Internal and external nitriding and nitrocarburizing of iron and iron-based alloys

INTERNAL AND EXTERNAL

NITRIDING AND NITROCARBURIZING OF

IRON AND IRON-BASED ALLOYS

TR diss

1722

J^Tf3

,in> ^ ^ INTERNAL AND EXTERNAL

NITRIDING AND NITROCARBURIZING OF

IRON AND IRON-BASED ALLOYS

INTERNAL AND E X T E R N A L

NITRIDING AND NITROCARBURIZING O F

IRON AND I R O N - B A S E D ALL<

PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus,

Prof. Drs. P.A. Schenck

in het openbaar te verdedigen

ten overstaan van een commissie

door het College van Dekanen daartoe aangewezen,

op donderdag 18 mei 1989

te 16.00 uur

door

MARCEL ADRIANUS J O H A N N E S SOMERS.

geboren te Vlissingen,

metaalkundig ingenieur

TR diss

1722

Dit proefschrift is goedgekeurd door de promotoren:

Prof. Dr. Ir. E.J. Mittemeijer

Prof. Dr. Ir. B.M. Korevaar

The work presented in this thesis is part of a research programme of the Foundation for Fundamental Research of Matter (Stichting FOM) and was supported financially by this foundation.

The work has been carried out in the divisions of 'Heat Treatment Science and Technology' and 'Physical Chemistry of the Solid State' of the faculty of 'Chemical Technology and Materials Science' of the Delft University of Technology.

Cover: SEM micrograph showing top view of the surface of a highly porous compound layer produced after 4 h nitrocarburizing of pure iron in a salt bath.

STELLINGEN

1. Binnen het vakgebied van de fysische chemie van de vaste stof verwordt de thermodynamische evenwichtsconstante te vaak tot een fitparameter waarin stilzwijgend activiteitscoëfficiënten zijn ondergebracht.

2. De aanduiding van de verbindingslaag op het oppervlak van genitreerde stalen werkstukken met de term "witte laag", is niet representatief voor haar bonte microstructuur; zij is louter het gevolg van gebrekkige lichtmicroscopie.

3. Het door Rickerby c.s. gevoerde pleidooi voor verwerping van het roosterdilatatiemodel ter verklaring van het fenomeen "excess nitrogen" in genitreerde, sterke interactie vertonende Fe-M (M = metaalatoom) legeringen, is gebaseerd op een onjuist gebruik van thermodynamische gegevens, een foute interpretatie van de elas­ ticiteitstheorie voor mispassende tweede-fase deeltjes en een irrelevant experiment.

D.S. Rickerby, S. Henderson, A. Hendry, K.H. Jack - Acta Metall. 34, 1986, p.1687.

Dit proefschrift.

4. De "unequivocal support" voor het optreden van "substitutional -interstitial solute - atom clusters", zoals voort zou vloeien uit nitreerexperimenten aan binaire Fe-Mo legeringen, is, in tegen­ stelling tot de bewering van Jack c.s., niet geleverd.

J.H. Driver, D.C. Unthank, K.H. Jack - Phil. Mag. 26, 1972, p.1227. Dit proefschrift.

5. De, conform normblad DIN 17014, in de duitstalige wetenschappe­ lijke literatuur gebezigde aanduiding "Diffusionsschicht" voor het gebied van het ferritische substraat waarbinnen de activiteit van de opgeloste stikstofatomen te laag is voor de vorming van een ijzernitride op de nitreertemperatuur, is ongewenst.

6. Naast de beoogde verbetering van de corrosieweerstand leidt een in de praktijk toegepaste naoxidatiebehandeling van genitreerde of genitrocarboneerde materialen tot verbetering van de tribolo-gische eigenschappen van de verbindingslaag.

Dit proefschrift.

7. De terminologie van de thermochemische oppervlaktebehandelin­ gen nitrocarboneren en carbonitreren is onlogisch.

8. Het promotiereglement van de Technische Universiteit Delft voor­ ziet onvoldoende in de situatie dat de voorzitter van de promotie­ commissie, in de persoon van de Rector Magnificus of d i e n s plaatsvervanger, naast "voortdurend leiding geven aan de discus­ sie" tevens actief opponeert.

Promotiereglement TU Delft, uitgave 1987.

