Alloy systematics in relation to the long periodic table

ALLOY SYSTEMATICS IN RELATION THE LONG PERIODIC TABLE

TO

H. E. N. STONE The Blackstt

Laborator).

Imperial

College.

London

SW7. England

Abstract-4 scheme is described for the subdivision of the Periodic Tsble. and examples are gt\sn tendencies and in related toptcs. with particular reference of its application in classifyin g aBoring to (a) alloys of iron. (b) beta-tungsten phases. ICI rare earth s)strms. also L’Co:. and (d) the allotropy of manganese and iron. R&u&.--On presente un schCma de subdivision de la classification piriodique des elements. et I’on montre des exemples de son application a la classification des conditions d’alliage et h des proprittis voisines, en insistant parriculiirement sur (a) les alliages de fer. (bi ies phases du type -‘rungstine p”. (c) la systemes de terres rsres, ainsi que UCo,. et (dt I‘ctllotropie du mangsntse et du fer. Zusammenfassung-Es wird ein Schema zur Untcrteiiung des periodtschen systems beschrieben: Anwendungen auf die Klassifizierung des Legierungscerhaltens und veru-andte Probleme ucrden legt: (a) die Legieruneen des Eisens. (b) beta-Wolfram-Phasen. (cl systeme seltener Erden. such und (di die Allotropic van Mangan und wn Eisen.

INTRODUCT Many types of proposal

ION

have been promulgated with the object of reducing to order the manifold behaviour in alloy systems. These have included the formulation of the Hume-Rothery rules. later work bq Raynor. Schubert. th2 geometrical aspect associated with th2 names of Laves and Frank. Pauling. EngelBrewer theory. and the more recent attempts of metal physicists to makr understandable the systematic variations in properties. Some accounts of all these are given in. for sxample, Refs. 1-S. Although thrre are some points of contact. such as the proposal of the Zintl line. and reference to the diagonal relation. thesr developments have, in the main. proceeded outside the context of strong involvement in the Periodic Table. The purpose of this paper is to attempt to show that a reformulation on this basis can provide a convenient and practical background to metallurgical practice. The emphasis here will be on the ciassificatory aspect. Obviously the question of mechanism is important. and this will be elaborated later, but a germinal idea has already been proposed [9]. In a sense. a reformuIation marks a return IO the standpoint of Tammann [IO]. but with the advantage that we may generalis from more extsnsive knowledge of alloy systems as the result of the labours of his school and many others. In this regard. our debt to the compilers of the encyclopaedia of phase diagrams [l l] cannot be undrrestimatzd. In the following proposal. incompatibility with other viewpoints is not necessarily to b2 inferred: pinpointing the dominant mechanism can often be difficult. and perhaps to a degree one must accept this as an inherent indeterminacy. Equally. there can bc

einipe dargcUCo,,

no glossing ovsr rssl differences: for euampls. if ~‘2 interpr2t gamma-brass (using ths conventional valency for zinc. and omitting thz ‘2~~2~s’ electrons) as Zn c 4Cuz-Zn’-Zn-Cu

+Zn. Zn

it follows that the effective e.‘crratio is much less than was considered in an earher theor!. Such an example is typical of the background to the present scheme. in that it is assumed that intermediate phases are chemical compounds and that. at least in principle. they may be interpreted and systematised in terms of chemical bonds. The object of the classification procedure is to establish between which (pairs 00 elements compounds form. to chart these on the Periodic Table. and to invent mnemonics to facilitate reference. Simple procedures for analysing the data have been used or developed [ 12-131. The memory aids that have been evolved consist of lines on the Table. generally vertically. and these hav2 been termed divides. A divide is placed in such a position that any element near to and on one side of a divide will form a compound or compounds with a counterpart element on the opposite side of that divide: if two elements are nrar to but on the same sidz of a divide. no compounds are formzd. and some other form of phase diagram. from solid solubility to liquid insolubility in type. is present. The Prriodic Table. with ditidss inserted. is illustrated in Fig. I. It will be noted that four divides are placed in this main body of the Tablr. Th2 ionic

260

STOSE:

ALLOY SYSTEMATICS

Fig. 1. A suggested division of the Periodic Table.

