iron nitride phases leads to an improved understanding of the Fe-N phase diagran1. Although consideration of thermodynamics indicates the state the system ...
THERMODYNAMICS, KINETICS, AND PROCESS CONTROL OF NITRIDING E. J. Mittemeijer and M. A. J. Somers As a prerequisite for the predictability of properties obtained by a nitriding treatment of iron based workpieces, the relation between the process parameters and the composition and structure of the surface layer produced 111ustbe known. At present, even the description of thermodynamic equilibrium of pure Fe-N phases has not been fully achieved. It is shown that taking into account the ordering of nitrogen in the c; and iron nitride phases leads to an improved understanding of the Fe-N phase diagran1. Although consideration of thermodynamics indicates the state the system strives f01~ the nitriding result is determined largely by kinetics. Nitriding kinetics are shown to be characterised by local near equilibria and stationary states at surfaces and intelfaces, and the diffusion coefficient of nitrogen in the various phases, for which new data are presented. The necessary background for process control of gaseous
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"I'
INTRODUCTION The nitriding/nitrocarburising of ferritic steel workpieces is a thermochemical surface engineering process the use of which is rapidly increasing. One reason for this current enhanced popularity lies in process versatility: new process variants have been developed which can be tuned to optimise resistance to fatigue, wear, and corrosion. In spite of these virtues, fundamental understanding is only fragmentary and it is therefore no surprise that the new developments have been achieved in a largely phenomenological way. Hence, a large and interesting playground is available here for the materials scientist. The present paper summarises recent progress in the understanding of the nitriding of iron. Knowledge of the nitriding of pure iron provides an essential general basis for the subsequent modelling of nitriding and nitrocarburising of Fe-C alloys and (otherwise alloyed) steels. The Fe-N phase diagram still causes much confusion. After an outline of the elements essential to 'reading' the standard metastable Fe-N phase diagram, recent results are presented on the thermodynamic equilibrium between iron nitrides and the nitriding medium, which make it possible to calculate the relevant part of the Fe-N phase diagram. It is suggested that the current version of the Fe-N phase diagram is not definitive. Thermodynamics allows description of states of equilibrium. In the practice of nitriding, equilibria are only asymptotically approached locally, e.g. at surfaces and interfaces. Often so called 'stationary states' are observed which are easily misinterpreted as equilibria. The occurrence of these local equilibria and stationary states during nitriding is discussed. Time and temperature dependent behaviour, as exhibited by the growth of the compound (nitride) layer at the surface and the development of the nitrogen diffusion zone underneath the compound layer, is governed by the diffusivities of the atomic
nitriding by monitoring the partial pressure of oxygen in the furnace using a solid state electrolyte is provided. At the time the work was carried out the authors were in the Laboratory of Materials Science, Delft University of Technology, Rotterdalnseweg 137, 2628 AL Delft, The Netherlands; Professor Mittemeijer is now also at the Max Planck Institute for Metals Research, Seestrasse 92, D-70174 Stuttgart, Germany and Professor S01ners is now in the Division of Metallurgy, Technical University of Denmark, Bldg 204, DK 2800, Lyngby, Denmark. Contribution to the 10th Congress of the International Federation for Heat Treatment and Surface Engineering held in Brighton, UK on 1-5 September 1996. © 1997 The Institute of Materials.