9. Het opdragen van, uit artikelen samengestelde, proefschriften aan personen van wie mag worden aangenomen dat ze het betreffende werk nooit zullen of kunnen lezen, benadrukt de overbodigheid van de samenbundeling.

10. Ter beschrijving van de opnametechniek van Compact Discs kan worden volstaan met een combinatie van twee in plaats van de huidige drie letters.

Marcel Somers Delft, 18 mei 1989

NAWOORD

Hoewel op de omslag van dit proefschrift slechts één naam prijkt, is de inhoud ervan het netto resultaat van de inspanning van velen. Een poging om een volledige lijst van bijdragenden samen te stellen is gedoemd te mislukken. Daarom wil ik eenieder die zich op enigerlei wijze heeft ingezet voor het welslagen van mijn verblijf aan de TU Delft, oprecht bedanken. Enkelen wil ik hier in het bijzonder dank toezeggen.

Mijn promotor Eric Mittemeijer voor zijn aanstekelijke enthousiasme, de inspirerende wetenschappelijke samenwerking op oneigenlijke tijdstippen en zijn bewonderenswaardige vermogen tot het bekennen van ongelijk.

Mijn promotor B. Korevaar voor het maken van kritische kanttekeningen, het uitspreken van ongeloof en het bieden van een grote mate van vrijheid bij de invulling van het onderzoek.

Hans van der Schaaf voor zijn twee rechterhanden, de continue beschikbaar­ heid en zijn bereidwillige ondersteuning bij de meest uiteenlopende werk­ zaamheden, waaronder de uitvoering van experimenten, het verzorgen van de lay-out van dit proefschrift en koek-en-zopie.

Pieter Colijn voor de genoeglijke lichtmicroscopische wandelingen en dwalingen door verbindingslagen en spoordwelingen.

Ruud Lankreijer voor de plezierige en vruchtbare samen- en wisselwerking tijdens de laatste anderhalf jaar van zijn studie metaalkunde.

Niek van der Pers voor uiterst waardevolle suggesties en bijdragen op het gebied van röntgendiffractie.

Daan Schalkoord, Wim Sloof en Denis Nelemans voor röntgenmicroanalyse. Dick de Haan voor transmissie-elektronenmicroscopie, waarvan het meren­ deel helaas niet is opgenomen in dit proefschrift.

Ted van Slingerland en Hans van der Schaaf verzorgden het tekenwerk.

Koos Jacobse en Louis Bakker namen het niet altijd even gemakkelijke fotografische werk voor hun rekening.

Olga Wens, Anke Kerklaan en Sandra Willermsen verzorgden het typewerk in de tijd dat ik nog niet de semi-permanente beschikking had over een computer.

Voorts wil ik mijn ouders, Jacqueline en Rob en Hans en Loes bedanken voor het door hen getoonde begrip en vertrouwen en hun ondersteuning in minder gemakkelijke periodes.

Science is like a two-partner game in which we have to guess the behaviour of a reality unrelated to our beliefs, our ambitions, or our hopes. Nature cannot be forced to say anything we want it to. Scientific investigation is not a monologue. It is precisely the risk involved that makes this game exciting.

Ilya Prigogine & Isabelle Stengers

Aan allen die dit proefschrift zullen gebruiken.

CONTENTS

List of publications iv

I . INTRODUCTION

1.1 Internal nitriding 7 1.2 External nitriding and nitrocarburizing 1 0

1.3 Development and relaxation of stress in thin nitride layers 13

I I . INTERNAL NITRIDING OF BINARY IRON-BASED ALLOYS

11.1 Excess nitrogen in the ferrite matrix of nitrided 17 binary iron-based alloys

11.2 Kinetics of nitride precipitation in Fe-AI and Fe-Si 65 alloys on nitriding

I I I . EXTERNAL NITRIDING OF IRON

111.1 Dependence of the lattice parameter of y' iron nitride, 81 Fe4Ni.x, on nitrogen content; accuracy of nitrogen

absorption data

111.2 Development and relaxation of stress in surface layers; 103 composition and residual stress profiles in y'-Fe4Ni.x

layers on cc-Fe substrates

111.3 Phase transformations and stress relaxation in 153 y'-Fe4N1.x layers during oxidation

IV. EXTERNAL NITROCARBURIZING OF IRON AND IRON-CARBON ALLOYS

IV. 1 Formation and growth of compound layer on gaseous 191 nitrocarburizing of iron: kinetics and microstructural

evolution

IV.2 Microstructural and compositional evolution of iron- 237 carbonitride compound layers during salt-bath

nitrocarburizing

SUMMARY 271 SAMENVATTING 277

Curriculum Vitae 283

List of publications

1. M.A.J. Somers, E.J. Mittemeijer- 'Formation and Growth of Compound Layer on Nitrocarburizing Iron: Kinetics and Microstructural Evolution', Surface Engineering 3, 1987, pp.123-137. (Chapter IV.1)

