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PHASE TRANSFORMATIONS IN IRON-RUTHENIUM ALLOYS UNDER HIGH PRESSURE?
L. D. BLACKBURNS, LARRY KAUFMAN3 and MORRIS COHEN1
At atmospheric pressure, iron-~thenium alloys containing less than 12 atom percent ruthenium exhibit a diffusionless a(b.c.c.) s y(f.e.0,) transformation on heating and cooling, while alloys containing 12-36 atom percent ruthenium exhibit a diffusionless e(h.c.p.) s y(f.c.0.) transformation. High pressure displaces the a + y reaction to lower temperatures, but shifts the E z y reaction to higher temperatures. These effects appear to be governed by the pressure dependence of the thermodynamic properties.
The application of pressure also produces a new transformation, cc * E, at room temperature in alloys which contain the a-phase at atmospheric pressure. Pressure-temperature diagrams at constant eom- position thus contain triple points involving a(b.c.c.f, y(f.c.c.) and e(h.c.p.). As the ruthenium content is increased, the t,riplo-point pressure decreases si~ificantly.
Comparison of the alloy pressur~~mperature diagrams with the high-pressure behavior of iron demonstrates that the pure metal also exhibits a triple point, at which the high-pressure, low-tempera- ture phase is E. A thermodynamic analysis has yielded values of AF a+~[ 211 for pure iron, thus establish- ing the relative stability of the e-phase in iron.
TRANSFORMATION DE PHASE SOUS PRESSION ELEVEE DANS LES ALLIAGES Fe-Ru
Lors d’un chauffage ou dun refroidissement B la pression atmospherique, les alliages Fe-Ru eontenant moins de 15% at. Ru, poss&lent une transformation sans diffusion a(c.c.) + y(c.f.0.); dams les memes conditions, les alliages contenant 12 a 36 % at. Ru possedent une transformation sans diffusion e(h,c.) + cc(o.f.e). Sous pression &e&e, la reaction x - y se deplace vers des tempkratures plus basses elors que la transformation E -+ y se deplace vers des temperatures plus &levees. Ces effets semblent 6tre en relation avec l’influence de la pression sur les proprietes thermodynamiques.
L’application d’une pression produit Bgalement une nouvelle transformation, a + E, qui apparait it la temperature ambiante dans les alliages contenant la phase a 8. la pression atmospherique.
Les diagrammes pression-temperature, a composition con&ante, contiennent des points triples pour lesquels existent siInultan~ment les trois phases a(c.c.), y(c.f.c) et l (h.c.p.). Lorsque la teneur en Ru s’accroit, on observe une diminution signifieative de la pression au point triple.
La comparaison entre les diagrammes pression-temperature et le eomportement sous haute pression du fer PUP, montre que le metal pur possede aussi un point triple pour lequel la phase l existe, sous haute pression et basse temperature.
Une analyse thermodynamique a fourni des valeurs de A&-e [T] pour le fer pur. Ceci prouve la stabiliti! relative de la phase E dans le Fe.
PHASEN~TMWA~DL~GE~ IN EISE~-RUTHE~~U~~-LEGIERUNGE~ UNTER HOHEM DRUCK
Eisen-Ruthenium-Legierungen mit weniger als 12 At. - % Ruthenium zeigen eine diffusionslose Unwandlung a(k.r.z.) $ y(k.f.2.) beim Hochheizen und Abkiihlen unter hohem Druck. Legierungen mit 12-36 At. - ‘4 Ruthenium zeigen eine diffusionslose e(hexagona1 dichtest gepackt) ;=t y(k.f.z.)- Umwandlung. Hoher Druck versohiebt die a + y-Reaktion zu niedrigeren Temperaturen, jedoch die E - _ y-Reaktion zu hoheren Temperaturen. Diese Effekte soheinen duroh die Druckabhiingigkeit der thermodynamisohen Eigenschaften kontrolliert zu werden.
