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The bearing of neutron scattering data on the Pauling theories of transition metals
ACTA
1462
METALLURGICA,
The bearing of neutron scattering data on the Pauling theories of transition metals* In 1938, Paulingci) advanced the view that, in transition metals, the bonding electrons are in hybrid spcl states. From a study of interatomic distances and other physical properties, he concluded that, in passing along the sequence K + Ca + SC - - - + Ni, the number of bonding electrons/atom at first increases steadily but that, at Cr, electrons begin to enter atomic 3d orbitals whose electrons are responsible for magnetic properties. Pauling noted that the highest saturation moment of 2.44,n per atom is reached in alloys of Fe and Co, and therefore postulated the existence of 2.44 atomic 3d orbitals, whilst the remaining 2.56 3d orbitals hybridise with 4s and 413 orbitals to produce hybrid bonding. Since the saturation moment of Fe is 2.22,n (i.e. less than the number of atomic 3d orbitals) Pauling proposed that 2.22 electrons/atom are in atomic 3d orbitals, leaving 5.78 electrons/atom for hybrid bonding, and this last number was assumed to remain constant in the series of elements Cr, Mn, Fe, Co, and Ni. This assumption was arbitrary and appears to have been made in order to give a regular increase of one in the number of electrons in atomic 3d orbitals for each step in the Periodic Table. This first Pauling scheme was used to interpret the structures and properties of many
VOL.
12,
1964
transition metal alloys, and numerous explanations were based on the assumption of the 2.44 atomic d orbitals which were imagined to exist in all three Transition Series. In 1953 Pauling@) advanced a theory of the ferromagnetism of iron, according to which each atom gave rise to 6 bonding electrons, and contained 2 electrons in atomic 3d orbitals, giving rise to a saturation moment of 2fiLB. The remaining 0.22,, of the saturation moment was regarded as arising from interaction between the atomic 3d electrons and the conductivity electrons, in a manner similar to that suggested by Zener. t3) In the 1960 edition of his book “The Nature of the Chemical Bond”, Paulingf4) rejected the configurations of his 1938 paper, and regarded the elements in Groups VIA to VIIIC in all three Transition Series as possessing a “valency” of 6, i.e. 6 bonding electrons/atom, in contrast to the 5.78 of the earlier view. In a recent paper Shull t5)has described experiments on neutron scattering by iron, and Fig. 1, which is taken from this paper, shows the magnetic spin density distribution in the (110) diagonal plane of the unit cell. This shows that the spin density is very small in the region midway between two atoms, t and is concentrated mainly round the individual atoms. This is consistent with the spin density which would be obtained by the superposition of magnetic atomic
Irqn nucleus
Iron nucleus FIG. 1. Magnetic spin density distribution in the (110) diagonal plane of the iron unit cell. Two neerest neighbour iron atoms are shown in this section. Very small density is to be noted in the mid-region between these atoms. (This figure is reproduced from e paper by Shull’6’.)