2. M.A.J. Somers, E.J. Mittemeijer- 'Porenbildung und Kohlenstoff-aufnahme beim Nitrocarburieren', Harterei-Technische Mitteilungen 42, 1987, pp.321-329.

3. W.G. Sloof, M.A.J. Somers, R. Delhez, Th.H. de Keijser, E.J. Mittemeijer-'Simultaneous Determination of Stress, Composition, Stacking-Fault Densities and Gradients Thereof in Surface Layers', in Residual Stresses in Science and Technology, eds. V. Hauk and E. Macherauch, DGM Informationsgesellschaft mbH, Oberursel (FRG), 1987, pp.493-500.

4. R. Delhez, Th. H. de Keijser, E.J. Mittemeijer, N.M. van der Pers, W.G. Sloof, M.A.J. Somers-'lnwendige Spanningen in Keramische Deklagen', Klei Glas Keramiek, No. 6, 1987, pp. 107-110.

5. M.A.J. Somers, E.J. Mittemeijer-'Development of e Carbonitride at the Compound Layer/Substrate Interface during Nitrocarburizing; Production of Compound Layers Deficient in y Carbonitride', in Heat Treatment '87 , The Metals Society, London, 1988, pp.197-202.

6. M.A.J. Somers, R.M. Lankreijer, E.J. Mittemeijer-'Excess-Nitrogen in the Ferrite Lattice of Nitrided Binary Iron-Base Alloys', Philosophical Magazine A, in press. (Chapter 11.1)

7. R.M. Lankreijer, M.A.J. Somers, E.J. Mittemeijer-'Kinetics of Nitride Precipitation in Fe-AI and Fe-Si Alloys on Nitriding', paper presented at Int. Conf. on High Nitrogen Steels '88, in press. (Chapter 11.2)

8. E.J. Mittemeijer, M.A.J. Somers-'A Model for Excess-Nitrogen Uptake in Nitrided Binary Iron-Base Alloys', paper presented at Int. Conf. on High Nitrogen Steels '88, in press.

9. M.A.J. Somers, N.M. van der Pers, D. Schalkoord, E.J. Mittemeijer-'Dependence of the Lattice Parameter of y' Iron Nitride, Fe4N-|.x, on Nitrogen Content;

Accuracy of Nitrogen Absorption Data', Metallurgical Transactions A, in press. (Chapter 111.1)

10. M.A.J. Somers, E.J. Mittemeijer-'Development and Relaxation of Stress in Surface Layers; Composition and Residual Stress Profiles in y-Fe4Ni_x Layers

on a-Fe Substrates', submitted for publication in Metallurgical Transactions A. (Chapter Ml.2)

1 1 . W.G. Sloof, M.A.J. Somers, R. Delhez, E.J. Mittemeijer-'Evaluation of Residual Stresses in Noncompact Surface Layers', paper presented at Int. Conf. on Residual Stresses 2', Nancy, 23-25 november 1988, in press.

12. M.A.J. Somers, E.J. Mittemeijer-'Phase Transformations and Stress Relaxation in •y'.Fe4N1.x Layers during Oxidation', submitted for publication in Metallurgical

Transactions A. (Chapter III.3)

13. M.A.J. Somers, P.F. Colijn, E.J. Mittemeijer-'Microstructural and Compositional Evolution of Iron-Carbonitride Compound Layers during Salt-Bath Nitrocarburizing', submitted for publication in Zeitschrift für Metallkunde (Chapter IV.2)

I. INTRODUCTION

1.1 Internal nitriding

1.2 External nitriding and nitrocarburizing

1.3 Development and relaxation of stress in thin nitride layers

I. Introduction

Nitriding, nitrocarburizing and carbonitriding are thermochemical surface treatments by which nitrogen or nitrogen and carbon are introduced into steel workpieces at elevated temperatures. The distinction between the first two processes and the latter one is based on the treatment temperature. Below about 863 K, nitrogen (-carbon) austenite (y; cf. phase diagrams in Figs.1 and 2 [1,2]) can not exist usually and the workpiece remains ferritic. Then, the treatment is defined as nitriding or nitrocarburizing. Above about 863 K a case of nitrogen (-carbon) austenite can develop and the process is denoted as carbonitriding. The research presented in this thesis applies to nitriding and nitrocarburizing of ferritic matrices and is thereby closely related with the majority of commercial process variants for nitrogen-based case hardening.

