The states of order and the phase diagram of Fe1−xSix, 0.06 ⪕ x ⪕ 0.20 , investigated by neutron scattering

Acta rnetall, mater. Vol. 42, No. 3, pp. 743 748, 1994 Copyright © 1994 ElsevierScience Ltd Printed in Great Britain. All rights reserved 0956-7151/94 $6.00 + 0.00

l'ergamon

THE STATES OF ORDER AND THE PHASE DIAGRAM OF Fel _ x Six, 0.06 ~< x ~< 0.20, I N V E S T I G A T E D B Y N E U T R O N SCATTERING K. H I L F R I C H L2, W. KOLKER 1'4, W. PETRY 3, O. S C H A R P F 3 and E. N E M B A C H 1 qnstitut ffir Metallforschung der Universit~it, D-48149 Mfinster, Germany, 21nstitut f/Jr Werkstofforschung des GKSS-Forschungszentrums, D-21500 Geesthacht, Germany, 3Institut Laue-Langevin, F-38042 Grenoble, France and 4Fa. W. Fette, D-21493 Schwarzenbek, Germany (Received 5 February 1993; in revised form 23 July 1993)

Abstract--The states of order of iron-silicon solid solutions with atomic fractions c of silicon between 0.06 and 0.2 have been studied in neutron scattering experiments. Up to 873 K, Fe4).06Si is short-range ordered. The structures of the other alloys can be described as follows. They are DO 3 long-range ordered at far lower c and higher temperatures than indicated in the current phase diagram: e.g. Fe4).099Si up to at least 900 K and Fe~).197Si up to at least 1473 K. The DO3-order parameter as well as the size of the antiphase domains decrease as the temperature is raised. Some phase boundaries shown in the current phase diagram turned out to be no phase boundaries at all: the respective lines have bearing only on the size of antiphase domains. Revisions of the current Fe-Si phase diagram are proposed.

Zusammenfassung--Die Ordnungszust/inde von eisenreichen Eisen Silizium-Legierungen wurden in Neutronenstreuexperimenten untersucht. Der Si-Atombruchteil c lag zwischen 0.06 und 0.2. Fe4).06Si kann bis zu 873 K als nahgeordnet bezeichnet werden. Die Strukturen der anderen Legierungen krnnen folgendermagen beschrieben werden. Sic sind noch bei sehr viel niedrigeren c und h6heren Temperaturen DO3-ferngeordnet als im zur Zeit aktuellen Phasendiagramm angegeben: z.B. Fe-0.099Si bis mindestens 900 K und Fe4). 197Si bis mindestens 1473 K. Sowohl der DO3-Fernordnungsgrad als auch die Gr6Be der Antiphasendom/inen nehmen ab, wenn die Temperatur erhrht wird. Es stellte sich heraus, dab einige im zur Zeit aktuellen Phasendiagramm eingezeichnete Phasengrenzen in Wirklichkeit keine solchen sind: tatsfichlich beziehen sich die dortigen Grenzlinien auf die Gr613e der Antiphasendom~inen. Die vorgelegten Ergebnisse legen Anderungen des Fe-Si-Phasendiagramms nahe.

Fe-Si-alloys have the D O 3 structure. The DOa longrange order parameter S and the size W of the antiphase domains varied with c and T. The c*(T)line in Fig. 1 turned out to be no phase-boundary: it has bearing only on W. Below results of extensive neutron scattering experiments are presented, c ranged from 0.061 to 0.197 and T from 623 to 1473 K. These measurements corroborate the just mentioned earlier findings [3, 4].

1. INTRODUCTION Figure 1 shows the iron-rich part of the iron-silicon phase diagram; it is based on critical assessments by Kubaschewski [1] and on extrapolations by Biichner [2]. There are three relevant phases: g, ~ , and ~2- The respective crystallographic structures are: disordered or short-range ordered A2, long-range ordered DO3, and long-range ordered B2. T h r o u g h o u t the following, the D O 3 elementary cell will be used to describe long-range ordered structures. Details can be found in Refs [3-5]. The nomenclature used below and the relevant equations have been published in a paper dealing with Fe-rich Fe-Al-alloys [5], whose structures are analogue to those of Fe-Si-alloys [7, 8]. The lattice constant a0 of the Fe-Si-DO3-cell varies slightly with the atomic fraction c of Si and with temperature T. ao(c = 0.095, T = 293 K) equals 0.5708 nm [6]. If short-range order is dealt with, the standard b.c.c, elementary cell will be used; its lattice constant is ao/2. On the basis of the results of recent neutron scattering experiments the present authors refuted that the B2 structure occurs for Fe-Si-alloys with c ~< 0.102 [3, 4]. They provided evidence that in the ranges 0.076~
2. EXPERIMENTAL METHODS AND RESULTS The Si-concentrations of the five cylindrical single crystals were: (0.061 _+ 0.008), (0.076_+ 0.002), (0.091 __ 0.005), (0.099 _+ 0.005) and (0.197 _+ 0.004). These compositions were obtained by electron microprobe analyses with wave-length dispersive spectrometers. Actually the Fe-0.099Si specimen is the one studied in Ref. [4]. The present more accurate analysis yielded, however, 0.099 instead of 0.102 for the Si-concentration. Length, diameter and axis orientation of the specimens were: 6 0 m m (Fe~).197 Si: 35 mm), 4 mm, and [T10], respectively. There was one exception: the Fe4).06t Si specimen had its axis along [010]; after tilting it through 45 ° it could be investigated like the other specimens. The 743

