Copper, copper alloys and the electron concentration concept

COPPER,

COPPER

ALLOYS

AND

THE N.

ELECTRON

CONCENTRATION

CONCEPT*

ENGELt

For a long time copper has been considered a one electron metal with a filled d-shell, thus being the first normal element after the transition metals. The properties of copper do not resemble those of the alkaline metals. It is shown that the properties and alloy behavior of the copper column metals are better accounted for if the filling of the d-shell is placed between copper and zinc, silver snd cadmium, or gold and mercury leaving copper, silver, and gold as transition metals. The f.c.c. phase extending through the iron~obal~nickel-copper diagrams is limited by the breakdown of the d-bonding at about 38% zinc. Increasing the average number of electrons above this limit causes electrons to fill the d-shells in copper, nickel or other transit,ion metals leaving one or zero outer electrons for the lattice control of the Hume-Rothery p, y and E phases. CUIVRE,

ALLIAGES DE CUIVRE ET LE CONCEPT CONCENTRATION ~LECTRONIQUE

DE

Pendant longtemps le cuivre a 8t8 consid&+ comme un m&al monoBlectronique, B couohe d saturbe, donc comme le premier element normal apr&s les mBtaux de transition. Les propri&&s du cuivre ne ressemblent pas 8. colles des m&aux alcalins. On montre que l’on rend mieux compte des propriWs et du comportement en alliage des m&aux de la colonne du cuivre si on fait intervenir la saturation de la oouche d entre le cuivre et le zinc, l’argent et le cadmium, ou l’or et le mercure, en laissant le cuivre, l’argent et I’or parmi les m&aux de transition. La phase c.f.c. occupant les diagrammes fer-cobaltnickel-cuivre est limit&e par la rupture de la liaison d & une concentration d’environ 38% en zinc. Un accroissement du nombre moyen d’klectrons au del& de cette limite entraine un remplissage des couches d dans le cuivre, le nickel ou les autres m&aux de transition, kissant> un ou zero i?lectron externe pour le contrele dans le rkseau des phases de Hume-Rother~ /I, y at. E. KUPFER,

KUPFERLEGIERUSGEN USD ELEKTRONENKONZENTRATION

DAS

MODELL

DER

Kupfer wurde lange Zeit als ein Einalektron+motall mit einor aufgefiillten d-&hale angesehen, also als das erste normale Element. nach den Uber~angsmetall~~. Die Eigenschaften von Kupfer gleichen nieht denen der Alkalimetalle. Es wird gezeigt, da13die Eigensehaften und das Legierungsverhalten der Metalle der Kupfergruppe besser verstanden werden kann, wenn die Auffiillung der d-Schale zwischon Kupfer und Zink, Silber und Kadmium oder Gold und Quecksilber erfolgt, d.h. Kupfer, Silber und Gold bleiben obergangsmetalle. Die k.f.z. Phase in den Eisen-Kobalt-NickelKupfer-Diagrammen wird duroh den Zusammenbruch der d-Bindung bei etwa 38% Zink begrenzt. Eine ErhGhung der durchschnitt~lichen Elektronenzahl oberhalb dieser Grenze fiihrt zur Au~~llung der d-Schale von Kupfer. Nickel oder anderer Ubergangsmetalle mit Elektronen, wobei ein oder kein iiul3eres Elektron fiir die Gittorkont,rolle dor @-, ;I- und s-Hume-Rothery-Phason iibrig bleiben.

Copper is generally accepted as a one electron metal whose d-shell is filled.(1) The support for this electron model is based on the observed diamagnetism, high electrical condu&ivity and the successful calculation a lattice parameter assuming the one electron model.@) In copper-zinc alloys the electron concentrations of the a, /I, y and Ephases are postulated such t’hat they are in agreement with the one electron copper atoms in the formation of these phases without regard to properties. Fuchs(2) has recognized that the oneelectron concept is not consistent with the elastic properties of copper. The one-ele~t:ron model of metallic copper is also not consistent with a number of other properties of copper such as melting point’, boiling point, vapor pressure, and certain aspects of alloying behavior. The purpose of this paper is to point out that a consistent explanation of the properties of copper can be achieved by the electron concentration concepts * Received April 21, 1966. t Metallurgy Department, School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Ga. ACT.4 METALLURGICA, K

VOL.

