The evanescent neutron wave diffractometer: On the way to surface sensitiveneutron scatteringH. Dosch, K. Al Usta, A. Lied, W. Drexel, and J. Peisl Citation: Review of Scientific Instruments 63, 5533 (1992); doi: 10.1063/1.1143841 View online: http://dx.doi.org/10.1063/1.1143841 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/63/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The intensity correlation function in evanescent wave scattering J. Chem. Phys. 132, 074704 (2010); 10.1063/1.3305328 Production of evanescent acoustic waves and their scattering by resonant targets J. Acoust. Soc. Am. 117, 2483 (2005); 10.1121/1.4787717 Evanescentwave forced Rayleigh scattering: A novel method for nearsurface diffusion investigations J. Chem. Phys. 104, 6901 (1996); 10.1063/1.471392 Critical Phenomena at Surfaces and Interfaces: Evanescent XRay and Neutron Scattering Phys. Today 46, 58 (1993); 10.1063/1.2809011 Evanescent wave excitation of the surface polariton J. Appl. Phys. 67, 22 (1990); 10.1063/1.345285

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The evanescent neutron wave diffractometer: On the way to surface sensitive neutron scattering

H. Dosch Sektion Physik der Universitiit Miinchen, D-8000 Miinchen 22, Germany

K. Al Usta and A. Lied Sektion Physik der Universitiit Miinchen, D-8000 Miinchen 22, Germany and Institut Laue-Langevin, P.O. Box 156X, F-38042 Grenoble Cedex, France

W. Drexel Institut Laue-Langevin, P.0. Box 156X, F-38042 Grenoble Cedex, France

J. Peisl Sektion Physik der Universittit Miinchen, D-8000 Miinchen 22, Germany

(Received 10 August 1992; accepted for publication 17 August 1992)

A novel experimental technique to observe the Bragg scattering of evanescent neutron waves is presented. The so-called EVA diffractometer, installed at the high-flux reactor of the Institut Laue-Langevin, allows the identification of neutron scattering from single crystal surfaces. We discuss the experimental setup, intensity, and resolution considerations and some first Bragg scattering signals from evanescent neutron waves excited at CaF,, InP, and MnFz single crystal surfaces. The experimental results are discussed within the framework of the so-called distorted wave Born approximation and within a dynamical scattering theory. The limitations of both theoretical approaches to describe the Bragg scattering of evanescent neutron waves are indicated.

I. INTRODUCTION

The phenomenon of total external reflection of neu- trons is a common phenomenon’ and widely applied today both in applied neutron optics, as in neutron guide tubes, as well as in surface science. Neutron reflectometry mea- surements allow one to obtain detailed information on the depth profiles of the average coherent and magnetic scat- tering length density across the surface or interface.2’3

In the last decade, there has been a growing interest in the microscopic in-plane structure of surfaces and inter- faces which is not accessible by simply measuring the spec- ular beam. This has sparked the development of a new experimental technique, glancing-angle x-ray scattering, which exploits the phenomenon of total external reflection and the associated limited penetration depth of evanescent x-ray waves. Examples of recent applications of this novel technique are the analysis of surface reconstructions (for a review see Feidenhans’14 and Robinson and Tweet’) and the investigation of surface-induced critical phenomena.6 Virtually all surface-sensitive x-ray scattering experiments have so far been carried out using x-rays provided by highly brilliant synchrotron radiation sources. Neutron scattering under the condition of total external reflection, however, is still in an early stage, since the low neutron flux available, the glancing-angle scattering geometry, and the low evanescent scattering cross section pose serious exper- imental problems in picking up the surface-sensitive neu- tron scattering signal.

Recently we have installed a new neutron diffracto- meter at the new cold source of the high flux reactor in Grenoble. This novel instrument allowed us to identify un- ambiguously neutron Bragg scattering from single crystal

surfaces. We will discuss in the following the experimental setup and some experimental results together with theoret- ical calculations (Sec. III). In Sec. II we give a short in- troduction to the elements of the theoretical aspects of neutron optics and of the Bragg scattering of evanescent neutron waves.

II. ELEMENTARY THEORY OF SURFACE SENSITIVE NEUTRON SCATTERING

A. Optical phenomena at total external reflection

A polarized, monochromatic neutron wave \I, (r) with wavelength ,l which travels in a medium characterized by an average coherent scattering length (b,) and an average magnetic scattering length (b,) * (the index f corre- sponds to the neutron spin parallel and antiparallel to the magnetic moment of the matter, respectively) experiences an index of refraction’

n,=l-S.fip=l-& (N,(b,)+N,(b,),)

where N, and N,,, are the number densities of all atoms and the magnetic atoms, respectively, and ( ainc + a,) is the to- tal dissipative cross section, including the incoherent scat- tering and absorption processes.7 Total external reflection of the neutrons occurs at a vacuum-medium interface for 6, > 0 with a critical angle

(2)

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I1

(cl p /a-o 8 ‘j -9; ,I2 ;,$ ----lOA -.- ,5A _ 4

3

;;5' :., *oh

\'..,. 2 lJ!L.

