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Lattice parameters of iron-carbon and iron-nitrogen martensites and austenites
S c r i p t a METALLURGICA e t MATERIALIA
LATTICE
V o l . 24, pp. 5 0 9 - 5 1 4 , 1990 Printed in the U.S.A.
PARAMETERS
OF IRON-CARBON
MARTENSITES
Pergamon P r e s s p l c All rights reserved
AND IRON-NITROGEN
AND AUSTENITES
Liu Cheng, A. Btttger, Th.H. de Keijser, E.J. Mittemeijer Laboratory o f Metallurgy, Delft University o f Technology, Rotterdamseweg 137, 2628 A L Delft, The Netherlands
(Received November 27, 1989) (Revised December 29, 1989) 1. Introdo¢tion and Preliminary Considerations A considerable amount of literature data on the lattice parameters of iron-carbon martensite (b.c.t. lattice of iron atoms) exists; see, for example, (1) and (2). Much less data arc available for iron-carbon austenite (f.c.c. lattice of iron atoms). Data on iron-nitrogen martensite and austenite are scarce too. In the course of a research project devoted to the tempering bchaviour of both iron-carbon and iron-nitrogen martensites, X-ray diffraction analysis of the aging-induced martensite-lattice changes revealed remarkable differences between the two martensites. For example, the c lattice parameter of iron-carbon martensite decreases considerably during aging at room temperature, whereas the c lattice parameter of iron-nitrogen martensite does not (3). Hence, it appeared desirable (i) to establish the dependencies of the lattice pararncters on interstitial content, in particular for iron-nitrogen rnartensite and austenite, and (ii) to compare, in this respect, both interstitial iron-based martensites and austenites. To this end a review of existing lattice-paran~ter data of both pure iron-carbon and pure iron-nitrogen as-quenched martensitic specimens is presented in this paper. The relations between lattice parameters and interstitial content are given in two ways: as a linear function of the atomic percentage of interstitial and as a linear function of the number of interstitiais per 100 iron atoms. In fast order approximation one may assume that the lattice parameter is linearly dependent on the number of solute atoms in the unit cell (4, 5). Then, for substitutionary dissolved atoms the lattice parameter would be linearly dependent on the atomic fraction of solute (i.e. Vtgard's relation; cf. (4)), whereas for interstitially dissolved solute atoms the lattice parameter would be linear dependent on the number of solute atoms per solvent atom, since solvent atoms at their (sub)lattice arc not replaced by solute atoms. However, because of the relatively large scatter of the experimental data to be discussed below for interstitial iron-based alloys, it is not possible at present to discriminate between the two types of latticeparameterfmterstitial-content relations. The temperatures pertaining to the lauice-parameter data have very often not been reported in the literature. Therefore it has to be assumed that these data have been obtained at "room temperature" (say 293-298 K). It should be recognized that this temperature uncertainty may contribute to the scatter of the data, in particular because the lattice parameters can change during aging at room temperature. 2. Iron-carbon Th~ until now generally adopted relations between lattice parameters (a and c) and atomic percentage dissolved
carbon,X~, read (2):
509 0 0 3 6 - 9 7 4 8 / 9 0 $ 3 . 0 0 + .00 C o p y r i g h t (c) 1990 P e r g a m o n P r e s s
plc
510
LATTICE PARAMETERS OF F e - C AND F e - N
f
Vol.
a = .28664 -,00028. x ~
(nm)
Da]
c = .28664 + .00247. X f
(ran)
[lb]
c/a = I + . 0 0 9 6 - X ~
2 4 , No.
3
[Ic]
Data, published in the last 50 years, on lattice parameters of iron-carbon martensite are presented as a function of X~, the number of carbon atoms per 100 iron atoms in Fig. la (data from (6-16)). Clearly, a large scatter occurs.The scatter can have several origins: for example, impurities dissolved in the martensite matrix and different experimental errors due to different methods used for lattice-parameter determination. Further, the presence of (nmcro)su'ess due to quenching from the austenite-phase field affects the lattice parameters; this can occur especially for thick specimens (see below). With these remarks in mind on evaluating the published data gathered in Fig. la, three sets of data ( 6, 15 and 16) appear the most reliable. Adopting .28664 nm as the lattice parameter of pure b.c.c, iron (JCPDS, card 6-0696), least-squares fitting of straight lines through these dat~, with the constraint a = c = .28664 nm and c/a = 1 for zero carbon content, yields (see also Fig.lb): a = .28664 - (.00028 :E .00002). X f
(rum) [2a]
a = .28664 - (.00027 + .00001)- X ~
c = .28664 + (.00256 + .00004). X~
(nm)
[2b]
c = .28664 + (.00243 + .00003). X ~ (rum) [2e]
[2c]
c/a = 1 + (.0095:1: .0001). ~ C
c/a = 1 + (.0100 + .0001). X f
3.1"
Fe-C maxtenslte
f
[2fl
Fe-C martensite
x
Honda et aL
-
Haog
=[
"7,
0
/
2.9
o Cadevilleet al. • Bernshteinet al.
2.8
6
8
10
r 12 X C
FIG. 1 a. Literature data for the lattice parameters of iron-carbon manensite as a function of carbon atoms per 100 iron atoms. The straight line is a least square fit through the data.