15, MARCH

1966

already proposed by the aut,hor.(3) Ma.ny properties and phase diagram formations m,ay be accounted for based on the postulate that metal lattices are dicated by the number of out,er electrons:(3-5J1) b.c.c. lattices are formed from atoms having one electron, h.e.p. lattices from two electrons, and f.c.c. lattices from three electrons. The electron concentration postulates have been broadened to apply not only to integer concentrations, but t’o ranges of electron concentration. Through an examination of solid solution stabilities in alloys between components having different outer electron concent,rations, it, has been found that, for example, t,he electron concentration of the f.c.c. lattice can vary from 3 t,o 2.25 electrons per atom.c3) Such electron ~oncentrat,ion variations are postulated to occur in transition metals where d-electrons also participate in bonding. Thus in transition metals an equilibrium between the concentration of outer (s + p)-electrons and inner d-elect,rons is established, which equilibrium is affected by average nuclear charge, temperature, pressure, etc. The number of ouber bonding electrons

557

ACTA

558

METALLURGICA,

TABLE 1. Bonding energies depending on shell and kind of electrons in kcal/g. atom per bonding electron

VOL.

15,

quantum

states

d

SSP

1 2

the atom,

which

does

not

figurations

copper

has a mixture

as follows:

of electron

con-

25 % Cu ls2 2s2ps 3s2pW

4$

and 75 % Cu ls2 2s2p6 3s2p6d0 4.9~~. Such a mixture

80 40 20 16 15 15

: 5 6

within

change dependent on bonding conditions, it is suggested that metallic

Shell no.

1967

of configurations outer

26 30 36

bonding

d-electron

yields the calculated electron

average of 2.5

concentration

and

the

8.5

in copper,

the

concentration.

Based on this electron

distribution

properties of the metal and the features of the copper and d-electrons

can be ascertained

from the lattices

alloys can be accounted

of the transition metals by the electron concentration rule smoothed graphically to fractional numbers. From

in which d-electrons

this electron

is illustrated

bonding

distribution

energies,

and the experimental

characteristic

total

contributions

to

bonding from each kind of electrons have been found for each period. t3) These contributions

are given in

Table 1. The measured bonding energies of copper, silver and gold indicate

that these three metals have close to

2.5 outer electrons

and 8.5 d-electrons

outer and 1.5 d-electrons calculated If the

participate

whereby

2.5

in bonding

as

from values in Table 1. electrons

ca

occupy

a predetermined

N,

that metallic

for.

First, it must be stated

copper and silver are transition participate

by the combination

diagram

C”

This

of neigh-

boring elements through the fourth and fifth periods. (Figs. 1 and 2). Figure 1 shows the elements Co-Ni-Cu-Zn-Ga-Ge combined

by

diagrams,

yielding

a combined

the number

of electrons

which

continuously sponding

their

from

diagram

neighbor

27 to 32.

to

to form

Ln

neighbor

phase

t.

in

increases

In Fig. 2, the corre-

for the fifth period

a phase diagram

phase

diagram

per atom

Here the elements Rh-Pd-Ag-Cd-In-Sn set of

metals

in the bonding.

in which

6.

FIG. 1. Phase diagrams of adjacent elements in the fourth period of the periodic chart yielding a survey over the continuous increase of electrons from 27 to 32 per atom. From Co to past Cu one wide range of f.c.c. lattice exist. This three electron field extends as far as unfilled d-shells exist. The melting point of Zn is about 250°C below the extension of the line through the melting points of Ni and Cu. The lowest melting point close to Ga is located almost 300°C below this line. The dotted line connecting the boiling points of the pure metals indicate a minimum at Zn. This suggests a filled d-shell and two outer electrons in this metal. The face centered lattice and the higher melting point of Cu suggest d-bonding and more than 2.25 outer electrons per atom.

is depicted. are combined

the number

of

ENGEL:

Rh

Cu

ALLOY

P*

AND

ELECTRON

CONCEPT

I”

Cd

R9

559

5.”