species involved. An area of considerable activity is the analysis of nitrogen diffusion in iron nitrides; such analysis is a prerequisite for modelling compound layer growth. The basis for a layer growth model and a summary of diffusion coefficient data are given in the penultimate section. The eventual practical application of nit riding models requires precise control, i.e. measurement and adjustment, of the process parameters. In fact, the execution of process control of (gaseous) nitriding has hardly changed since the advent of commercial nitriding in the 1920s; thus, the nit riding power of the furnace atmosphere has been characterised by the volume fraction of ammonia measured at the outlet of the furnace, and so on line adjustment of the chemical potential of nitrogen in the furnace atmosphere has not been possible. In this sense, and as compared to carburising, nitriding is old fashioned. However, a breakthrough in practice, at least for gaseous nitriding, is near with the application of commercially available oxygen sensors (solid state electrolytes). The background for such process control is provided in the final section of this review. THERMODYNAMICS Interpretation of Fe-N phase diagram Thermodynamics identifies the state a system tends towards by defining an equilibrium from the condition of minimal energy. Phase diagrams normally indicate the stable state(s) to be expected as a function of temperature and composition at constant pressure. Against this background, considerable confusion regarding the interpretation of the standard Fe-N phase diagram,l and in particular identification of the a (ferrite), (austenite), and y'-Fe4N1-x and c;-Fe2N1-z phase fields (Fig. 1; analytical expressions for the a/a + "I', a + "1'/"1', "1'/"1' + c;, and "I' + c;/c; phase boundaries are given in Table 1), may arise. The published Fe-N phase diagram does not describe the equilibrium between Fe and N 2 at "I
Surface Engineering
1997
Vol. 13
No.6
483
484
Mittemeijer
and Somers
Thermodynamics,
kinetics,
and process
control
of nitriding
........ 1200
state is independent of the route taken to reach that state. Therefore, nitriding in an NH3-H2 gas mixture can be viewed as the sum of the (hypothetical) reactions
~ •..... t1000
(1)
!N2¢[N] NH3¢!N2 giving
800 lX+l'
o
5
where [N] represents N dissolved in M. In equation (3) it is assumed that equilibrium has been established. This means the occurrence of 'local equilibrium' at the workpiece surface (see section 'Local equilibrium and stationary state' below). Hence, the fugacity of the (hypothetical) N 2 gas in equilibrium with M as present in equations (1) and (2) can be calculated from equation (2) as
10
15
20
25
•••.
eN
30
(at%)
1 Phase diagram for binary Fe-N system atmospheric
pressure. For example, the reaction
4Fe + t(l - x)N2
-»
Fe4N1-x
1'1/2 = K(2)p
JN2
requires at 773 K and 105 Pa a consumption of Gibbs energy of about 50 kJ mol-1, and thus significant formation of y' iron nitride does not occur under these circumstances. However, the reaction
Table 1
T
a/a + y'
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+ y' /y'
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y'
Surface Engineering
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623-870
Vol. 13
. (4)
2
Nitriding potential, Lehrer diagram, and absorption isotherms Thermodynamic equilibrium between Fe and the NH3-H2 gas mixture requires that the chemical potentials of nitrogen in gas and solid phase are equal. Adopting the same reference state for nitrogen in the gas and solid phases, it follows for the nitrogen activity in the solid at the solid/gas interface aN thatS aN = f~~2 /( p~J1/2 =
(p~J-1/2
K(2)(PNH3/PU;)
=
(p~J-1/2
4541 ) exp ( -T-1'32 y'
"41 { 1 -
exp [7558 - -T
-1 { 1 - exp [7558 - --
4
+ 8/8
1997
/p3/2 H
Equations describing phase boundaries in Fe-N phase diagram as occupancy of nitrogen sublattice yf$) (t/J = u, y', e) with formulas to transform yf$) into atomic fraction of nitrogen [N] and nitrogen concentration ef$) in mol m-3 given in footnote: T is range of valid temperatures in K, rf$!o is reference nitriding potential for phase t/J in Pa -1/2, 11 is number of nitrogen sites per iron site, NAv is Avogadro's number, Vet/»~is volume of phase t/J per iron atom; values and equations for calculation of rf$!o, 11, and Vet/»~ are given in Table 2 and values of rN,Klw in Table 3 (data taken from Ref. 2)
Phase boundary
y' h'
NH3
where PNH3/PU; follows from the (actually occurring) equilibrium in equation (3) and K(2) is the equilibrium constant for equation (2). The virtual N2 pressures (fugacities) can easily amount to several gigapascals for the equilibria between Fe and NH3-H2 gas mixtures and this makes it evident that N2 gas is not suitable for producing iron nitride from Fe, and that away from the interface between the gas and Fe-N phases where equilibrium can be established (see above), at normal temperatures and pressures a strong tendency exists for decomposition of the Fe-N phase concerned.