I 'y< 1 9 __'> .;'

0 0 05 10 15 20

Ott=<

FIG. 1. Total external reflection of neutrons from a vacuum-sol id inter- face: (a) incident, reflected, and transmitted (evanescent) neutron waves; (b) neutron reflectivity vs incidence angle for various values of the root mean square roughness p; (c) transmitted neutron intensity vs incidence angle for various values of the root mean square roughness p; (d) pene- tration depth I, vs incidence angle for various values of fl/6.

When the incidence angle ai of the impinging neutron beam is below a:, a specularly reflected beam occurs, while inside the med ium the neutron wave decays expo- nentially into the z direction [Fig. 1 (a)]. The neutron wave field Y * (r) at the interface at z=O decomposes accord- ingly into

W*(r)= I e’k~lt’ll(eik~+R~~e-ik~~), for z<O e’k4’ll T,? eikL*‘, for z > 0 9 (3)

where kill is the wave vector component parallel to the interface, ki,= k sin ai the vertical component in the vac- uum and

k,!z* = k ,/sin2 ai- 26, + 243 (4)

the refracted z component in the med ium (k = 21~/,l). The Fresnel coefficients RI and TP read*

Ti” = 2kiz kiz- kiz*

k,+ key ’ R” =--

k,+ k;z ’ (5)

Both intensities, the specularly reflected neutron beam, IRf- IR”j2 [Fig. l(b)], and the “evanescent neutron wave” inside the sample, If Cd 1 TF I2 [Fig. 1 (c)l, are ex- ploited in the experimental setup described below.

The specular intensity gives the information on the depth profile of the average nuclear scattering length den- sity (b,) (z) and (when polarized neutrons are applied) of the magnetic scattering length density (b,) A (z). This has been very successfully exploited in the past by Felcher and coworkers,3 Penfold and Thomas,’ and many others. The transmitted evanescent intensity can be used to extract surface-related correlation functions6 Inserting kLA (4) into Eq. (3) we find

5534 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992

FIG. 2. Schematic scattering geometry of a glancing angle neutron Bragg scattering experiment from Bragg planes perpendicular to the interface.

V, * (r) =e~kil~rltT,~ei Re(kiz* Iz,--z’[,~,

where (6)

ZT= IIm{kL*}I-’ (7)

is the evanescent penetration of the distorted neutron wave field [Fig. 1 (d)]. For ai < aC the penetration depth is typ- ically z 100 A, while Re{kL*} E-0, thus an evanescent neutron wave occurs which travels parallel to the surface and decays exponential ly into the med ium. This wave field can be used to excite neutron Bragg scattering from the med ium close to the interface. The experimental setup and some neutrons scattering experiment exploiting evanescent neutron waves will be described now in some detail.

B. Evanescent neutron scattering in distorted wave Born approximation

The scattering geometry for the observation of evanes- cent neutron scattering is shown schematically in F ig. 2: The incident beam undergoes total external and gives rise to the specular beam, while the evanescent neutron wave field encounters a kinematic scattering cross section and is observed at a scattering angle 28 in the surface and at a grazing exit angle of which is kept around the critical angle. W ithin the distorted wave Born approximation (DWBA) one treats the optical phenomena associated with the total external reflection exactly and the scattering from the evanescent neutron wave field in the first Born approximation. Neglecting for the moment magnetic scat- tering ( (b,) A = 0) this yields a very simple semikinematic neutron scattering intensity observed in the detector’

J(Q')=l~(qTi)~s(Q!>s (8) where 1, is the incident neutron intensity and S(Q’) = 1 F(Q’) I* semi-infinite structure factor with

F(Q') =JYQll,Q:)

e-‘QII*rl&+ll s m 0

N( rll,z)ei@dz.

(9) In (9) b, is the coherent scattering length, N( r,,,z) the

number density of the nuclei. Tf in (8) is the transmission function of the scattered neutron wave associated with the

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FIG. 3. Neutron scattering depth A vs glancing exit angle a/for InP and CaF, and various values of a/a,

exit angle as and obtained from Eq. (5) by replacing the index i by f. The perpendicular momentum Qi within the semi-infinite medium reads

Q~=k;i-k,!z=K~+i/A, (10)

and determines via the so-called “scattering depth” A,”

A= 1 Im{Qi} 1 -I, (11) the surface sensitivity of the neutron scattering process un- der consideration. Figure 3 shows A as a function of the grazing exit angle CL/ for various incidence angles CZ~ En- hanced surface sensitivity is accordingly achieved only when both glancing angles are less than the critical angle of the substance. In Eq. (10) the wave vector component k;= of the scattered neutron beam is obtained from Eq. (4) after replacing the index i by f.

It will be demonstrated during the description of the experiments that a useful evanescent neutron intensity is so far only achievable when near-surface Bragg scattering is excited, its structure factor reads”

1 =~(QI+t,,) Il-JQh 12’

The DWBA-a/-profiles of the evanescent neutron Bragg scattering intensity based on Eqs. (8)-( 12) will be dis- cussed below in some detail together with experimental results on InP and CaF, single crystal surfaces.

