Nuclear Instruments and Methods in Physics Research B 207 (2003) 447–452

www.elsevier.com/locate/nimb

Anomalous x-ray scattering on molten levitated samples

L. Hennet a,*, D. Thiaudi�eere a, C. Landron a, J.-F. Berar b,M.-L. Saboungi c,d, G. Matzen a, D.L. Price a,d

a Centre de Recherche sur les Mat�eeriaux �aa Haute Temp�eerature, 1d, avenue de la Recherche Scientifique,

45071 Orl�eeans cedex 2, Franceb Laboratoire de Cristallographie, 25, rue des Martyrs, 38042 Grenoble cedex 09, France

c Centre de Recherche sur la Mati�eere Divis�eee, 1bis, rue de la F�eerollerie, 45071 Orl�eeans cedex 2, Franced Argonne National Laboratory, Argonne, IL 60439, USA

Received 23 December 2002

Abstract

In a single diffraction measurement, on a multi-component high-temperature liquid, the measured SðQÞ and GðrÞ areweighted averages of the partial functions for the different atom pairs, and different structural models can be consistent

with the experimental data. In order to obtain more specific structural information, we have combined aerodynamic

levitation and laser heating with the anomalous x-ray scattering technique to study the structure of liquid yttrium oxide

at high temperature. The results are in good agreement with the previous experiments and computer simulations. This

combination represents a powerful technique for obtaining reliable partial structure information in complex high-

temperature liquid materials.

� 2003 Elsevier Science B.V. All rights reserved.

PACS: 61.20.)p; 61.10.EqKeywords: Synchrotron; Anomalous x-ray scattering; Levitation

1. Introduction

In the past, the combination of containerless

technique and x-ray scattering has enabled struc-

tural studies of high-temperature liquids above the

melting point and in the supercooled state [1–3].

However, the information obtained on a multi-component liquid with such diffraction experi-

* Corresponding author. Tel.: +33-2-3825-5513; fax: +33-2-

3863-8103.

E-mail address: hennet@cnrs-orleans.fr (L. Hennet).

0168-583X/03/$ - see front matter � 2003 Elsevier Science B.V. All r

doi:10.1016/S0168-583X(03)01077-2

ments is limited because the measured structure

factor SðQÞ and the corresponding pair correlationfunction gðrÞ are weighted sums of the partial

functions for the different atom pairs, so that

various structural models can be consistent with

the experimental results.

High-intensity synchrotron radiation sourceshave enabled the development of more selective

methods such as anomalous x-ray scattering

(AXS), frequently used on amorphous and glass

materials [4]. At high temperature, only a few

studies have been made, using classical furnaces, on

relatively low melting point compounds [5]. In this

ights reserved.

448 L. Hennet et al. / Nucl. Instr. and Meth. in Phys. Res. B 207 (2003) 447–452

paper we describe an application of the AXS tech-

nique to study the structure of molten materials at

very high temperature using containerless condi-

tions (aerodynamic levitation and laser heating).To test the feasibility of this approach, we chose

to study liquid Y2O3 (yttrium oxide or yttria) be-

cause some work has already been carried out on

this system. A few years ago, Krishnan et al. [6]

determined the structure using x-ray diffraction.

Following this experimental work, two molecular

dynamics (MD) computer simulations were per-

formed [7,8]. The two simulations are in goodagreement with the experimental data but lead to

contradictory results. Alvarez et al. [7] found a

substantial sub-stoichiometry of the sample during

the heating process, while Belonoshko et al. [8]

obtained results under stoichiometric conditions

that agreed well with the experimental data.

Fig. 1. Detailed view of the high-temperature chamber: laser

beam (a), focusing mirror (b), flat mirror (c), levitator (d), py-

rometer (e), x-ray beam (f), x-ray collimator (g), direct beam

stop (h).

2. Experimental aspects

2.1. Beamline description

The experiments were carried out at the French

CRG beamline D2AM at the ESRF (Grenoble,

France). This beam line is situated on a bending

magnet and is dedicated to structural investiga-tions using anomalous scattering. A detailed de-

scription can be found in [9]. The optics consist of

a double Si[1 1 1] crystal monochromator sur-

rounded by two platinum-coated mirrors. Hori-

zontal focusing is achieved by bending the second

crystal and the second mirror is used to focus the

beam in the vertical plane.