4Fe + (1 - x)NH3 -» Fe4N1-x + ~(1- x)H2 produces at 773 K and 105 Pa a release of Gibbs energy of about 20 kJ mol-1. Thus, iron nitrides such as y'-Fe4N1-x and 8-Fe2N1-z can be produced at atmospheric pressure and normal temperatures (500-1000 K) by reaction of Fe and NH3-H2 gas mixtures. The Fe-N phase diagram that is established on this basis then represents the equilibria between Fe and NH3-H2 mixtures, or, more generally phrased, it represents the equilibria between Fe and a medium of largely variable chemical potential of nitrogen (see below). Such equilibria can only occur at the interface of Fe and the medium concerned. The vitriding of the solid M (e.g. ferrite, austenite, or iron nitride) in an NH3-H2 gas mixture can formally be conceived as a result of bringing N2 gas into contact with M under a certain pressure. This statement is based on the fact that the Gibbs energy (and thus the chemical potential) is a state variable, which means that the value of the Gibbs energy of a
a
. (3)
NH3¢[N]+~H2
600
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(2)
+~H2
623-870
NO.6
5·758
X
10-2
T
+ 6·621
+ 2·978 + In (
.r(y') N,O,
-
r
1 N,rx/y
+ 2·978 + In
( .r(y') N,~
')J} ~:t)J} ~,y~~y
rN,o
-
r'
IN,r/e
IN,o
x 10-4T - 5·345 x 10-7T2
0·94242 - 6·621 x 10-4T
+ 5·345
x 10-7T2
K(2)rN
(5)
Mittemeijer and Somers
Ammonia
1 800
3
10
Thermodynamics,
kinetics,
Equilibrium
content (vol.-%)
30
60
103
102 800
80
and process
pressure
control
485
of nitriding
PN .. (aIm)
104'
6
105
10
/"
1000
1000
700
0
900
;-600
:s
roQ)
g ~::J
0
800
y'
~500
:s
ex
a>
T§
E
~500
y'
a>
0-
a> I-
a> I-
900
;-600
"§
ex
800
700
g ~::J T§ a>
0.
E
a> I-
a> I-
700
400 300
y
700
400 (a)
(b)
600 0.1 1 Nitriding potential rN (atm-1/2)
0.01
600
300
10
100
10
1000
Nitrogen activity aN
a variation of temperature with nitriding potential (Lehrer diagram): NH3 contents in NH3-Nz mixtures at 1 atm corresponding to nitriding potentials are also given; b variation of temperature with nitrogen activity (reference state Nz gas at 1 atm): (equilibrium) pressure PN2 (to be read as fugacity fN2) follows from equation (4) or equation (5) with P~2 = 1 atm
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2
Phase boundaries for Fe-N system
with fN2 as the fugacity of the (hypothetical) as present in equations (1) and (2) and
rN == PNH /PY;
.
3
content. Absorption isotherms for IS-Fe2N1-z are shown in Fig. 3. Summaries of data on the dependencies of nitrogen activity and nitrogen content on nitriding potential and temperature are provided in Refs. 2 and 8. Analytical expressions for the absorption isotherm data for a-Fe, y'-Fe4N1-x, and IS-Fe2N1-z, providing the relations between the atomic fraction of nitrogen dissolved (at the surface) [N], and the nit riding potential rN, are given in Table 4. The analytical expression given in Table 4 for the absorption isotherm for IS is, in contrast with the other expressions, empirical in nature and holds so long as (local) equilibrium between ISand the NH3-H2 gas mixture is realised. At relatively high temperatures stationary states, rather than thermodynamic equilibria, occur beyond a certain critical content of dissolved nitrogen in ISat the gas/solid interface: for example, at 823 K this happens above [N] ~ O·3 (see Fig. 3). Such stationary states occur at increasingly higher temperatures for increasingly smaller dissolved nitrogen contents. Note that the analytical expressions for the phase boundaries in the Lehrer diagram are obtained from the expressions given in Table 4 by substitution of rN by rN,rx/y' or rN,y'/p depending on the phase boundary considered, from Table 3.