! I B

t

H

tie

Li

Be

N

0

F

Ne

Na

41g

P

S

Cl

A

K

Ca

As

Se

Br

Rb

Sr

Sb

Te

I

Kr ! Xc

Cs

Ba

I

/ Al Ti

V

Zr

Nb

Si

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

MO

Tc

Ru

Rh

Pd

Ag

Cd

In

/

Ge I Sn

I/

I Hf

Ta

W

Re

Transition metal divide

OS

Ir

Pt

I

AU

I

Composite divide

divide. though not under that name, is familiar from inorganic chemistry, and the covalent divide from semiconductor science, with its Group IVB elements and III/V compounds. The position of the former is given by the 2n' recurrence of the rare gases, and the latter by that of half an octet away from the rare gases. The ordinal positions of the other two divides are given by cutting the row of 18 elements in the ratio 1.62:1 (Ref. 13). The term compositr divide was coined to suggest a mixed character. However, complexity also occurs af the transition metal divide-the existence of the latter was only realised at a later stage. The formula above for gamma brass is in terms of ionic and co-ordinate bonds, gnd metallic nature enters with the excess electrons, but it is not implied that this is the only type of constitution. and work remains to be done on the details of the divides in the transition metals. It will be appreciated that simplicity has been achieved in Fig. 1 at some expense in accuracy. It is not possible. in a single account, to present all its modifications and limitations; several descriptions, from different angles, are necessary fully to appreciate the structure of the Periodic Table in this context. However, it is essential to make two points here. Firstly, what may be termed the zone of influence of a divide does not generally coincide with the block of elements up to the adjacent divides on either side. Sometimes it extends further than an adjacent divide, sometimes less: nearly always it extends two elements to each side of a divide. Secondly, the simple straight lines which represent the transition metal and composite divides in Fig. 1 are oversimplifications. This is in particular contrast with the ionic divide. To take the composite divide: alloying systematics often appear consistent with a broadening of the line in a manner which may be schematically illustrated thus:

Ionic divide

Covalent dir ide

The reason lies perhaps in the s-d -shear’ hypothesis quoted earlier [13]. However this may be. it means we need to be on our guard for changes of regime occurring at some point in the broadened divide. Note that if we exaggerate the broadening. we have the belt of metals from Mn to Bi in the Long Periodic Table which can display low valencies. and that there is a certain symmetry in that to the left of the divide in the First Long Period we have ferromagnetic elements. and to the right in the Second and Third Long Periods we have some strongly diamagnetic elements. To turn to the case of the transition metal divide: this often appears broadened to a wedge shape, the latter consisting approximately of the following V

Cr MO W

elements Mn Tc Re,

and the fundamental basis may lie in the ‘complex anion’ hypothesis [ 121. The remainder of the paper consists of a series of illustrations in some detail of the scheme outlined. The first is concerned with the most industrially important metal. others are more esoteric.

SYSTEIMATICS

OF IRON

ALLOYS

This has been covered by Desch [I j] and Weverj Schubert [16]: though these authors worked on the basis of the. effect of alloying elements on the stability of the gamma-iron structure, there is a strong resemblance to the present classification. For example, iron forms solid solutions generally with the elements between the transition metal and composite divides. and these are also gamma stabilisers. Another common feature is the following block of elements which are insoluble in iron. cu Ag

Cd Hg

In Tl

Pb

Bi

PO.

STONE:

ALLOY SYSTE!&ATICS

261

Table I. Occurrence ofihe structure Cr,Si (or beta-\V). ,415

.Lf -

Ti, V,

[I

Ir

Pt

Au

Hg

_

-

---

.-

CO

xi

‘;r”

E;

z Ir

----pr

1

:%I?;

OS

Rh Ir

Pt

_

-

--

OS

Ir

_--

-

-

Au

j_

-

-

Cr3

iRu OS Zr3

I

Vfil

component

I_

-

-

III

IV

-

-

/

I I

Group of the 3’ componsnt

si

v

1

Sb

[

i

-

I 5

-

Ga

cir

As

I

1

;;

5”!?