744

HILFRICH et al.: THE STATES OF ORDER OF Fet _~Six

preparation of the specimens has been detailed elsewhere [4, 5, 9]. They were homogenized for 24 h at 1273 K. Neutron scattering experiments have been performed as described in Refs [5, 8]. The direction of the incident neutrons was [0.594, 0.594,-0.543] and [0.089,0.089, -0.992], when the (002)- and (111)-reflection was studied, respectively. This applies to 2 = n e u t r o n wave l e n g t h = 0 . 3 1 n m , and a0 = 0.5708 nm. In this case the Bragg angles 0002and Oii I were 32.9 ° and 28.1 °, respectively. The temperatures T at which the scattering cross-section 0a'/0f~ [5] has been determined, are indicated in Fig. 1. The error limits of T were about ___10 K. For c >i 0.076, the specimens were kept at T during the neutron scattering experiments. For c = 0.061 and T ~< 873 K, quenched specimens have been studied at ambient temperature. It has been proved that for T ~< 873 K the equilibrium state of order can be quenched in [4]. Some data are shown in Fig. 2. There Oa'/O~loo~ and Oa'/Ofllm are plotted vs the scattering angle 20 [5]. At 20 > 100 °, parts of the (113)- and of the (113)-reflections are visible in the (002)- and (111)-diagrams, respectively. The data are representative of the states of thermodynamic equilibrium. Reaching a certain temperature from higher or lower ones yielded identical results for da'/O~. The reduced DO3 longrange order parameters Shkl (S = S/Smx(e), equation (3) of Ref. [5]) and the domain sizes Whkt are derived

from curves like those shown in Fig. 2. The relevant procedures have been laid down in Refs [3, 5]. Shk~ depends on integrals over such curves and Whkt on their peak-widths. (hkl) indicates the two superlattice reflections (002) and (111). Some results for S00E,Slil, Woo2 and Wm are presented in Table 1. The error limits of Shkt are estimated to be around 25%. Their major part stems from the approximations made in their evaluations [3, 5]. Since in the present investigation broad reflections were of prime interest, the instruments were configurated accordingly. This had the consequence that very narrow reflections could not be accurately measured [5]. This applies e.g. to those of Fe-0.197Si studied at 1173 K [Fig. 2(c)]. In such cases (i) Shkt is not quoted and (ii) only lower limits are given for Whkt. When short-range order is considered, the lattice constant equals ao/2 and the (002)- and (111)-reflections should be given the indices (001)- and d_!!~ ~-2 2 2 / , respectively. For the sake of uniformity the former indices are kept, however. The most important results are: (1) Except for the Fe4).061Si specimen at 1073 K, all others showed (002)- as well as (111)-reflections at all temperatures. The latter ones indicate DO 3order. (2) c t> 0.076: at elevated temperatures the (002)reflection is higher and narrower than the (111)reflection. For the above mentioned experimental reasons, this may not hold for very narrow peaks

[51. 1500 -

(3) As T is raised, Whkt and Shktdecrease.