III. THE EVANESCENT NEUTRON WAVE DIFFRACTOMETER

A. Description of the experimental setup

The “evanescent neutron wave diffractometer” (EVA) has been installed 1989/90 at the new neutron guide hall of the high flux reactor of the Institut Laue-Langevin (ILL) in Grenoble.” EVA is supplied with moderately cold neu- trons which are produced at the new horizontal cold source (a cylindrical DzO container with diameter + = 2 1

5535 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992

FIG. 4. Schematic view of the EVA diffractometer: (a) side view: Ct, C,, and C, are slits; 7’ denote evacuated beam tubes; M is the monochro- mator, F the Be filter and MO the monitor counter; the detector D records the specular intensity, the position sensitive detector (PSD) the o, pro- files of the evanescent Bragg scattering . (b) Closeup of the sample ma- nipulation stage: the heavy-duty goniometer had including the 4-x seg- ments, the ai segment, the x-y-z stage and the o circle are shown. The shown neutron beam corresponds to Fig. 2. The intensity profiles (black) in the PSD will be discussed in the main text.

cm kept at T=23 K) and directed to the experiment by the curved neutron guide H53, which has a total length of 41 m and a cross section of A=dHxdy=60 mmX120 mm. The H53 guide has a NiS8 coating and consequently a spectral critical angle a,JA= 1.8 mrad/A. Note here that the vertical and horizontal beam divergence (aJ at the end of the neutron guide is 2aoc, i.e., a,=20 mrad at ;Z =5.5 A. Activation measurements with Au foils per- formed by the ILL at the end of the neutron guide gave a total flux (integrated over all wavelengths) of $- 1.0 X 10” n/(cm’ s), the spectral distribution is a Maxwellian associated with T=23 K, but modified by the curved neu- tron guide, resulting in an average wavelength of illcl=6.5 A and a spectral flux of &$/S/l.= 8 x 10’ n/(cm2 s A) at ;1=5.5 A.

Figure 4 gives a schematic side view of the Tanzboden- type EVA diffractometer. At the moment the instrument is supplied with monochromatic neutrons of wavelength /z = 5.5 A (i.e., the incident energy is Ei=2.70 meV) as reflected from a PG(002) monochromator (doo2=3.355 A) which has a size of dodov= 60 mm x 10 mm, a mosaic spread of qy= 30 min, and a reflectance of RM=0.85. The monochromator angle is 8,=55.05” for /2=5.5 A. A cooled Be filter (Be) suppresses higher harmonics in the

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(a) topview :

(b) sideview: PSD

d 0"

FIG. 5. Slit arrangement at EVA: (a) horizontal slits; (b) vertical slits (for explanation see the main text).

reflected neutron beam. Intensity variations in the mono- chromatic beam are controlled by a monitor counter (MO) after the Be filter. Various Cd-slit systems are used to re- duce the horizontal and vertical beam size and beam di- vergence of the incident, reflected, and surface-scattered neutron beams (Fig. 5). In order to achieve the necessary surface sensitivity, the vertical divergence a& of the inci- dent neutron beam has to be ;typically of the order 0.2~~~ thus o~~c=O.5-1.0 mrad, this is achieved by two vertical slits [Sty and Szy in Fig. 5(a)] separated by Li2=1710 mm, giving

, 4Y-t-d2Y UipF

42 (13)

With typical vertical slits sizes of dly=0.5 mm and dzy =0.2 mm this results in a vertical divergence of a&=0.4 mrad and a vertical beam size oiv at the sample position which is according to Fig. 5 (a)

ajv=dzv+a;vLm, (14) i.e., ~~~~-0.4 mm (L2s=400 mm). Thus, the vertical re- duction of the neutron phase space is ry= (c$oiv)/ (2a,gov) -5 x 10m4-5 x 10B5(!) The use of the horizontal slit system SIH, SzH, and SsH will become clear below in the context of evanescent Bragg scattering, they are, however, in general relaxed to some 20-30 mm each (depending on the actual sample size), and, thus, do not reduce the hor- izontal divergence provided by the neutron guide and the subsequent PG(O02) reflection,

ff~,=[(2~~sin8nr)24(2a,)2]“2 (15) giving u&2”. The energy resolution of this setup is quite generally12 [see also Fig. 5 (b)]

Aa -=cot e, kwd2+ bw?)2+ (w?)

a ai+atf4q2 with ai = 2ds/LMS~2’ [LMs=2 m is the distance mono- chromator sample and ds a typical linear sample dimen- sion, see Fig. 5 (b)]. The second term is associated with an eventual lattice parameter spread ha, in the monochro-

5536 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992

mator crystal (see below). With this setup A,%/,% results to 5.0~ 10M3. The neutron flux expected at the sample posi- tion can be estimated to be