"
Bemsht,in ,t al. r
2.9
/
2.8
4
o Cade,~ille.st ai.
/
+ Moss m Lysaket al.
2
/
3.0
• Fletcher + Lipsonet al. • Mazur • A,-buzov
,
0
r
o Ohman
3.0"
0
[2d]
/
3.1"
"7
(nm)
a = .28664 - .00027 X c
i
i
|
i
i
2
4
6
8
I0
r 12 XC
FIG. I b. Selected data for the lattice parameters of iron-carbon martensite; the straight lines correspond with Eq. 2(t and 2e.
Vol.
24, No.
3
LATTICE
PARAMETERS
OF Fe-C AND Fe-N
511
The dependence of the volume per iron atom on carbon content is obtained as (least-squaresfit,forced through .011776 Pan3 forzero carbon content): V = .011776 + (.000081 + .000003). X~(nm) [2g]
V = .011776 + (.000077 + .000002)- X~ (nm 3)
[2hi
In the above presentation (¢qs. [2a-h]) it has been assumed that the lattice spacings measungt from the martensitic specimens are not affected by residual (macro)stress. This may be correct for the majority phase (i.e. martensite) in thin foils quenched from the austcnite-phase field, as is demonstrated by the following stress measurements performed by the present authors. Pure iron foils of thickness 100 g m wcr¢ carburized at 1115 K in a gas mixture of 99.1 vol.% H 2 and .9 voL%CO at atmospheric pressure, leading to a carbon content of ~ C = 5.3. The austenitized foils were quenched in brine. Adopting a stateof plane stressfor the surface-adjacent,X-ray probed rnartensite,applicationof the sin2~/method for stressevaluation(see,for example, (17))shows thata small stressof 130 (:I:20) M P a occurs in the iron-carbonrnartensite (full details are found in (3)). It can be shown in a straightforward manner that such a minor stress can not explain at all the large scatter in Fig. la.It may thus be understood that in particular the data reported in (15), obtained from high purity ironcarbon martensidcfoils, show a relatively small scatter (Fig. lb). However, a pronounced stress can occur in the austenite phase of martensidc specimens, even if they are of the thin-foil type. If a small stress is present in the majority mar~nsite phase, the balance of forces requires that the minority austcnite phase is subjected to a larger stress of opposite nature. In view of the usually very small amount of retained austcnite (a few percent) even a pronounced stress in the austcnite can thus occur. Further, it does not appear likely that a state of plane stress can be assumed for the retained anstenite. Pracdcally all martcnsite probed in the X-ray experiment is surface adjacent and, as a consequence of mechanical equilibrium, its stress component perpendicular to the surface is zero. However, the small amount of retained austenite in the X-ray probed surface layer is dispersed and thus it is generally not adjacent to the surface. So, for the retained austenite a triaxial state of stress appears probable. The lattice parameter of the retained anstenite in Fe-Mn-C martensidc specimens ofcoastant compositiondecreased as the amount of martensite increased (18) (the amount of martensite was varied by changing the quench temperature). This suggests that, overall, retained austcnite is in a state of (hydrostatic) compression as a direct consequence of the change of specific volume (about 4%) on transforming austenite into martensite. Against this background lattice-parameter data for austenite are considered below. Least-squares fitting of a straight line through literature data for the lattice parameter of retained austenite in Fc-C martcnsitic specimens as a function of carbon content (6,7,11,19) affords (Fig. 2): a = (.3553 + .0001) + (.00105 + .00002). X
g
r
(nm) [3al
a = (.3556 :t: .0001) ÷ (.00095 + .00001). X C (nm) [3bl
;e:Z:to
i
g •:,
3.61 -
"~ 3 . 5 9 " 3.57 -
3.55
.
0
2
.
.
4
•
IVlazur
o
Wrazej
.
,
6
8
10 x r 12 C FIG. 2. Literaturedam for the latticeparametersof retained austenite in iron-carbon martensitic specimens as a function of the number of carbon atoms per I00 iron atoms. The straight line corresponds with Eq.3b.
512
LATTICE PARAMETERS OF F e - C AND F e - N
Vol.