FIG. 2. The phase diagrams of adjacent elements in the fifth period of the periodic chart yields a survey of a continuous increasing number of electrons from Ru to Sn. From Rh to past Ag one wide range of f.c.c. lattice exist with an almost straight decline of the melting points. This field extends as far as unfilled d-shells exist. The melting point of Cd is below this line. The boiling points drop linearly from Ru to Pd with a break at Pd and faster from Pd to Cd, due to the appearance of non-d-bonding 4d1° shells which start forming between Pd and Ag. From the point where the d-shells are filled between Ag and Cd the boiling points increase due to an increasing number of bonding electrons.

electrons

rises from

45 to 50.

diagrams are extended

To the left in both

fields of f.c.c. lattices covering

the area from Co to Cu + 40%

Zn and from Rh to

Ag + 40%

are formed

Cd.

No compounds

these metals as is common

for neighboring

between transition

metals except those in the middle of the period. To the right of Zn and Cd are diagrams normal

metals

participate factors,

(those

in which

in bonding).

varying

from

combinations

In contrast Ag-Cd

is general

agreement

distribution

that

the

between

and that d-electrons

participate

in bonding.

such as Ga and In, are normal

phases

eutectic (or peritectic) is rare in

normal metals. are formed

only

participate

and,

therefore,

in bonding.

only

where the d-shell is filled. transition

metal bonding

To the left of this point, prevails,

of this point, normal metal bonding show

many

intermetallic

phases.

with

electrons

Going from left to right over

in the and the

metals

outer

the diagrams of Figs. 1 and 2, there must be a point

In this

the Cu-Zn

There is

likewise general agreement that the metals to the far d-shells

formation

transition

such as Co and Rh, to the far left in the diagrams of

filled

Compound

such as

prevails in the elements,

right,

to this behavior,

diagrams

There

metal electronic

size

of neighboring

case, intermetallic In-Sn system.

metals,

1.069 to 1.097, the solid solu-

bilities are low and consequently diagrams are formed.

with normal

Zn, Ga or Sn.

Figs. 1 and 2. This means that the d-shell is unfilled

no d- or f-electrons

In spite of favorable

Ni, Pd or Fe, alloyed

and to the right dominates.

This

crossing point or the end of the transition metal region can be determined by the following argument.

These phases are of the same nature as those found in

Within

several diagrams

electrons will be placed in the d-shell, filling up this

between

transition

metals,

such as

the transition

metal

bonding

region,

added

ACTA

560

METALLURGICA,

VOL.

15,

1967

there should still be some d-bonding

retained

and Cd (and close to none in Hg). heat of vaporization

is much greater than the latent

heat of melting, the boiling points probably indicators

in Zn

Since the latent

of the bonding

energy.

Of special interest is the uniform, line for t’he decline

almost straight,

of the melting

t’hrough Ag in Fig. 2.

are better

points

The melting

from

point

Rh

of Cd is

approximately

200°C below this straight line.

fourth period,

Fig. 1, the slope of the melting point

In the

curve is almost the same between Ni and Cu and the melting

point

of Zn is located

the extrapolation bonding

of this line.

about, 250°C below

This indicates that the

in Cd and Zn is weaker than expected

extrapolated metals.

from

Because

the properties

if

of the transition

of the “ferromagnetic”

core in the

three metals Fe, Co and Ni, these metals exhibit the same melting points and the melting point curve does not increase beyond

Ni, corresponding

to the rise in

the fifth period. The boiling

points

drop similarly.

If Cu and Ag

are considered one electron metals their boiling points should be related to the normal metals to the right in the diagrams.