In Legierungen, welche die a-Phase bei atmosph~risch0m Druck enthalten, fiihrt die Einwirkung eines Druckes ebenfalla zu einer neuen DL + e-Umwandlung bei Raumtem~rat~. Druck-Tem~ratur- Diagramme enthalten folglich bei konstanter Legierungszusammensetzung einen Tripelpunkt zwischen den Phasen a(k.r.z.), y(k.f.2.) und e(hexagona1 dichtest gepackt). Mit zunchmendem Rutheniumgehalt nimmt der Druck am Tripelpunkt marklich ab.
Ein Vergleich der Druck-Temperatur-Diagramme der Legierungen mit dem Verhalten von Eisen bei hohem Druck zeigt, daB beim reinen Metal1 ebenfalls ein Tripelpunkt auftritt, an dem E die Phase bei hohem Druck und niedriger Temperatur ist. Eine thermodynamische Analyst? hat Werte fiir AFa-e [T] in reinem Eisen ergeben und somit die relative Stabilit&t der e-Phase in Eisen sichergestellt.
1. INTRODUCTION
The application of high pressure may have impor- For example, polymorphism becomes more common
tant effects on phase relationships in metals and alloys. when both temperature and pressure are variables, rather than temperature alone. Pressure also changes
t Received May 6,1964. This research was sponsored by the the temperatures of melting and polymorphic trans- Metallur~ Branch, Office of Naval Research, W~hing~n, D.C. under Contracts Nom 2600(00)-NR 031-627 with
formations, and may thus permit a direct study of
ManLabs Inc., and Nonr-1841-35 with the Massachusetts solid phases at temperatures beyond their normal Institute of Technology, and is based on a doctoral thesis submitted to the Department of Metallurgy, M.I.T. in May
range of stability at atmospheric pressure. Detailed
1963 by L. D. Blackburn. studies of such effects may well provide new insight to $ Formerly Department of Metallurgy, M.I.T., presently
Lieutenant USAF, Air Force Materials Laboratory, Wright- the understanding of lattice stability of metals, and it
Patterson Air Force Base, Ohio. is in this context that the present investigation on the 5 ManLabs, Inc.. Cambridge, Mass. ff Department of Metallurgy, Massachusetts Institute of
iron-~thenium system was conducted.
Technology, Cambridge, Mass. The iron-ruthenium phase diagram exhibits only
ACTA METALLURGICA, VOL. 13, MAY 1965 533
534 ACTA METALLURGICA, VOL. 13, 1965
three solid phases at temperatures below 1400°C:
a(b.c.c.), y(f.c.c.) and an extensive r(h.c.p.) solid solu-
tion. These phases interact via a eutectoid transfor-
mation :
y(9.3 a/o Ru) 2 x(4.8 a/o Ru) + ~(23.5 a/o Ru)
at approximately 500”C.(1) This reaction is very slug-
gish, however, and even with slow heating and cooling,
it is replaced by two diffusionless phase transforma-
tions. Alloys containing less than 12 at. y’ ruthenium
exhibit an a 2 y transf or a ion, while alloys con- m t
taining 12 to 36 at. “/o ruthenium undergo an E 2 y
reaction.‘2) It is the pressure dependence of these dif-
fusionless reactions which is of interest here.
A high-pressure study of the iron-ruthenium system
offers an intriguing possibility for clarifying the phase
relationships in pure iron. It is well established that
at room temperature iron undergoes a pressure-in-
duced transformation at a pressure of 133 kb.(3y4y5)
The structure of this high-pressure, low-temperature
polymorph has been tentatively identified as either
face-centered cubic(3p6T7) or hexagonal close-packed.(5*s)
Now, the iron-ruthenium phase diagram contains an
h.c.p. solid solution extending from 23.5 to 100 at. y0
ruthenium. Coupled with the hypothesis that pure
iron is h.c.p. above 133 kb, this diagram suggests that
additions of ruthenium to iron may progressively lower
the transformation pressure for the b.c.c. + h.c.p.
reaction, and eventually produce a stable h.c.p. phase
at atmospheric pressure. Judicious alloying with ru-
thenium may, therefore, allow the production of the
high-pressure form of iron at pressures below 133 kb,
thus facilitating the X-ray identification of the struc-
ture in question. Compositional extrapolation of the
transformation pressures might then verify that the
reaction in the alloys is the same as that occurring in
pure iron.