During the experiment, the spot size at thesample position was 0.5 mm vertically and 1 mm

horizontally. Scattered x-rays were detected over

an angular range of 3–125� with a NaI scintillatorcoupled to a graphite [0 0 2] analyzing crystal, giv-

ing an effective scattering vector Q range of 0.5–15�AA�1 with an energy resolution of about 0.15 keV.

2.2. Sample preparation

Spherical samples were prepared by melting

high-purity (99.9%) yttria powder, pressed under

an isostatic pressure of 250 MPa, in an aero-

dynamic levitator with a CO2 laser beam and then

cooling to room temperature. They had a nominal

diameter of 2.7 mm, corresponding to a weight of

about 50 mg.

2.3. High-temperature setup

A detailed description of the complete setup can

be found elsewhere [10,11]. Fig. 1 is a schematic

view of the high-temperature chamber. The

spherical sample is situated on a levitator in the

center of the chamber. This device consists of aconvergent–divergent nozzle, enabling the flow of

a regulated gas jet onto the sample from below.

This enables the sample to remain in a stable po-

sition during the heating phase without any con-

tact.

This chamber was mounted on the center of the

7-circle goniometer of the beam line. The samples

were heated using a 125 W CO2 laser focused onthe sample by means of mirrors. The melting point

of Y2O3 is 2731 K and the measurements were

performed at 2770 K, determined with a single

wavelength pyrometer using a value of the emis-

sivity taken from [6].

L. Hennet et al. / Nucl. Instr. and Meth. in Phys. Res. B 207 (2003) 447–452 449

3. Principles

3.1. AXS method

The principle of the method is widely developed

in Price and Saboungi [12] and we give here only

a few details applied to the case of Y2O3. The

average structure factor can be expressed as a

weighted sum of the different partial structure

factor Sij:

SðQÞ ¼X

i;j

WijðQÞSijðQÞ; ð1Þ

where i and j represent the atoms Y (yttrium) andO (oxygen). In the Faber–Ziman formalism [13],

the measured coherent scattered intensity is related

to these partial structure factors through the for-

mula

IcohðQÞ ¼X

i;j

cicjfif �j ðSijðQÞ � 1Þ þ

X

i

cifif �i ; ð2Þ

where ci is the atomic concentration of the elementi and fi ¼ f 0i ðQÞ þ f 0

i ðEÞ þ if 00i ðEÞ is the atomic

scattering factor, containing anomalous dispersioncoefficients f 0

i and f 00i that depend on energy. Fig. 2

shows the variations of f 0 and f 00 for yttrium and

oxygen around the Ka absorption edge of yttrium

(17.038 keV).

The principle of the method is to perform

measurements at two energies, one just below the

edge (17.01 keV) and one further below the edge

Fig. 2. Variations of the anomalous dispersion terms f 0 and f 00

of yttrium and oxygen as a function of energy.

(16.75 keV). Fig. 2 shows that f 0Y changes drasti-

cally while f 0O remains constant. By performing the

difference of the two coherent intensities (see Eq.

(2)), it is possible to remove the contribution of theO–O partial structure factor. We obtain finally the

yttrium structure factor:

SYðQÞ ¼X

i

W AYiðQÞSYiðQÞ; ð3Þ

Wij and W AYi can be evaluated with the following

equations, using atomic scattering factors and

anomalous dispersion coefficients taken from the

literature [14–16]:

WijðQÞ ¼cicjfif �

jP

cicjfif �j

�� ��2 ; ð4Þ

W AYiðQÞ ¼

ciReðfiðQÞÞPciReðfiðQÞÞ

: ð5Þ

3.2. Scattering processes

Fig. 3 is a schematic representation of the dif-

ferent scattering processes occurring at the angle

2h ¼ 90�, during the near edge experiment at 17.01keV on Y2O3 in addition to the elastic scattering.

AXS experiments are made at energies below

the absorption edge to avoid fluorescence effects,nevertheless some resonant Raman scattering

(RRS) is present in the near edge experiment. For

Fig. 3. Schematic representation of the different scattering

processes occurring with a yttria sample during the near edge

measurement at 17.01 keV.

Fig. 4. Yttrium resonant Raman scattering intensity at an in-

cident energy of 17.01 keV (squares) and calculated absorption

450 L. Hennet et al. / Nucl. Instr. and Meth. in Phys. Res. B 207 (2003) 447–452

yttrium, the Ka and Kb RRS peaks are expected at

14.93 and 16.75 keV. Due to the analyzer resolu-

tion (0.15 keV), both RRS peaks are resolved and

do not influence the measurement of the elasticpeak.