T (K]

3. DISCUSSION 1300'

0

O0

3.1. c = 0.061 0

1100'

T. o . . . . . . -¢. . . . . . 0 O 0 0

900'

0 0 o o

700

o o

j

Ct 1

500

Up to 873 K, this specimen may be described as short-range ordered; at 1073 K no order is noticeable. The curves plotted in Fig. 2(a) have been obtained by fitting the equation meant for short-range order (equation (11) of Ref. [5]) to the data. Eleven shortrange order parameters ~i and three size effect coefficients fli have been allowed for. Since the 10th coordination shell contains two groups of crystallographically non-equivalent sites, ~i0 comprises two independent parameters: ~t10a and ~10b. The fitted curves represent the data quite well. Since there are broad (11 l)-reflections up to 873 K, the short-range order resembles DO3-order. 3.2. c >~ 0.076

300

o

o.&

o. 8

o.;2

oJ6

¢

aio

Fig. 1. The Fe-rich part of the Fe--Si phase diagram after Kubaschewski [I] and Biichner [2], c -- atomic fraction of Si. The y-phase is not shown. The dashed line marks the Curie temperatures To. For the concentrations and temperatures indicated by O, neutron scattering experiments have been performed. The thick lines indicate the critical concentrations c*(T) and c*(T) defined in Section 3.2.

All specimens show (002)- as well as (111)- reflections at all temperatures studied (Fig. 1). This indicates DO3 long-range order. Below about 900 K, the reduced DO3 long-range order parameters S0o2as well as s m agree--within the error limits--with their theoretical upper limit 1.0. For 0.076 ~< c ~< 0.099, 900 K is high above the ~--}~2-phase transition supposed by Kubaschewski [1]. W002and Wm are not less than 1.5a0 even at 1273 K. W m/> 1.5a0 and s m - 1.0

HILFRICH et al.: THE STATES OF ORDER OF Fe I_xSi~ imply that even for c = 0.076 the positions of more than four Si atoms are strictly correlated: they all occupy sites in the D sublattice [5]. For (c = 0.076, T = 1023 K), (c = 0.091, T = 1023 K) and (c =0.099, T = 1273K) the equation describing short-range order (equation (11) of Ref. [5]) can represent the data with fourteen adjustable parameters. They have, however, unreasonable values. Since only two scans through k-space, namely through the (002)- and through the (111)-reflections, have been measured, the fitting procedure has too much freedom: it assigns meaningless values to Oa'/d~lk for k-vectors outside of the measured range. It cannot be excluded that the mentioned equation can represent data sets covering the entire k-space with reasonable ~i and fli; but at any rate a host of ct~would be necessary. In view of this, these alloys are described as DO 3 long-range ordered--at least up to the following temperatures: c = 0.076--773 K; c = 0 . 0 9 1 and 0.099--900K; c = 0 . 1 9 7 - - 1 4 7 3 K . 1473 K is the highest temperature studied. At these temperatures, which are high above those for which Kubaschewski [1] expected DO3-order (Fig. 1), the antiphase domains are relatively small (Table 1). In a short-range order description not less than 20 coordination-shells would have to be allowed for; i.e. not less than about 30 parameters would be required. The "DO3 long-range order small domain model", however, involves only three of them: s, W0o2 and WI~. The temperature limits quoted above for

745

c ~<0.099, are more conservative than those given earlier [4]. Since all experimental data are representative of the states of thermodynamic equilibrium, the antiphase domain boundaries which lead to the decrease of W0o2and WII 1 a s Tis raised, are also in thermodynamic equilibrium. W002and W~l~are unique functions of T and c: Wo02(c, T) and Will(c, T). Approaching T from above or from below yields the same results. At the phase boundaries c~(T) and c~(T) drawn by Kubaschewski [1] and Bfichner [2] (Fig. 1) neither S0o2 nor Sill changes significantly (Table 1). Evidently c*(T) and c*(T) in Fig. 1 do not indicate phase transitions, i.e. changes of crystallographic structures. These lines have bearing only on Woo2 and Wll 1 -

As the c*(T)-line is approached either from low concentrations or from high temperatures, Woo2 increases strongly. W002is derived from the width B0o2 which is raised by antiphase domains with v~-displacement vectors, but not by those with v2-displacement vectors [5]. Therefore one can conclude that to the left of the c*(T)-line, vl-antiphase domain boundaries are in thermodynamic equilibrium. Their density ( = total area per unit volume) decreases, the closer one gets to the c~'(T)-line. Disregarding a geometrical factor whose order of magnitude is unity, this density equals 1/W002. Evidently the variation of Woo:/ao with c/c* resembles critical behaviour. The approach of s002 and of W002 to their equilibrium

c =

(a) T = 623 K

T = 623 K ~

0.061

.

aft o

,•

o

Of/ ¢:J]

2'0

~o

s~

do

,~o 2'0 t°l

2'o

T = 873 K (00.'2)

4'0

6'0

do

,go 20 [ ° ]

8'0

8'0

,do i o [°]

T = 873 K (111) °°

:l 0

J

z'0

,'0

I

~o

I

80

o

2'0

Fig. 2. (a) Caption on p. 747. AMM 42/3~K

~o

746

HILFRICH et al.: THE STATES OF ORDER OF Fe l_xSix c

(b)