2. EXPERIMENTAL MATERIALS AND PROCEDURE
The compositions, structures and volume relation-
ships of the four alloys used in this investigation are
listed in Table 1. Alloys A, B and C undergo an a + y
transformation on heating and cooling, while alloy D
undergoes an E* y reaction. Comparison of the
lattice parameters of these alloys with the data of
Raub and Plate(l) shows that the metastable product
phases, u and E, have the same composition as the
parent phase, y; therefore, both transformations are
diffusionless. Metallographic observations have indi-
cated that the u z y reaction is martensitic.
The molar volume relationships shown in Table 1
are derived from the measured lattice parameters and
from extrapolation of the X-ray data of Raub and
Plate(l) and Abrahamson.(9) Based on the generaliza-
tion that pressure stabilizes the phase of smaller molar
volume, the data in Table 1 indicate that pressure
should lower the transformation temperatures for the
CL & y reaction but should raise the temperatures for
the E ;~?r y reaction.
Transformation temperatures for the diffusionless
reactions were determined from electrical resistance-
temperature curves. Atmospheric pressure experi-
ments were conducted in an argon atmosphere, and
the high-pressure experiments were conducted in a
high-pressure assembly described elsewhere.(l’Vl)
Pressure calibration was based on the transitions in
bismuth at 25.6 kb and in thallium at 36.7 kb, and on
the pressure dependence of the cc e y transformation
in pure iron. Temperatures were measured with chro-
mel-alumel thermocouples uncorrected for the effect,
of pressure on the e.m.f.
Isobaric resistance-temperature cycles on a given
specimen were recorded at ascending pressure incre-
ments, these increments being varied from one speci-
men to the next to avoid possible thermal history
effects. Several heating and cooling cycles were run at
each pressure, with as many as 17 cycles being obtained
on a single specimen over a range of pressures. Metal-
lographic observation of specimens showed no evidence
of contamination from materials used in the high-
pressure cell.
An entire heating and cooling cycle (25°C -+ 900°C
- 25°C) for each resistance-temperature curve was
accomplished in approximately 7-9 min. However,
varying the heating and cooling rates within the limits
of the equipment. had no effect on the measured trans-
formation temperatures.
TABLE 1. Compositions, structure and volume relationships of iron-ruthenium alloys
Alloy Composition, a/o Ru Structure at 25°C A Va-~t(25”C), cm3/mol AV rz~(25”C) cma/mol AVe-~(25”c) oma/mol ___-
A 5.7 tc -0.19 -0.35 to.16
: 7.7 G( -0.20 -0.36 +0.16 8.8 -0.22 -0.37
D +0.15
15.4 -0.29 -0.44 +0.15
t AVa-y E VY - Vu..
BLACKRURN et ul.: PHASE TRANSFORMBTIONS UNDER PRESSURE 535
I . I i MO-
, \ I I
0 5 10 is 20
ATOM PERCENT RUT(IENIUM
FIG. 1. Transformation temperatures and Curie tempera- tures of Fe-Ru alloys.
3. EXPERIMENTAL RESULTS
1. Transformations at atmospheric pressure
The transformation-start temperatures on heating
(AZ+’ and AZ+‘) and on cooling (M,Y-” and Mr”) under atmospheric pressure are shown as a, function of composition in Fig. 1. In addition to the transforma- tion temperatures, the resistance-temperature curves revealed the Curie temperatures Ti, of the u-phase; these findings are included in Fig. 1. The present results are in good agreement with those of earlier investigat1ions.(1~12~13)
A recent application of the regular solution model of Kaufman and Cohen(14) to the iron-ruthenium sys- tem has yielded values of APa+’ for the diffusionless tr~nsform~tiou as a function of temperature and corn- position. From this, it is possible to calculate T&a s r), which is defined as the temperature at which AY”’ = 0 for a given composition. Figure 1 shows a comparison of these calculated values of T,, with the experimental values of 4(M, + A,). In view of the excellent agreement shown in Fig. 1, the relation T,, = g(M, + A,) was used to evaluate T, for the a s y reaction at higher pressures. Although a lack of thermodynamic data precludes a calculation of T&E + y), it was also assumed that T, = 4(&f, + A,) for this reaction.