24,
No. 3
An extrapolation of lattice-parameter data of Fe-Mn austenite (20), measured from specimens fully austenitic at room temperature, to zero manganese content yields .3573 nm for the lattice parameter of pure f.c.c, iron at room temperatme. From a comparison with eq. (3) it may then be suggested that the retained austenite in Fe-C specimens overall experiences a (hydrostatic) compressive swain of about .5%. The dependence of lattice parameter on carbon content for unstra/ned austenite can be derived by adopting a linear relation and combining the value of .3573 nm for f.c.c, iron with a few data (21) for iron-carbon specimens measured at elevated temperature where the specimens are fully austenitic (and thus strain-free) and then corrected for thermal expansion. Itis obtained: a = .3573 + .00075. X f
(nm)
[4a]
a = .3573 + .00070. X ~
(nm)
[4b]
(nm 3)
[4<1]
and the dependence of the volume per iron atom on carbon content is: V ffi .011404 + .000072 • X f
(nm 3)
[4c]
V = .011404 + .000067. X~
For the martensitic foil discussed above (X~ = 5.3) eq. [4d] gives a = .3610 nm. The experimental value obtained from this foil by utilizing the {220} reflection of the retained austenite is .3596 nm. This suggests that the retained austenite in this foil is subjected to a compressive strain of about .4%, in agreement with the above evaluation of literature data. 3. Iron-Nitro~,en Adopting a value for the lattice parameter of pure b.c.c, iron identical to that implied by eq. [2}, the dependencies of the lattice parameters of iron-nitrogen martensite on nitrogen content have been obtained here by least-squares fitting of straight lines through reported data (22-24), with the constraint a ffi c = .28664 nm and c/a = 1 for zero nitrogen content (Fig. 3): a ffi.28664 - (.00018 +.00003)" X
(nm)
[Sa]
a = .28664 - (.00017 4- .00002) X N
(nm) [Sd]
c = .28664 + (.00263 4- .00006) • X
(nm)
[Sb]
c = .28664 + (.00242 4- .00006)" X N
(nm) [5el
[Se]
c/a ffi 1 ÷ (.0090 4- .0002)" X N
c/a ffi 1 + (.0098 4- .1~12) • X
[5t]
f where X N and Xrlq denote atomic percentage of dissolved nitrogen and number of dissolved nitrogen atoms per 100 iron atoms, respoctivety. The relation between the volume per iron atom and nitrogen content is (leastosqUares fit, forced through .011776 nm3 for zero nitrogen content): V = .011776 + (.000092 4- .000004)" X f
(nm 3)
[5g]
V = .011776 + (.000085 4- .000003)" XrN (nm 3)
[5h]
ALl literature data used have been obtained from thin foll specimens*. The possible role of residual stress has been assessed here by nitriding a pure iron foil of 100 ~tm thickness at 923 K in a gas mixture of 96 vol.% H 2 and 4 vol.% r NH 3 at atmospheric pressure, leading to a nitrogen content of X N = 5.8. Proceeding as described with the iron-carbon martensitic foil,application of the sin2v method demonstrated that within experimental accuracy (:I:20 MPa) no stress occurred in the martensite phase. As discussed above for retained h'on-carbon austenite, a negligible stress for the major, martensite phase does not imply that the stress in the dispersed, minor, austenite phase is insignificant. Lattice-parameter data of retained austenite for various nitrogen contents are given in (22-24, 26). Least-squares fitting of a straight line yields (Fig. 4): a = (.3562 + .0004) + (.00093 4- .00006). X
(nm) [6al
a - (.3566 + .0004) + (,00080 4- .00005)- X N (nm) [6bl
" Homogeneous. relatively thick tron-mtrogen austenRe spectmens (martensltic after quenching} can not be made by nttridmg femte foils tn the austenRe-phase field because of agtng-induced recombination of dissolved mtrogen atoms into N2 molecules, leading to severe porosity (see {25)}.
Vol.
24,
No.
3
LATTICE
PARAMETERS OF F e - C
AND F e - N
513
From a comparison with the latticeparameter of pure f.c.c,iron at room temperature (.3573 nm; cf. section 2) it
can be concluded that, analogous to retained iron-carbon austenite, retained iron-nitrogen austenite in Fe-N specimens overall experiences a compression. The dependence of lattice parameter on nitrogen content for unstrmned austenite can be derived by combining the value of .3573 nm for f.c.c, iron with a few data (26) taken from iron-nitrogen specimens which are fully austenitic (and thus strain-f~ee) at room temperature and by adopting a linear relation. It is obtained: a = .3573 + .00080. X f
(nm)
[7a]
a = .3573 + .00072" XrN
(nm)
[7b]
and the dependence of the volume per iron atom on nitrogen content is V = .011404 + .000077 • X f
3.1"
(nm 3)
V = .011404 + .000069 • X rN
[7c]
3'67 t
Fe-N martertstte
(nm3)
[7d]
Fe-N austenlte
r
a=
c = .28664 + .00242 X N
.~+
~ 3.C:~3 "7 3.61 ---
Fe-C
t= 3.59
3.0 ¸
n Jack + Bose & Hawkes o Bell & Owen
"7
/
3.57 3.55
0
d
= o
Jack Boll &Owen
+
Bose & Hawkes
•
Paranjpe et al.
,
,
,
,
,
2
4
6
8
10
r 12 X
2.9
r
a = .28664 - .00017 X N
N
FIG. 4. Literature data for the lattice parameters of retained austenite in iron-nitrogen martensitic specimen as a function of the number of nitrogen atoms per 100 iron atoms. The straight line corresponds with Eq. 6b. 2.8 "t" 0
2
4
6
8
10
r 12 X
N
FIG. 3. Literature data for the lattice parameters of iron-nitrogen martensite as a function of the number of nitrogen atoms per 100 iron atoms. The straight lines correspond with Eq. 5d. and 5e.
4. C o m v a r i s o n o f C a r b o n a n d N i t r o g e n Martensite~
It is generally accepted that the interstitiallydissolved carbon and nitrogen atoms in martensite occupy ( at least dominantly) octahedral intersticesof the iron b.c.t,lattice.In pure b.c,c,iron the six iron atoms surrounding such a site form an irregularoctahedron. In martensite the two furst-nearest-neighbouriron atoms are pushed away in opposite directions along the c axis by the misfittinginterstitial,in conjunction with a minor closing in of the four second-nearestneighbour iron atoms. Thereby the octahedron becomes more regular (tewagonal distortion;cf.(27)).The dissolved carbon and nitrogen atoms have bonds of strongly covalent nature with the surrounding iron atoms (28).The covalent radius of carbon is largerthan thatof nitrogen (29).Thus one might expect a largerunit cellfor iron-carbon martensitethan for ironnitrogen martensite.Thisis not observed (section3).