Si Gs

-is

-

1

I

_~~~

G3 In -

G? Sri Pb

Sb Bi

Si Gs -

-1 --i7

i

-

.&I Ga -

-1

,

-

-

Sn

Sb

3

7

I’

6

Ga -

-

/

Nb3

Mo,

Ta3

-

4

9

6

Au

Be

5

With elements to the left of the transition metal divide (Fig. I). iron is a compound former. though due to the (helpfully sluggish) formation of Fe-0 sigma phase, chromium could be claimed to be an exception. and there is an extensive degree of solid solution with vanadium. With elements between the ionic and composite divides. iron is a compound former. With elements to the right of the ionic divide in Fig. I. insolubility exists. SYSTEMATICS BETA-TUNGSTEN

-

OF PHASES

The information is largely condensed into Table 1. derived from Schubert [ 173 and Hume-Rothery ef al. [ L8], with an outer frame giving totals by row and column which has been added by the writer. Not included are Zr,Sn, Mo,Zr, MoTc, W,Si and W,O; though not stated. there are no X components from Group VIIA. it is clear that .iI components come from immediately to the left of the transition metal divide. most frequently from Group VA. and the X component. with the exception of Mo3Zr. always from the right hand side of that divide. There is a minimum in the frequency of occurrence where the X component is from Group IIB-again a divide correlation. The simplest valency scheme to cover these facts overall would be to assign bivalencies to both &I and X atoms. in covalent lattice fashion. However. if a Goldschmidt diagram [I91 (where lines on the Periodic Table are drawn between all the pairs of components) is drawn from the material in Table I

13

it will be found that the greatest probability of finding a beta-Ct’ structure occurs near or at points and directions in the Periodic Table Mhich may be expressed as Cr - Ir and Sb +-Ga respectively. The Cr - Ir direction approximates to the most Favourable condition for the formation of ionic bonds in intertransition metal compounds which would be predicted from Fajans’ rule [?O]. and we therefore infer some donation from the .Y atom to ;\I atom(s): this may not be simply of the nature of a ‘static’ charge transfer, but perhaps involve an outer-electron --+ d-hole type resonance [9]. GROllP IliA WITH THE RARE EARTH IMETALS The matter of the systematics of the rare earths may be approached by a roundabout route. a route which has its measure of interest. as follows. If we consider potassium as basis metal for alloying. we find (subject to some uncertainty due to gaps in knowledge) that no compounds are formed with elements to its right in the First Long Period. untiI we come to the K-Zn system, where a compound Zn,,K is formed. and compounds are further formed with Ga and Ge. We repeat the procedure with Ca as the assumed base metal. and so on as follows: _________~” ~_____-___-_--_-_________---------co__-_________________--------------cu Sc______________Mn ir______Cr “_______&+* C;--Mn

262

STONE:

ALLOY SYSTEMATICS

ition in the Periodic Table uith respect to the divides. For many elements this is true. but others. notably the transition metals. display dual or many sided character. For example. manganese in some instances behaves like a bivalent element such as zinc, though in a system such as Cu-Mn the predominant effect appears to be stabilisation of the face centred structure-it is an interesting exercise to see how nearly one may reproduce the Cu-Mn diagram by &perposition of the Cu-Zn and Zn-Mn systems. It is agreed that alpha manganese has lattice sites of different electronic nature. The stability of the sites vvill change with temperature and different types of site will form. and with these considerations in mind we can present a useful test of the present ideas. For simplicity we shall assume (Table 7) only two internal species (such as X, and zt,) for each allotrope. and for brevity it is convenient to make USCof a system of labelling blocks of slements A,, .-l:. etc. [XL 1-I). In its general character. alpha manganese is similar to intertransition metal phases such as sigma which form “across the transition metal divide”, and as such it may be coded A, .-I2 (Table 2). Beta manganese has been described as an electron compound [29]. and accordingly we may suppose that multiplicity of electron states in the solid again exists. but that in this instance some of the manganese atoms function as a B, element such as zinc whilst others retain .J character, so that the overall constitution may be coded as .A:B,. Gamma manganese is generally miscible with other .A1 elements and soft like closepacked A2 elements [30]. and it is reasonable to suppose that it is A,Az in type. In this structure. it is probably that internal differentiation is small and that atoms are structurally and electronically nearly equivalent. In delta manganese. further activation has occurred, and the structure may perhaps be repre-

