THERMODYNAMIC FUNCTIONS OF AN Fe-Mn SOLID SOLUTION FORMED

BY THE Fe(n, p)Mn REACTION*

R. SMITH? and R. SHUTTLEWORTH?

A dilute solution (I.. = 3 x 1O-B) of maneanese in iron was formed bv neutron irradiation of nature1 iron Feh4(n, p)Mn5* &d by means of the Knudsen effusion technique the quantity p,/x”, where p, is the partial pressure of manganese, w&s estimated for temperatures between 1073°K and 1673OK. The Raoult& activity coeffiAent was 0.3 and the variation with temperature was small corresponding to a partial heat of solution of 1.25 kc&l/g-atom, (even though the cohesion energy of manganese is 33 kc&l/g- atom less than that of iron). The value 0.3 arises from the positive excess entropy of solution. It is suggested that this excess entropy is primarily due to changes of the electronic specific heat of solution rather than changes in the lattice vibrations.

FONCTIONS THERMODYNAMIQUES D’UNE SOLUTION

SOLIDE FeMn FORMEE PAR LA REACTION Fe(n, p)Mn

Lea auteurs ont forme une solution diluee (zu = 3 x 10-B) de manganese dans le fer, par irradiation neutronique defer nature1 FeS4 (n, p)MnS4; en utilisant la technique d’effusion de Knudsen, ils on testime la qua&e p,,/x, oh p, est la pression partielle de manganese,-pour lea temperetures comprises entre 1073’K et 1673’K. Le coefficient d’activite de Reoult Btait 0.3 et sa variation avec la temuerature Btait faible, correspondant B une chaleur partielle de solution de 1,25 koal/at. gr (bien que l’energie de cohesion du manganese soit de 33 kcal/at. gr moindre que celle du fer). La valeur 0,3 provient d’un exces positif de l’entropie de mise en solution. de resultat suggitre que cet exces d’entropie eat dti au premier chef B une mod&cation de la chaleur de mise en solution Blectronique plut6t qu’8. une modification des conditions de vibration du reseau.

TBERMODYNAMISCHE FUNKTIONEN EINER BE1 DER Fe(n, p)Mn-REAKTION GEBILDETEN Fe-Mn-LEGIERUNG

Durch Neutronenbestrahlung von natiirlichem Eisen entstand bei der Rertktion Fes4(n, p)Mn5* eine verdtinnte L&sung (2, = 3 x 10-e) von Mangan in Eisen. Mit Hilfe der Knudsenschen Effusionstechnik wurde die GrijBe pJx,, wo p, der Pertialdruck von Mangan ist, im Temperaturbereich 1073°K bis 1673°K ebgeschiltzt. Der Reoultsche Aktivitiltskoeffizient war 0.3 und die Temperaturabhiingigkeit war klein, entsprechend einer partiellen Liisungsw&rme von 1.25 kcal/g-Atom (obwohl die Kohiisionsenergie von Mannan um 33 kc&l/e-Atom kleiner ist als die von E&en). Der Wert 0.3 rtihrt von dem nositiven tfber- schz der Liisungse~ropie her. Es wird vorgeschlagen d&3 diese tfberschuflentropie hauptsiiohlich auf Ver&nderungen der elektronischen spezillsohen Losungswiirme und weniger auf Ver&nderungen der Gitterschwingungen zurtiokzuftihren ist.

INTRODUCTION TABLE 1. Transition metals

In Table 1 are given values of the sublimation

energies,@) melting poinW) and atomic radiic2) of the

3d-transition metals. The system Fe-Mn is particu-

larly interesting because as pointed out by Hume-

Rothery@) manganese is anomalous in having the

lowest cohesion of all the transition elements, the

cohesion energy being 33 kcal/g-atom less than that of the adjacent element iron. However, measurements

by Kendall and Hultgren t4) show that iron-manganese

solid solutions have only a small exothermic heat of

formation (-1.2 kcal/g-atom for a 50/50 f.c.c. alloy).

Vapour pressure measurements of McCabe and his

collaborators(s-7) show that concentrated iron- mang-

anese solid solutions deviate only slightly from Raoult’s law.

