mentation in particular for applications in condensed- matter research. Their basic principles are largely understood, at least in a semiquantitative manner. In spite of significant progress achieved in the past it is felt, however, that there are only a few materials which ap- proach the theoretical limits for their performance, whereas most others fall far behind. The manufacture of highly efficient monochromator crystals, i.e. engineering an appropriate mcirocrystalline defect structure, requires skill and imagination. For this reason this presentation is frequently oriented towards applied aspects whereas it is not concerned primarily with diffraction theory.

The major problems to date relate to the question of how a suitable defect structure can be created in real materials either by some kind of plastic deformation or by introducing appropriate defects during the growth process of the material. In many cases it is not obvious what the optimum defect structure should look like to achieve the desired diffraction properties.

A further aspect concerns the availability of large single crystals of sufficient quality. Additionally, it is a non-trivial task to make a homogeneous defect struc-

ture in a large volume of the order of 100 cm 3. A recent example is given by the strong effort to grow large Be single crystals of high structural fidelity, which could be readily transformed into monochromator materials. Un- doubtedly, there has been continuous progress over the years. However, achieving a crystalline quality sufficient for the normal plastic deformation procedure has turned out to be very hard. Therefore, the search for new proced- ures which are less dependent on high perfection of the starting material has become very desirable.

The present paper is not intended to describe the history of the development of monochromators. After some remarks referring to the usual plastic deformation, 1 shall concentrate on some newer procedures while restricting myself to common materials. A key feature is homogeneity. I shall demonstrate on some examples how progress has been achieved in particular areas. I shall not mention here monochromators for polarized beams, or monochromators made from rarely exploited materials like covalent bonded crystals or from exotic materials like isotopic 58Ni.

Beam focusing by crystal optics is also an important issue in the design of monochromators. However, this subject has been treated extensively in arecent workshop and the interested reader is referred to Ref. [1].

0921-4526/95/$09.50 ~ 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 1 9 5 ) 0 0 3 2 2 - 3

918 A. Magerl/ Physica B 213&214 (1995) 917 921

2. Diffraction and crystals

Diffraction is based on Bragg's law

2 = 2dsin 0, (1)

where the interplanar spacing d and the Bragg angle 0 define the reflected wavelength 2. In addition extinction plays an important role. For ideal crystals it increases the reflected bandwidth to a finite but still very narrow wavelength range (typically in the range of A2/2-~ 10-s), which represents an outstanding resolution. However, the intensity contained in this narrow bandwidth is too low for most practical applications.

For this reason defects are introduced which should widen the bandwidth according to the logarithmic deriv- ative of Eq. (1):

A2 Ad : c o t ( 0 ) A0 + - - , (2)

2 d

where Ad and A0 represent uncertainties for the lattice spacing and for the Bragg angle, respectively. A gain factor for the intensity of typically a factor of 100-1000, as compared to the case of an ideal crystal, is often desirable.

According to Eq. {2) either the orientation of the lattice planes or the regular interplanar spacing can be relaxed. Although these two defect structures may not be com- pletely independent they are generally considered to be complementary. In the first case, it is referred to as a mosaic crystal, and this type is quite generally used in today's instrumentation. The second case refers to gradi- ent crystals. They are more difficult to produce and for this reason they are rarely exploited.

Mosaic and gradient crystals have quite different dif- fraction properties and they define resolution elements of complementary shape as illustrated in Fig. 1. Increased flexibility in instrument design is possible if both types of monochromators are available [-2].

3. Making monochromator crystals

3.1. Plastic deformation of big crystals

The more traditional method of making mono- chromator crystals consists of choosing carefully large single crystals of high quality (with the exception of pyrolytic graphite). Gamma-ray diffraction is a parti- cularly powerful means for this task. The absorption for electromagnetic radiation is reduced by many orders of magnitude as compared to usual X-rays because of the short wavelength used (e.g.)~ = 0.018 A for a Cs source). It becomes possible to analyze the bulk of massive

°N mosaic crystal

gradient crystal

Fig. 1. Although the accepted phase-space elements in the inci- dent beam (left side) may be the same for a mosaic crystal (top) and a gradient crystal (bottom) the shapes of reflected phase- space volumes are very different (right side).

