201. The Nature o f the Metallic Bond. III

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1 No. 8] The Nature o f the Metallic Bond. III Atomic Interactions in Alloys. I By San-ichiro MIZUSHIMA, M.J.A., and Isao Ichishima Tokyo Research Institute, Yawata Iron and Steel Co. Ltd., Ida, Kawasaki-City (Comm. Oct. 12, 1966) I. Phase Diagrams and Aggregation of Atoms. In our previous papersl''2' we proposed a tentative explanation of both cohesive energy and crystal structure in terms of the wave functions of the individual atoms. In the case of transition metals which occupy the greater part of the periodic table, cohesive energy and crystal structure can be explained roughly by the number of d-electrons and the way in which d-orbitals (in the sea of conduction electrons) change with atomic number. We now turn to alloys for which phase diagrams provide us with an important tool. As will be seen from previous papers, our intention lies not in the application of such diagrams to practical problems, but rather in the understanding of diagrams in terms of atomic interactions. In other words, we try to understand an assembly of different kinds of atoms as we did in Parts I and II for crystals consisting of atoms of the same kind. Let us first consider alloy systems consisting of two kinds of atoms miscible in all proportions. This will give us information about the degree of similarity of the nature of individual atoms within which two different kinds of atoms can form a homogeneous phase in all proportions. It is quite natural that the neighboring elements in the periodic table (or diagonally neighboring elements) will form usually such a phase; for example, Cu-Ni, Ni-Pd, and Co- Pd systems. As two kinds of atoms become more dissimilar, they will not be miscible in all proportions. This is particularly the case at lower temperatures, where the individual nature of atoms becomes relatively more important, as we have seen in Parts I and II. In Ni-Pt and Au-Cu systems the energy will be almost independent on the arrangement of atoms at higher temperatures. However, at lower temperatures, where the thermal energy is low, a periodic arrangement of two kinds of atoms decreases the local accumulation of energy, since the atomic size of one component is considerably different from that of the other. This will be one of

2 914 S. MIZUSHIMA and I. ICHISHIMA [Vol. 42, the factors to explain the order-disorder transformation. That the size effect is not the only factor of the explanation is easily seen from the comparison of Ni-Pt with Ni-Pd systems and Au-Cu with Ag-Cu systems. Pd is not much different in size from Pt, but Ni-Pd system shows no ordered structure even at room temperature. Both Au and Ag have nearly the same size, which is due to the lanthanide contraction occuring in Au with fourteen f electrons. Notwithstanding nearly the same size of Au and Ag, solubility of Cu in Ag is quite different from that of Cu in Au. This may have something to do with the electronegativity of Aucore which is much higher than that of Ag-core. This difference in electronegativity may contribute to the difference in the attractive force between cores of different kinds, probably through the change of state of conduction electrons, (this including of course exchange forces. See ref. 4 of Part I.) This might be a more important factor determining order-disorder transformation. We should like to add that in the quantitative discussion on this problem we have to take into account the entropy of mixing. II. Bias of Electron Cloud and Electronegativity. In simple salts where we have two kinds of atoms with large difference in electronegativity, one or more electrons are transferred completely from one atom to another to form anion and cation. Therefore, all the electrons are localized in ions, and the electrostatic force plays most important part in the formation of the crystal. In molecules electrons are also localized, but valence electrons are shared among few atoms. However, in many cases electron clouds are biased, resulting in permanent dipole moments of polar molecules. A situation similar to this may apply to conduction electrons of alloys and they are more concentrated about one kind of cores than another. This may contribute in a way to the binding of different kinds of atoms, an extreme one having a structure almost equal to that of salt crystals mentioned above. In other words we consider the gradual transition from one extreme type of binding to another in alloys. This transition in the binding type is naturally governed by the ionization potential and electron affinity of the atoms forming alloys. However, both of them are concerned with isolated atoms and what is more desirable is something like electronegativity related to both component atoms. In the case of a molecule this is understood as the power of an atom to attract electrons to itself and, therefore, is a measure by which a polarity of a molecule may be determined. The concept of electronegativity of an atom in a simple molecule,

3 No. 8] Nature of Metallic Bond. III 915 as it stands, will not be strictly applicable to atoms in alloys. However, it certainly helps us to take some measures in studying new aspect of alloys. Quite a few alloys form intermediate phases over a range of compositions. Those containing IVb, Vb, and VIb group elements often form intermetallic compounds with simple whole number ratios of component atoms. In Ia and ha group elements we can treat eth metallic crystals rather simply as consisting of cores and conduction electrons. However, they often form intermetallic compounds with IVb, Vb, and VIb elements in the states which are not much different from those of metallic salts, because there is large electronegativity difference. Even in Ca-Tl system electrons are attracted to Tl so much as to form a state close to Ca++T1~-. Tl-r has three outer p-electrons and forms a cubic crystal by p-bonds given rise to by quantum mechanical resonance among these p-orbital structures, while Ca++ ions enter into the body-center to become electrically neutral. III. Ionization Potential of Transition Elements. In Parts I and II it was shown that the binding by d-orbitals plays most important role in cohesive energy and crystal structure of transition metals. In alloys containing them as one component d-orbitals play a part in binding, but deformation of d-orbitals as well as the change of the number of the electrons in the presence of foreign atoms should be taken into account. In order to get a rough idea by which we may find a clue to this problem, we should like to consider the third ionization potentional. This is the potential of removing a d-electron further from M++, which is an ion obtained by removing two electrons already from the corresponding atom. Roughly speaking we are intersted in removing one electron from the d-shells in the sea of conduction electrons. As shown in Fig. 1, the first ionization potential of transition elements does not change much with atomic number. However, if we plot the third ioni- Fig. 1. Ionization potential.