FIG. 3. The explanation of the Cu-Zn diagram. The top figure (a) is a schematic phase diagram. The middle diagram (b) indicates the concentration of atoms with open d-shells expressed as 3d* and atoms with closed d-shells indicated by 3di0. At the c( phase limit there is slightly less than 50% 3d8 atoms or slightly less than 100% 3ds atoms. In the B phase almost all atoms exhibit 3di0 shells. The bottom diagram (c) gives the electron concentration or the number of outer lattice controlling electrons per atom. This concentration is 2.5 at pure copper, decreases to 2.25 through the tc phase and drops to about 1.5 in the ,!I phase. Thereafter the electron concentration increases uniformly to 2 at pure Zn creating the y and E Hume-Rothery electron concentration phases.

shell and thereby d-electrons.

decreasing

Consequently,

the number

hypothetic room beyond

Cd.

extrapolating

Likewise

be below

boiling

room

To illustrate

the

from

boiling

electron

of copper

in Fig. 3. The

scheme in the alloys of copper

elements

is described

under

to outer electronic bonding.

concentration

or the number of outer bonding electrons

per atom is given. Pure metallic copper is, according to bonding energy calculations, d-electrons solid state.

assumed

to

have

an average

and 2.5 outer electrons This distribution

is different

and 2 should, therefore, exhibit increasing melting and

and only one outer electron is determined

boiling

copy.

melting

point

The minimum

curves should,

of

in the boiling and

therefore,

indicate

the

cross over point where the d-shell becomes filled. From the figures, the boiling points, indicated by the

This change of electron

This leaves Cu

one kind of copper

melting

another

as transition a minimum

metals.

The

close to Ga and between

In (and at Hg in the sixth period)

points Cd and

indicating

that

is due to 1.5

bonds than

is used to excite 1.5 electrons from the 3 d-level to an

clear cut minimum and Ag

by spectros-

distribution

bonds and 1.5 outer electron

outer 4 sp-level. In this way, an equilibrium

exhibit

from that

the fact that more energy is released in forming d-electrons

8.5

atoms in a gas, where 10 d-electrons

dotted line on Figs. 1 and 2, can be seen to exhibit a at Zn and Cd.

of

per atom in the

in free copper

electrons per atom.

the phase

diagram and at the bottom of the diagram the electron

of bonding

in the number

of copper

as a transition

diagram is depicted

distribution

and normal

melting and boiling points

an increase

In

if extrapolated

The normal metals within the field covered by Figs. 1 with

of a

Sn and

point

temperature

the alloys

metal, the Cu-Zn

the d-shell is filled, added electrons must all go to the

points

point

silver metal would be below

from Ge and Ga beyond Zn.

Within the normal metal region, in which

outer shell and contribute

temperature,

would

must decrease as the number of electrons per atom is increased.

The extrapolated

one electron

atoms

kind of copper

It is the great bonding

is established

with closed

between

d-shells and

atoms with unfilled d-shells. contribution

from d-electron

bonds (see Table 1) which makes the excited state of

Cu ALLOY

EXGEL:

copper with

atoms closed

possible.

Addition

of normal

inner shells prevents

AND

metals

the formation

of

d-bonds between copper atoms and the added atoms. Preventing

the formation

of d-bonds

will eliminate

the source of energy used to excite d-electrons the concentration Especially

and

of unfilled d-shells must decrease.

when the d-electron

concentration

exceeds

9, each copper atom will have less than one unpaired d-electron

on the average;

atoms

because

there are no neighbor

d-electrons.

cannot

as a result, a number

copper

At

equilibrium

participate

this

atoms with unpaired

d-electron

a catastrophic

pattern.

of

d-bonding

concentration

the

becomes rather sensitive to an increase in

total electron concentration create

with

because any increase will

breakdown

At this concentration

of the d-bonding

the equilibrium

also be sensitive to temperature

will

will have

two

direction.

The filled inner cores of the alloy atoms

will break d-bonds,

both

acting

thus causing

in the same

electrons

to move

from the outer shell to the d-level in the copper atoms. This electron movement

within the copper atoms will

increase the concentration

of the filled d-shell atoms

faster than would the addition alone.

of closed shell atoms

The second effect becomes

the added atoms contribute per atom.

pronounced

when

more than 2.25 electrons

The excess above 2.25 electrons per atom

will increase the outer electron concentration

whereby

561

CONCEPT

will be Cu 3d10 4s1 atoms giving a total concentration of approximately

56%

of atoms with filled d-shells.