Metal

SC Ti V Cr Mn Fe co Ni

Sublimation Goldschmidt energy at 29S°K Melting point

radii ( A) (kcal/g&om) (“C)

1.60 82.00 1400 1.45 112.6 1677 1.36 122.8 1917 1.28 95.00 1903 1.31 66.73 1244 1.27 99.83 1539 1.26 101.6 1495 1.24 101.3 1465

In the present study a dilute solution of radioactive

MrP was formed@) in iron by the fast neutron reaction

* Received September 28, 1964. t Department of Metallurgy, University of Leeds.

Fes4(n, p)Mn s4. The total atomic fraction of manga-

nese in the alloy was 3 x lo4 but because of the high

specific radio-activity of the manganese the partial vapour pressure could be determined ; simultaneously the partial pressures of the iron could be determined

using radioactive FeS9. Measurements on dilute solutions are revealing since for these solutions it is.

possible to neglect interaction between solute atoms

and because the configurational entropy is that of a

ACTA METALLURGICA, VOL. 13, JUNE 1965 623

624 ACTA METALLURGICA, VOL. 13, 1965

random distribution of atoms. The present paper continues the work of Pyle,(gslo) who studied dilute solutions of Ag, Ga, Ge and Zn in liquid Cu; of Johnson(n12) who studied solution of Kr in liquid Ag, Pb, Sn, Cd and In and of McLellan and Shuttleworth(13) who studied Ag and Au in solid Cu.

The thermodynamics of metallic solutions have recently been reviewed by Alcock and 0riani(14) and by Kleppao5) ; they emphasize the importance of measuring both the excess enthalpy HE and the excess entropy SE. The present method enables the initial slopes of these excess quantities to be determined.

= H,+ - H,O r,=O

= s,+ - x,0 x,=0

(2)

HE and SE tend to zero as the atomic fraction x, tends to zero or to unity. The notation of equations (1) and (2) is that of McLellan and Shuttleworth: the sub- scripts u and v refer respectively to the components manganese and iron, the superscript+ refers to an infinitely dilute solution in which the subscript is the solute, the superscript0 to an infinitely dilute solution in which the subscript is the solvent. Thus H,+ - H,O

is the increase of enthalpy when a manganese atom is transferred from pure manganese to pure iron ; S,+ - SUo is corresponding increase of entropy apart from the ideal configurational entropy.

If the enthalpy of the manganese and the dilute solution of manganese in iron can be estimated by counting bonds

H,O = $zE,, (3)

H,+ = zE,, - $zE,, (4)

where the term -$zE,, is the energy necessary to form a vacancy in iron into which a manganese atom can be placed. Then

H,+ - H,O = 0 if E,, = i(E,, + E,,,) (5)

Thus even when E,, and E,,, have very different values HE may still be small.

Non-zero of S,+ - S,O may arise since forming the alloy may change the vibrational spectra,03) the degree of order of the magnetic moments,06) or the elec- tronic specific heat.(14) Measurements of the magnetic susceptibility of iron-manganese alloys have been made by Sedov(l’) and of the electronic specific heat by Gupta, Cheng and Beck(ls) (addition of 11% manganese to iron increases y from 8 to 34 Cal/g-atom/ “K2).

EXPERIMENTAL

The thermodynamic functions of the Fe-Mn solid solution were determined by measuring the partial pressure of manganese in equilibrium with the solution. A Knudsen effusion method was used and the vapour condensed on a target cooled by liquid nitrogen; the apparatus was that previously used by the authors(ig) to measure the vapour pressure of pure iron. The manganese and iron content of the condensate were determined by means of a y-ray spectrometer. Since manganese is very much more volatile than iron (exp 33,00O/RT N 105) it was necessary to avoid depleting the sample of manganese and therefore necessary to restrict the measurements to small effusion times (10 min at high temperatures). For this reason more accurate values were obtained by measuring the ratio of the partial pressures of iron and manganese and using the previously determined pressure of iron.