The utility of nitriding/nitrocarburizing ranges from improving the wear resistance of the tiny sphere in a ball point to enhancing the fatigue life of crankshafts of large trucks.

In practice, nitriding and nitrocarburizing treatments can be performed in gas mixtures (with main constituents NH3, H2 and CO), in

salt baths (usually composed of a mixture of KCNO and KCN) or in plasmas (generated by a glow discharge in a gas atmosphere usually composed of N2, H2 and CH4). The major part of the work presented in

this thesis (chapters II and III) deals with treatments in N H3/ H2 gas

mixtures. Therefore, as an introduction, the principal characteristics of nitriding pure iron in such gas mixtures are briefly indicated below.

If, at the surface of an a-iron specimen, local equilibrium exists with the gas mixture, the occurring phase at the surface is determined by

1200

t

Fig.1. Iron-rich part of the binary Fe-N phase diagram [1].

2;</t •C—tL Fe, c. X.c

A\Y\

V/ A

,/x

\ V

V

Atomic Percent Nitrogen

temperature and nitrogen activity; the latter depends on the partial pressures of NH3 and H2. A pictorial description is afforded by the

so-called Lehrer diagram (Fig.3 [3]). On this basis distinction can be made between two cases, viz. internal and external nitriding.

In the first case, nitrogen is only interstitially dissolved in the a-iron lattice and a nitrogen diffusion zone results in the surface-adjacent part of the specimen (Fig.4 [4]). The existence of a nitrogen concentration-depth profile in internally nitrided materials can be associated with a compressive-macrostress profile in the surface region. In the second case also iron nitrides are formed at the surface (regions y and e in Figs.1 and 2) and a compound layer is produced on top of the diffusion zone (Fig.4).

O 8 0 -^ " \ ' 4 0 - N . & >v Oi ^ J ok-J 1 1 1 1 600 8 0 0 1000 - ► T ( K )

Fig.3. Stable phases at the surface of an, originally pure, iron specimen being nitrided at a temperature T in a gas mixture of ammonia and hydrogen, containing a nitrogen content denoted by NH3 [3].

Fig.4.

Subdivision of the nitrided case in a diffusion zone and a compound layer, as formed on nitriding, originally pure, iron [4].

N(*C) E-FC2(N,C),.X Tf-F«4(N,C),.X 1 in iron B - F C1 6NZ Tf'-Fc4N,.x (N) interstitial compound layer diffusion zone ,

For nitrided steels, the diffusion zone leads to improvement of the endurance limit and the compound layer is responsible for better tribological properties as compared to untreated material. Further, it was recognized recently that the presence of an iron-nitride surface layer leads to a better corrosion resistance. An oxidation treatment in addition to the nitriding treatment can lead to a further improvement of the protection against corrosive media.

The aim of this thesis is twofold. On the one hand, its purpose is to contribute to the body of fundamental knowledge of the physical chemistry of the solid phase, in particular, solid-state precipitation, kinetics of diffusion-layer growth and development and relaxation of residual stress in thin layers. On the other hand, it is meant to provide a better insight into the phenomena occurring during nitriding and nitrocarburizing processes as performed in commercial praxis. To this end, the research described in the present work concerns model systems, as pure Fe, Fe-C alloys and binary Fe-M (M=metal) alloys.