64 $o(a;pA =-jg ~K&c&-q+;~) (17)

and, thus, for a vertical divergence of a/,= 1 mrad, (bo=7 x IO5 n/cm 2 s. The actually observed value is 4. ( 1 mradf =2x 105n/cm2 s). The totally available intensity at the sample position is then determined by the area d&dzy of the second slit, thus, typically lo=&&2&2v~2X 10’ n/ ( cm2 s) X 3 cm X 0.02 cm= 5 X IO4 n/s. Notice, however, that the number of useful neutrons which are actually in- tercepted by the sample surface depends on the sample surface area Fs (typically 2 cm X 2 cm) and the incident angle ai (typically 5X 10-3), thus, Is=##‘@iti2X IO5 n/ (cm2 s) ~4 cm2X5X 10m3= lo4 n/s. As we shall see be- low, the scattering cross section for evanescent Bragg scat- tering is very low, consequently, the feasibility of such experiments depends crucially upon Is and the neutron- and gamma-background in the experimental hall. After a careful shielding the background (neutrons and gammas) was 2 counts/l0 min, as observed in one pixel of the posi- tion sensitive detector and 3 counts/min as observed in the specular beam detector. When the wavelength spread of the impinging neutron could further be relaxed to say A&’ A=O.O2,the gain in 4. would roughly be one order of mag- nitude without losing the surface sensitivity of the method. Currently, we are operating the instrument with two iden- tical PG(O02) crystals misaligned horizontally by Awl1 = 2q ( = 1.2”) resulting in a wavelength spread of AUil =0.012, thereby gaining a factor of roughly 2 in the incident intensity. For the future we are exploiting the fea- sibility of several approaches to increase Ad/a: the use of a monochromator system with a large lattice constant (as mica) which would decrease 0, and thus increase the term “Cot e&f” in Eq. ( 16) or the use of a monochromator setup with an appropriate intrinsic spread AaM in the lattice con- stant aM, giving rise to the additional term (A&a), in Eq. ( 16). The latter may be achieved with Si-Ge gradient crys- talsi3 which exhibit a fixed hay, with insulating crystals (such as CaF,) exposed to a sufficiently strong tempera- ture gradient across the thickness of the crystal, or with an oscillating monochromator crystal setup. l4 By varying the temperature gradient or the oscillation amplitude, respec- tively, the effective AaM may eventually be tuned in a cer- tain range and adjusted to the experimental requirements. The instrument is furnished with two detectors, a conven- tional He3 detector in the forward direction at a variable distance between 1.2 m and more than 2 m. This detector is used to measure specular effects and can be moved in the vertical direction by a stepping motor. A position sensitive detector (PSD; ORDELA) is mounted on the detector arm which can be moved on the Tanzboden to an arbitrary scattering angle 29 between 0” and 125”. It is used to mea- sure af profiles of evanescent Bragg scattering (at an in- plane scattering angle 20#0) and, when moved to the forward direction (20=0), to observe specular and diffuse offspecular effects. The PSD system is mounted 1920 mm

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, primary a, = 3 3mral

* beam . experiment

- gaussian fit

200 300 ZK, (channel number I

FIG. 6. Example of the recording of the primary and the specularly reflected neutron beams by the PSD system.

away from the sample and measures the neutron scattering along a 200 m m wire perpendicular to the surface with a spatial resolution between 1.5 and 2 m m (depending on the high voltage which is applied), i.e., with an af resolution of ajV=0.8-1.0 mrad. The PSD is carefully shielded with boron and cadmium.

Figure 4(b) shows a close-up of the heavy-duty goni- ometer head which supports the sample and the sample environment. It consists of two chi segments (tc, and x) which allow a precise alignment of the sample surface par- allel to the incident beam. This alignment is most conve- niently performed using the specular beam detector by measuring the incident angle ai in terms of the spatial separation of the primary and specular beam (Fig. 6). The width of the specular beam gives as a byproduct the wav- iness of the sample surface. A z stage allows then to move the surface precisely (within an accuracy of 1 pm) into the beam which has a vertical width of typically 0.4 m m [see Eq. ( 14)]. A special chi segment (ai) with a radius of 650 m m is then used to adjust the wanted grazing incidence angle ah which can again precisely (AaizO.1 mrad) be monitored by the specular beam detector system. The sam- ple may then be rotated by 360” by the w circle on top of the ai segment without affecting the grazing incidence con- dition. The entire instrument is equipped with stepping motors and controlled by a special operating system (AL- IBABA) run on a PDPl 1. It allows to compose arbitrary scans in ai and Q,, and also the online readout of special regions of interest of the multichannel analyzer attached to the PSD system. For future operation with polarized neu- trons a spinflip selector is already implemented in the AL- IBABA code.

B. Performance of reflectivity measurement

Measurements of specular reflectivity profiles are car- ried out in the angle-dispersive mode, i.e., by variation of the angle of incidence ai at a fixed wavelength (usually /l. = 5.5 A). When the surface of the system under investi- gation exhibits a certain intrinsic waviness, the angular (a/) width of the reflected neutron beam is broadened and

5537 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992

(a) a< =6.05 mrad 6;,=0.5 mrad I

10-b 0 12 3 4 5 6 IS 9

=1/Q<

1.2 ,111,1,,1,1111,1111,1111(11,,

FIG. 7. (a) Neutron reflectivity profile from a polished float glass ob- tained in the angle-dispersive mode: at each incidence angle the specular ar profile is measured and fitted to a Gaussian (see insets); theoretical curves for various values of surface roughness are shown; (b) scaling form of surface illumination function Q(x).

usually varies slightly with ai, thus, in order to measure the total specular intensity, the af distribution of the specular intensity is scanned for each setting of ai by means of the PSD (see, e.g., Fig. 6) or by a vertical scan of the conven- tional detector. By this also eventually present scattering background underneath the specular intensity can be ac- counted for. Close to the critical edge sufficiently high an- gular resolution is obtained by setting the vertical slits to typically dlV=0.45 m m and d,,=O.2 m m , resulting in c& =0.4 mrad or d, y= 0.45 m m and d, y= 0.45 m m , resulting in &=0.5 mrad, at larger values of a/a, the steep drop in the reflected intensity may be countered by relaxing a$ accordingly. (Note that for a given value of al” the inci- dent intensity is maximal at this setup for dlH=dzH.)