LETTERS
TO
states. Equally electrons in band states with wave functions and approximated as linear combinations of atomic d orbitals would give the same results. On either interpretation, the description of the magnetic electrons is in terms of little modified and little hybridised atomic d functions; the non-spherical nature of the spin density results from selective population of the 5 cl states available. Shull and Yamada(Q (also Shullc5)) have shown by neutron scattering methods that interaction between 49 and 32 electrons will give rise to a negative and not to a positive magnetisation. This means, therefore, that the second Pauling view of a positive contribution 3d interaction is of 0.22,s for conductivity/atomic incorrect, and it is unlikely that any model is correct which gives Fe atoms in a state with a moment of exactly 2pB. Of the Pauling approaches, the first is, therefore, now the more probable. As has been shown elsewhere (Hume-Rothery’7)) the assumption of the same constant valency for all the elements from Group VIA to VIIIC in all three Transition Series is not in agreement with the facts, and modified schemes have been suggested. The exact electronic configurations of these transition metals are still in dispute, but it is satisfactory to know that the magnetic electrons are exclusively d like, and that atomic electronic structure may still be significant in the solid. The author acknowledges helpful discussion with Dr. W. M. Lomer and Dr. S. L. Altmann. W. HUME-ROTHERY Department of Metallurgy University of Oxford References L. PAULINO, Phys. Rev. 54, 899 (1938). L. PAULINQ, PTOC.Nut. Acud. Sci. 89. 551 (1953). C. ZENER, Phys. Rev. 81, 440 (1951); 62, 463 (1951); 83, 299 (1951). L. PAULINO, The Nature of the Chemical Bond. Cornell, New York (1960). C. G. SHULL, Electronic Structure and Alloy Chemistry of the Transition Metals. , D. 69. Interscience. New York (1963). 6. C. G. SHULL and Y. YAMADA, J. Phys. Sot. Japan, Suppl. B, BIII, 17, 1 (1961). 7. W. Hum-ROTHREY, Atomic Theory for Student8 of Metallurgy, p. 378. Inst. of Metals (1962); also W. HUMEROTHERYand B. R. COLES,Advanc. Phye. 3, 149 (1954). &
* Received July, 2 1964. i Jn Fig. 1, the upper left end lower right hand corners are the positions of two atoms which are nearest neighbours.
Electron microscope observations of the formation of 0 from 0’ in A14% Cu* In the early stages of an investigation of precipitation at grain boundaries, an Al4% Cu alloy has
THE
EDITOR
1463
given incidental information on the formation of 0 phase from the transitional 0’ phase. A sheet specimen 0.005 in. thick, was solution treated at 500°C and transferred to an ageing furnace at 380% for 15 min. Electron microscope examination of thin foils revealed plates of 0’ containing two types of rod-like 0 particles. Figures 1 and 2 are from foils oriented respectively with [510],, and [3Ol],i directions approximately parallel to the electron beam. The 0’ phase forms as (OOl), platelets on the {lOO},i matrix planes. Two orientations of the 0’ plates, A and B, are parallel or almost parallel to the electron beam in the Figs. 1 and 2. The third 0’ plate orientation is almost perpendicular to the electron beam, that is at a shallow angle to the foil surface. Such plates contain 0 rods (v, w, x, y and z in Figs. 1 and 2). Rods v, w, x and y are at angles of 12” to 13’ to one of the two (loo),, directions in the plane of the 0’ plate (this is near to the value 11’ 18’ for a (510),, direction). It can be seen from the edge-on view of the 0’ plates A and B that the rod axes lie in the plane of the 0’ plates. The orientation relationship between rods such as v, w, x, y and the matrix was obtained by electron diffraction from five different 0’ plates, and is: [lOOI, 11[lOOI*,; [Oil],
11[001],1 (orientation 1)