samples like a 10 cm thick Cu. In addition, these controls can be performed without extinction playing a significant role. Careful analysis of the starting material means that there are no small-angle grain boundaries present (within the resolution of the instrument) and that there is a con- stant (and low) reflectivity for the entire sample volume. Selected pieces are prepared from the single crystals (typi- cal block size in an area of 25 cm 2 and a height of 10 cm) which are then subject to plastic deformation. The press- ing is frequently done along a low-symmetry direction to initiate gliding on only a few gfide systems. This establishes a desired anisotropic mosaicity. Metals or semiconductor materials deformed at elevated temperature are favored for this procedure because of their pronounced plastic properties. The desired orientation for the mono- chromator crystals is obtained by properly slicing the large blocks. As an advantage it can be noted that well- defined glide systems can be initiated. Indeed this proced- ure works well for a number of monochromator materials like Cu. This case is particularly favorable, because of the pronounced work hardening of this material and the clean glide system that can be excited when the deformation is performed at elevated temperatures.

Inherent disadvantages of this procedure relate to a stronger plastic deformation in the middle of the sample as compared to the ends. This imposes practical limits for large crystal blades. Additionally, in- homogeneous deformation is a frequently encountered problem. It may result from an unidentified defect in the

A. Magerl / Physica B 213&214 (1995) 917-921 919

starting material which leads to macroscopic gliding of part of the crystal.

Quality control at a high-energy beam line station on a synchrotron source with a photon flux greatly exceed- ing any gamma-ray diffractometer would be very desir- able. This would help to reduce the failure rate during the final stages of plastic deformation.

3.2. Locally imposed plastic deformations

Locally imposed deformations may reduce some of the above risks and hold promise for the creation of a homo- geneous reflectivity over large volumes. This is of special importance for difficult materials like the semiconductors or crystals of moderate quality. A particularly successful story has been written by Brookhaven National Laborat- ory I-3]. The local deformation is achieved by pressing thin blades (e.g. Ge) already suitably cut in a cylindrically shaped die. This leaves very little room for macroscopic gliding. By assembling a number of these thin blades, monochromator crystals with high reflectivity and with very smooth well- shaped rocking curves have been obtained.

The strength of this technique is demonstrated in Fig. 2. Fig. 2(a) shows the rocking curve of an unde- formed Cu crystal (3 mm thick) of moderate quality. This crystal has a small-angle grain.boundary which actually runs all along the crystal. This would normally exclude it from any further processing. However, the double peak structure does not evolve during the bending deforma- tion shown in Fig. 2(b) (d). In contrast it is absorbed after three bending cycles, and a well-behaved smooth rocking curve is obtained.

This procedure may become of special importance for Be, which has a pronounced subgrain structure. It has not been possible in the past to deform as-grown crystals because macroscopic gliding along the grain boundaries prohibits homogeneous deformation. However, mosaic- ity can be nicely introduced as shown in Fig. 3, when the crystals are first sliced into thin blades and then bent [4].

More detailed investigations demonstrate that the ends of the blades do not deform well. This may relate to the different boundary conditions for the gliding or to an ill-defined deformation mode. It should also be noted that it is advantageous to deform with a large radius of curvature and with a large number of bending cycles. Applying only one or a few bending cycles at a small radius gives less satisfactory homogeneities. Best results may be obtained when working with a continuously varying bending radius.

i , I i I , i i i I . . . . 1 , , , J 1 0 0 -

a) 80-: ! ~

~ 6 0 -

4 0 2

2O -"

0 2 I I I

~ 0 .

~ 20,

10,

. . . . i . . . . i . . . . i . . . .

50 t c)

30

20

10

0 , .

, i i i I i , i L I i i ~ i I i i i i 5°i fl)

3o2 ~

~2o2

Io

o . . . . i . . . . i . . . . I . . . .

- 1.0 -0.5 0.0 0.5 1.0

rocking angle [°]

Fig. 2. Gamma-ray rocking curves for the 2 0 0 reflection from a 3 mm thick Cu crystal. The as-grown crystal (a) has a small- angle grain boundary. Nevertheless smooth rocking curves de- velop after 1, 2 and 3 bendings with a radius of 200 mm as shown in (b), (c) and (d), respectively.

volumes. Recently a systematic study of the reflectivity of crystals coupled to ultrasound transducers was conduc- ted by Hock et al. [5, 6]. A gain factor of up to 50 could be measured for the 1 1 1 reflection by exciting a perfect Si crystal with a LiNbO3 transducer. In addition the line shape is absolutely symmetric and the peak reflectivity remains very close to 100%. This technique, although likely limited to high-resolution applications, has the further merit that it allows to vary the compromise be- tween intensity and wavelength selectivity with no need of changing the monochromator crystal.