The angular dependence of the Compton scat-

tering energy is given by

E0 ¼ E

1þ 0:00392E sin2 h; ð6Þ

where E is the incident energy (17.01 keV). At lowangle the Compton scattering is superposed with

the elastic peak and has to be removed in subse-

quent analysis. At angles above 50�, the Comptonpeak is resolved and does not influence the elasticpeak any more.

coefficient AðQÞ (line).

4. Data analysis

4.1. Procedure

The coherent scattered intensity is extractedfrom the experimental measurements using the

method of Wagner [17]. Following this procedure,

the measured scattering intensities were corrected

for detector dead time, air scattering, multiple

scattering and Compton scattering.

• The air scattering, appreciable only at small an-

gles, was recorded in a separate measurementwithout any sample and subtracted.

• The multiple scattering was eliminated analyti-

cally by using the procedure of Warren and

Mozzi [18].

• The Compton scattering intensities were calcu-

lated using data from Balyuzi [19].

The resulting intensity IðQÞ normalized to theprimary beam intensity I0ðQÞ is proportional to thecoherent intensity:

ISðQÞI0ðQÞ

¼ AðQÞIcohðQÞ; ð7Þ

AðQÞ is an attenuation term related to the sample

geometry and calculated by a numerical integra-

tion of the optical path of the x-ray beam over theirradiated volume of the sample.

Since it is an absorption process, the RRS in-

tensity is expected to be proportional to AðQÞ, andwas used to fit the geometrical parameters: samplesize and position in the beam at high temperature.

For this step, absorption coefficients were calcu-

lated using the x-ray cross-sections compiled by

McMaster et al. [20].

Fig. 4 shows the good agreement between the

KaRRS intensity recorded at 14.93 keV in a sep-

arate measurement and the calculated values of

AðQÞ, confirming the validity of the integration.

4.2. First results

The average structure factor SðQÞ measured at16.75 keV and the yttria structure factor SYðQÞ areshown in Fig. 5 and are very similar. This shows

that the partial structure factor S0–0 has a limitedcontribution to the total SðQÞ, consistent with thevalue W0–0 ¼ 0:064 calculated from Eq. (4).

The corresponding average pair correlation

function GðrÞ and yttrium pair correlation function

GYðrÞ are shown in Fig. 6. Calculating the differentweighting factors with Eqs. (4) and (5) we get

GðrÞ ¼ 0:557GY–Y þ 0:379GY–O þ 0:064GO–O;

GYðrÞ ¼ 0:735GY–Y þ 0:265GY–O:ð8Þ

In GðrÞ, five peaks are observed at 2.26, 3.67, 6.77,9.75 and 12.9 �AA. These values are in good agree-

Fig. 6. Average pair correlation function GðrÞ measured at

16.75 keV and yttrium pair correlation function GYðrÞ for liquidY2O3 at 2770 K. The upper curve has been shifted up by 0.5 for

clarity.

Fig. 5. Average structure factor SðQÞ measured at 16.75 keVand yttrium structure factor SYðQÞ for liquid Y2O3 at 2770 K.

The upper curve has been shifted up by 1 for clarity.

L. Hennet et al. / Nucl. Instr. and Meth. in Phys. Res. B 207 (2003) 447–452 451

ment with the previous work [6]. The first can be

ascribed to Y–O nearest-neighbor pairs and the

second to a combination of O–O and Y–Y corre-

lations.

In GYðrÞ, the first peak is also at 2.26 �AA but in

this case the second peak is due only to Y–Y pairs

and its position is around 3.74 �AA. The combinationof these results with Eq. (8) leads to an O–O dis-tance around 3.06 �AA. These values are in good

agreement with the MD simulations of Bel-

onoshko et al. [8] and those of Alvarez et al. [7] in

the stoichiometric case, in contradiction with the

sub-stoichiometry conclusions.

5. Conclusion

The AXS method was successfully applied to

study the local environment of yttrium in high-

temperature liquid yttrium oxide. The results are

in good agreement with previous experimental

work and MD simulations. This work shows that

the combination of aerodynamic levitation and

AXS is a powerful technique for obtaining reliablepartial structure information in complex high-

temperature liquid materials.

Acknowledgements

This work was financially supported by the

CNRS and the contract ‘‘XI�eeme plan Etat/R�eegionCentre’’. DLP and MLS were supported by the US

Department of Energy, Office of Science, under

Contract W-31-109-ENG-38. The authors are

grateful to P. Melin, Y. Auger and the D2AM staff

for their technical help and H. Chaudret for

computer support of the control systems.

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