In adding Ga or Ge, the effect of the increased number of outer electrons is the more important the electronic distribution After the catastrophic

breakdown

copper atoms supply only one outer bonding electron per atom and very few copper

At 50 % Zn the overall electron concentration

becomes

slightly

producing

over 1.5 outer electrons

the b.c.c.

1.7 electrons per atom as indicated Fig. 3.

The diagram

most d-quantum electron

influences of an equilibrium, will be proportional

The result will be a

Since

both

effects

arc

the two effects together

to the effect of all electrons

in

indicates

concentration

further

will raise the

of outer electrons from 1.5 to

the y brass and the e brass phases

become stable at about 21 electrons per 13 atoms and 7 electrons per 4 atoms, respectively, by Hume-Rothery.‘s) alloyed

If copper,

as pointed

with other normal metals carrying

a greater

number of outer electrons per atom, the same breakdown of the d-electron bonding will occur at approximately the same average number of electrons per atom because of the equilibrium of d-electrons

between the concentrations

and outer electrons.

The phase limit of

the CIphases is, therefore, determined

by the lowering

electrons below 2.25

Increasing the amount of alloying

elements within the ccphase region will simultaneously decrease the number

of d-electron

bonds

and outer

electron bonds, whereby melting paints(3) and Young’s modulus(3,g) decrease.

for

is lower for p brass than for both pure copper

and

Au

exceeds

0.4 electrons

reached.

In terms

alloys.

When

this

difference

per atom, the 0: phase limit is of the equilibrium

between

3d1’J 4$ atoms and Cu 3ds 4s~~ atoms, 25%

Cu

of the

first kind are present in pure Cu. In adding zinc, the main closed

factor

is an increase

d-shells which

in the concentration

of

Actually

pure zinc, in agreement

the Young’s

with the bonding

The limit

of the u phase constitutes

range of the catastrophic

breakdown

With increasing temperature

At the

phase.

This will favor an electron

limit of the M phase, about 30% of the copper atoms

closed

d-shells.

in the copper

atoms.

quantum

TABLE 2. Per cent of atoms with given electron distribution

Cu 3ds atoms cu 3d’O atoms Alloy 3&o atoms* Sum of 3d1° atoms * Experimentally

Cu-Zn tL

Cu-Ga rx

Cu-Ge c(

15 25

43.5 18.5 38 56.5

42.7 37.5 19.9 57.4

44.8 43.4 11.8 55.2

determined

CIphase limit.“)

that

of the

high

Electrons

the critical of d-bonding.

temperature

will

gaseous

distribution move

with

from

outer

states to d-levels and break d-bonds

as the

temperature

PIWe cu

and

pattern of

the electron distribution

approaches

distribution

modulus

Fig. 3.c3s5)

in the

electronic

causes a slight change

out

silver or gold are

the d-shell and the outer shell minus eleven per atom Cu, Ag

of

that

states are occupied.

electrons per atom.

conditions.

at the bottom

in the middle

the zinc content

2.0, whereby,

per atom,

phase which is stable to about

to the equilibrium

d-bonds.

atoms have unfilled

d-shells.

of the number of outer bonding

of

of the d-bonding,

above 38 % Zn, 19.9 y0 Ga or 11.8 % Ge, most of the

several electrons will be transferred to the d-level due breakdown

influence on

among the Cu atoms as can

be seen from Table 2.

Increasing

change.

Normal metals added to make dilute copper solutions influences,

ELECTROX

increases.

Because of this shift of outer

electrons to d-levels, determining electrons

the concentration of latticewill diminish with increasing

temperature. therefore, elevated bilities

The border

move

to

temperatures. increase

with

lower

line of the M. phase will, zinc

concentrat,ions

at

It is normal that solid solutemperature.

