Since most of the physical properties of a high-temperature liquid material are related to its atomic arrangement, it is important to develop methods to probe the local environment of the atoms in the sample. At very high temperature, the use of conventional furnaces presents major problems. In particular, the sample can be contaminated by the container and its structure thereby corrupted. One solution is to perform experiments under contactless conditions [1].

As opposed to crystals, liquids are disordered systems for which the structure is generally described in terms of distribution functions for interatomic distances and bond angles. In particular, the pair correlation function G(r) is proportional to the probability of finding an atom at a distance r from another taken at the origin. Such pair-distribution functions are directly accessible from the structure factor S(Q) obtained with classical X-ray diffraction measurements. However, the information obtained on a multi-component liquid with such diffraction experiments is limited because the measured average structure factor S(Q) and the corresponding pair correlation function G(r) are weighted sums of the partial functions for the different atom pairs, so that various structural models can be consistent with the experimental results. One solution is to use anomalous X-ray scattering (AXS) which is a more selective technique.

We have performed AXS experiments on levitated liquid yttrium oxide (Y2O3) at 2770 K. The measurements were carried out at two energies below and above the yttrium K absorption edge at the BM02 beamline. The principle of the method [1,2] is to subtract the two measured intensities to extract the yttrium structure factor SY(Q), containing information on the local environment of yttrium atoms.

Figure 47 shows the X-ray-weighted average structure factor S(Q) and the yttrium structure factor SY(Q) obtained on the high-temperature liquid. The sharpness of the first peak at Q = 2.07 Å-1 in both S(Q) and SY(Q) is remarkable and implies a relatively long-range of chemical ordering in the liquid.


Fig. 47: Average structure factor S(Q) measured at 16.75 keV and yttrium structure factor SY(Q) for liquid Y2O3 at 2770 K.


The corresponding average and yttrium pair correlation functions G(r) and GY(r) obtained using a classical Fourier transform of S(Q) and SY(Q) are shown in Figure 48. G(r) is the weighted average of the partial functions for the three atomic pairs: Y­O, Y­Y and O­O whereas GY(r) involves only Y­O and Y­Y. By combining the two results we have derived bond distances and coordination numbers for all three pairs. The two first peaks in GY(r) corresponds to Y­O and Y­Y nearest-neighbour pairs giving distances of about 2.26 Å and 3.74 Å respectively. We estimated the O­O distance to about 3.06 Å. The values obtained for the Y­O and Y­Y coordination numbers, slightly below 7 and 12, respectively, together with the position of the sharp main peak in S(Q), which coincides with the strongest Bragg peaks of the high-temperature H-type solid phase, imply that the close packing of this phase is preserved on melting.


Fig. 48: Average pair correlation function G(r) obtained at 16.75 keV and yttrium pair correlation function GY(r) for liquid Y2O3 at 2770 K.


This work shows that the combination of aerodynamic levitation, laser heating and AXS is a powerful technique for obtaining reliable partial structure information in complex high-temperature liquid materials.

[1] L. Hennet, D. Thiaudière, C Landron, J.-F. Bérar, M.-L. Saboungi, G. Matzen, D.L. Price, Nucl. Instrum. Meth. B, 207, 447-452 (2003).
[2] D.L. Price and M.L. Saboungi, in Local Structure from Diffraction, S.J.L. Billinge, M.F. Thorpe (Eds), Plenum Press, New York, 23-33 (1998).

Principal publication and Authors
L. Hennet (a), D. Thiaudière (a), C. Landron (a), P. Melin (a), D.L. Price (a), J.P. Coutures (b), J.-F. Bérar (c) and M.-L. Saboungi (d), Appl. Phys. Lett., 83, 3305-3307 (2003).
(a) CRMHT, CNRS, Orléans (France)
(b) IMP, CNRS, Perpignan (France)
(c) ESRF
(d) CRMD, CNRS, Orléans (France)