The [lOOI, direction is perpendicular to the 0’ plate, It follows from symmetry considerations that there are four possible 0 orientations for each 0’ plate, all of which are present in Fig. 2 (i.e. v, w, x and y). The orientation relationship is the same as that observed by Heimendahl and Wassermann(l) when 0 formed from 0’ at 45O”C, but the details of the morphology of the @ particles were not given. The orientation of one rod axis is shown on the right hand side of Fig. 3; all rods form in (032)e directions. The rods are clearly defined and have very straight sides so that a simple explanation of their shape might be expected. If the morphology of the @ phase arose entirely from a highly preferred growth direction then it might be expected to be the same as that in the melt, in which case the growth direction is [OOl],. Since the rods form in this case with an (032 )e axis and only that (032)e axis which is almost parallel to an (051),i direction, it is apparent that the growth direction is dependent on the orientation of 0 with respect to the matrix. It might be expected that the preferred direction of growth would correspond to a zone axis of planes of easy fit with the matrix and high atomic density. (The rods are growing in the Al matrix at the stage observed
1462
METALLURGICA,
The bearing of neutron scattering data on the Pauling theories of transition metals* In 1938, Paulingci) advanced the view that, in transition metals, the bonding electrons are in hybrid spcl states. From a study of interatomic distances and other physical properties, he concluded that, in passing along the sequence K + Ca + SC - - - + Ni, the number of bonding electrons/atom at first increases steadily but that, at Cr, electrons begin to enter atomic 3d orbitals whose electrons are responsible for magnetic properties. Pauling noted that the highest saturation moment of 2.44,n per atom is reached in alloys of Fe and Co, and therefore postulated the existence of 2.44 atomic 3d orbitals, whilst the remaining 2.56 3d orbitals hybridise with 4s and 413 orbitals to produce hybrid bonding. Since the saturation moment of Fe is 2.22,n (i.e. less than the number of atomic 3d orbitals) Pauling proposed that 2.22 electrons/atom are in atomic 3d orbitals, leaving 5.78 electrons/atom for hybrid bonding, and this last number was assumed to remain constant in the series of elements Cr, Mn, Fe, Co, and Ni. This assumption was arbitrary and appears to have been made in order to give a regular increase of one in the number of electrons in atomic 3d orbitals for each step in the Periodic Table. This first Pauling scheme was used to interpret the structures and properties of many
VOL.
12,
1964
transition metal alloys, and numerous explanations were based on the assumption of the 2.44 atomic d orbitals which were imagined to exist in all three Transition Series. In 1953 Pauling@) advanced a theory of the ferromagnetism of iron, according to which each atom gave rise to 6 bonding electrons, and contained 2 electrons in atomic 3d orbitals, giving rise to a saturation moment of 2fiLB. The remaining 0.22,, of the saturation moment was regarded as arising from interaction between the atomic 3d electrons and the conductivity electrons, in a manner similar to that suggested by Zener. t3) In the 1960 edition of his book “The Nature of the Chemical Bond”, Paulingf4) rejected the configurations of his 1938 paper, and regarded the elements in Groups VIA to VIIIC in all three Transition Series as possessing a “valency” of 6, i.e. 6 bonding electrons/atom, in contrast to the 5.78 of the earlier view. In a recent paper Shull t5)has described experiments on neutron scattering by iron, and Fig. 1, which is taken from this paper, shows the magnetic spin density distribution in the (110) diagonal plane of the unit cell. This shows that the spin density is very small in the region midway between two atoms, t and is concentrated mainly round the individual atoms. This is consistent with the spin density which would be obtained by the superposition of magnetic atomic
Irqn nucleus
Iron nucleus FIG. 1. Magnetic spin density distribution in the (110) diagonal plane of the iron unit cell. Two neerest neighbour iron atoms are shown in this section. Very small density is to be noted in the mid-region between these atoms. (This figure is reproduced from e paper by Shull’6’.)