The partial pressure p,, of a component u is related to the mass that effuses from an orifice of area as in time t by the Knudsen equation.@O)

where w, is the mass of the component u which condenses on a target radius r at a distance 1 from the orifice.

The weight of manganese on the target w, is deter- mined from A,’ the manganese radioactivity of the target and AuS the manganese radioactivity of a sample of the solution of mass w.

(7)

where x, is the atomic fraction of manganese in the solid solution, x,(M,/M,,) the weight fraction and M,, the average atomic weight of the solid solution. Thus

A similar equation holds for the iron solvent v. Therefore

P& 1’2

P&V (9)

In the present measurements xv was essentially unity. The quantity in equation (9) can be measured accu- rately since any uncertainties due to the short effusion times might be expected to affect the effusion rates of the manganese and the iron by the same amount.

SMITH AND SHUTTLEWORTH: THERMODYNAMIC FUNCTIONS

The pure iron used in this work was supplied by BISRA and according to spectrographic analysis all impurities were present at a concentration of <O.Ol wt. %. The manganese impurity was estimated by activation analysis using the 2@r half-life isotope Mn56 and a concentration of 3.2 x low4 wt. % found. The iron samples were rolled into foils (0.006 x 0.4 x

20 cm) sealed in silica and irradiated in the Harwell pile for a week at a neutron tlux of 1.2 x 1012 neutrons/ cm2/sec. y-emitting isotopes of iron and manganese were formed by the reactions FeQs(n, y)Fe5Q and Fe54(n, p)Mns4. Each sample was effused at one temperature and the vapour condensed on a target cooled by liquid nitrogen. The temperature was then increased to 1673’K and all(s) the manganese evapor- ated from the foil, and the fraction r2/(r2 + Z2) of the manganese condensed on a second target. All determinations were made on the face centred cubic solution except for those at 1073°K and 1673°K which were body centred cubic.

Due to the grea:er volatility of manganese than iron it is vital to ensure that the surface of the alloy is not appreciably depleted during effusion. The effusion times were chosen so that the amount of manganese that effused through the orifice was about 10 % of the

amount that was within a distance m of the surface. The value of D the diffusion coeillcient of manganese in f.c.c. iron was taken from Wells and Mehl.t21) No data appears to be available on the diffusion of manganese in b.c.c. iron and so the values of the self diffusion coethcient of b.c.c. iron were used. Because of the very high diffusion rates in the b.c.c. structure effusion rates were reliable down to 1073°K.

Materials from the two targets and a sample of the alloy from which all the manganese had been evapor- ated were dissolved in acid and assayed with a y-ray spectrometer. The Mns4 and FebQ spectra of neutron irradiated natural iron have been given previously(s); the activity of the Mna is about 1% that of the Fe59 and the energies of the Mns4 and Fe5Q are 0.84 MeV and 1.09 MeV. Because of the greater volatility of the manganese the condensate on the target is pre- dominantly manganese but iron can be estimated in the presence of the manganese because of the greater y-energy. Values of (AUG/aQt)(r2 + 12)/r2 and AuS/w and the corresponding quantities for iron are given in Table 2.

Values of PJx, at 1473°K and above were calculated using equation (9) and values of p,,/x, given by the equation

pc = pm antilog (- T,/T) (10)

635

626 ACTA METALLURGICA, VOL. 13, 1965

TABLE 3. Values of parameters used to calculate pu/x,, p,/xu, f and u. Derived for a mean temperature of 1307°K

Atomic fraction Temperature manganese range (“C) id’;~~~~m i~~~~~~m

2.303 RT,

fm CT13 T* in kcaI~g-atom Reference

-- 0 1000-1500 135.6 21240 97.19 19 0.000003 800-1400 3.911 13540 61.94 This work 0.000003 80&1400 0.2123 186.1 0.85 This work 0.000003 800-1400 0.1250 7491 34.28 This work 1 802-927 19.90 13760 62.98 5

The values of poo and T8 corresponding to the mean l/T’K temperature, 1307”K, were calculated from the iron vapour pressure data measured previously(le) and are given in Table 3. At 1373’K due to the small effusion time it was not possible to measure A,’ and the value of ~~~~~ was determined from equation (8).

