Structure of High-Temperature Levitated Liquids Probed by High-energy
X-ray Diffraction – Relationship between Liquid Structure and GlassForming AbilityIntroduction

High-brilliance and high-energy X-rays are one of the greatest advantages of SPring-8.

The use of high-energy X-rays allows us to measure diffraction patterns up to high 	 values of the momentum transfer in reciprocal space in transmission geometry, using	 
small scattering angles and small correction terms. This fortunate combination provides
more detailed and reliable structural information of not only disordered materials(glasses, liquids and amorphous materials) but also nanoparticles and mesoporousmaterials. The use of the levitation technique allows us to achieve deeply supercooledstates, because there is no interface between the liquid and a container wall. Hence we
can obtain new metastable materials (glasses) from the supercooled levitated liquid. In

this practical session, we will try to levitate an oxide melt at a temperature beyond 2,000T 5L HF<A: 4 6BA<64? ABMM?8 ?8I<G4GBE -8 J<?? ?84EA ;BJ J8 64A B5G4<A E8?<45?8
7<99E46G<BA 74G4 4A7 ;BJ J8 4A4?LM8 G;8 74G4 HEG;8E@BE8 J8 J<?? GEL GB C8E9BE@
structure modelling of disordered materials on the basis of diffraction data employing acomputer simulation technique, in order to understand the relation between the structureof a liquid and its glass forming ability.

High-energy X-ray diffraction techniqueIn this practical session, we measure diffraction from disordered materials, that do notexhibit Bragg peaks due to the lack of long-range periodicity. -8J<??HF8the two-axis

diffractometer dedicated for disordered materials (see Fig. 1 [1]). The energy of incident
X-rays is 61.4 keV obtained by a Si 220 monochromator. The scattered X-rays from thesample are collected by a Ge detector using a conventional θ - 2θ FG8CF64A@8G;B7-8
4A4?LM8G;87<99E46G<BAC4GG8EA4A7B5G4<A458E-Ziman total structure factor S(Q) [2] by

the following equation,

S(Q) =I(Q) − f (Q)
2f (Q)= ∑ c ic j

2+1Re f i (Q) f j (Q)

[ij∗

f (Q)

2] S (Q) = ∑ w (Q)S (Q),
ij

ij

ij(1)

ij

where S(Q 64A 58 B5G4<A87 5L 4 ABE@4?<M4G<BA B9 G;8 6BEE86G87 X-ray scattering

intensity I(Q). The pair distribution function g(r) and total correlation function T(r) are

obtained by a Fourier transformation of S(Q),Q max
1
Q[ S(Q) −1]sin(Qr)dQ2
2π ρr 01 ∞ Q max
r'[gij ( r') −1]⋅ wij (Q)cos[Q(r − r')]dr'dQ,= 1+πr −∞ 0g(r) = 1+∫(2)∑ ∫ ∫ij

T (r) = 4πρ r ⋅ g(r)(3)

where Q is the absolute value of wave number (Q = (4 π/λ) sinθ, 2θ: scattering angle, λ:wavelength of incident x-rays) and < > means the average per one atom; ci and fi(Q)represent the atomic fraction and the atomic form factor of component i, respectively.
wij(Q), Sij(Q), and gij(r) are the weighting factor of i-j correlations for X-rays, partial

structure factor for i-j correlations, and the partial pair distribution function for i-jcorrelations, respectively. ρ is the 4GB@<6 AH@58E 78AF<GL -8 64A 4FF<:A 4GB@<6
correlation peaks and derive the coordination number by integrating the area under the
peak in the real-space function.

Vacuum chamber

Receiving slits

Ge detector

I0 monitor
Incident slit
2

Fig. 1 Photograph of the two-axis diffractometer for disordered materials for typicalroom temperature measurement.
Aerodynamic levitation technique

One of the major experimental difficulties in studying materials at extremely hightemperatures is unwanted contamination of the sample through contact with thecontainer. This can be avoided by suspending the samples through levitation. Thistechnique also makes metastable states of matter accessible, opening up new avenues tonew materials for technological applications.

In the aerodynamic levitation technique [3], a sample is levitated by gas flow in aconvergent-7<I8E:8AGABMM?8<AJ;<6;8EABH<??<9BE68FCHF;the sample back to the axis
B9 G;8 ABMM?8 )G45?8 ?8I<G4G87 F4@C?8F 64A G;8A 58 ;84G87 5L 4 - &2 laser. Thecondition for levitation is derived from the law of momentum conservation applied to acontrol volume that contains the sample:!12$∫ #" 2 ρµ + p&%dA = Mg,(4)where ρ, μ and p are the gas density, vertical gas flow velocity and gas pressure,respectively, and Mg is the sample weight. The integral is performed over the surface A

of the control volume.

Figure 2(a) F;BJF4F6;8@4G<6I<8JB96BA<64?ABMM?8HF879BE48EB7LA4@<6?8I<tation.
*LC<64?F<M8B9G;8F4@C?8<FN @@ in diameter. The typical experimental set up foroxide melts is shown in Fig. 2(b). During this practical session, we will try to levitate aliquid Al2O3 droplet at a temperature above(a)

T

(b)
SampleConical nozzle

Focusinglens

MirrorPyrometer

SR X-rays

Laser beam
CCD camera

Conical nozzle

Gas

Fig. 2

Schematic view of the 6BA<64? ABMM?8 4 4A7 C;BGB:E4C; B9 the aerodynamiclevitation apparatus (b).