4 916 S. MI~USHIMA and I. ICHISHIMA [Vol. 42, nation potential of ion cores M++ of transition elements against the atomic number, we see that the behavior is similar to that of the ionization potential of nonmetallic elements plotted against the atomic number. Therefore, the fact that ionization potential of M++ of transition metals behaves similarly as that of nonmetallic elements with p valence electrons may throw light upon the binding of d-electrons in the sea of conduction s-electrons of transition metals. In other words the nature of this binding may be understood to some extent by p-binding of nonmetals. Since the ionization potential of M+ (2nd ionization potential) is equal to the electron affinity of M++ in absolute value, we may calculate the electronegativity of M++ of transition metals as the mean value of the ionization potential and the electron affinity. In the case of molecules this corresponds to the electronegativity of the Mulliken type, which is different from that of Pauling. In the case of pure metals the electronegativity defined above can be used in our discussion. In the former part of transition elements of the first long period, where the electronegativity of M++ is low, a d- electron may be fairly released from the core. However, in the latter part where the electronegativity is high, the core becomes so electronegative that it will attract even the conduction electrons. This will be shown by the magnetic measurement on Ni that the number of conduction electron per atom amounts only to 0.6. It will be seen that the notation M++ does not necessarily mean that two electrons are always transferred from an atom to the conduction band, but has been used for the sake of convenience as a basis on which the idea is proposed. Sigma phase or a hard, brittle intermediate phase (such as FeCr) occurs in many binary alloys of transition metals. (One of IVa, Va, and VIa elements often forms sigma phase with one of VIIa, VIII1, VIII2, and VIII3 elements). The occurence of such a phase may be explained by the analogy of a nonmetallic compound with p valence electrons mentioned above. If the electronegativity difference between two atoms, A and B is not so large, the molecule AB becomes more covalent, but if the difference is large, AB becomes more ionic. Anyhow the actual state of the molecule is represented by al/ca;b + b~ra+b- formed by linear combination of the wave functions corresponding to the normal covalent structure A ; B and the ionic structure AB. In other words we have a system resonating between covalent and ionic structures and the system is stabilized by the resonance energy. The same would apply to the alloys of transition metals mentioned

5 No. 8] Nature of Metallic Bond. III 917 above: i.e, the resonance between ionic and covalent structures formed by d-orbitals may play important part in stabilizing sigma phase with high hardness. IV. Alloys of Transition Metals. Alloys and compounds containing transition elements include interesting ones other than those mentioned above; for example, a series of systems formed by a transition element and one of those of Vb and VIb group elements. Roughly speaking the latter has larger atomic volume and higher electronegativity. Therefore, their atoms in general have nearly closed packed structures by themselves and sites available to atoms of transition elements are tetrahedral positions or octahedral positions (in some cases the structure may be deformed). If the electronegativity difference betweem two atoms is so large as in MnO, the conduction (valence) electrons of Mn are absorbed in the p-shell of 0 to form an ionic crystal M++O. The difference between ionic radii becomes larger than that between atomic radii to allow all the octahedral sites available to Mn++ so that the crystal of MnO becomes of NaCI-type. Here, p-orbitals of 0^r overlap d7-orbitals of Mn++ to result in superexchange (antiferromagnetism). So we have again bonds of both ionic and covalent character which stabilize MnO crystal, resulting in high melting point. This is an extreme case, but a bond similar to this has to be taken into consideration, when p-orbital of nonmetallic element overlaps d-orbital of transition element. Furthermore, as mentioned in Part II, as the principal quantum number gets higher, binding becomes more metallic. What has been stated above about VIb and Vb elements may have to be taken into account to a certain extent in the discussion on IVb and IIIb elements. Let us consider the opposite case, in which metal atoms are large enough to form closed packed structures by themselves. Therefore, the crystals show essentially metallic properties. Transition metals, Ti, V, Zr, Nb, Hf, Ta, etc, forming interstitial alloys with small atoms, C and N, are examples of this kind. They also form alloys of NaCI-type in which d-orbital of transition element will overlap p-orbital of C or N. Therefore, again we may consider bonds of both covalent and ionic character, resulting in formation of alloys with high hardness. In the case of similar interstitial alloys of Cr, Mn, Fe, Co, and Ni the size of solute atom is not large enough to leave sufficient room for interstitial atoms, e.g., Fe-C. Therefore, the lattice in the vicinity of each solute atom is considerably deformed. However, since C atom has strong atomic

6 918 S. MIZUSHIMA and I. ICHISHIMA [Vol. 42, orbital character and Fe core has incomplete 3d-shell, we may consider a binding of covalet nature between C and Fe atoms. Furthermore this binding will be stabilized by the resonating ionic structure which results from the electronegativity difference between the solute and solvent atoms. This binding will in turn affect the state of conduction electrons from which we can reasonably consider long range effect of solute atoms. Thus we see that it will leave too many problems behind, to explain the effect of solute atoms away as the problem of lattice distortion only. IV. Summary. The importance of the consideration of electronegativity difference between component atoms of alloys has been emphasized. For those containing transition elements quantum mechanical resonance between ionic structure and covalent structure formed by d-orbitals something like that of molecules have been considered. In conclusion we would like to repeat that this series of papers has a significance as a whole and, therefore, if only a part of it will be picked up without any attention to the remaining part, it will make no sense. References 1) S. Mizushima and I. Ichishima: Proc. Japan Acad., 42, 783 (1966), 2) --: Ibid., 42, 789 (1966).

- A polar molecule has an uneven distribution of electron density, making it have ends (poles) that are slightly charged.

14 POLARITY and shape: - A polar molecule has an uneven distribution of electron density, making it have ends (poles) that are slightly charged. POLARITY influences several easily observable properties.