514
LATTICE
PAL~dqETERS
OF
Fe-C
AND
Fe-N
Vol.
24,
No.
3
Recent calculations (30) of the electronic structure around the interstitials may provide an explanation: the bond strengths were calculated for a cluster of 14 iron atoms around an interstitial as a function of displacements of first- and second-nearest-neighbour iron atoms. It was found that a displacement of the two first-nearest-neighbour iron atoms, such that an approximately regular octahedmn results, stabilizes in particular the cluster. This is attended by the occurrence of a positive ionicity of carbon (transfer of charge to neighbouring iron atoms), while the nitrogen atom for this state is nearly neutral (30). It may then be understood that especially the carbon atom in martensite is smaller than the value referred to above, suggesting that the difference in size between carbon and nitrogen atoms becomes smaller when dissolved in martensite. The present evaluation of literature data suggests that in martensite the size of a nitrogen atom is even somewhat larger than that of carbon: the a lattice parameter is larger for the same amount of interstitials, while, within experimental accuracy, an identical c lattice parameter is observed (cf. Fig. 3). The following tentative explanation is proposed. From the calculated electronic structure around the interstitials it follows that for the same displacement of the two first-nearestneighbour iron atoms, the b.c.t, structure is more stable (i.e. larger total bond strength) for dissolved carbon than for dissolved nitrogen. This is in particular caused by a strength of the bond between the dissolved interstitial and the four second-nearest-neighbour iron atoms which is larger for carbon than for nitrogen (see Figs. 3, 4 and 5 in (30)). The bond strengths between the interstitial and the first- and third-nearest-neighbour iron atoms are practically the same for carbon and nitrogen. The bond strength between the interstitial and the second-nearest-neighbour iron atoms can be associated with the a lattice parameter. Thus, it may be understood that a slight difference exists between the a lattice parameters of both martensites.
References I. 2. 3. 4. 5. 6. 7. 8. 9. I0. II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
C.S. Roberts, Trans. AIME 197,203 (1953). D.H. Jack, K.H. Jack, Mat. Sci. Eng. II, I (1973). Liu Cheng, N.M. van der Pets,Th.H. de Keijser,EJ. Mittemeijer,in preparation. J.W. Christian,"The Theory of Transformationsin Metals and Alloys",part I,2ridedn.,p. 198, Pergamon Press,Oxford (1978). J.D.Eshelby, Solid State Phys. 3, 79 (1956). E. Ohman, JISI 123,445 (1931). K. Honda, Z. Nishiyama, Sci, Rpts. Tohoku. Imp. Univ. Ser. I, 21,299 (1932). G. Hagg, JISI 130,439 (1934). S.G. Fletcher,Sc.D. Thesis, Massachusetts Instituteof Technology, 1943. H. Lipson, A.M.B. Parker,JISI 149, 123 (1944). J. Mazur, Nature 166, 828 (1950). M.P. Arbnsov. DAN SSSR 74, 1085 (1950). S.C. Moss, Acre Metall.. 15, 1815 (1967). L.I.Lysak, S.A. Aptemyuk, Yu.M. Polishchuk,Fiz. Metal. Metalloved. 35, 1098 (1973). M.C. Cadeville,J.M. Friedt,C. lamer, J. Phys. F.: Metal Phys. 7, 123 (1977). M.L. Bernshtein,L.M. Kaputkina, S.D. Prokoshkin, Phys. Met. Me~dl. 52, 127 (1981). R. Delhez, Th.H. de Keijser,E.L Mittemeijer,Surf.Eng. 3, 331 (1987). Y. Tanaka, K. Shimizu, Trans. JIM 21, 42 (1980). WJ. Wrazej, Nature 166, 828 (1950). A.R. Troiano, F.T. McGuire, Trans. AIME 31,340 (1943). N. Ridley, H. Stuart,L. Zwell, Trans. AIME, 245, 1834 (1969). K.H. Jack, Proc. Roy. Soc. 208, 200 (1951). T. Bell,W.S. Oweo, JISI 205,428 (1967). B,N. Bose, M.F. Hawkes, Trans. AIME 188, 307 (1950). EJ. Mittemeijer,M. van Rooijen. I.Wierszyllowski,H.C.F. Rozendaal, P.F. Colijn,7- Me,tallkde74, 473 (1983). V.G. Paranjl~, M. Cohen, M.B. Bever, C.F. Floe, Trans. AIME lSg, 261 (19.50). LD. Fast,"Interactionof Metals and Gases", Vol. 2, p. 3, MacMillan (1971). H. Adachi, S. Imoto, Trans Jap. Inst.Met. 18, 375 (1977). W.B. Pearson, "The CrystalChemistry and Physics of Metals and Alloys",p. 135, Wiley, New York (1972). M. Morinaga, N. Yukawa, H. Adachi, T. Mura, J. Phys. F: Met. Phys. 17, 2147 (1987).