2. Trans~o~~t~o~ at high pressures
In alloys A, B and C, the application of pressure
lowers both Ma+“” and A,“+‘, which is expected since y has the smaller molar volume (see Table 1). How- ever, as the pressure is increased, a new reaction re- places the CL G y transf ormation in these alloys. This behavior is illustrated by the resistance-temperature curves shown in Figs. 2 and 3. Figure 2 presents the curves for all four alloys at atmospheric pressure and reveals the difference in hysteresis loops between the a ri: ^J and E ~ti: y transformations. Resistanee-tem- perature curves of alloy B at higher pressures are shown in Fig. 3. Comparison of these figures illustrates quite clearly that at pressures above 42 kb, the CI s y reaction vanishes and the E $sy reaction appears; that is, E replaces ct as the low-temperature phase.
This conclusion was verified by high-pressure X-ray diffraction experiments performed by Professor John Jamieson of the Department of Geology, university of Chicago. He found that on applying it pressure of approximately 90 kb at room temperature, alloys A, B and C contained both b.c.c. u a,nd h.c.p. E; i.e., pres- sure induces an E + E tr&nsformation. Both the resist- ance-temperature work and the X-ray diffraction experiments demonstrated that E is not retained when
26- I ATMOSPHERE
3
zoo 1
500 FJ 903
TE&K=ERAT”RE,-C
FIG. 2. Resistance-temperature curves for Fe-Ru ELIIOJTJ at atmospheric pressure.
536 ACTA METALLURGICA, VOL. 13, 1965
v: I0 Co I
MO 500 700 903
TEMPERAT”RE,~C
FIG. 3. Resistance-temperature curves for 7.7% Ru alloy at high pressures.
the pressure is released, but rather it reverts to u via
the reverse reaction, E -+ a.
Several experiments utilizing isothermal resistance-
pressure cycles were performed in an attempt to meas-
ure the transformation pressures for the u z E reac-
tion. Unfortunately these efforts were unsuccessful.
It is felt that one or both of the following factors may
explain this inability to detect the dc --, E transforma-
tion : (1) the equipment had insufficient pressure capa-
bility to produce appreciable transformation ; or
(2) the transformation occurs gradually over a broad
pressure range, and thus the resistance change is too
gradual to be detected.
The first of these factors is not necessarily inconsis-
tent with the results of resistance-temperature cycling,
where E definitely was produced. In these experiments
it is likely that E formed from y rather than cr; that is,
the first cycle reactions may be u % y 2 E, subse-
quent cycles then showing only E = 1’. However, this
possibility could not be conclusively demonstrated,
since the “settling” of the high-pressure cell on the first
heating cycle always produced an irregular resistance-
FIG. 4. Transformation temperatures vs. pressure for 5.7 at. ‘A Ru alloy.
temperature curve which was difficult to interpret
accurately.
Quantitative results of the transformation behavior
in alloys A, B and C are presented in Figs. 4-6, which
show the variation of the transformation temperatures
and T,, with pressure. In addition to the entree of the
E s y reaction at high pressures, these plots reveal
that as the ruthenium content is increased, this reac-
tion occurs at lower pressures. Thus, in alloy C, the
I I I 1 I
OO 10 20 so 40 so PRESSURE , KILOBAf?S
FIG. 5. Transformation temperatures vs. pressure for 7.7 at. % Ru alloy.
