Comment on the Interpretation of the First Peak of the Rdf of Amorphous Metals

The first peak of the RDF has been calculated for the dense random packed (DRP) and Ni3P structures with a gaussian broadening of the atomic positions. It is found that the position of the broadened first peak of the RDF of DRP is 2 % greater than the hard sphere diameter. The contributions of Ni-Ni and NI-P pairs to the first peak of the RDF of amorphous Ni-P are discussed by comparing this peak to the calculated broadened peaks. Introduction. Structural models for amorphous metals which are currently most widely accepted are based on a dense random packing (DRP) of hard spheres. Bernal [l] first considered such structures in detail as a structural model for monatomic liquids ; it was subsequently suggested [2-51 that such DRP structures could provide suitable models for amorphous monatomic solids in particular, amorphous metals. In considering such a model, the effective hard sphere diameter, D,,,, of the atoms comprising the glass must be specified. This can be done by matching the experimental radial distribution function (RDF) to that for hard spheres. However, the determination of D,,, is complicated by experimental uncertainties and by the fact that amorphous metals generally are alloys containing elements which may differ in size and which do not interact identically to hard spheres. Cargill [5] first compared in detail an amorphous metal RDF to that for a DRP structure. He matched the second through fifth peak maxima of the function [p(r)/po] for amorphous Ni-P to that of Finney [6] for DRP and, noting that the Goldschmidt radii of Ni (*) Supported by Allied Chemical Corporation. (t) Former address : Materials Research Center, Allied Chemical Corp., Morristown, N. J., 7960, USA. and P differ by only 3 %, determined a D,,, of 2.42 A, 3 % less than the Goldschmidt radius of Ni. Polk 17, 81 pointed out the possible importance of compositional short range order and atomic size differences in the structure of amorphous Pd-Si and Ni-P. He showed [8] that it was topologically possible to have a random packed structure that approximated the short range order of Pd,Si and Ni,P by considering, as a first order approximation of such a structure, the structure obtained by placing the Si or P in the larger voids inherent in a dense random packing of inetal atoms. The Goldschmidt diameter of the metal atom was chosen as its D,,, while the metal-metalloid distances were proposed to be similar to those in the crystalline phases. Cargill and Cochrane [9] have reported that a least squares fit of 4 ~ r [ ~ ( r ) pO] of DRP and that of Ni,,P,,, excluding the region of the first peak, results in a D,,, of 2.46 W while the first peak position (R,, defined as the midpoint at 314 maximum) for Ni,,P,, occurs at 2.56 W. They suggest that the Ni-Ni separation is increased 3 % from that of DRP with the Ni Goldschmidt radius, (2.49 A) because of the introduction of P, while the higher r peaks suggest a lower D,, since they are due to configurations containing both Ni-Ni and Ni-P distances. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975210 C2-56 D. E. POLK AND D. S. BOUDREAUX Dixmier and Duwez [l01 observed small shoulders 011 the lower side of the first peak for Pd-Ni-P alloys and attributed these shoulders to the shortened metalphosphorus distance. Such shoulders were also found for CO-P and Ni-P alloys [g]. The RDF of dense random packings of hard spheres of two different sizes have been investigated by Sadoc et al. [l l]. In this paper, the first peak of the RDF has been calculated for the DRP structure of one sphere size and the Ni,P structure with a gaussian broadening of the atomic positions. The DRP peak is compared to that for Ni,P and amorphous Ni-P in order to determine the D,,, of Ni in these structures. Finally the separation of the Ni-P and Ni-Ni contributions to the first peak of amorphous Ni-P is discussed. Calculation of broadened peaks. The RDF used for DRP is that reported by Finney [6] in the form of a histogram for a hard sphere diameter of D = 1.00 and AD = 0.02. This was scaled to a D of 2.50 h; to approximate the Ni diameter. The number of pairs given in Finney's data for 1.00 (i. e., contact) were all assigned the distance 2.50 on the revised scale, while the number of pairs for 1.00 < D < 1.02 were distributed uniformly among the values 2.51, 2.52, 2.53, 2.54 and 2.55, etc. The first peak of the RDF for DRP with D = 2.50 is represented by the histogram of figure 1. FIG. 1. Finney's RDF of DRP with Denr of 2.50 iP [6] plotted as the histogram. The curve is this RDF after a gaussian broadening of 4 nup(u). Assuming that an atom at distance v from the origin atom undergoes thermal vibration with a gaussian shaped amplitude in all three dimensions, it is the function rp(r) which undergoes gaussian broadening, Thus the function rp(r) has been gaussian broadened and reconverted to the broadened 4 nr2 p(r) which is plotted as the curve in figure 1. The broadening was chosen so as to produce a peak height of -21, similar to those observed for amorphous metals. For the broadened peak, R, (the midpoint at 314 maximum) is at 2.55 A, i. e., 2 % greater than the hard sphere diameter. This shift is due primarily to the asymmetric shape of the first peak of the DRP stmcture ; broadening v 2 p(r) instead of vp(r) would provide almost as great a shift. The asymmetry of the original peak remains measurable ; at half-maximum, the peak has a width of 0.21 h; to the left and 0.25 A to the right of the r of the peak's maximum. Based on the data reported by Rundqvist et al. [l21 for the Ni3P structure, a broadened first peak of the RDF was calculated in the same manner for this structure. The Ni and P contributions were weighted by their respective atomic numbers. Figure 2 displays