1.1 Internal nitriding

The uptake in ferrite of nitrogen from a gas mixture comprising ammonia and hydrogen can be characterized by the following overall reaction:

N H3^ Na +§ H2 (1)

where Na denotes nitrogen dissolved in the octahedral interstices of the

b.c.c. iron lattice. From the equilibrium constant, K, of this reaction it is immediately obtained for the activity of nitrogen in ferrite, aN:

fNH3

aN = K. 3 / 2 , (2)

fn2

where fj is the fugacity of gas component i. Replacing fugacities by partial pressures p,, and nitrogen activity by nitrogen concentration, cN,

it follows :

PNH3

C N = K'. 3/2 , ( 2 a )

PH2

where K' incorporates K and the various activity coefficients. The ratio

3/2

pN H /PH2 is normally referred to as the nitriding potential and is

denoted by rN. Normally, the activity coefficients can be taken as

constants and K' can be adopted as an effective equilibrium constant. For sufficiently low rN's at a certain temperature, no iron nitrides are

formed. On cooling from the nitriding temperature, the maximum nitrogen content dissolvable in ferrite decreases rapidly (Fig.1) and, consequently, N tends to precipitate. According to the metastable Fe-N phase diagram (Fig.1), the iron nitride to be expected is y ' - F e4N1.x, but

an intermediate nitride precipitate cc"-Fe1 6N2 can occur too [5,6]. This

a" iron nitride is the only nitride to precipitate (coherently) at room

temperature in quenched nitrogen ferrite and, thus, is the same nitride that is responsible for the occurrence of overageing of steel containing nitrogen as an impurity. The reason that a" can precipitate in favour of

y' in supersaturated ferrite is the similarity of parent a and precipitate

a" lattice (b.c.c. and b.c.t. sublattices of iron atoms, respectively; merely a rearrangement of nitrogen atoms suffices), whereas precipitation of y' (f.c.c. sublattice of iron atoms) requires a significant rearrangement of iron atoms.

In iron-based Fe-M alloys (M stands for metal atom), nitrogen atoms interstitially dissolved in the oc-iron lattice can interact with substitutionally dissolved alloying-element atoms to give MNn nitride,

according to:

NH3 + Ma£ M Nn+ f H2 . (3)

Different types of alloying elements can be discerned, viz.:

strong nitride formers: after nitriding the microstructure is

characterized by a relatively sharp case-core boundary. In the nitrided case practically all M has precipitated. In the core nitrogen is virtually absent. Nitriding kinetics are predominantly controlled by nitrogen diffusion in ferrite. The plate-like nitrides formed have an f.c.c. sublattice of M atoms and the interface between the broad faces of the platelets and the matrix is coherent. Alloying elements belonging to this category are Ti and V. Homogeneous nitride formation in alloys containing strong nitride formers has frequently been observed to be associated with the uptake of an amount of nitrogen in excess of the sum of the lattice solubility in ferrite and the nitrogen incorporated in the stoichiometric nitride. For this

phenomenon of fundamental interest, in Chapter 11.1 a model is presented that provides a quantitative description of enhanced nitrogen solubility in the ferrite lattice due to the hydrostatic lattice dilation caused by misfitting nitride particles. The model is tested using all known excess nitrogen data presented in the literature.

weak nitride formers: after nitriding the microstructure is

characterized by a very faint (or no) case-core boundary in conjunction with a virtually constant nitrogen concentration. Nitriding kinetics are predominantly controlled by diffusion of alloying elements in the ferrite. Due to a large crystallographic difference between the nitrides (usually hexagonal) and the ferrite lattice, the nitride/matrix interface is incoherent. Heterogeneous precipitation of this kind of nitride is immensely facilitated by the presence of dislocations. Further, production of dislocations during precipitation accelerates nitriding kinetics on prolonged nitriding. For this self-accelerating nitride precipitation process a kinetic model is provided in Chapter II.2. The model is tested using data of nitriding Fe-AI and Fe-Si alloys.

nitride formers of intermediate strength: depending on temperature

and alloying-element concentration (e.g. Cr,Mo), nitriding behaviour varying between those of the above mentioned, extreme cases can be obtained.

1.2 External nitriding and nitrocarburizing

If the nitrogen activity imposed is larger than that corresponding with the maximum nitrogen lattice solubility in a-Fe, Y'-Fe4N1_x can

nucleate at the outer surface. Separate nuclei grow into the iron substrate and along the iron surface. As long as no isolating y' layer has been formed, diffusion of nitrogen through ferrite is possible, which can be conceived as a by-pass for the relatively slow diffusion of nitrogen atoms through the y' phase. After the formation of an isolating y' layer, surface-layer growth is controlled by nitrogen diffusion through the layer.