Subsequently. with manganese as solute; a new sequence is initiated: it forms solid solutions rather than compounds with elements to its right. until zinc is reached. The manner in which successive changes in systematics occur at points to be expected from Fig. 1 and the Introduction i notable. In general. the rare earth metals behave similarly to scandium. yttrium and each other in alloys with &transition metals: manganese is rhs first element in the First Long Period with which they usually form a compound. and compound formation with other elements is sensibly uniform. Cerium and yttrium do not form compounds until iron is reached. and lanthanum not until cobalt. When we consider alloys between the rare earths. we find that these are largely solid solution systems. except that one type of compound, the samarium structure, may be formed. For formation of this structure [‘l-27]. it is necessary to have. as components. rare earths to the left and right of samarium in the Periodic Table. Prediction of the compositions at which the samarium structure is stable may be made using either the principle of average atomic number. or by constructing a synoptic diagram of a type devised by the author [13]. The way in which known samarium structures group themselves along hyperboiae in such a plot (not illustrated) in a manner analogous to inter-d transition compounds [ 141 suggests that this. exceptionally, is an instance where 4f’involvement exists. in conformity with the view of Gschneidner and Valetta [27].

THE ALLOTROPY OF fRON AND MASGANESE So far in this paper it has been assumed that an element has a fixed character depending on its pos-

Table 2. Part of the periodic table. showing divides (A. above). and a schematic description &heallotropes of manganese (B. below).

A,

-A(--

elements

-

-

8,

Ti

v

cr

Mn

Fs

Co

Ni

Co

Zn

tr

Nb

Mo

Tc

Ru

Rh

pd

Ag

Cd

Composite diwde

Tronsitioo rnetoi

divide

y, -

y,,

of the constitution

As

Se

Br

fn covoL?nt divide

“y - MN”(iii) “8 - MN” (iv)

IOlliC

divide

of

STOVE:

ALLOY

SYSTEM.4TICS

263

“C

Fig. 2. Hypothetical effective group number

vs temperatures of decomposition, of manganese (x) and iron (0).

sented as one across the composite divide (A?B, and Table Z-point B iv). We now plot the average Group Number suggested by these electronic configurations against melting,’ decomposition points, since the latter are indicators of stability. This is done in Fig. 2. in which the averare given age positions of 1. 8. 7 and d manganese by the arithmetic means of (VI and VII), (VII and IIB). (VIIIC and IB) and (IB and IIB). respectively, groups VIIIB, VIIIC. IB and IIB being counted as 9. 10, 11 and 12 respectively in assessing the position on the abscissa. It will be noted that an approximately straight line relationship obtains. and that the result is supported by a similar exercise for the element iron and its allotropes. The overall picture, in terms of rising temperature, is of increase of effective atomic number and of changes in the electronic character of manganese atoms as divides are passed. with results which are particularly suited as a description of the Proteus-like character of manganese in its physicochemical behaviour. THE WVES

PHASE L’Co2

This is an interesting variation on the theme stated in the last section. The physical and metallurgical data on which this interpretation is based have been given elsewhere (31.373. It suffices to say that the data indicate that a certain critical or ideal stoichiometric ratio exists. and aIso that cobalt-rich compounds as a group (e.g. UCO~,,~) react differently

Fig. 3. Schematic description of UCo, of varying Co/U ratio in terms of a subdivision of the Periodic Table.

