BL04B2: Structure of High-Temperature Levitated Liquids Probed byHigh-energy X-ray Diffraction – The Relationship between LiquidStructure and Glass Forming 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 highvalues 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 disordered materials (glasses,liquids and amorphous materials) than it has hitherto been available. On the other hand,use of the levitation technique allows us to achieve deeply supercooled states, because
there is no interface between the liquid and a container wall. Hence we can obtain newmetastable materials (glasses) from the supercooled levitated liquid. In this practicalsession, we will try to levitate an oxide melt at a temperature beyond 2,000 ˚C by using
a conical nozzle levitator. We will learn how we can obtain reliable diffraction data andhow we analyze the data. Furthermore we will try to perform structure modelling ofdisordered materials on the basis of diffraction data employing a computer simulation
technique, in order to understand the relation between the structure of 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. We will use the 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 step scan method. Weanalyze the diffraction pattern and obtain Faber-Ziman total structure factor S(Q) [2] by
the following equation,

(1)where S(Q) can be obtained by a normalization of the corrected X-ray scattering
intensity I(Q). The pair distribution function g(r) and total correlation function T(r) areobtained by a Fourier transformation of S(Q),(2)(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-j
correlations, respectively. ρ is the atomic number density. We can assign atomic
correlation peaks and derive the coordination number by integrating the area under the
peak in the real-space function.

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. This
technique 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-divergent nozzle in which Bernouilli forces push the sample back to the axisof the nozzle. Stable levitated samples can then be heated by a CW CO2 laser. The
condition for levitation is derived from the law of momentum conservation applied to acontrol volume that contains the sample:(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) shows a schematic view of conical nozzle used for aerodynamic levitation.
Typical size of the sample is ~ 2 mm 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 2000 ˚C.
(a)

(b)

Fig. 2 Schematic view of the conical nozzle (a) and photograph of the aerodynamiclevitation apparatus (b).

Reverse Monte Carlo simulation
One may realize after the experiment that diffraction data yield only one-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 reverse Monte Carlo (RMC) method [4,5] has been shown to be a useful tool
to construct a three-dimensional structural model of disordered materials using mainly
experimental diffraction data. In the RMC simulation technique the atoms of an initialconfiguration are moved so as to minimize the deviation from the experimental
diffraction data, using a standard Metropolis Monte Carlo algorithm [6]. 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 synthesize
Al2O3 glass, from the point of view of glass forming ability.
References

[1] S. Kohara, M. Itou, K. Suzuya, Y. Inamura, 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 Materials”, Cambridge University Press,
2010.
[4] R. McGreevy and L. Pusztai, Mol. Simul. 1, 359 (1988).
[5] R. McGreevy, J. Phys.: Condens. Matter 13, R877 (2001).
[6] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, J.
Phys. Chem. 21, 1087 (1953).