P Villars, J Daams, Y Shikata - A new approach to describe elemental-property parameters - страница 1

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Chemistry of Metals and Alloys

Chem. Met. Alloys 1 (2008) 1-23 Ivan Franko National University of Lviv www.chemetal-journal.org

A new approach to describe elemental-property parameters

Pierre VILLARS[1]*, Jo DAAMS[2], Yoshihiro SHIKATA2, Krishna RAJAN3, Shuichi IWATA4

1 Material Phases Data System (MPDS), CH-6354 Vitznau, Switzerland

2 Meijo University, Nagoya, Japan

3 Iowa State University, Ames, IA-50011, U.S.A

4 The University of Tokyo, Tokyo, Japan

* Corresponding author. E-mail: villars.mpds@bluewin.ch

Received December 21, 2007; accepted February 17, 2008; available on-line March 31, 2008

The atomic number (AN) of the elements together with their 'periodic number' (PN) were found to form an efficient pair for the discussion of metallurgical and structural problems. The periodic number PN represents a different enumeration of the elements, emphasizing the role of the valence electrons. In contrast to the atomic number, PN depends in details on the underlying Periodic Table of the elements. As a first result we describe the elemental-property parameters 'atomic size SZa' and 'atomic reactivity REa', derived from fits to various experimental and theoretical data sets. These two parameters can be approximated as simple functions of AN and PN:

SZa = ksz [log (AN + 1)] [kpN - (log PN)3], REa = kRE {[log (AN + 1)] [kPN - (log PN)3]}-1 = ksz (SZa)-1, where kPN is a scaling factor, and ksz, kRE are fit parameters for a fit to experimental data. We argue that all elemental-property parameter patterns are derived from AN and PN. AN and PN represent fundamental elemental-property parameters independent from each other. Any pattern, which shows well-defined functional behavior within each group number GN, as well as within each main quantum number QN, can be included. On the example of compound formers/non-formers in binary, ternary and quaternary chemical systems we demonstrate that a quantitative link exists between material properties and AN, PN (or simple functions of both) of the constituent elements.

Electronegativity / Atomic radii / Chemical elements


Most of the chemical elements are well characterized by quite a number of experimental and theoretical elemental-property parameters, such as the atomic number AN, experimental and theoretical radii, ionization potential, bulk modulus, melting temperature, etc. On plotting these elemental-property parameters versus AN respectively PN, a vast majority of them can be grouped into distinctly different patterns. As examples, three of these patterns are shown in Figs. 1-3.

Elemental-property parameters belonging to the same pattern are qualitatively similar, although they are quantitatively different. The elemental-property parameters used in this work are listed in Tables 1a and 1b. In Table 1a the two fundamental pattern groups and in Table 1b four examples of derived pattern groups are given.

Our investigations revealed that the elemental-property   parameters  not   only   characterize the chemical elements themselves but also reflect quantitatively their interaction behavior between each other, which thus opens the possibility to predict physical or chemical properties of multinary systems.

Fundamental elemental-property parameters: Atomic Number AN and Periodic Number PN

Looking closer at the data sets listed in Tables 1a and 1b we notice that integer parameter values are only found in the first two patterns (Table 1a). The only comprehensive ones are AN and PN. The atomic number AN and the periodic number PN (the possibly misleading name for PN was chosen to have a neutral designation for different variants of this parameter) define, in a different way, the position of each element in the Periodic System (or Periodic Table) of the elements. AN is a simple count of the protons of the nucleus, which is equal to the total number of electrons of this element. The periodic number PN isх' >*>><

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Fig. 1 Eight elemental-property parameters (normalized to their maximum values) belonging to the atomic-size group (Table 1b), plotted versus periodic number PNME.

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Fig. 2 Eight elemental-property parameters (normalized to their maximum values) belonging to the atomic-reactivity group (Table 1b), plotted versus periodic number PNME.


Table 1 (a) The 13 elemental-property parameters considered grouped into the two fundamental groups, the atomic number AN pattern group and the periodic number PN pattern group. (b) The 26 elemental-property parameters considered grouped into the four derived groups, the atomic size pattern group, the atomic reactivity pattern group, the atomic affinity pattern group, and the atomic density pattern group.


I) Atomic number pattern group_

AN: Atomic number QN: Main quantum number AM: Atomic mass [1]

nc(C): Nuclear effective charge according to Clementi [2] nc(S): Nuclear effective charge according to Slater [3] cma(Mo): Coefficient of mass attenuation for Mo Ka [2] cma(Cu): Coefficient of mass attenuation for Cu Ka [2]

aes: Atomic electron scattering factor [2]_

II) Periodic number pattern group_

PNME: Periodic number according to Meyer [4]

PNMD: Periodic number according to Mendeleyev [5]

PN(P): Periodic number MN according to Pettifor's sequence [6]

VE: Valence electron number

GN: Group number_


i) Atomic size pattern group_

R(Z): Pseudo-potential radii according to Zunger [7]

Ri(Y): Ionic radii according to Yagoda [2]

Rc(P): Covalent radii according to Pauling [2]

Rm(WG): Metal radii according to Waber and Gschneidner [8]

Rve(S): Valence electron distance according to Schubert [9]

Rce(S): Core electron distance according to Schubert [9]

R(M): Radii according to Miedema (derived from his V2/3 compilation) [10]

R(VD): Radii according to Villars and Daams (derived from their V compilation) [11]

ii) Atomic reactivity pattern group_

EN(MB): Electronegativity according to Martynov and Batsanov [12]

EN(P): Electronegativity according to Pauling [1]

EN(AR): Electronegativity according to Allred and Rochow [2]

EN(abs): Absolute electronegativity [9]

IE(first): First ionization energy [1]

CP(M): Chemical potential according to Miedema [10]

wf: Work function [1]

n(WS): n(Wigner and Seitz) according to Miedema [10]_

iii) Atomic affinity pattern group_

Tfus: Temperature of melting [1]

Tvap: Temperature of boiling [1]

AHvap: Enthalpy of vaporization [1]

AHfus: Enthalpy of melting [1]

A Hatom: Enthalpy of atomization [1]

A Hsurf(M): Surface energy according to Miedema [10]

CE(B): Cohesion energy according to Brewer [13]

VC: Isothermal volume compressibility [13]_

iv) Atomic density pattern group

DX: X-ray density [1] Dm: measured density [1]



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