Reverse Monte Carlo simulation&A8 @4L E84?<M8 49G8E G;8 8KC8E<@8AG G;4G 7<99E46G<BA 74G4 L<8?7 BA?L BA8-dimensional

structural information. To reveal the complicated structure in disordered materials, it isnecessary to construct 3-dimensional atomic configurations on the basis of diffraction

data. The E8I8EF8$BAG84E?B($) method [4,5] has been shown to be a useful tool

to construct a three-dimensional structural model of disordered materials using mainly

8KC8E<@8AG4?7<99E46G<BA74G4 AG;8($F<@H?4G<BAG86;A<DH8G;84GB@FB94A<A<G<4?
6BA9<:HE4G<BA 4E8 @BI87 FB 4F GB @<A<@<M8 G;8 78I<4G<BA 9EB@ G;8 8KC8E<@8AG4?

7<99E46G<BA74G4HF<A:4FG4A74E7$8GEBCB?<F$BAG84E?B4?:BE<G;@16]. Here, we try togenerate a 3-dimensional atomic configuration of liquid Al2O3 that is consistent withdiffraction data. Then we will try to understand the reason why we cannot syntheF<M8
Al2O3 glass, from the point of view of glass forming ability.

Beamline practiceIn this practice, we try to perform high-energy x-ray diffraction measurement onlevitated liquid Al2O3 and try to model structure of liquid Al2O3 by means of reverse$BAG84E?B)<@H?4G<BAHF<A:K-ray diffraction data.
High-energy x-ray diffraction measurement	  -e measure x-ray diffraction from levitated liquid Al2O3 @8?G<A:CB<AG
using high-energy x-rays (E=61.4keV) from SPring-8.

T5L

	  The starting material is a crystalline Al2O3 bead whose diameter of 2 mm. The sample<F?8I<G4G875L7EL4<E4A7<F;84G875L4

measured by a pyrometer.

-&2 laser. Temperature of the sample isExperimental details

1. Put a Al2O3 bead on the tope of 6BA<64?ABMM?8

2. Adjust the position of mirror, pyrometer, and 64@8E4

3. Exit from the experimental hutch and levitate and melt the sample.

4. Open down stream shutter (DSS) from the computer and carry out a quick scanin the range of 0.3 < 2θ < 17TJ<G;4Ftep of 0.1Tand 200 msec dwell time to makesure sample is liquid.

5. Adjust the postion of sample by scanning the sample in X, Y, and Z directions.
6. 4EELBHGlong time measurement with a 2θ step of 0.05T and 10 sec dwell time

7. Repeat the scan to obtain sufficient statistics.
Data analysis	  Data analysis of raw diffraction data is performed using our originally developed
6B78 J;<6; E8DH<E8F -4I8@8GE<6F :BE (Fig. 3). The raw data are corrected for

CB?4E<M4G<BA 45FBECG<BA 4A7 546>:EBHA7 4A7 G;8 6BAGE<5HG<BA B9 B@CGBA F64GG8E<A:
J4FFH5GE46G87*;86BEE86G8774G4F8GFJ8E8ABE@4?<M87 to give the Faber-Ziman total
structure factor S(Q), and the pair distribution function G(r), total correlation function

T(r), radial distribution function N(r) are obtained by a Fourier transformation of S(Q).

ρ is atomic number density (Å-3).
G(r) =4πρr(g(r)-1)(4)

T(r)= G(r)+ 4πρr(5)N(r)=r G(r)+ 4πρr2 =r T(r)(7)

T(r)= 4πρrg(r)(6)

More detailed information is available in user’s manual of PDFgetX code developed by
Prof. S. J. L. Billinge et al (See chapter 5 of attached pdf file).

Fig. 3 GUI of data analysis code for PDF.
RMC simulation	  ($F<@H?4G<BAJ4FCEBCBF875LMcGreevy and 'HFMG4< in 1988. Two major opencodes ($POT [7] and ($'EB9<?e [8] are available. However we use the mostprimitiI8($6B7878I8?BC87<A ($ [4] BA'5864HF8<G<Fthe best code toHA78EFG4A7QJ;4G<F($R'?84F8G4>84?BB>4G4GG46;87GHGBE<4?7B6H@8AGF9BE($before the practice.
References[1] S. Kohara, $ GBH")HMHL4/ A4@HE4, Y. Sakurai, Y. Ohishi, and M. Takata, J.
Phys.: Condens. Matter, 19, 506101 (2007).

[2] T. E. Faber and J. M. Ziman, Phil. Mag. 11, 153 (1965).

[3] D.-L. Price, “High-Temperature Levitated MaterialsR4@5E<7:8+A<I8EF<GL'E8FF

2010.

[4] R. McGre8IL4A7#'HFMG4<Mol. Simul. 1, 359 (1988).

[5] R. McGreevy, J. Phys.: Condens. Matter 13, R877 (2001).

[6] N. Metropolis, A. -(BF8A5?HG;$ N. Rosenbluth, A. H. Teller, and E. Teller,
J. Phys. Chem. 21, 1087 (1953).

[7] ;GGCJJJFM9><;HNAC;LFE@6BC8A<A:;G@?
[8] http://www.rmcprofile.org/Main_Page.