By way of example the reflectivity profile obtained from float glass (mainly SiO,; surface area 90 m m X 120 m m ; a,=6.05 mrad for ;1= 5.5 A) is shown in Fig. i’(a) together with theoretical fits, including surface roughness and the deviation of the specular intensity from unity at ai<a, which is a geometric effect as caused by the a,- dependent illumination of the surface (with size I,) : As- suming a Gaussian beam profile exp( -z/aiv)2 the effec- tive reflectivity at ai( >O) is

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10

(b) % 12

(cl T MnFt

(0011 Oberfl iche

FIG. 8. (a)-(c) Neutron Bragg scattering under grazing angles from MnF, and CaF2 surfaces for various experimental conditions: (a) purely magnetic MnF,( 100) reflection from a MnF2(CKll) surface observed for O/CL,= 1 and completely relaxed horizontal slits S 2~, S,, (see the inset); the thick fulI line is the evanescent surface Bragg reliection Bragg beam (see the main text), the dashed line are spurious Bragg scattering from the edges of the crystal; (b) ( 111) Bragg scattering from the CaF2(21 1) surface observed for q/q= 1.0 and for appropriately set horizontal slits (see the inset); (c) case (a) for appropriately set horizontal slits.

(18) C. Performance of evanescent Bragg scattering

whereR(aJ isgiven by Eq. (5) andoivbyEq. (14). @(x) is the normalized illumination function which has the scal- ing form

l/2 @(x)=(T)-“2x

s t? -‘c*d( (x)0). (19)

- l/2

Before evanescent neutron Bragg scattering is recorded the reflectivity profile of the single crystal surface is care- fully analyzed, since it provides the calibration of the glancing incidence angle ai and the sample surface “hori- zon” defined by af=O at the position sensitive detector. In addit ion useful information on the surface roughness, sur- face waviness, and (if not exactly known) on the associ- ated critical angle a, is obtained.

As shown in F ig. 7(b) a(x) varies smoothly between Q , In order to pick up glancing angle Bragg scattering, =0 for x=0 and a,= 1 for x;>6. In this reflectivity mea- the incidence angle is set to ai=ac (for intensity reasons) surement the instrumental resolution has been chosen to and the position sensitive detector is set to the expected a;,=05 mrad, implying oi,==0.5 m m , i.e., IJcrL,=200. scattering angle 2ehkl associated with the Bragg point Ghkr Furthermore c+= 1.75 mrad, as given by the detector slit. (which lies in this scattering geometry in the sample sur- The specular reflectivity can be traced down to 1 R 1 2 face, see F ig. 2). Then the sample is rotated about its sur- = 10-5-10-6. It should be noted that the performance of face normal until the Bragg law is exited. In F ig. 8 we show one of these reflectivity profiles usually takes typically 30 by way of example nuclear ( 111) Bragg scattering excited to 40 h, which is roughly three times the data collection from a CaF, (211) surface and pure magnetic ( 100) Bragg time needed with dedicated time-of-flight reflectometers at scattering observed on a MnF,( 001) surface.‘5 When the modem neutron spallation sources. However, this “effi- horizontal slits S2, and S,, [Fig. 5(b)] are fully relaxed ciency” difference between the two experimental methods [see the inset of F ig. 8(a)], an af distribution as shown in has to be put into a correct perspective: W h ile in the time- F ig. 8(a) for the MnF, case may eventually be observed: of-flight mode the detector is usually set at af=2a, and In addit ion to the evanescent Bragg scattering which is integrates over a certain reflection angle range as given by picked up by the PSD between af=O and af= 3a, (thick the detector aperture, here the performance of an af scan curve) various additional peaks are observed. Some of over the specular intensity at each setting of the incidence them (dashed curves) are due to spurious scattering from angle aj allows the proper numerical integration over the the edges of the crystal which are directly “visible” by the pure specular intensity and the proper subtraction of the PSD [see the inset of F ig. 8(a)]: There, small, slightly diffuse scattering around and underneath the specular m isoriented crystallites, as probably created by the me- peak. This correction becomes important for large values chanical polish of the surface create this unwanted Bragg of ai, whenever the surface under investigation exhibits a scattering, which, however, can simply be eliminated by significant roughness. By way of example two of such aJ narrowing the slits S’,, and S’,, properly [inset of F ig. profiles at ai= 20 mrad and ai= 50 mrad are shown in the insets of F ig. 7(a). The hatched areas are the obtained

8(b)], then an af distribution as shown in F igs. 8(b) (CaF,) and 8(c) (MnF,) is finally observed, typically

specular intensities. W h ile at ai< mrad the diffuse scat- consisting out of three more or less separated peaks. This tering is negligible, it becomes dominant at larger angles of feature is in strong contrast to the x-ray case, where only incidence. W e argue here that discarding this diffuse scat- the evanescent surface peak (thick curve) is detectable. In tering (here 0.12 counts/s) lim its the reflectivity range the neutron case, the usually negligible absorpt ion cross that is accessible and, in addition, would eventually lead to an incorrect reflectivity profile and, accordingly, to a

section allows that a neutron beam which enters the crystal

wrong experimental value of the roughness parameter p. by one side edge subsequently undergoes Bragg scattering and can leave the sample by another side edge without