=

0.099

Dc/

(002) ,=T= 703K , T = 753 K ,, T -- 7 7 3 K ° T = 823 K o T = 1025 K

¢q

O

0

I

I

40

60

80

I

I

I

I

I

20

40

60

80

100

20

'-

i

100

20

[°1

20

["1

(111)

O-

oT= 703K , T = 753 K ,, T = 7 7 3 K oT = 8 2 3 K o T = 1025 K O"

vv O

0

Fig. 2. (b) Caption on facing page.

values has been studied for Fe-0.076 Si and for Fe--0.099 Si. These parameters were measured as functions of time at 663 K (c = 0.076) and 623 K (c = 0.099) [10]. The c* (T)-line in Fig. 1 has an analogous meaning for Will as the c* (T)-line for W0o2. To the left of the c* (T)-line antiphase domain boundaries with v2-displacement vectors are in thermodynamic equilibrium. On the basis of the present experimental data it is not possible to determine c* (T) in the range 620-960 K, because the error limits of c and T are too large. Kubaschewski's and Biichner's supposed ct2*'-~(ct2+ ~l)-phase boundary probably follows c~(T).

Vl-antiphase boundaries have higher specific energies than rE-boundaries because the former ones create wrong nearest neighbours whereas the latter ones disturb only next-nearest neighbour relations. This difference in energy explains why Vl-boundaries are found at lower Si-concentrations than VE-bOundaries, i.e. why c*(T) is smaller than c*(T). Antiphase boundaries are thermodynamically stabilized by their configurational entropy. They are believed to fluctuate in time and space [5]. There was no indication for a gradual transition from DO3- to B2-1ike order as T is raised. If at higher temperatures Si atoms preferred sites in the C sublattice to those in the A and B sublattices [5], the ratio

HILFRICH et al.: THE STATES OF ORDER OF Fe]_~Si~

747

(c)

c = 0.197 au

T=

a

1173K

T = 1173 K

(111)

(002)

R.

i

i

~--~

2O

-

40

6o

aO

too

[0]

0

40

6o

80

6o ,

~

mo '

2o

I*!

!

a,'~

T=1373K

/

aa m

T = 1373 K

e

an ~

(002)

(111)

O"

o

o

~

4o

~

too 2 0

T = 1473 K

aft

i

20

I*l

~a

'

J

i

4O

" ' m~ 2 0 L.1 [

T = 1473 K

m

m

8fl

(002)

(111)

tO

el"

/

o

0

i

'-

i

40

;

i

6o

"1!

80

=;

i

~

7

20 ['1

o

'

6o '

loo ' 2e

[°1

Fig. 2. Experimental results: do'/0tl vs 20, &r'/Ot~in [barn sterad I atom-q. Note the different ordinate scales. (002)- and (111)-reflections are shown. (a) Fe-0.061Si, the curves represent a fit of equation (11) of Ref. [5] (short-range order) to the data. (b) Fe-0.099Si, the lines just connect the data; supposed phase transitions [1, 2]: (DO3 + B2).-.B2 (the (111)-reflection should disappear): at about 720 K; B 2 ~ A 2 (the (002)-reflection should disappear): at about 770K. (c) Fe-0.197Si, some data have been smoothed by averaging over several detectors, the linesjust connect the data; supposed phase transition [1, 2]: DO3 ~ B2 (the (111)-reflection should disappear): at about 1350 K.

soo2/sm would increase with T. This is actually not the case. The Fe-rich part of the Fe-Si phase diagram shown in Fig. 1 should be revised to allow for the present findings. For Fe-Al-alloys with compositions around Fe3 A1, for which Kubaschewski [7] supposed similar phase transitions as for the present Fe-Si-alloys, the present

authors [5] defined critical temperatures T*(c), 1 ~< i ~< 3. The inverse functions to c*(T) had to be used because for Fe-A1 Tg (c) was rather flat. Qualitatively the results for Fe-Si and F e - A l are the same: (i) supposed DO3-~-~B2-,-~A2-phase transitions do not occur; (ii) supposed phase boundaries indicate changes of Whu. There is, however, a difference: shu of Fe-Si-alloys decreases already at temperatures at