N 2 gas (6)
as the nitriding potential (in German: Nitrierkennzahl, KN) with the dimension of pressure -1/2. The activity of nitrogen and the chemical potential of nitrogen in the gas phase are governed by rN, irrespective of the total pressure of the NH3-H2 gas mixture (the partial pressures of the gas components, given their mole fractions, do depend on the total pressure). Usually nitrogen gas at atmospheric pressure and at the temperature concerned is selected as the reference state. Then the numerical value of a~ can be interpreted as the (hypothetical, equilibrium) fugacity (in atmospheres) of the N2 gas in equations (1) and (2). It follows from the above discussion that phase fields for the Fe-N system can be presented not only in the usual Fe-N phase diagram but also in a T -rN diagram as well. This is realised in the so called Lehrer diagram (Fig. 2).9 The phase boundaries in the phase and Lehrer diagrams indicate equilibria between the corresponding solid phases and the NH3-H2 gas mixture. At these phase boundaries the nitrogen activities are equal for the solid phases in equilibrium (cf. equation (5)). The dependence of nitrogen activity on composition is different for each Fe-N phase. These relationships can be derived from the absorption isotherms which depict the relation at constant temperature between nitriding potential and nitrogen Table 2
Structure of Fe-N phases, ordering of nitrogen atoms, and prediction of Fe-N phase diagram The solid Fe-N phases of practical interest can all be described as interstitial solid solutions: they are based
,.~;o,
Values and equations referred to in Tables 1, 4, and 5 for calculation of 11, and V(~) (data taken from Refs. 2-4): is reference nitriding potential for phase t/J in Pa -1/2, n is number of nitrogen sites per iron site, V(~) is volume of phase t/J per iron atom, T is temperature in K, and a(~), c(~) are iron sublattice parameters in nm
,.~;o
Phase
In
Cf.-Fe
-11'56+
r(c/J) N,o
11
9096
3
T
-12·5
+
-4'92
+
6·35 x 103 T 3·59
X
T
103
V(c/J)
del)
= 0·28663
+ 0'20505y~)
aU) = 0·37988 a(£)
= 0·25813
c(£)
= 0·42723
0'095315(i - y~'»)
+ 0·0389yW + 0'0318yW
Surface Engineering
1997
Vol. 13
NO.6
486
Mittemeijer and Somers
Thermodynamics,
kinetics,
0.50 ...--Fe2N
and process
·
!t ~.~.
c
-.- -T ---0--
~~
. c
00 0
c
c
.
~
.....•
of nitriding
···············0························································o···························~······· o
0.45
control
-\-:s- --_ .
00
o
_.-.~.-
.
0.42
0.40
o 673 K
0.40
o 698 K
0.38
b.
•
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A
-
0.36
0.35
---. fit 773 K _._.. fit 823 K ----- fit 673-823 K
i
*
723 K 773 K 823 K fit 673-723 K
0.34
...--Fe3N
··.···· · D:.O'1.. 0.4
0.2
0.0
Q:.Q2
Q.:Ql
Q:.Q.4
0.6
Q.:Q~
0.8
.
1.0
(£)
rN / rN,o
3
Absorption isotherms for E-Fe2Nl-z showing relation between normalised nitriding potential rN/rff!o and occupancy of nitrogen sub lattice yff) (= [N]/( 1 - [N]), [N] being atomic fraction of nitrogen). Full line represents fit to experimental data in temperature range 673-723 K given in Table 4, where equilibrium is established between gas mixture and solid state. Absorption isotherms at 773 and 823 K can not be represented by this equation for normalised nitriding potentials above certain maximum value, which decreases with increasing temperature. Absorption isotherms at 773 and 823 K represent stationary states between gas mixture and solid state for range of normalised nitriding potentials where these absorption isotherms deviate from drawn line. Inset shows absorption isotherms in temperature range 673-823 K for nitrogen contents up to yff) = 0·42 ([N] = 0'2958) 1
on an Fe sublattice and an N sublattice composed of all octahedral interstices of the Fe sublattice. Only a fraction of the N sublattice is occupied by nitrogen atoms. In lJ.- Fe [N], with bcc Fe sublattice, and in y-Fe [N], with fcc Fe sublattice, the nitrogen atoms are more or less distributed randomly over the sites of their own sublattice. In y'-Fe4N1-x, with fcc Fe sublattice, and in 8-Fe2N1-z, with hcp Fe sublattice, the nitrogen atoms show long range ordering on their own sublattice (e.g. see Ref. 10). There is a history of attempts to model the thermodynamics of the Fe-N system (for literature see Ref. 2). Until very recently, the expressions used for the Gibbs energies of the Fe-N phases were based on the Hillert-Staffanson approachll,12 for interstitial
Table 3