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being totally eliminated by absorption processes. Since this bulk beam [“R’ in Fig. 8 (b)] suffers no refraction effects at all, it is expected at of= --ab provided that the Bragg planes are orientated exactly normal to the surface [see Fig. 8(c)]. The two other peaks result from the Bragg scattering of evanescent neutron waves: After Bragg scat- tering of the evanescent neutron wave field there is a cer- tain probability, as given by the transmission function Tf, that the Bragg-reflected evanescent neutron wave field which travels parallel to the surface is refracted out of the surface. This process leads to the pure surface peak [de- noted “S’ in Fig. 8(b)] which we have considered in the scattering theory above [Eqs. (8), ( 12)]. The nonrefracted part of evanescent Bragg scattering (denoted “T” in Figs. 8(b), 8(c)] leaves the sample by one edge and conse- quently occurs at the sample horizon, af=O, again as- sumed that the Bragg planes are ideally normal to the surface [Fig. 8 (c)l. The observation of this T beam (which is mediated by the negligible absorption) proves in a very nice way the existence of evanescent neutron waves inside the crystal, it should be noted, however, that the surface sensitivity of this beam is only moderate, since it is given by the penetration depth Ii of the evanescent neutron wave field [Eq. (7) and Fig. 1 (d)] and not by the scattering depth A [Eq. ( 11) and Fig. 31 associated with the pure surface peak.

(a)

Bragg planes

ai(mrad)

We conclude from this that the proper identification of the most surface sensitive glancing angle neutron Bragg scattering requires both the precise control of the incidence angle oi and the meticulous analysis of the af distribution of the scattered intensity. We think it is fair to say that previous attempts to observe pure surface-sensitive neutron scattering have to be considered with care, because this crucial point has not properly been taken into account.16

FIG. 9. (a) Definition of the surface miscut A& (b) a/--q relation of the .S-, T-, and B-neutron Bragg beam for a given nonzero surface miscut 4.

The observed deviations of the B- and T-beam position from CL/ = -aC and 0, respectively, in the CaF2 case [Fig. 8(b)] is due to a miscut of the (211) surface by A@=55 mrad. By definition, A+> 0 when the reciprocal lattice vector Ghkl is pointing out of the crystal surface [Fig. 9 (a)] and A+<0 otherwise. As can be verified by the reader quite simply, then the B and T beam occur at

nated by the hot spot of the beam. The full symbols show the simultaneous intensity variation of the specular beam which monitors the incident intensity along the entire sur- face. The control, whether this intensity peaks at the same z position of the sample as does the Bragg intensity, can be used to check that the active area SF is properly located in the center of the surface.

In the last years we have investigated a series of single crystal surface by evanescent neutron Bragg scat- tering, such as Si(llO), CaF,(?ll), InP(ilO),*iV1’ and

1 -ai+A@ sin 0, for the B beam

af= - (af-26)“2+2A@ sin 8, for the T beam (20)

and the situation becomes more complex. For a reliable disentanglement of the various beams the variation of the af positions of the various Bragg peaks in the PSD has to be studied, while the incidence angle is scanned. By this analysis the various Bragg contributions can unambigu- ously be identified p‘a,-arrelations;” Fig. 9(b)] and, as a byproduct, the surface miscut AQ, is obtained from Eq. (20).

200

7 2 100 c s

. specular intensity

0 evanescent

After the surface sensitive evanescent Bragg peak has been identified, the sample height can be adjusted properly within the incident beam. Figure 10 shows the surface Bragg scattering (open symbols) as a function of the z translation [see Fig. 4(b)]: The intensity maximum corre- sponds to the optimum sample position, where the active area of the surface [SF in the inset of Fig. 8(b)] is illumi-

0 25

FIG. 10. Vertical adjustment of the sample surface into the neutron beam: intensity variation of the specular beam (full symbols) and the ( 100) magnetic Bragg beam at the MnF*(OOl) surface vs sample z trans- lation.

5539 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992 Evanescent neutron wave 5539 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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0.14 , I I I 1

(a) 4 x 0,25 l

. l

2 AA A 2 A - -2

0.07

ts

“-8’

Am B L

‘WJ O&

CaF (111)

Qilf& = 0 0.68 l 0.87 l 1.04

A 1.19

affac

InP(111)

0 0 0 0

OA A% 0 A Am

aiIac = o 0.71 o 1.02 A 1.31

FIG. Il. Observed raw data of evanescent Bragg scattering from (a) the CaF,(211) and (b) the InP( 110) surface for various incidence values.

MnF2(O01).t5 The motivation for the investigation of the first three systems was

0.4

0

g 0.8 z 'W .E .5 z 0.4 r-4 f E ki c

0

0.8

0.1

(

( 1) to gain experience with this new neutron scattering technique,

1 2 3 af Iac

(2) to get some clues which parameters determine the feasibility of evanescent Bragg scattering,

(3) To test, whether the DWBA is an appropriate theoretical concept to describe the af profiles of the observed neutron scattering.