748

HILFRICH et al.: THE STATES OF ORDER OF Fel_xSix Table 1. Results for the reduced order parameters s002and sll I and the domain sizes Woo2/ao and Supposed c T[K] phases~ Soo2 Woo2/ao slit 0.076 663 • 0.80 4.3 1.02 873 • 0.74 3.4 0.90 1023 • 0.57 2.9 0.76 1273 • 0.58 2.3 0.56 0.099 703 °tl + ~2 0.79 25 1.02 753 ~2 0.79 16 1.06 773 ct 0.87 12 1.12 823 ~ 0.80 7.4 0.92 1023 ~ 0.58 3.5 0.68 1273 a 0.60 2.0 0.47 0.197 1173 a~ >40 1273 ~1 >40 1373 ~2 >40 0.56 1473 a2 > 40 0.47 aPhases expected on the basis of Kubaschewski's [1] and Biiehner's [2] phase diagram shown in Fig. 1.

which Whkl still exceeds 1.5a0. This contrasts with the observations for Fe-Al-alloys. The present model "DO3 long-range order with small antiphase d o m a i n s " obviously implies a generalization of the definition of long-range order: (i) antiphase domain boundaries are in thermodynamic equilibrium at elevated temperatures; (ii) the longrange order parameter has to be determined for individual domains first and then averaged over them. As long as Whkl exceeds a0 significantly, this model is preferred to that of short-range order. The latter one can represent only the broadest o f all diffraction peaks with a reasonable number of ~ . The long-range order model .requires only three parameters: s, W0o2 and W l l I . Only if Wh,~ is close to or below a0, the short-range order model may be applicable. The reasons why the small antiphase domains have been overlooked in earlier investigations, have been given elsewhere [4, 5]: to be visible in the transmission electron microscope, domains should not be much smaller than the thickness t o f the thin foil. t will have been between 30 and 100nm. The creation of antiphase boundaries next to c * ( T ) may produce thermal effects which resemble those caused by phase transitions.

4. CONCLUSIONS On the basis of the experimental data and the above analysis the following descriptions of the states of order o f Fe-rich Fe-Si-alloys are given: 1. Fe--0.061 Si is short-range ordered up to at least 873 K. F o r c i> 0.076, the specimens are DO3 longrange ordered up to at least the following temperatures: c = 0 . 0 7 6 - - 7 7 3 K ; c =0.091 and 0 . 0 9 9 - about 9 0 0 K ; c = 0 . 1 9 7 - - 1 4 7 3 K . These temperatures are high above those at which Kubaschewski [1] expected D O 3-Order. If the diffraction peaks observed at the quoted temperatures were to be described by

Wm/ao Wla~/ao 1.9 1.5 1.5 1.6 4.9 3.2 2.9 2.4 1.4 1.5 >40 >40 13.2 4.3

a short-range order model an unreasonably high number of parameters would be needed. The D O 3 long-range order model involves only three of them. N o B2-order has been found at any temperature. 2. The DO3 long-range order parameter as well as the size of antiphase domains decrease as the temperature increases. 3. The lines marked c * ( T ) and c * ( T ) in Fig. 1 are no phase boundaries, at which crystallographic structures change. These lines have bearing only on the size of antiphase domains. To the left of the c * ( T ) line, antiphase domain boundaries with v~-displacement vectors are in thermodynamic equilibrium. The analogue holds for v2-boundaries to the left of the c~' (T)-line. The present results suggest revisions o f the current [1, 2] F e - S i phase diagram. Acknowledgements--Thanks are due to Professor Dr R. Wagner and Dipl.-Phys. Th. Ebel, GKSS, for various help. K. Nembach, M. S., is thanked for growing single crystals.

REFERENCES

1. O. Kubaschewski, Iron-Binary Phase Diagrams, p. 136. Springer, Berlin (1982). 2. A. R. Bfichner, Arch. Eisenhiittenwes. 53, 189 (1982). 3. W. K61ker, R. Wagner and E. Nembach, J. Phys. F: Metal Phys. 18, 2513 (1988). 4. K. Hilfrich, W. K61ker, W. Petry, O. Sch/irpf and E. Nembach, Scripta metall, mater. 24, 39 (1990). 5. K. Hilfrich, W. Petry, O. Sch/irpf and E. Nembach, Acta metall, mater. 42, 731 (1994). 6. F. Lihl and H. Ebel, Arch. Eisenhiittenwes. 32, 489 (1961). 7. O. Kubaschewski, Iron-Binary Phase Diagrams, p. 5. Springer, Berlin (1982). 8. K. Hilfrich, Th. Ebel, W. Petry, O. Sch/irpf and E. Nembach, Scripta metall, mater. 25, 1857 (1991). 9. G. K6tter, K. Nembach, F. Wallow and E. Nembach, Mater. Sci. Engng All4, 29 (1989). 10. K. Hilfrich, W. Petry, O. Sch/irpf and E. Nembach, Z. Metallk. 84, 255 (1993).