3.4. Precipitation o f impurity atoms

3.3. Ultrasonic excitations

Ultrasonic excitation of crystals is another exotic means of obtaining homogeneous reflectivities over large

A homogeneous distribution of structural defects in a large crystal volume can also be created through the precipitation of defect atoms. This has been demon- strated previously for the system NbHx, where hydrogen

9 2 0 A. Magerl / Physica B 213&214 (1995) 917 921

undeformed 3000] I

Y- 1000

0

4O

20

10

-.50

2 bend ing cycles

tsoo

1°°°i

i /~ '¢,,

411 ~

0.0 .50 -2.0 -1.0 0.0 1.0

rocking angle [" ]

Fig. 3. X-ray rocking curves of a 11 00) reflection. The corres- ponding crystal planes are parallel to the surface ofa 1 mm thick and 50 mm long Be blade. The first 5 mm on each side are not shown for the sake of clarity. The macroscopic bending on the left-hand side is insignificant. It is introduced during the spark- erosive cutting. The deformed blade on the right has some residual macroscopic ripples.

can be introduced in large quantities in the Nb host at about 700°C [7]. At sufficiently high temperatures the hydrogen forms a lattice gas and the host retains its cubic structure. In contrast, at reduced temper- atures, the hydrogen precipitates, forming many little clusters of a highly concentrated hydride phase which has a different structure. The misfit with the host lat- tice results in strongly disturbed volumes ~round the precipitates.

In a more recent study the precipitation of oxygen in Czochralski-grown Si has been used [8,9]. Here the oxygen is already introduced with a maximum concen- tration of 8 × 1017 atoms/'cm 3 during the crystal growth process. At room temperature the oxygen is super- saturated. However precipitation is prohibited due to the very low oxygen mobility. In an appropriate annealing cycle, the conditions can be chosen such that the oxygen precipitates into many small SiO2 clusters which push numerous dislocation loops into the surrounding Si host. A significant gain in intensity which may exceed a factor of 10 can be readily obtained in spite of the low initial defect concentration. The temperature cycle chosen allows one to tune the gain factor.

Some monochromator SiOx crystals have come into operation for special applications like high-resolution diffraction or neutron topography. In these cases a mod- erate bandwidth, but a large and very homogeneous neutron beam, is requested.

For many applications gain factors of about 10 may be insufficient. However the procedure is still very interest- ing because the defects created are homogeneously dis- tributed throughout the entire volume of the crystal. They may serve as very finely distributed nucleation centers for additional dislocations which are created when plastic deformation in a more traditional manner is added later to boost the bandwidth by one or two more orders of magnitude.

3.5. Sil ~Gex 9radient crystals

Gradient crystals represent another approach to- wards a high-performance monochromator. Their diffraction properties have already been shown sche- matically, for the in-plane component, in Fig. 1: the reflection is of a simple mirror type, and the shape of the resolution element reflects the properties of the incident beam. Consequently a large bandwidth can be reflected into a given direction. It is only limited by the gradient. In addition there is no increased divergence of the beam in th e direction perpendicular to the diffraction plane, which avoids vertical blurring of the diffracted beam [2].

The smooth variation of the lattice spacing can be obtained by a variety of techniques. Actually, an ultra- sonically excited crystal can be viewed as a dynamic gradient crystal, and a bent perfect crystal eventually with an asymmetric reflection is a special case of a gradi- ent crystal with particular focusing properties. Another type of gradient crystal has been presented by Alefeld [11]. He exposed a CaFz crystal to a temperature gradi- ent of 230 K which gave an intensity increase of a factor of 37. This technique is routinely available on the thermal backscattering spectrometer IN13 at the ILL, where a gain factor on the order of five can be made available. However all these techniques require a complex crystal environment, and it appears that an intensity gain of the order of 1000 is out of reach.