For an imposed nitrogen activity allowing the formation of e-Fe2N1_x,

e nuclei develop on top of y' nitride. This is possible even before the establishment of a continuous y' layer. Eventually, a dual phase e(top)/y'(bottom) compound layer results.

A peculiar feature of Fe-N phases, in particular of iron nitrides, is the occurrence of porosity. This porosity is a consequence of the metastability of Fe-N phases with respect to nitrogen gas at normal pressures. Thermodynamical equilibrium between a solid Fe-N phase and a gas mixture requires that the chemical potential of nitrogen in the gas phase is imposed on the solid phase at every location. Away from the gas/solid interface Fe-N phases tend to decompose, because of an equilibrium partial nitrogen gas pressure, which is very high: about 4000 atm for y' nitride and even higher for e nitride. The driving force for the precipitation of N2 is largest in material near to the gas/solid

interface, where the highest nitrogen activity occurs. Pore formation is discussed and interpreted on the above basis at several places in this thesis.

A discussion on the role of porosity in the attainment of a state of equilibrium between gas atmospheres and iron nitrides is given in Chapter 111.1. Lattice parameter-composition data, determined in the present work, provide a tool to choose among different sets of literature data that describe the amount of nitrogen incorporated in y' as a function of the composition of ammonia/hydrogen gas mixtures at various temperatures (so-called absorption isotherms).

Under commercial conditions, compound layers are usually produced on (carbon-containing) steel substrates by means of a nitrocarburizing treatment. According to the ternary Fe-N-C phase diagram (Fig.2), the e phase can contain a considerably larger amount of carbon than y' phase. Thus, in practice, the availability of two carbon sources (substrate and nitrocarburizing agent) will lead to a stabilisation of e phase at the expense of i phase.

Unlike the case of external nitriding of pure iron, a straightforward prediction of the constitution of the compound layer produced on nitriding of steel or nitrocarburizing of iron and steel is not possible from the corresponding Fe-N-C phase diagram, because kinetics of the absorption of both nitrogen and carbon in the layer determine to a large extent the microstructure of the layer and vice versa.

The role of the carbon originating from the nitrocarburizing agent on the kinetics and the microstructure of the compound layer is not understood. For example, one peculiar observation is the existence of a carbon accumulation in the compound layer near the interface with the substrate, regardless of the presence of carbon in the substrate. In chapter IV.1 the influence of a small addition of carbon monoxide, to an ammonia/hydrogen gas mixture (only 3 vol.-% CO), on compound-layer formation on pure iron is described. As will be demonstrated, initially

w 1000

t

Part of the binary Fe-N phase diagram containing y'-phase region [7].

(for relatively short treatment times) the carbon addition to the nitriding gas has a negligible influence on the constitution of the layer produced. However, on continued treatment the establishment of coalesced pores (channels), in open contact with the gas mixture, provides the possibility of local carbon absorption at some depth below the outer surface. By this mechanism the microstructure of the layer is altered dramatically.

The presence of carbon in the substrate, in the form of cementite, can bring about a preferential nucleation of e phase on cementite (see Fig.2) at the beginning of nitriding/nitrocarburizing, due to the relatively large carbon solubility in e as compared to y', that is facilitated by the crystallographic similarity of e carbonitride and cementite (h.c.p and orthorhombic sublattices of iron atoms, respectively). In Chapter IV.2

the development of the compound layer during commercial salt-bath nitrocarburizing of iron and iron-carbon substrates is described.

1.3 Development and relaxation of stress in thin nitride layers

Surface layers are widely applied for improvement of surface-related properties. It is well recognized that residual stresses in the layers can largely govern their properties. However, fundamental knowledge on the development and relaxation of residual stresses in surface layers does only exist fragmentarily.

A y'-nitride layer on an a-iron substrate can be conceived as a model system for layer/substrate assemblies characterized by a thermal

misfit at the layer substrate interface and a c o m p o s i t i o n a l misfit within the layer due to the composition-depth profile.

The analysing technique used in this work for the determination of residual stress is X-ray diffractometry (XRD). The simultaneous determination of residual stress-depth and composition-depth profiles in y' layers ( f has a small homogeneity range, Figs.2 and 5 [7]) by XRD is cumbersome, because unraveling of stress and compositional variations, both leading to spacing gradients, is necessary. However, unique results can be attained: simultaneous changes in nitrogen content and stress of only 0.02 at.-% N and 50 MPa on a depth change of less than 1.5 (im have been determined (Chapter III.2).