BLACKBURN et al.: PHASE TRANSFORMATIONS UNDER PRESSURE 537
FIG. 6. Transformation temperetures vs. pressure for 8.8 at. % Ru alloy.
cc & y reaction has already disappeared at 16 kb. The M,, A, and T, temperatures for this reaction were calculated using the same pressure dependence meas- ured in alloy B.
The transformation behavior of alloy D at high pressures is shown in Fig. 7. This alloy exhibits the l $ y reaction at atmospheric pressure, and M:+,
A:‘Y and T&E e y) are raised as the pressure is in-
I I ! I I I I
900 t
200’ I I I I 0 10 20 30 40 50
PRESS"RE.KILOBARS
FIG. 7. Transformation temperatures vs. pressure for 15.4 at. % Ru alloy.
creased. No new transformations occur in this alloy,
supporting the conclusion that the high-pressure phase
in the lower ruthenium alloys is E.
4. DISCUSSION
1. Pressure dependence of a 22 y and E 212 y reactions
The pressure dependence of the diffusionless phase transformation in these iron-ruthenium alloys is in qualitative agreement with the generalization that pressure stabilizes the phase of smaller molar volume; thus Mi+, and At+?’ decrease with increasing pressure, while MT’E and AfY increase.
A quantitative prediction of the pressure depend- ence of those diffusionless transformations requires a knowledge of A Vu+y, A F+’ and the driving forces at
M, and A, as functions of temperature and pressure.(16) Using the only available data for AFa+Y,(15) an approx- imate calculation of the pressure dependence of Ml’“,
A:?’ and T,(a 2 y) was carried out. This calculation is identical to thst used by Kaufman et al. for the iron- nickel system.u7) Table 2 compares the calculated and experimental transformation temperatures at several pressures for alloy A. The calculated values of AZ+7 are
somewhat low, but considering the approximations required in the calculations, the agreement evidenced in Table 2 indicates that the pressure dependence of the u e y reaction is governed by changes in the thermodynamic properties under pressure.
Unfortunately, the lack of thermodynamic data for the E & y transformation prohibits a similar calcula- tion for this reaction. In general, the behavior of this reaction is consistent with the fact that E has the smaller molar volume, suggesting that the variation in the thermodynamic properties with pressure is the controlling factor. The only exceptions to this gener- alization occur in alloys B and C, where AZ-Y de- creases as the pressure is raised. This anomalous result may be due to unknown changes in Al++” with tem- perature and pressure, or to changes in nucleation behavior or transformation mechanism under pressure.
2. Composition dependence qf the high-pressure
transformati0n.s
An important feature of the present investigation is the appearance of E as the high-pressure, low-tempera- ture phase in iron-ruthenium alloys. Since the phase transformations are diffusionless, Figs. 4-7 may be treated as binary analogues of the pressure-tempera- ture diagrams for one-component systems. Thus, the T,, curves in these graphs are the boundaries between the single phase fields in this type of pressure-temper- ature diagram. In alloys A, B and C, TO(u e 7) end T&E JFs y) intersect, to give a triple point. There
538 ACTA METALLURGICA, VOL. 13, 1965
TABLE 2. Comparison of experimental and calculated transformation temperatures for 5.7 a/o Ru alloy at high pressures
P, kb
0 569 722 646 655 10 461 697 579 480 661 5s5 20 382 672 527 421 604 519 30 332 643 488 353 553 463 40 278 613 446 289 507 413
should, of course, be a third branch intersecting at the
triple point corresponding to T,( tc G e). Although the
latter curve could not be quantitatively measured,
the experimental demonstration of the direct u -+ E
transformation shows that it exists. Therefore, it is
concluded the the diffusionless transformations in iron-
ruthenium alloys do exhibit triple point behavior. The
pressure and temperature parameters of the triple
points (which vary with the ruthenium content) are
denoted as P, and T, in Figs. 4-6.