LETTERS
TO
states. Equally electrons in band states with wave functions and approximated as linear combinations of atomic d orbitals would give the same results. On either interpretation, the description of the magnetic electrons is in terms of little modified and little hybridised atomic d functions; the non-spherical nature of the spin density results from selective population of the 5 cl states available. Shull and Yamada(Q (also Shullc5)) have shown by neutron scattering methods that interaction between 49 and 32 electrons will give rise to a negative and not to a positive magnetisation. This means, therefore, that the second Pauling view of a positive contribution 3d interaction is of 0.22,s for conductivity/atomic incorrect, and it is unlikely that any model is correct which gives Fe atoms in a state with a moment of exactly 2pB. Of the Pauling approaches, the first is, therefore, now the more probable. As has been shown elsewhere (Hume-Rothery’7)) the assumption of the same constant valency for all the elements from Group VIA to VIIIC in all three Transition Series is not in agreement with the facts, and modified schemes have been suggested. The exact electronic configurations of these transition metals are still in dispute, but it is satisfactory to know that the magnetic electrons are exclusively d like, and that atomic electronic structure may still be significant in the solid. The author acknowledges helpful discussion with Dr. W. M. Lomer and Dr. S. L. Altmann. W. HUME-ROTHERY Department of Metallurgy University of Oxford References L. PAULINO, Phys. Rev. 54, 899 (1938). L. PAULINQ, PTOC.Nut. Acud. Sci. 89. 551 (1953). C. ZENER, Phys. Rev. 81, 440 (1951); 62, 463 (1951); 83, 299 (1951). L. PAULINO, The Nature of the Chemical Bond. Cornell, New York (1960). C. G. SHULL, Electronic Structure and Alloy Chemistry of the Transition Metals. , D. 69. Interscience. New York (1963). 6. C. G. SHULL and Y. YAMADA, J. Phys. Sot. Japan, Suppl. B, BIII, 17, 1 (1961). 7. W. Hum-ROTHREY, Atomic Theory for Student8 of Metallurgy, p. 378. Inst. of Metals (1962); also W. HUMEROTHERYand B. R. COLES,Advanc. Phye. 3, 149 (1954). &
* Received July, 2 1964. i Jn Fig. 1, the upper left end lower right hand corners are the positions of two atoms which are nearest neighbours.
Electron microscope observations of the formation of 0 from 0’ in A14% Cu* In the early stages of an investigation of precipitation at grain boundaries, an Al4% Cu alloy has
THE
EDITOR
1463
given incidental information on the formation of 0 phase from the transitional 0’ phase. A sheet specimen 0.005 in. thick, was solution treated at 500°C and transferred to an ageing furnace at 380% for 15 min. Electron microscope examination of thin foils revealed plates of 0’ containing two types of rod-like 0 particles. Figures 1 and 2 are from foils oriented respectively with [510],, and [3Ol],i directions approximately parallel to the electron beam. The 0’ phase forms as (OOl), platelets on the {lOO},i matrix planes. Two orientations of the 0’ plates, A and B, are parallel or almost parallel to the electron beam in the Figs. 1 and 2. The third 0’ plate orientation is almost perpendicular to the electron beam, that is at a shallow angle to the foil surface. Such plates contain 0 rods (v, w, x, y and z in Figs. 1 and 2). Rods v, w, x and y are at angles of 12” to 13’ to one of the two (loo),, directions in the plane of the 0’ plate (this is near to the value 11’ 18’ for a (510),, direction). It can be seen from the edge-on view of the 0’ plates A and B that the rod axes lie in the plane of the 0’ plates. The orientation relationship between rods such as v, w, x, y and the matrix was obtained by electron diffraction from five different 0’ plates, and is: [lOOI, 11[lOOI*,; [Oil],
11[001],1 (orientation 1)
The [lOOI, direction is perpendicular to the 0’ plate, It follows from symmetry considerations that there are four possible 0 orientations for each 0’ plate, all of which are present in Fig. 2 (i.e. v, w, x and y). The orientation relationship is the same as that observed by Heimendahl and Wassermann(l) when 0 formed from 0’ at 45O”C, but the details of the morphology of the @ particles were not given. The orientation of one rod axis is shown on the right hand side of Fig. 3; all rods form in (032)e directions. The rods are clearly defined and have very straight sides so that a simple explanation of their shape might be expected. If the morphology of the @ phase arose entirely from a highly preferred growth direction then it might be expected to be the same as that in the melt, in which case the growth direction is [OOl],. Since the rods form in this case with an (032 )e axis and only that (032)e axis which is almost parallel to an (051),i direction, it is apparent that the growth direction is dependent on the orientation of 0 with respect to the matrix. It might be expected that the preferred direction of growth would correspond to a zone axis of planes of easy fit with the matrix and high atomic density. (The rods are growing in the Al matrix at the stage observed