solid solutions. In this approach the Fe-N phases are conceived as binary (sub) regular solutions. Deviations from ideal mixing behaviour are described according to the Rettlich-Kister formalism,13 which uses a series development for the 'excess' Gibbs energy. Only the first term of this series can be interpreted physically. Such descriptions are in principle unsuited for alloy phases that exhibit long range ordering. The reasonable fit of the Fe- N phase diagrams calculated on such a basis with the experimental Fe-N phase diagram (Fig. 1) relies on the use of a relatively large number of (unphysical) fit parameters which are refined using the experimental composition-temperature data of the Fe-N phase diagram itself. A last example of this approach for the Fe-N system is
Equations describing nitriding potential rN,Klw at phase boundaries of phases Lehrer diagram for given temperature ranges Tin K (data taken from Ref. 2)
K
and
(J)
T
a-Fe/y'-Fe4N1-x
Surface Engineering
1997
Vol. 13
NO.6
573-863
4555 --12'88
623-900
60536 )1/2 - 9·63+ ( -T- - 56,85 or
T
-
(2150)2
T
18 708
+ -T-
- 21·46
in
Mittemeijer and Somers
Table 4
Thermodynamics,
kinetics,
and process
control
of nitriding
487
Equations describing N absorption isotherms for Fe-N phases as occupancy Y~) of nitrogen sublattice: is reference nitriding potential for phase t/J in Pa -1/2, It is number of nitrogen sites per iron site, NAv is Avogadro's number, V(rp) is volume of phase t/J per iron atom, and T is temperature in K; values and equations for calculation of It, and V(rp) are given in Table 2 (data taken from Refs. 2, 3, and 5); for Y~) expressed in terms of N content and concentration see caption and footnote to Table 1
r~!o
"~!o'
Phase a-Fe 1
1
4: - 4:exp
(
3
2·98-
7·56X 10 T
)
(r~:~ rN ) -r- -;w> N
(r
1 65·9x 10-3 exp N-2·57 ) -2W
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rN,o
provided by Refs. 4, 14, and 15. As soon as the same description of the thermodynamics is used to calculate the nitrogen absorption isotherms for the and 8 phases, large discrepancies with the corresponding experimental data oCCUr.2,3,16 Recently it has been proposed that the thermodynamics of the and 8 phases should be described on the basis of the Gorski-Bragg- Williams model for long range ordered solid solutions incorporating pairwise interaction on the N sublattice.2,3,5,16 The occurrence of ordering derives from the repulsion among N atoms. This interaction is likely to be largely strain induced: the nitrogen atoms do not fit well in the octahedral interstices and pronounced local distortions of the Fe sublattice result.17 The Gorski-Bragg-Williams approach is especially suited for this type of interaction, because it extends over a relatively long distance.1s The results obtained with this approach applied to the and 8 phases2,3,16 demonstrate that the experimental nitrogen absorption isotherms for the and 8 phases can be well described using, with reference to the earlier treatments discussed above, only a few, physically relevant fit parameters. The phase boundaries in the Fe-N phase diagram calculated correspondingly, on the basis of thermodynamics that accounts for ordering of nitrogen in the and 8 iron nitrides, agree well with the most reliable experimental data. A discrepancy occurring for the ("If + 8)/8 phase boundary at relatively high temperature may at least partially be related to the "If
"If
"If
N,o
(r
- 95·3x 10-3exp N-26'9-:w-) 'N,o
occurrence of stationary states at the 8-NH3/H2 interface, implying that the corresponding data presented in the standard, experimental Fe-N phase diagram (Fig. 1) do not necessarily represent thermodynamic equilibria in the sense discussed above. The development of the Gorski-Bragg-Williams model for long range ordering of interstitials in the octahedral interstices of a hexagonal close packed lattice, as holds for nitrogen in 8 iron nitride, led also to a derivation of the ground state structures for this system,16 among them the two corresponding to the two types of nitrogen ordering observed.lO Further, the calculations indicate that at sufficiently low temperature the 8 phase may decompose into two phases each exhibiting one of these two types of ordering.16 Recent M6ssbauer data suggest that this does happen.3 This would imply that a two phase region appears in the, until now single, 8 phase field of the Fe-N phase diagram at relatively low temperatures.
"If
"If
Table 5
LOCAL EQUILIBRIUM AND STATIONARY STATE Local equilibrium The solid Fe- N phases as depicted by the Fe- N phase diagram (Fig. 1) can be conceived as phases in equilibrium with a medium having a specific, chemical potential of nitrogen, which is equivalent to equilibrium with N2 gas at very high pressure. Such equilibria can only occur at the interface of the solid state with the medium concerned, as an NH3-H2 gas
Effective