The establishment of triple points for iron-ruthe-
nium alloys, in which all the phase have been identified,
immediately suggests a comparison of these alloys with
pure iron, where the phase relationships are still in
doubt. This comparison is made in Figs. 8 and 9,
where P, and T, are plotted as functions of composi-
tion. The extrapolation of the alloy data to pure iron is
in very good agreement with the triple-point param-
eters for iron proposed by Johnson, Stein and Davis.(s)
It should be emphasized that Fig. 8 shows the com-
positional variation of the triple-point pressure at a
Fro. 8. Variation of triple-point pressure (P*) with composition.
I
0 JOHNSON ET AL 124)
0 PRESENT INVESTIGATION
*x5 --__
--_ ----_ l l
0
1 I I I 2 4 6 B
ATOM PERCENT R”THENl”M
FIG. 9. Variation of triple-point temperature (T,) with composition.
temperature of approximately 450°C, not the trans-
formation pressure at 25°C. Accordingly, the alloy
data do not extrapolate to a pressure of 133 kb at room
temperature in pure iron, but to a lower pressure char-
acteristic of the triple point. However, additional
workos) by J. S. McCallum and J. C. Jamieson on ten
alloys containing O-6 a/o ruthenium? has yielded qual-
itative information on the composition dependence of
the actual CI --+ E transformation pressure at room tem-
perature. Table 3 summarizes the h.c.p. reflections
which were observed in these alloys under pressures of
approximately 90 kb and 130 kb. The increase in the
number of h.c.p. reflections at a given pressure indi-
cates that the u ---f E transformation pressure is de-
creasing with higher ruthenium contents, leading to
the formation of more E at the test pressure. These
data demonstrate that the transformation pressure
does not rise sharply with decreasing ruthenium con-
bent but varies smoothly to a value quite close to
t These alloys were kindly supplied by Dr. E. P. Abrahemson of the Watertown Amenal during the final stages of this inves- tigation.
BLACKBURN et al.: PHASE TRANSFORMATIONS UNDER PRESSURE 539
TABLE 3. High-pressure X-ray diffraction results on the c( + e transformation at 25°C (after J. S. McCallum and J. C.
Jamiesono*‘)
Alloy composition,
at. ‘A Ru
0.00 0.53 1.00
1.55 2.02 2.57 3.43 3.96 4.50 5.12 5.65
H.C.P reflections observed P m QOkb P es 130kb
none none none
none n0IIe none none none none
t;;.;\(Ref. 5)
(lO:l), trace of (11.0) and (10.3)
I::.:\ (lo:o), (lO.l), (ll.O), (10.3) (lO.l), (ll.O), (10.3) (lO.O), (lO.l), (ll.O), (10.3) (lO.O), (lO.l), (ll.O), (10.3) (lO.O), (10.1), (ll.O), (10.3) (lO.O), (lO.l), (ll.O), (10.3)
133 kb. This result also provides strong support for the
validity of the extrapolation of the triple-point pres-
sures in Fig. 8.
From these considerations of the iron-ruthenium
data, it is evident that pure iron does indeed contain
a triple-point, and that the high-pressure, low-temper-
ature form of iron is hexagonal close-packed. This
conclusion has recently been verified by very high-
pressure X-ray diffraction experiments.(1g~20)
3. Thermodynamics of h.c.p. iron
The transformation data on these iron-ruthenium
alloys can now be used to further advantage in devel-
oping the thermodynamic properties of the h.c.p. form
of iron.
Previous high-pressure studies of the pure metal
have yielded no information on the E z y reaction in
iron. However, in the alloys studied here, it is found
that cZT~“~)/~P = 3.3”C/kb. Using this value of
dT&P and the known triple-point pressure and tem-
perature, the temperature at which y and E would be
in equilibrium in pure iron at atmospheric pressure is
estimated to be approximately 400’K. This is an im-
portant piece of information in t!ie following analye&.
Following the treatment of Kaufman et aZ.,@l) the
heat capacity of e-iron is considered in terms of lattice,
electronic and magnetic contributions :
GDQ[T] = C, f (1 + 10-4T) + yET + CDEw[T] (1) [I where 8’ is the Debye temperature of e-iron
y’ is the electronic specific-heat coefficient
C,E@ is the magnetic contribution to the heat
capacity.