Porosity (=noncompactness) implies the presence of internal free surfaces. Perpendicular to a free surface, no stress component can exist. Accordingly, comparing the stress level in compact and porous y' layers, porosity in y' layers can be thought to bring about 'relaxation' of the residual stresses.

Phase transformations can also induce stress relaxation. During annealing of a y' layer at a temperature below the nitriding temperature, the composition of the y' phase changes, especially for relatively low nitrogen contents as occurring in the substrate/adjacent part of the layer (see Fig.5 [7]), leading to development of a-iron precipitates in the layer. Simultaneous with this phase transformation, stress relaxation occurs in the Y ' -| ay er / a-s ub s t r a t e assembly, as is

demonstrated and discussed in Chapter III.3.

References

[ 1 ] O. Kubachewski-lron-binary phase diagrams, Springer-Verlag, Berlin (1982). [ 2 ] F.K. Naumann, G.K. Langenscheid, Arch. Eisenhüttenwes. 36, 1965, p.677. [ 3 ] E. Lehrer-Z. Eletrochem. 36, 1930, p.383.

[ 4 ] P.F. Colijn, E.J. Mittemeijer, H.C.F. Rozendaal-Z. Metallkde. 74, 1983, p.620. [ 5 ] L.J. Dijkstra-J. Metals 1, 1949, p.252.

[ 6 ] K.H. Jack-Proc. R. Soc. 208A, 1951, p.216.

[ 7 ] Z. Przylecki, L. Maldzinski-Proc. 4th Int. Conf. 'Carbides, Nitrides and Borides', Poznan/Kolobrzeg, Poland (1987), p.153.

II. INTERNAL NITRIDING OF BINARY IRON-BASED ALLOYS

11.1 Excess-Nitrogen in the Ferrite Lattice of Nitrided Binary IronBased Alloys

-M.A.J. Somers, R.M. Lankreijer, E.J. Mittemeijer

11.2 Kinetics of Nitride Precipitation in Fe-AI and Fe-Si Alloys on Nitriding

-R.M. Lankreijer, M.A.J. Somers, E.J. Mittemeijer

EXCESS NITROGEN IN THE FERRITE MATRIX OF

NITRIDED BINARY IRON-BASED ALLOYS

M.A.J. Somers, R.M. Lankreijer* and E.J. Mittemeijer

Laboratory of Metallurgy, Delft University of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands Now with: Plastics and Rubber Research Institute TNO, Schoemakerstraat 97, 2628 VK Delft, The Netherlands

Abstract

On nitriding ferritic Fe-M (M=Ti,V,Cr,Mo) alloys three types of absorbed nitrogen atoms can be distinguished: (i) nitrogen incorporated in the stoichiometric nitride; (ii) nitrogen adsorbed at the nitride/matrix interface and (iii) nitrogen dissolved in octahedral interstices of the ferrite lattice. As compared to pure ferrite, enhanced nitrogen lattice solubility is observed for the ferritic matrix of Fe-M alloys. This excess nitrogen can be ascribed to an average lattice dilation induced by the volume misfit between nitrides and matrix. A model is developed for a quantitative description of the amount of excess nitrogen in ferrite. The treatment originates from an application of a theory due to Eshelby, developed originally for the case of elastic distortions by point imperfections, in conjunction with the thermodynamics of stressed solids. The model is applied to published data on excess nitrogen in various Fe-M alloys where coherent nitrides develop. The dependence of the amount of excess nitrogen in Fe-M alloys on type of alloying element can be explained in terms of an interaction parameter weighing up the contributions of chemical and strain energy changes occurring on precipitation of nitrides.

1. Introduction

On nitriding pure iron, nitrogen can be dissolved in the octahedral interstices of the iron-matrix lattice. If alloying elements are present, nitrogen atoms can be bonded to alloying-element atoms leading to the precipitation of nitrides at the nitriding temperature.