FIG. 12. Experimental data compared with theoretica calculations within the DWBA (full curve) and a dynamical Bragg scattering theory (dashed curve) for CaF, and some incidence angles (see the text).

The antiferromagnet MnF, has been investigated around the bulk NCel temperature and first results on surface- and interface-dominated thermodynamic behavior have been obtained. This will :be published in detail else- where. I5

nescent Bragg scattering intensity is of the order of only l-2 counts/l0 s in the PSD pixel associated with the crit- ical angle (af/ac= 1). As was discussed above, the identi- fication of the surface Bragg scattering requires the record- ing of the af profile, thus, the use of a PSD system seems indispensable for such neutron scattering experiments.

We will discuss some typical results obtained at the CaF,(Tll) and InP(i10) surfaces. They have been cho-

In Fig. 12 we show for some incidence angles theoret-

sen, because they exhibit distinctly different absorption, ical fits to the normalized af profiles of the CaF,( 111)

namely’ /3=1.8~10-‘~ for CaF, and p=5.2X10-8 for reflection within the DWBA approximation (full lines)

InP. The critical angles associated with A=55 A are a, and a dynamical scattering theory18 including instrumental

=6.2 mrad and a,=4.2 mrad for CaF, and InP, respec- resolution, in particular the af resolution of the PSD

tively. In both cases the ( 111) Bragg scattering signal ex- (c+O.35a,) which has a strong influence on the ob-

cited from evanescent neutron waves have been measured served intensity distribution (dashed curve). We find good

and analyzed for a,=Wa, and for various values of ai agreement of both theories with the experimental profiles

around ac [Figs. 11(a), 11(b)]. The experimental chal- for CYi<a, [Figs. 12(a), 12(b)] and a slightly better agree-

lenge is quite apparent by inspection of Fig. 11: The eva- ment of the dynamical theory than the DWBA for ai> a, [Fig. 12(d)]. Note that in all three cases the Bragg condi-

5540 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992

0.8

(b) Oi /ff,=1.04

(cl (Yi /a~ = 1.19

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tion is not exactly fulfilled, thus, the dynamical and semi- kinematical treatment should provide essentially the same results. A significant deviation between theory (both kine- matic and dynamic) is observed for ai close to a,: The kinematic theory shows a smaller width and the dynamical theory a much too broad width than observed in the nor- malized spectra. This is due to the fact that the semikine- matic theory overestimates the scattering depth for ai> a, which is in this theory then only given by the absorption cross section, while the dynamical theory underestimates the scattering depth, since it assumes full (Bragg) extinc- tion, whenever the Bragg condition is fulfilled. Neutron Bragg scattering from any nonperfect crystal which exhib- its low absorption (as CaF2) is strongly affected by pri- mary and/or secondary extinction effects (in the x-ray case the photoabsorption is usually strong enough to wipe out these effects), thus, also in ‘the regime of evanescent neu- tron waves such effects have to be properly included. A grazing angle neutron Bragg scattering theory which ac- counts for such phenomena has not yet been formulated. When grazing angle Bragg scattering will become a more frequently applied tool for the study of inter-facial phenom- ena in a systematic and quantitative way, there will cer- tainly come up the need for an appropriate evanescent neu- tron Bragg scattering theory. Figure 13 shows the theoretical calculations for the glancing-angle neutron Bragg scattering in the case of (the more strongly absorb- ing) InP. Here it appears as if the DWBA theory (full curve associated with a surface waviness of An,=0.6a,) does a satisfactory job.

1 .I

0.8

0.5

0.2

2 0.8

E 2

2 0.5 .E 2! f-4 j 0.2

b c

Ui lUc =I.31

0.8

IV. OUTLOOK AND POSSIBLE APPLICATIONS

0.5

0.2

During the shutdown of the reactor the EVA diffrac- tometer will be upgraded:

( 1) the option to work with polarized neutrons will be installed;

%

-1 0 1 2 af I a,

3 4 5

(2) the possibility of new monochromator systems will be explored (as indicated above);

(3) the option to work with an analyzer crystal will be installed which allows (a) to measure purely elastic and (b) to analyze the spin state of the neutron after total reflection from a magnetic surface.

FIG. 13. Experimental data compared with theoretical calculations within the DWBA (full line: waviness An,=O.(ia; dashed-dotted line: An,=0.24 a,) and a dynamical Bragg scattering theory (dashed line: An,=0.24a,) for InP and some incidence angles (see the text).

The performance of evanescent neutron scattering faces, due to the low scattering intensity, severe experimen- tal problems. So, we would not recommend to carry out a glancing angle neutron scattering experiment, if the same results are also accessible to glancing angle x-ray scatter- ing, where highly brilliant synchrotron radiation sources are available. On the other hand, there are many intriguing problems of current interest related to surface and interface science which are not or only very hardly accessible to x rays. Some of them will be listed in the following, subdi- vided into three classes.

is exploited. Consider by way of example the case of a Ni surface covered by, say, 1 pm of Ti. Since Ti has a negative coherent scattering length, no total external reflection oc- curs at the vacuum-Ti interface, however a strong optical effect at the Ti-Ni interface. The small absorption of neu- tron within the Ti coating allows the implantation of a strong evanescent neutron wave field at the Ti-Ni interface and the subsequent study of inplane structural and mag- netic properties across the interface (see Ref. 6). In a sim- ilar manner organic substances can be investigated.