LATTICE
V o l . 24, pp. 5 0 9 - 5 1 4 , 1990 Printed in the U.S.A.
PARAMETERS
OF IRON-CARBON
MARTENSITES
Pergamon P r e s s p l c All rights reserved
AND IRON-NITROGEN
AND AUSTENITES
Liu Cheng, A. Btttger, Th.H. de Keijser, E.J. Mittemeijer Laboratory o f Metallurgy, Delft University o f Technology, Rotterdamseweg 137, 2628 A L Delft, The Netherlands
(Received November 27, 1989) (Revised December 29, 1989) 1. Introdo¢tion and Preliminary Considerations A considerable amount of literature data on the lattice parameters of iron-carbon martensite (b.c.t. lattice of iron atoms) exists; see, for example, (1) and (2). Much less data arc available for iron-carbon austenite (f.c.c. lattice of iron atoms). Data on iron-nitrogen martensite and austenite are scarce too. In the course of a research project devoted to the tempering bchaviour of both iron-carbon and iron-nitrogen martensites, X-ray diffraction analysis of the aging-induced martensite-lattice changes revealed remarkable differences between the two martensites. For example, the c lattice parameter of iron-carbon martensite decreases considerably during aging at room temperature, whereas the c lattice parameter of iron-nitrogen martensite does not (3). Hence, it appeared desirable (i) to establish the dependencies of the lattice pararncters on interstitial content, in particular for iron-nitrogen rnartensite and austenite, and (ii) to compare, in this respect, both interstitial iron-based martensites and austenites. To this end a review of existing lattice-paran~ter data of both pure iron-carbon and pure iron-nitrogen as-quenched martensitic specimens is presented in this paper. The relations between lattice parameters and interstitial content are given in two ways: as a linear function of the atomic percentage of interstitial and as a linear function of the number of interstitiais per 100 iron atoms. In fast order approximation one may assume that the lattice parameter is linearly dependent on the number of solute atoms in the unit cell (4, 5). Then, for substitutionary dissolved atoms the lattice parameter would be linearly dependent on the atomic fraction of solute (i.e. Vtgard's relation; cf. (4)), whereas for interstitially dissolved solute atoms the lattice parameter would be linear dependent on the number of solute atoms per solvent atom, since solvent atoms at their (sub)lattice arc not replaced by solute atoms. However, because of the relatively large scatter of the experimental data to be discussed below for interstitial iron-based alloys, it is not possible at present to discriminate between the two types of latticeparameterfmterstitial-content relations. The temperatures pertaining to the lauice-parameter data have very often not been reported in the literature. Therefore it has to be assumed that these data have been obtained at "room temperature" (say 293-298 K). It should be recognized that this temperature uncertainty may contribute to the scatter of the data, in particular because the lattice parameters can change during aging at room temperature. 2. Iron-carbon Th~ until now generally adopted relations between lattice parameters (a and c) and atomic percentage dissolved
carbon,X~, read (2):
509 0 0 3 6 - 9 7 4 8 / 9 0 $ 3 . 0 0 + .00 C o p y r i g h t (c) 1990 P e r g a m o n P r e s s
plc
510
LATTICE PARAMETERS OF F e - C AND F e - N
f
Vol.
a = .28664 -,00028. x ~
(nm)
Da]
c = .28664 + .00247. X f
(ran)
[lb]
c/a = I + . 0 0 9 6 - X ~
2 4 , No.
3
[Ic]
Data, published in the last 50 years, on lattice parameters of iron-carbon martensite are presented as a function of X~, the number of carbon atoms per 100 iron atoms in Fig. la (data from (6-16)). Clearly, a large scatter occurs.The scatter can have several origins: for example, impurities dissolved in the martensite matrix and different experimental errors due to different methods used for lattice-parameter determination. Further, the presence of (nmcro)su'ess due to quenching from the austenite-phase field affects the lattice parameters; this can occur especially for thick specimens (see below). With these remarks in mind on evaluating the published data gathered in Fig. la, three sets of data ( 6, 15 and 16) appear the most reliable. Adopting .28664 nm as the lattice parameter of pure b.c.c, iron (JCPDS, card 6-0696), least-squares fitting of straight lines through these dat~, with the constraint a = c = .28664 nm and c/a = 1 for zero carbon content, yields (see also Fig.lb): a = .28664 - (.00028 :E .00002). X f
(rum) [2a]
a = .28664 - (.00027 + .00001)- X ~
c = .28664 + (.00256 + .00004). X~
(nm)
[2b]
c = .28664 + (.00243 + .00003). X ~ (rum) [2e]
[2c]
c/a = 1 + (.0095:1: .0001). ~ C
c/a = 1 + (.0100 + .0001). X f
3.1"
Fe-C maxtenslte
f
[2fl
Fe-C martensite
x
Honda et aL
-
Haog
=[
"7,
0
/
2.9
o Cadevilleet al. • Bernshteinet al.
2.8
6
8
10
r 12 X C
FIG. 1 a. Literature data for the lattice parameters of iron-carbon manensite as a function of carbon atoms per 100 iron atoms. The straight line is a least square fit through the data.
"
Bemsht,in ,t al. r
2.9
/
2.8
4
o Cade,~ille.st ai.