This relation can then be integrated to yield an ex-
pression for the free energy of E-iron:
FyT] = Hoc + Fe + FE’[Tl - iyeT (2)
where HOC is the enthalpy at O”K, based on Ho” G 0.
It is now assumed that yE = ycl = y’ and also that
FCp = 07. Then, by employing the known values of
F”[T],(21) AFZ+E(=FE - F”) can be formulated in
terms of the parameters 8’ and Ho’. These parameters
are then fixed by requiring: (1) that AFa+<[T] yield
reasonable agreement with the calculated equilibrium
temperature of y 2 E at one atmosphere (i.e. the tem-
perature at which AFx’E[T] intersects the known
function A F”“[ T]) ; (2) that A Fa+E[ T] yield a reason-
able value for the melting temperature of E-iron (i.e.
the temperature at which AFa-<[T] intersects the
known function AF”‘L[T]) ; and (3) that the melting
point and Debye temperature of h.c.p. iron conform
to the Lindermann relation.(21) Table 4 summarizes
the parameters for c-iron which result from these cal-
culations and compares them with the corresponding
parameters for u and y iron.
Figure 10 shows the variation at one atmosphere of
the calculated AF”“, AF”‘Y and AF”‘L functions
with temperature. These curves indicate that at T =
O”K, E-iron is more stable than y-iron. As the temper-
ature is increased, AF”’ decreases because E has a
larger entropy than CI. However, y has a still larger
t Recent measurements of the Mossbauer effect in iron at 25°C and high pressures by Nicol and Jurat2*J and by Pipkorn et al.“@’ indicate that h.c.p. iron is not ferromagnetic. An earlier study’z1j yielded the result ya = yy.
TABLE 4. Thermodynamic properties of a, y and E iron.
Phase ?‘[ T = O”K] z;; cal
H, moi 8°K cal cal
?’ mol - (“K)2 pr mol
7.061 0 432 12 x 10-a
Y (31)
E
7.216$ 6.695 $ 1303 432 12 x 10-a
6.731 1150 375 12 x IO-4 V]T] = V[T = 0](1 + 2.043 x lo-“T + 1.520 x lo-8T2) cma/mol
3wc( T] (ref. 21) PYP[ T]
(ref. 21) 0
$ The two values of B[T = O”K] given for f.c.c. correspond to a high moment-high volume and a low moment-low volume state. (a)
540 ACTA METALLURGICA, VOL. 13, 1965
FIG. 10. Free ener~-~rnper~tu~ rel&ions for the a(b.c.c.),y(f.c.c.),t-(h.c,p.)andliquidformsofFeat 1 atm.
entropy, so y becomes more stable than E at tempera- tures above 39O’K. At higher temperatures, the mag- netic contribution to the entropy of a-iron becomes important, producing a minimum in AP”+. This minimum, indicating a small value of AL?‘~, is con- sistent with the very steep slope of the u e E boundary in the pressure-temperature diagram (i.e. d T,,(a*Ftt)/d P = AVaJC/ASCL’E). It should be noted that this calcu- lation also yields values of AFC+‘[TJ, which is simply the difference between AP”E and APa++’ in Fig. 10.
The free energy functions AFa+E,Ali’“Y and AIW”‘, coupled with the known volume relationships (see Table 4), can now be applied to calculations of the phase boundaries in the pressure-temperature dia- gram, since at the boundaries
AF[T, P] = 0 (3)
On the basis of the foregoing and t,he earlier re- sults,t2n the a/e boundary is defined by
Ai\Fa+[T, P] = 0 = AFa+[T] + 23.9PAV’a-E[T] (4)
The u/y boundary is defined by?
AF’-“[T, P] = 0 = -1303 + Pup[T]
- RT In (1 - y[T, P])
+ 23.9P(VC([T] - V”[T]) (5)
t Equation (5) corrects a typographical error in equation (39) of Ref. 21 in which the P in the last term was omitted.