A. The study of buried, organic and isotope- decorated interfaces

B. The study of surface fields on surface-related magnetism

The inplane structure of deeply buried interface can be studied by this technique in an elegant way when the iso- tope dependence of the coherent scattering length density

The study of interfacial magnetism allows the system- atic investigation of the influence of surface fields on the magnetic structure near surface and interfaces. Examples hereof are the interface between two ferromagnets with

5541 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992 Evanescent neutron wave 5541 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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different Curie temperatures and the interface between a the “INlOc-group” (Professor J.-B. Suck and B. Frick). ferro and an antiferromagnet. Also in these cases the low This work was supported by the Bundesminister fir For- absorption of neutron in matter is advantageous. schung und Technologie under Grant No. 03PElLMU2.

C. The experimental test of the predictions of the renormalization group theory on semi-infinite criticality

By measuring the order parameter near the surface of an antiferromagnet (as MnF,) a new surface-related crit- ical exponent Pi is accessible. The renormalization group prediction” fir -0.8 has already been confirmed in the fer- romagnet Ni (Ref. 20) and in the binary alloy Fe,A16. To show the universality of this value of &, an experiment at the surface of an antiferromagnet is missing. First success- ful attempts have already been undertaken.15 Surface- induced decay of the critical order parameter fluctuations has been observed in FesAl” yielding another universal critical surface exponent 7 = I,52 f 0.04 in agreement with the theoretical prediction. lr4 In order to test its universality, experiments at a ferromagnetic surface would be desirable. The surface-dominated critical spin fluctuations create an evanescent diffuse off-specular neutron scattering around the specular beam which contains the information upon Yi *9

ACKNOWLEDGMENTS

The authors are grateful to A. Freund and B. Dorner for helpful discussions during the construction of the in- strument. N. Givelet and P. Ledebt developed the EVA computer control system. The help, financial support and the hospitality of the Institut Laue-Langevin during the last years is greatly appreciated. We gratefully acknowl- edge the kind cooperation with the neighboring neutron experiments, the “~6-group” (Professor D. Dubbers) and

‘V. F. Sears, Neutron Optics (Oxford University Press, New York, 1989).

2J. Penfold and R. K. Thomas, Condens. Mat. 2, 1369 (1990). ‘G. P. Felcher, Phys. Rev. B 24, 1595 ( 1981); G. P. Felcher, R. D.

Hilleke, R. K. Crawford, J. Haumann, R. Kleb, and G. Ostroski, Rev. Sci. Instrum. 58, 609 (1987).

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‘From Eo. ( 1) one finds that the extinction coefficient /3 is related with a,= (an+Uinc) by the relation @=4.758x 10-‘0p[g/cm3]cr,[bn]~[;/~, where A is the mass number of the periodic table. For other useful relations see the Appendix of Ref. 6.

*M. Born and E.Wolf, Principfes of Optics (Pergamon, Oxford, 1980). %. Dietrich and H. Wagner, Z. Phys. B 59, 35 (1985).

‘OH. Dosch, B. W. Batterman, and D. C. Wack, Phys. Rev. Lett. 56, 1144 (1986); H. Dosch, Phys. Rev. B 32, 2137 (1987).

” K. Al Usta, H. Dosch, A. Lied, and J. Peisl, Physica B 173, 65 (1991). ‘* K. Dorner, Acta Crvst. A 28. 3 19 ( 1972). “A. Magerl, Nucl. In&urn. Methods A 240, 414 (1990). 14R. Hock, T. Vogt, J. Kulda, 2. Mursic, H. Fuess, and A. Magerl

(preprint ). “K. Al Usta, H. Dosch, and J. Peisl (unpublished). ‘6J. F. Ankner, H. Zabel, D. A. Neumann, and C. F. Majkrzak, Phys.

Rev. B 40, 792 (1989). “K. Al Usta, H. Dosch, A. Lied, and J. Peisl, in Surface X-Ray and

Neutron Scattering, Springer Proceedings in Physics, Vol. 61, edited by H. Zabel and I. K. Robinson (Springer, Heidelberg, 1992).

‘*A. Zeilinger and T. J. Beatty, Phys. Rev. B 27, 7239 (1983); A. M. Afanase’v and M. K. Melkonyan, Acta Cryst. A 39, 207 (1983); N. Bernhard, E. Burkel, G. Gompper, H. Metzger, J. Peisl, H. Wagner, and G. Wallner, Z. Phys. B 69, 303 (1987).

19H. W. Diehl and S. Dietrich, 2. Phys. B 42,65 (1989), 43, 315 (1989). *“S F. Alvarado, M. Campagna, and H. Hopster, Phys. Rev. Lett. 48, 51

(;982). “L. Mailander, H. Dosch, J. Peisl, and R. L. Johnson, Phys. Rev. Lett.

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5542 Rev. Sci. Instrum., Vol. 63, No. 12, December 1992 Evanescent neutron wave 5542 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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