/
+ Moss m Lysaket al.
2
/
3.0
• Fletcher + Lipsonet al. • Mazur • A,-buzov
,
0
r
o Ohman
3.0"
0
[2d]
/
3.1"
"7
(nm)
a = .28664 - .00027 X c
i
i
|
i
i
2
4
6
8
I0
r 12 XC
FIG. I b. Selected data for the lattice parameters of iron-carbon martensite; the straight lines correspond with Eq. 2(t and 2e.
Vol.
24, No.
3
LATTICE
PARAMETERS
OF Fe-C AND Fe-N
511
The dependence of the volume per iron atom on carbon content is obtained as (least-squaresfit,forced through .011776 Pan3 forzero carbon content): V = .011776 + (.000081 + .000003). X~(nm) [2g]
V = .011776 + (.000077 + .000002)- X~ (nm 3)
[2hi
In the above presentation (¢qs. [2a-h]) it has been assumed that the lattice spacings measungt from the martensitic specimens are not affected by residual (macro)stress. This may be correct for the majority phase (i.e. martensite) in thin foils quenched from the austcnite-phase field, as is demonstrated by the following stress measurements performed by the present authors. Pure iron foils of thickness 100 g m wcr¢ carburized at 1115 K in a gas mixture of 99.1 vol.% H 2 and .9 voL%CO at atmospheric pressure, leading to a carbon content of ~ C = 5.3. The austenitized foils were quenched in brine. Adopting a stateof plane stressfor the surface-adjacent,X-ray probed rnartensite,applicationof the sin2~/method for stressevaluation(see,for example, (17))shows thata small stressof 130 (:I:20) M P a occurs in the iron-carbonrnartensite (full details are found in (3)). It can be shown in a straightforward manner that such a minor stress can not explain at all the large scatter in Fig. la.It may thus be understood that in particular the data reported in (15), obtained from high purity ironcarbon martensidcfoils, show a relatively small scatter (Fig. lb). However, a pronounced stress can occur in the austenite phase of martensidc specimens, even if they are of the thin-foil type. If a small stress is present in the majority mar~nsite phase, the balance of forces requires that the minority austcnite phase is subjected to a larger stress of opposite nature. In view of the usually very small amount of retained austcnite (a few percent) even a pronounced stress in the austcnite can thus occur. Further, it does not appear likely that a state of plane stress can be assumed for the retained anstenite. Pracdcally all martcnsite probed in the X-ray experiment is surface adjacent and, as a consequence of mechanical equilibrium, its stress component perpendicular to the surface is zero. However, the small amount of retained austenite in the X-ray probed surface layer is dispersed and thus it is generally not adjacent to the surface. So, for the retained austenite a triaxial state of stress appears probable. The lattice parameter of the retained anstenite in Fe-Mn-C martensidc specimens ofcoastant compositiondecreased as the amount of martensite increased (18) (the amount of martensite was varied by changing the quench temperature). This suggests that, overall, retained austcnite is in a state of (hydrostatic) compression as a direct consequence of the change of specific volume (about 4%) on transforming austenite into martensite. Against this background lattice-parameter data for austenite are considered below. Least-squares fitting of a straight line through literature data for the lattice parameter of retained austenite in Fc-C martcnsitic specimens as a function of carbon content (6,7,11,19) affords (Fig. 2): a = (.3553 + .0001) + (.00105 + .00002). X
g
r
(nm) [3al
a = (.3556 :t: .0001) ÷ (.00095 + .00001). X C (nm) [3bl
;e:Z:to
i
g •:,
3.61 -
"~ 3 . 5 9 " 3.57 -
3.55
.
0
2
.
.
4
•
IVlazur
o
Wrazej
.
,
6
8
10 x r 12 C FIG. 2. Literaturedam for the latticeparametersof retained austenite in iron-carbon martensitic specimens as a function of the number of carbon atoms per I00 iron atoms. The straight line corresponds with Eq.3b.
512
LATTICE PARAMETERS OF F e - C AND F e - N
Vol.