Values of (~,/x,)/&,jzJ, and pJx, are given in Table 2.

RESULTS AND DISCUSSION

The present results refer to an atomic fraction 3 x lo* of manganese in LX. iron. McCabe and his collaboratorsc5) have given corresponding results for an atomic fraction 0.3 (1 temperature), atomic fraction 0.5 (3 temperatures) and for pure manganese over a temperature range 1075°K to 1200’K. All these results* are presented in Fig. 1, where log p,/x, is plotted against l/!PK.

Verhaegen, Smoes and DrowartP) have shown that the vapours of the transition metals are essentially monatomic. The chemical potential of a perfect monatomic gas is given by

@ = kTln 1 ~3~/2 1 p

03/2--*-e - (11) 1 @I2 M3/2 QTbi2

where Q is the electronic partition function of atoms in the gas

Q = xv7 t+fkT iw

For mangan~e atoms all electronic states except the lowest can be neglected so that Q, = 6 the multi- plicity of the lowest state. Even at moderate tempera- tures iron atoms are excited and in the neighbourhood of 1500°K Q can be taken from the series expansion.(r@

* McCabe’s experimental results for pure manganese were actually made on &manganese and it was necessary to derive corresponding values for unstable f.c.c.-manganese. Each experimentally determined vapour pressure was inoreased by a factor (1 + AO/kT) ~1.03 where AG is the difference of free energy between f.c.c. manganese and /?-manganese and which has been tabulated by Christian.‘*B) The value of pm was calculated from the entropy of manganese derived from low temperature specific heat data and the experimental vapour preesures were used to calculate Ta; the values of p o. and I$ given in Table 3 correspond to a mean temperature of 1307°K.

The chemical potentials of the solute and solvent of a dilute solution are given by(13)

pus = H,+ - TX,+ + kT In x,

(14) p s = H,” - Tk3vo + kT In xv 21 )

Since for equilibrium the chemical potentials in the gas

and in the solid must be equal the vapour pressures of the pure components can be written in the form:

iso -= xv”

Pu” -= %”

and the partial pressure of the solute

104/ToK

9 8- 7 6

TEMPERATURE IN ‘c

FIG. 1. The variation of the partial pressure of manganese over Fe-Mn alloys with concentration t, and tempera-

ture T.

SMITH AND SHUTTLEWORTH: THERMODYNAMIC FUNCTIOXS 627

It is convenient sometimes to compare the partial pressure of the solute to the pressure of the pure solute and somet~es to the pressure of the pure solvent. Thus the quantities f (Raoultian activity coefficient) and o are defined

(19)

the quantity H,+ - H,@ is the change of energy per atom when manganese is dissolved in a large amount of iron, H,+ - H,,@ is the change of energy when in pure iron an iron atom is replaced by a manganese atom ; S,+ - Sue and S,+ - S,O are defined corre- spondingly. Analogous to equation (10) it is possible to write :

c = 0, antilog (- T,/T) f = f co antilog (- IP,IT)

WV

a, ’ s,+ - se0

=exp - t

) k ,

f, = exp (- ‘%’ I, “‘)

(21)

(22)

In Fig. 2 log f and log G are plotted against l/!P’K and in Table 3 the numerical values of the parameters are given.

For an ideal solution f is unity; Fig. 1 shows that in ~on~entra~d solutions f is only slightly less than unity but for a dilute solution f falls to 0.3. Further- more Fig. 2 shows this value offarises from the entropy of solution and not from the heat of solution. The value of H,+ - H,O, the partial heat of solution at infinite dilution, is $0.85 kcaljg-atom so that in contrast to the results that Kendall and Hultgren(4) obtained for a 50/50 solution the heat of solution is endothermic. The value of (IS’,+ - SUo)/k is +1.55. Again this contrasts with the result that McCabe et d.(7) deduced for concentrated solutions from their own vapour pressure measurements and the results of Kendall and Hultgren that the excess entropy SE/k = -0.47. It is important to realise that the value derived for SW+ - SW0 does not depend upon combining the present experimental work with that of McCabe for pure manganese ; a value of u, and hence

tO’/T “I(

TEMPERATURE IN *C

FIG. 2. The variation of u and f (Raoultian activity coefficient) with temperature for a f.o.c. Fe-Mn solution

containing 3 X IO-* at. oA Mn.

s,+ - SVo can be derived from equation (19j and the difference of entropies of the pure components s,o - SW0 is known from low ~rn~rat~e specific heat data.