melting

for the allotropes

from those that are uranium-rich. It is perhaps more likely that. electronically. cobalt atoms retain the same character. whilst uranium is many-sided. On this basis. the following scheme (Fig. 3) is proposed. Ideal UCoz (Fig. 3a) is thought to be a close approach to a covalently bonded infinite lattice. whilst cobalt- and uranium-rich (Fig. 3b and c) have analogy with a .q2.d2 solid solution such as kin-Co and a ‘Hume-Rothery’-type system such as Co-_Zn respectively. The essential notion is that, depending on the stoichiometry. the nature of the uranium electronic contribution to the lattice changes. Acknowledgements-Several examples have been given of the application of a scheme to clarify the systematics of alloy behaviour. Many of the alloys discussed have been prepared in the course of everyday work. It is a pleasure to acknowledge the stimulation quirements of the Metal Physics of the scheme.

offered by the varied reGroup in the formulation

REFERENCES 1. W. Hume-Rothery. R. Haworth. The Srrlrcrure

E. Smallman and C. W. of .Cletals and AIloxs. The

Metals and Metallurgy Trust, London (1969).

2. W. Hume-Rothery and B. R. Coles, Atomic Theory for Srudents of .Vetallurg_v. Institute of Metals. London (1969). 3. K. Schubert. KrisMsrrukturen xeikomponentiger Phasen. Springer. Berlin (1964. 4. Idem. Srrucrure and Bonding. 33, 139-177 (19771. 5. L. Pauling. The .Varure of rhe Chemical Bond. Cornell University Press. Ithaca (1960). 6. Seung-am Cho. kra .MetaU. 25, 1085-1094 (1977). 7. D. G. Pettifor. CALPHAD. 1, 305-321 (1977). 8. J. Friedel and C. %l. Sayers. J. Phys. thiar. appl. 38. 697-705 (1977). 9. H. E. N. Stone, J. Marer. Sci. 11. 1576-1577 (1976). 10. J. R. Partington General and Inorganic Chemistry. p. 250, Macmillan. London (1967). I I. M. Hansen and K. Anderko. Constiturion 01~Binary Alloys. McGraw-Hill. New York (1958) and supplements edited by R. P. Elliott (1965) and F. A. Shunk (1969).

264 12. 13. 14. i5. 16. 17. 1% 19. 20. 21. 22. 23.

STONE:

ALLOY SYSTEMATICS

H. E. N. Stone. J. Jfnrrr. Sci. 9. 607-613_(1973). f&m. i&f. II. ‘0 l-206 ( 1957). I&m. z. .~fer~f~~.68. 679481 (1977). C. H. Desch. .~f~ru~~~grup~~,p. 364. Longmans. London (19X). Ref. 3. p. I-U. Ref. 3. p. 150. Ref. I. p. 212. H. J. Goldschmidt. J. Inst. Merals. 97, 178 (1969). H. E. N. Stone, Z. .Cferaifli. 69, 598-599 (1978). K. N. R. Taylor and M. I. Darby. Physics of Raw Earrh Solids. p. 69. Chapman and Hall. London(l972). F. H. Soeddina. R. M. Valetta and A. H. Daane. Trans. rl.S..LI.‘JS, 483-491 (1962). J. D. Speiaht. 1. R. Harris and G. V. Raynor. J. lesscorwnon .tirrds 15.3 17-330 (1968).

24. I. R Harris and G. V. Rqnor. ibid. 17. 336-339 (L969). 3. L. Tissot and A. Blaise. JI. appl. Phrs. 41, i18Q-1182

(1970). 26. I. R. Harris. C. C. Koch and G. V. Raynor. J. Jess-corn-

MOM.!4erals. 11, 436-454 (1966). Jr. and R. M. Valetta. Acrn .Metall. 16, 477-481 (1968). A. F. Wells. Srrucrirral Inorganic Chemistry, p. 971. Oxford University Press. Oxford (1962). Ref. I. p. 229. . H. O’NeiiL ~~d~e~s ~~~~su~e~~~c of Met& and Altoys. pp. IOS. 192, Chapman and Hall. London (1967). J. Kiebik and B. R. Coles. Proc. Im. Cotif an &fagnetism. Amsterdam (1976). H. E. N. Stone, J. IWafer. Sci. Accepted for publication.

27. K. A. Gschneidner

28. 29. 30.

31. 32.