24,
No. 3
An extrapolation of lattice-parameter data of Fe-Mn austenite (20), measured from specimens fully austenitic at room temperature, to zero manganese content yields .3573 nm for the lattice parameter of pure f.c.c, iron at room temperatme. From a comparison with eq. (3) it may then be suggested that the retained austenite in Fe-C specimens overall experiences a (hydrostatic) compressive swain of about .5%. The dependence of lattice parameter on carbon content for unstra/ned austenite can be derived by adopting a linear relation and combining the value of .3573 nm for f.c.c, iron with a few data (21) for iron-carbon specimens measured at elevated temperature where the specimens are fully austenitic (and thus strain-free) and then corrected for thermal expansion. Itis obtained: a = .3573 + .00075. X f
(nm)
[4a]
a = .3573 + .00070. X ~
(nm)
[4b]
(nm 3)
[4<1]
and the dependence of the volume per iron atom on carbon content is: V ffi .011404 + .000072 • X f
(nm 3)
[4c]
V = .011404 + .000067. X~
For the martensitic foil discussed above (X~ = 5.3) eq. [4d] gives a = .3610 nm. The experimental value obtained from this foil by utilizing the {220} reflection of the retained austenite is .3596 nm. This suggests that the retained austenite in this foil is subjected to a compressive strain of about .4%, in agreement with the above evaluation of literature data. 3. Iron-Nitro~,en Adopting a value for the lattice parameter of pure b.c.c, iron identical to that implied by eq. [2}, the dependencies of the lattice parameters of iron-nitrogen martensite on nitrogen content have been obtained here by least-squares fitting of straight lines through reported data (22-24), with the constraint a ffi c = .28664 nm and c/a = 1 for zero nitrogen content (Fig. 3): a ffi.28664 - (.00018 +.00003)" X
(nm)
[Sa]
a = .28664 - (.00017 4- .00002) X N
(nm) [Sd]
c = .28664 + (.00263 4- .00006) • X
(nm)
[Sb]
c = .28664 + (.00242 4- .00006)" X N
(nm) [5el
[Se]
c/a ffi 1 ÷ (.0090 4- .0002)" X N
c/a ffi 1 + (.0098 4- .1~12) • X
[5t]
f where X N and Xrlq denote atomic percentage of dissolved nitrogen and number of dissolved nitrogen atoms per 100 iron atoms, respoctivety. The relation between the volume per iron atom and nitrogen content is (leastosqUares fit, forced through .011776 nm3 for zero nitrogen content): V = .011776 + (.000092 4- .000004)" X f
(nm 3)
[5g]
V = .011776 + (.000085 4- .000003)" XrN (nm 3)
[5h]
ALl literature data used have been obtained from thin foll specimens*. The possible role of residual stress has been assessed here by nitriding a pure iron foil of 100 ~tm thickness at 923 K in a gas mixture of 96 vol.% H 2 and 4 vol.% r NH 3 at atmospheric pressure, leading to a nitrogen content of X N = 5.8. Proceeding as described with the iron-carbon martensitic foil,application of the sin2v method demonstrated that within experimental accuracy (:I:20 MPa) no stress occurred in the martensite phase. As discussed above for retained h'on-carbon austenite, a negligible stress for the major, martensite phase does not imply that the stress in the dispersed, minor, austenite phase is insignificant. Lattice-parameter data of retained austenite for various nitrogen contents are given in (22-24, 26). Least-squares fitting of a straight line yields (Fig. 4): a = (.3562 + .0004) + (.00093 4- .00006). X
(nm) [6al
a - (.3566 + .0004) + (,00080 4- .00005)- X N (nm) [6bl
" Homogeneous. relatively thick tron-mtrogen austenRe spectmens (martensltic after quenching} can not be made by nttridmg femte foils tn the austenRe-phase field because of agtng-induced recombination of dissolved mtrogen atoms into N2 molecules, leading to severe porosity (see {25)}.
Vol.
24,
No.
3
LATTICE
PARAMETERS OF F e - C
AND F e - N
513
From a comparison with the latticeparameter of pure f.c.c,iron at room temperature (.3573 nm; cf. section 2) it
can be concluded that, analogous to retained iron-carbon austenite, retained iron-nitrogen austenite in Fe-N specimens overall experiences a compression. The dependence of lattice parameter on nitrogen content for unstrmned austenite can be derived by combining the value of .3573 nm for f.c.c, iron with a few data (26) taken from iron-nitrogen specimens which are fully austenitic (and thus strain-f~ee) at room temperature and by adopting a linear relation. It is obtained: a = .3573 + .00080. X f
(nm)
[7a]
a = .3573 + .00072" XrN
(nm)
[7b]
and the dependence of the volume per iron atom on nitrogen content is V = .011404 + .000077 • X f
3.1"
(nm 3)
V = .011404 + .000069 • X rN
[7c]
3'67 t
Fe-N martertstte
(nm3)
[7d]
Fe-N austenlte
r
a=
c = .28664 + .00242 X N
.~+
~ 3.C:~3 "7 3.61 ---
Fe-C
t= 3.59
3.0 ¸
n Jack + Bose & Hawkes o Bell & Owen
"7
/
3.57 3.55
0
d
= o
Jack Boll &Owen
+
Bose & Hawkes
•
Paranjpe et al.
,
,
,
,
,
2
4
6
8
10
r 12 X
2.9
r
a = .28664 - .00017 X N
N
FIG. 4. Literature data for the lattice parameters of retained austenite in iron-nitrogen martensitic specimen as a function of the number of nitrogen atoms per 100 iron atoms. The straight line corresponds with Eq. 6b. 2.8 "t" 0
2
4
6
8
10
r 12 X
N
FIG. 3. Literature data for the lattice parameters of iron-nitrogen martensite as a function of the number of nitrogen atoms per 100 iron atoms. The straight lines correspond with Eq. 5d. and 5e.
4. C o m v a r i s o n o f C a r b o n a n d N i t r o g e n Martensite~
It is generally accepted that the interstitiallydissolved carbon and nitrogen atoms in martensite occupy ( at least dominantly) octahedral intersticesof the iron b.c.t,lattice.In pure b.c,c,iron the six iron atoms surrounding such a site form an irregularoctahedron. In martensite the two furst-nearest-neighbouriron atoms are pushed away in opposite directions along the c axis by the misfittinginterstitial,in conjunction with a minor closing in of the four second-nearestneighbour iron atoms. Thereby the octahedron becomes more regular (tewagonal distortion;cf.(27)).The dissolved carbon and nitrogen atoms have bonds of strongly covalent nature with the surrounding iron atoms (28).The covalent radius of carbon is largerthan thatof nitrogen (29).Thus one might expect a largerunit cellfor iron-carbon martensitethan for ironnitrogen martensite.Thisis not observed (section3).