It is noteworthy that although the enthalpies of pure iron and manganese differ by 33 kcal/g-atom the heats of solution are small. An explanation of this must presumably await an explanation of the small cohesive energy of manganese.

Mc~l~an and ~~uttleworth calculated an expression for the part of S,+ - XV0 due to change in lattice vibrations on the assumption that the solvent was an elastic continuum and contained a spherical cavity into which a solute atom of a different radius was inserted.

(23)

where p is the shear modulus of the solvent, /? the linear thermal expansion coefficient of the solvent and 6 the size factor. The equation is least likely to be wrong when 8 is small. Manganese and iron have essentially the same atomic weight and are almost the same size 6 = 3 % and values calculated from the equation using the data ~fKiister@~) is 0.525 compared to the e~erimentally determined value 2.08.

628 ACTA METALLURGICA, VOL. 13, 1965

Analogous to the results obtained by Oriani(ls) 4. W. B. KENDALL and R. HULTOREN, Trans. Amer. Sot.

for Fe-Ni it is probable that the magnetic moment Met. 58, 199 (1961).

5. J. F. BUTLER, C. L. MCCABE and H. W. PAXTON, Tram.

of manganese is not much changed on solution in iron, Amer. Inat. Min. (Met&) Engra 221, 479 (1961).

iEnd that in the pure components and in the solution 6. J. H. SMITE, H. W. PAXTON and C. L. MCCABE, Trans.

Amer. Inst. Min. (Met&.) Engrs 221, 896 (1961).

the electron spins are uncoupled so that the magnetic 7. J. H. SMITH, H. W. PAXTON and C. L. MCCABE, J. Phye.

disordering will make only a negligible contribution Chem. 68, 1345 (1964).

8. R. SMITH and R. SHUTTLEWORTH, J. AppZ. Rad. Isotopes, to the excess entropy. to be published.

Kleppa pointed out that for the electronic specific 9. T. PYLE and R. SHUTTLEWORTH Radioisotopes in ScientijZc

Research, edited by R. C. EXTERMANN (UNESCO Con-

heat C, = yT, then provided y is constant the ference, Paris, 1, 1957) U.N. Publication.

electronic entropy S, = y T. Low temperature meas- 10. T. PYLE, Thesis, University of Leeds, Leeds, England

(1959).

urements suggest that the values of y for iron and 11. G. W. JOHNSON and R. SHUTTLEWORTH, Phil. Mag. 4,

manganese have the normal values of 8 x lo4 957 (1959).

12. G. W. JOHNSON, Phil. Mag. 9, 943, (1961). and 11.2 x lo4 Cal/g-atom/cleg2 however the addition 13. R. B. MCLELLAN and R. SHUTTLEWORTH, J. Phys. Chem.

of an atomic fraction 0.11 of manganese to iron Solids 24, 453 (1963).

14. R. A. ORIANI and C. B. ALCOCK, Trans. Amer. Inst. Min. increases the value of y (I*) from 8.10-4 to 33.1 X lo4 (Metall.) Engrs 224, 1104 (1962).

Cal/g-atom/deg2. This corresponds to yE = 25 x lo-+’ 16. 0. J. KLEPPA, Metallic Solid Solutions, edited by J.

FRIEDEL and A. GUINIER. W. A. BENJAMIN, New York

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18. K. P. GUPTA, C. H. CHEN~ and P. A. BECK, J. Phys. Chem. seriously. However the physical origin of the excess Solids 25, 73, (1964).

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(Metall.) Engrs, to be published. 20. R. SPEISER and J. W. SPRETNAE, Vacuum MetaZZurgv,

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