Frc, 11. Calculated pressure-temperature relations in Fe.
where y[T, P] is the fraction of high magnetic mo-
ments in f.c.c. iron at a given temperature and pres- sure, and Vro is the molar volume of the low magnetic moment form in f.c.c. ironcal’ Finally, the y/c bound- ary is defined by
AFY-E[T, P] = AFY-“[T, P]
+ APa-‘[T, PJ = 0 (6)
Equation (6) is solved numerically by adding equation (4) to equation (5).
Figure 11 shows the calculated pressure-tempera- ture diagram of iron. These results are in good agree- ment with experimental observations of the phase relationships. Thus, the thermodynamic analysis yields values of AFa+<[T] which are consistent with the observed behavior of pure iron.
It is interesting to note that the computed free- energy difference between the f.c.c. and h.c.p. forms of iron at 0°K and one atmosphere is 150 cal/mol. This difference is about three times the corresponding free- energy difference in cobalt. On this basis, the stacking fault energy of y iron would be estimated at about 30 ergs/cm2 or three times that of cobalt.
The principal difference between the computed P-T diagram (Fig. 11) and the observed version (Fig. 1 of Ref. 21) is the location of the triple-point. Johnson,
BLACKBURN et al.: PHASE TRANSFORMATIONS UNDER PRESSURE 541
Stein and Davis@) put the triple-point at about 800°K
and 110 kb as opposed to the computed values T, = 750°K and P, = 92 kb in Fig. 11. There are at least
two reasons for these discrepancies. First, the present
calculations are based on idealizations required for
simplifications and for the purpose of eliminating un-
known parameters. Secondly, the experimental shock-
wave measurements of the u e y branch,(*) which were
performed “isothermally”, exhibit pressure over-
shooting of the order of 10 to 20 kb between 850 and
1150°K. This overshooting can be readily seen in
Fig. 1 of Ref. 21.
Thus, the current differences between the computed
and observed triple-points arise from uncertainties in
both the calculations and the measurements. Resolu-
tion of these differences will require more detailed
studies along both lines.
5. SUMMARY
1. The application of pressure lowers the transfor-
mation temperatures of the diffusionless b.c.c. 2 f.c.c.
reaction, but raises that of the diffusionless f.c.c. z
h.c.p. reaction in iron-ruthenium alloys. The pressure
dependence of these transformations is controlled pri-
marily by the variation in the thermodynamic proper-
ties with pressure.
2. In addition to the diffusionless transformations
observed on heating and cooling, u-phase alloys exhibit
a pressure-induced b.c.c. z h.c.p. reaction at room
temperature.
3. Fixed-composition pressure-temperature dia-
grams for the binary iron-ruthenium alloys show a
triple-point between the b.c.c., f.c.c. and h.c.p. phases.
As the ruthenium content is increased, the triple-point
pressure decreases markedly, while the triple-point
temperature remains essentially constant.
4. A comparison of these diagrams with the high-
pressure behavior of pure iron demonstrates that the
pure metal also exhibits a triple-point, with the high-
pressure, low-temperature structure being h.c.p.
5. A thermodynamic analysis has yielded values for
the free-energy differences between the b.c.c. and h.c.p.
phases in pure iron which are consistent with the
experimentally observed behavior.
6. ACKNOWLEDGMENTS
The authors are indebted to Professor John C.
Jamieson and Dr. J. Stewart McCallum of the Univer-
sity of Chicago for performing the high-pressure X-ray
diffraction experiments pertinent to this investigation,
and to Mr. J. Elling of ManLabs for assistance in the
experimental program. They also wish to thank
Dr. E. P. Abrahamson of Watertown Arsenal for fur-
nishing some of the iron-ruthenium alloys.
The General Electric Fellowship at M.I.T. which
provided financial support for one of the authors
(L. D. B.) is gratefully acknowledged.
1. 2. 3.
4.
5.
6.
7.
8.
9. 10.
11.
12. 13. 14.
15. 16.
17.
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