Single-crystalline binary alloys with a gradual modifi- cation of the composition have been proposed as an alternative way of synthesizing gradient crystals, and Sil-xGex seems a particularly good example: the lattice constant of germanium exceeds the lattice constant of silicon by 4%, and the alloy crystallizes over the entire concentration range in the cubic diamond structure. Fur- thermore the scattering cross-sections of the two con- stituents are very favorable for thermal neutron scatter- ing [12]. There has been a recent effort to make large Sil-xGex single crystals by a low-pressure chemical va- por deposition process [13, 14]. This epitaxial growth technique combines very high growth rates with reason- ably good crystal quality, while the growth temperature can be maintained well below the melting temperature in

A. Magerl/Physica B 213&214 (1995) 917 921 921

evident from the large extension in the AG±/G direction. The sample in Fig. 4(b) represents the intensity map of

a smooth gradient with 0 < x < 0.03 deposited in an 800 gm thick layer. It shows again first a sharp Bragg spot at AGII/G = 0, which is followed by a continuous distribution extending smoothly out to AGII/G = - 1.3 x 10-3. Note that this longitudinal width exceeds

the Darwin width of the crystal by a factor of 70! At the same time there is very little mosaicity observed, which underlines the high crystalline fidelity of this binary gradient crystal. Samples with a stepped concentration profile with AGII/G = 15 x 10 3, i.e. 700 times the exten- sion of the Darwin width, have already been synthesized.

-2

-1

4. S u m m a r y

The present paper underlines defect engineering as a key issue for recent developments in the field of neutron monochromators . It is felt by the author that significant improvements have been achieved recently for usually applied materials, and others are still possible. Several developments mentioned have already found practical applications, whereas others are just about to reveal their potential.

Mr. K.D. Liss has made a big effort in helping me to prepare this manuscript. I thank him very much.

r

' I

AG~ 10 3] G

Fig. 4. Intensity maps near the 2 20 Bragg peak of a Si~ -xG% crystal with two fixed concentrations x = 0.03 and x = 0.06 (top) and a Sia_xGex crystal with a continuous variation of 0 ~< x ~< 0.036 (bottomt. The Si substrate peaks appear at the coordinates (0, 0).

a regime where the crystal is still rigid enough to avoid the development of long-range defects.

Fig. 4(a) shows a mapping of the intensity in the vicin- ity of a 2 2 0 Bragg peak for a sample which contains the Si substrate peak (at AGql/G = O) and which has two synthesized layers with x = 0.03 and x = 0.06 (located at about AGII/G = - 1 x 10 - 3 and AGII/G = 2 × 1 0 - 3 ) .

Each layer has a thickness of 30 gm. Note that this sample with the stepped change in concentration x has a significant perpendicular width, i.e. mosaicity, as is

R e f e r e n c e s

[1] A. Magerl and V. Wagner (eds.), Nucl. Instr. and Meth. A 338 (1994).

[2] K.-D. Liss and A. Magerl, Nucl. Instr. Meth. A 338 (1994) 90. [3] J.D. Axe, S. Cheung, D.E. Cox, L. Passell, T. Vogt and

S. Bar-Ziv, J. Neutron Res. 2 (3) (1994) 85. [4] C. May, P. Klimanek and A. Magerl, Nucl. Instr. and

Meth., to be published. [5] R. Hock, T. Vogt, J. Kulda, Z. Mursic, H. Fuess and

A. Magerl, Z. Phys. B 90 (1993) 143. [6] R. Hock, K.J., Nucl. Instr. and Meth. A 338 (1994) 38. [7] J.R. Schneider and N. Stump, Nucl. Instr. and Meth. 125

(1975} 605. [8] A. Magerl, K.-D. Liss, J.R. Schneider and W. Zulehner, in:

Proc. int. Conf. on Slow Dynamics in Condensed Matter, Fukuoka, Japan, 1991, eds. K. Kawasaki, M. Tokuyama and T. Kamakatsu (ALP, New York, 1992) p. 479.

[9] K.-D. Liss, A. Magerl, J.R. Schneider and W. Zulehner, J. Appl. Phys. 70 (1991) 1276.

[10] See various contributions in Ref. [1]. [11] B. Alefeld, Z. Phys. 228 (1969) 454. [12] H. Maier-Leibnitz and F. Rustichelli, Patentschrift,

1816542, Deutsches Patentamt (1968). [13] R. Madar, E. Mastromatteo, A. Magerl, K.-D. Liss and

C. Bernard, Surf. Coatings Technol. 54-55 (1992) 229. [14] A. Magerl, K.-D. Liss, C. Doll, R. Madar and E. Steichele,

Nucl. Instr. and Meth. A 338 (1994) 83.