The

opposite

behavior of the Cu (Ag and Au) Mphase solid solutions

ACTA

562

METALLURGICA,

with normal element additions is explained by the electron concentration concept, assuming Cu to be a tradition metal. All of the excellent work published by Hume-Rothery et al., showing that maximum solubility in the u phase, melting point depression, etc. depend on the electron concentration, can therefore be explained by a decrease of the concentration of outer electrons in Cu to 2.25 per atom just a,s well as by an increase to 1.4 per atom. The dilution concept is in agreement with thermodynamic properties, strength properties, alloy behavior of the Cu-column metals and other transition metals. According to the electron concentration concept, copper is the last transition metal in which the d-shell is not completely i‘llled. Moving to the next element with higher nuclear charge will complete this filling up process which is synonymous with the breakdown of d-electron bonding over the binary diagram. The major part’ of this process takes place between the limit of the a phase or the three electron range and the ,E!?phase, Fig. 3. Within the a phase range, addition of Ni atoms will increase the number of d-bonds and the addition of Zn atoms will decrease the number of d-bonds approximately proportional to the atomic per cent of each. This is illustrated by Greer and BucknalP who measured the Young’s modulus of a series of Cu-Ni-Zn alloys and found the modulus of the Cu to be 21 x 1O+6psi increasing or decreasing by 8.5 x lo-‘-* per atomic per cent added Ni or Zn. If one d-electron contributes 8.5 x 1O+6to the Young’s modulus, copper should have 8.5 d-electrons leaving 1.5 bonding d-electrons and 2.5 outer bonding electrons since the contribution to bonding strength of outer electrons is about half that of d-electrons.(3) (Table 1). According to this rough approximation, the contribution to the Young’s modulus is 8.5 x 1O+6psi per bonding d-electron and 3.6 x 1O+6psi per outer bonding electron. When other transition elements to the left of the copper group are alloyed with normal elements, very similar electronic changes take place. When Ni or Fe, for example, is alloyed with Zn, the excess electrons added with the Zn at,oms in the d&_&e solutions of TABLE 3. Electron distribution in a or ,8 and y phases a phase

/I and y phase

cu 18%zs=p~ 3s~pW-6 4qF Ni I-2-3sepW 48p2 Many atoms 3sapSd1* 4spa c&o I-2.3ssp8d1@481, ,BCo 1.2.3szpW 4spp

Cu I.+ 2s=p= 3sapw0 48’ Si 1-2-3~*pW~ 4s”~~ Co I-2.3s=pW

&sop0

The 3s*pW0 configuration is suggested as a carrier of ferromagnetism if present in conoentrations higher than about 5076.

VOL.

15,

1967

Ni or E’e will distribute themselves between inner and outer electrons according to the equilibrium conditions until the outer electron oon~entration is diminish~ to 2.25. The lattice will then change and the transition element atoms will, at higher Zn concentrations, take up all their electrons in the d-shell because of the ovcrall increased electron concentration. At higher zinc ~oneentrat~ions, the transition metal atoms will not contribut,e any outer bonding electrons and will, t,herefore, not contribute lattice controlling electrons, in agreement with Hume-Rothery’s rules.(*) The fact, that the transition elements to the left of the Cu column has to be ascribed zero electrons in forming /3, y and E phases is a good demonstration of the postulate that only outer electrons are lattice controlling. The electron distribution in the Ni atoms is different in the cc phase from that in the /3, y and s phases in analogy to the distribution in Cu. This is illustrated in Table 3 for Cu, Ni and Co atoms. From Table 3 it can be seen that the transition metals contribute almost three outer electrons to the u phase and only one for Cu and none for Ni and Co in the p and y phases. This is due to the fact that the transition bonding range extends to about 40% zinc or cadmium. This can be seen in Figs. l-3 as the limit of the f.c.e. a range, Below this limit the d-shells in the t,ransition metal atoms Co, Ni and Cu are unfilled and d-electrons participate in bonding. In alloys with higher zinc contents (or corresponding Ga or Ge contents) the catastrophic breakdown of d-bonding has taken place and d-shells are practically filled or filled to formation of neutral transition element atoms. Under these conditions copper will contribute one outer bonding electron and earlier transition metals contribute no outer lattice cont,rolling electrons. In the transition metal zone. i.e. when the average atlomie number is below 29.4,47.4 or 79.4 respectively, transition metal atoms will assume the electron distribution indicated in Fig. 3(b) and contribute the number of outer electrons indicated by the upper line in Fig. 3(c). Beyond the transition bonding zone, i.e. when the average atomic number is above 29.5, 47.5 or 79.5 respectively, transition met,alatoms will behave as d-electron acceptors and yield one or no outer bonding electrons as indicated by the lower dotted line in Fig. 3(c). flume-Rothery considers t#he latter inte~retation only and extends the electron distribution as found in the normal metallic bonding range [the lower curve in Fig. 3(c)] beyond its natural limita’tion, the lower limit of the ,!3phase. The postulate that copper is a one electron metal does not agree with copper being