514
LATTICE
PAL~dqETERS
OF
Fe-C
AND
Fe-N
Vol.
24,
No.
3
Recent calculations (30) of the electronic structure around the interstitials may provide an explanation: the bond strengths were calculated for a cluster of 14 iron atoms around an interstitial as a function of displacements of first- and second-nearest-neighbour iron atoms. It was found that a displacement of the two first-nearest-neighbour iron atoms, such that an approximately regular octahedmn results, stabilizes in particular the cluster. This is attended by the occurrence of a positive ionicity of carbon (transfer of charge to neighbouring iron atoms), while the nitrogen atom for this state is nearly neutral (30). It may then be understood that especially the carbon atom in martensite is smaller than the value referred to above, suggesting that the difference in size between carbon and nitrogen atoms becomes smaller when dissolved in martensite. The present evaluation of literature data suggests that in martensite the size of a nitrogen atom is even somewhat larger than that of carbon: the a lattice parameter is larger for the same amount of interstitials, while, within experimental accuracy, an identical c lattice parameter is observed (cf. Fig. 3). The following tentative explanation is proposed. From the calculated electronic structure around the interstitials it follows that for the same displacement of the two first-nearestneighbour iron atoms, the b.c.t, structure is more stable (i.e. larger total bond strength) for dissolved carbon than for dissolved nitrogen. This is in particular caused by a strength of the bond between the dissolved interstitial and the four second-nearest-neighbour iron atoms which is larger for carbon than for nitrogen (see Figs. 3, 4 and 5 in (30)). The bond strengths between the interstitial and the first- and third-nearest-neighbour iron atoms are practically the same for carbon and nitrogen. The bond strength between the interstitial and the second-nearest-neighbour iron atoms can be associated with the a lattice parameter. Thus, it may be understood that a slight difference exists between the a lattice parameters of both martensites.
References I. 2. 3. 4. 5. 6. 7. 8. 9. I0. II. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
C.S. Roberts, Trans. AIME 197,203 (1953). D.H. Jack, K.H. Jack, Mat. Sci. Eng. II, I (1973). Liu Cheng, N.M. van der Pets,Th.H. de Keijser,EJ. Mittemeijer,in preparation. J.W. Christian,"The Theory of Transformationsin Metals and Alloys",part I,2ridedn.,p. 198, Pergamon Press,Oxford (1978). J.D.Eshelby, Solid State Phys. 3, 79 (1956). E. Ohman, JISI 123,445 (1931). K. Honda, Z. Nishiyama, Sci, Rpts. Tohoku. Imp. Univ. Ser. I, 21,299 (1932). G. Hagg, JISI 130,439 (1934). S.G. Fletcher,Sc.D. Thesis, Massachusetts Instituteof Technology, 1943. H. Lipson, A.M.B. Parker,JISI 149, 123 (1944). J. Mazur, Nature 166, 828 (1950). M.P. Arbnsov. DAN SSSR 74, 1085 (1950). S.C. Moss, Acre Metall.. 15, 1815 (1967). L.I.Lysak, S.A. Aptemyuk, Yu.M. Polishchuk,Fiz. Metal. Metalloved. 35, 1098 (1973). M.C. Cadeville,J.M. Friedt,C. lamer, J. Phys. F.: Metal Phys. 7, 123 (1977). M.L. Bernshtein,L.M. Kaputkina, S.D. Prokoshkin, Phys. Met. Me~dl. 52, 127 (1981). R. Delhez, Th.H. de Keijser,E.L Mittemeijer,Surf.Eng. 3, 331 (1987). Y. Tanaka, K. Shimizu, Trans. JIM 21, 42 (1980). WJ. Wrazej, Nature 166, 828 (1950). A.R. Troiano, F.T. McGuire, Trans. AIME 31,340 (1943). N. Ridley, H. Stuart,L. Zwell, Trans. AIME, 245, 1834 (1969). K.H. Jack, Proc. Roy. Soc. 208, 200 (1951). T. Bell,W.S. Oweo, JISI 205,428 (1967). B,N. Bose, M.F. Hawkes, Trans. AIME 188, 307 (1950). EJ. Mittemeijer,M. van Rooijen. I.Wierszyllowski,H.C.F. Rozendaal, P.F. Colijn,7- Me,tallkde74, 473 (1983). V.G. Paranjl~, M. Cohen, M.B. Bever, C.F. Floe, Trans. AIME lSg, 261 (19.50). LD. Fast,"Interactionof Metals and Gases", Vol. 2, p. 3, MacMillan (1971). H. Adachi, S. Imoto, Trans Jap. Inst.Met. 18, 375 (1977). W.B. Pearson, "The CrystalChemistry and Physics of Metals and Alloys",p. 135, Wiley, New York (1972). M. Morinaga, N. Yukawa, H. Adachi, T. Mura, J. Phys. F: Met. Phys. 17, 2147 (1987).