Investigation of decomposition of the PdB_y solid solution by time-resolved X-ray powder diffraction

T. G. Berger¹, A. Leineweber¹, E. J. Mittemeijer¹, M. Knapp²

¹Max Planck Institute for Metals Research, Heisenbergstr. 3, 70569 Stuttgart, Germany.

²Institute for Materials Science, Darmstadt University of Technology, Petersenstr. 23, 64287 Darmstadt, Germany.

The palladium-rich terminal solid solution PdB_y (fcc arrangement of Pd, B randomly occupies interstitial octahedral sites) shows an interstitial solubility of B up to approximately PdB~_0.20 above about 450°C and two-phase areas as well as several low temperature phases at lower temperatures. A remarkable feature of the PdB_y solid solution is a miscibility gap with a critical temperature of T_crit = 410°C (Figure 1) [1, 2] which covers at the monotectic temperature of T_mono = 312°C a composition range of about 0.03 < y < 0.10.

This work presents the results of X-ray powder diffraction investigations (CuKa₁ radiation in Bragg-Brentano geometry and synchrotron radiation with l = 1.1315 Å on the B2, HASYLAB, Hamburg) performed on initially homogeneous PdB_y alloys (y = 0.050, 0.065) which were first quenched from 800°C (i.e. ‘within’ the single phase solid solution field) and then annealed at 340°C and 355°C, (i.e. ‘within’ the miscibility gap) for various periods of time. The decomposition of the solid solution into a boron-rich solid solution phase and a boron-poor solid solution phase is clearly visible due to the corresponding splitting of the Bragg reflections. However, even after the longest applied heat-treatment times (8 weeks at 340°C and 2 weeks at 355°C), still considerable diffraction-line broadening remains.

The diffraction-line profiles were fitted, applied to several reflections simultaneously, in a Rietveld like fashion [3], considering a convolution of several line-broadening contributions:

1. The instrumental line-broadening

2. A quasi-continuous composition distribution density function p(y), which was approximated by a step-function between y = 0 and y = 0.12 with equal concentration intervals of dy in the range of 0.0005 - 0.002 (value chosen depending on the resolution of the diffraction data), and adopting a Vegard’s law behaviour for the lattice parameter of PdB_y [4]:

a = 3.8920 Å + 0.6882 Å×y

3. Anisotropic microstrain-broadening due to internal stresses according to Refs. [5, 6]

The use of small step sizes for p(y) leads to strong correlations between the p(y) values of adjoining compositions y'-dy, y', y'+dy. This problem can be overcome by incorporating 'penalty functions' in the overall fitting procedure which add to the c² value due to the deviation of the fitted from the observed profile. This penalty function increases with the square of the second derivative of p(y) for each value of y; the second derivative is especially large if 'unnatural' fluctuations of p(y) occur.

Figure 1: Section of the Pd-B phase diagram with the miscibility gap [8].	Figure 2: 311-Diffraction peak group (Pattern taken using synchrotron radiation with λ = 1.1315 Å).

The diffraction-line broadening due to variation in composition as expressed by p(y) also masks line broadening due to microstresses (e.g. due to dislocations). However, the latter contribution is clearly detectable due to its usually significant anisotropy (which derives from the Pd crystals intrinsic mechanical anisotropy) [5], whereas broadening due to composition variations is isotropic for cubic crystals [7].

The time-dependent changes of p(y) can be summarised as follows:

i. For short annealing times a distinct boron-rich phase (relative to the initial solid solution’s composition) and a distinct boron-poor phase appear, whereas the solid solution of the original composition is still present. The compositions of the product phases are closer to the initial composition than predicted by the phase diagram.

ii. The fraction of the original phase decreases (and finally disappears) and the two product phases increase with annealing time. Simultaneously, the compositions of the product phases ‘move’ towards the respective equilibrium values.

iii. Upon increasing annealing times an apparently stable composition distribution p(y) is reached, which however, does not correspond to the sum of two delta functions located at the two boundary compositions of the miscibility gap at the annealing temperature. Instead, an apparent probability for intermediate concentrations occurs in the form of ‘tails’ connected with the two maxima of p(y) towards intermediate y (see Fig 2).

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3. TOPAS, General Profile and Structure Analysis Software for Powder Diffraction Data, V2.0, Bruker AXS GmbH, Karlsruhe, Germany.

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