ENGEL:

Cu

ALLOY

AND

part of the f.c.c. transition metal range and its properties as an extension of the transition metal properties, nor does it agree with the alloy behavior of the metal. The consequence of this extrapolation beyond its natural limits, that nickel and earlier transition metals are zero electron elements, is not acceptable. From Table 3 it can be seen that copper and nickel contribute no d-electrons in the /3, y and E phases, whereas, Co (and, therefore, also Fe and Mn) have unpaired d-electrons and, therefore, participate in d-bonding in these phases. Under extreme conditions the transition metal atoms may take up excess electrons and become negative ions as, for example, in TiC(lO‘~l) or in some phases with NiAs str~l~tures as, for example, Co, Fe and Mn sulfides. The limit of the a phase, according to the author, is caused by a diminuation of the outer electron concentration to 2.25 per atom for both the aCuZn, aNiZn and @CoZn phases. According to HumeRothery the limiting electron ~on~entrat~on should be 1.4 per atom for the CuZn system and about 0.8 for the NiZn system and even less for the phase in the CoZn system. CONCLUSION

It has been pointed out that the electron concentration concept leads to the electron distribution cu ls2 2s2p638213W.54sipi.5 in pure copper. This reconsiders copper as a transition metal which agrees with the properties of copper especially as related to neighboring elements in the periodic chart. It also agrees with the alloy behavior of copper and silver. Alloying copper and silver with

ELECTRON

CONCEPT

563

neighbor transition elements causes the number of d-electron bonds to increase, whereby, melting points, boiling points, strength and coefficient of elasticity increase. Alloying with normal metals (B group) causes the number of d-electron bonds to drop, lowering the melting point, boiling point and elastic properties. At the limit of the a phase, the d-bonding pattern breaks down catastrophically and the electron distribution in the metals Cu, Ni, Ag, Pd changes to filled d-shells when more B group alloy elements are added. In the Hume-Rothery ,9, y and E phases these elements behave as normal metals with essentially filled d-shells. REFERENCES 1. N. F. MOTT and H. JONES, The Theoryof the Properties of Metal8 and Alloys. (1936); F. SEITZ, The Modern Theory of SoZids. McGraw-Hill (1940); F. SEITZ,The Physics of Met&s. McGraw-Hill (1943). 2. K. FUCHS, Proc. R. Sot. 151, 585 (1935). 30,53, 75 (1949); N. ENOEL, 3. N. EHOEL, Kern. ~~n~8bZ. Kern. ~ua7~,~sb~. 30, 97, 105, 113 (1949). 4. L. BREWER, Prediction of High Temperature Me&&c Phase Diagrams, U.C.R.L. 10701, Ernest 0. Lawrence Radiation Laboratory, University of California, Berkeley (1963). 5. N. ENGEL, The Electron Concentration Ckmcept a& Diffusion, D#.&on an Body Centered Cubic Metala, 87. Am. Sac. Met. (1964). 6. L. BREWER, T~Tmody~~rn~ and Phyaicas Pipette of the Elements OeneraJ Chemistry and Met~l~rgy, Vol. IQ-B, Division IV, Plutonium Project Record, National Nuclear Energy Series by L. L. Quill et al. 7. M. HANSEN, ConstGution of Binary Alloys. McGraw-Hill

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8. W. HUME-ROTHERY, The Stvuctul-e of Metals and Alloys, The Institute of Metals, Monograph & Report Series No. 1,London /1950). 9. J. B.'GREER 8nd I?.H. BUCKNALL. Am. Sot. X8&b Trans. Q. 57, 559 (1964). 10. N. ENGEL, Powder Metall. Bull. 7, 8 (1954). 11. N. ENGEL, Am. Sot. Metal8 Trans. Q. 57, 610 (1964).