Because of the technological importance of the nitriding process for the improvement of fatigue, tribological and anti-corrosion properties (Source book on nitriding 1977, Mittemeijer 1984), there is a distinct need to understand the precipitation behaviour of ferritic iron-based alloys on nitriding. The corresponding, mostly recent, research has revealed some nitride-precipitation phenomena of fundamental interest. Undoubtedly, one of the most intriguing features concerns the occurrence of so-called excess nitrogen, particularly in Fe-Cr (Hekker, Rozendaal and Mittemeijer 1985), Fe-V (Pope, Grieveson and Jack 1973, Yang and Krawitz 1984) and Fe-Ti alloys (see for example Jack 1976, Podgurski and Davis 1981, Rickerby and Jack 1981, Rickerby, Henderson, Hendry and Jack 1986). The amount of excess nitrogen, [N]e x c, can be

defined as the total amount of nitrogen absorbed, [ N ]t o t, after

subtraction of the amount of nitrogen incorporated in the stoichiometric equilibrium nitride, [ N ]M N (where M stands for alloying

element), and the amount of nitrogen in the specimen which would be dissolved in its ferrite matrix if the equilibrium solubility valid for

[ N ] e x c - [ N ] , o , - [ N ]MNn- [ N ] °a (1)

(square brackets denote fractional quantities, i.e. weight or atomic f r a c t i o n ) .

Major amounts of excess nitrogen occur in alloys containing minute, coherent, nitride platelets (Hekker et al. 1985, Pope et al. 1973, Yang

and Krawitz 1984, Jack 1976, Podgurski and Davis 1981, Rickerby and Jack 1981, Rickerby et al. 1986, Phillips and Seybolt 1968); it is noted that these platelets have also been denoted as clusters/zones (see first footnote of section 2 and Appendix A).

Apart from a purely phenomenological description in terms of interaction coefficients (Pulkkinen 1983), a number of interpretations of the excess-nitrogen phenomenon have been presented in the literature, but these have no general validity and are of conflicting nature (compare especially for the Fe-Ti system: Jack 1976, Podgurski and Davis 1981, Rickerby and Jack 1981 and Rickerby et al. 1986). This paper intends to provide a model for the amount of excess nitrogen in iron-based alloys containing a homogeneous distribution of initially coherent nitride platelets. The treatment originates from an application of a theory due to Eshelby (1956), initially developed to describe elastic distortions introduced by point imperfections in a matrix, in conjunction with thermodynamics of stressed solids (Li, Oriani and Darken 1966). An earlier description of excess nitrogen in Fe-Ti alloys after one specific nitriding treatment departed from the same basis (Podgurski and Davis 1981). The general treatment of the present paper provides a wider applicability, as will be demonstrated by application to published data for nitrided Fe-M alloys (in particular M=Cr,V,Ti).

2. Sites for excess nitrogen

The amount of nitrogen absorbed by iron-based alloys on nitriding in a N H3/ H2 gas mixture at a specific temperature can be expressed as a

3/2

function of the nitriding potential, rN ( = P N H3^ P H2 )■ T n i s function is

usually designated as an absorption isotherm. Each point of an absorption isotherm corresponds to the maximal amount of nitrogen

taken up by the specimen at the specific nitriding potential chosen (after a homogeneous, constant nitrogen concentration has been attained). This amount can be conceived as the equilibrium amount of absorbed nitrogen, provided that appropriate prenitriding has been performed, implying that the platelet morphology remains the same during determination of the absorption isotherm. To this end,

M

..—

I

I

I

Fig.1.Schematic presentation of an absorption isotherm, i.e. the total amount of nitrogen absorbed, [N]tol, as a function of nitriding

potential, rN. Three (energetically) different types of nitrogen

can be discerned (see text), viz.:

I: nitrogen incorporated in the stoichiometrical equilibrium nitride MNn;

II: nitrogen adsorbed at the platelet/matrix interface; III: nitrogen interstitially dissolved in strained ferrite.

prenitriding at a temperature well above the temperature of the isotherm concerned is preferred.

As follows from experimental data, the absorption isotherm can be schematically presented as in Fig. 1 (e.g. see Podgurski and Knechtel 1969, Jack 1976, Podgurski and Davis 1981, Rickerby and Jack 1981, Rickerby et al. 1986). Three types of absorbed nitrogen atoms can be distinguished (Podgurski and Davis 1981):

I. Nitrogen (strongly) bonded to M in the corresponding stoichiometric nitride. As compared with nitrogen of types II and III, this nitrogen can not be removed easily by, for example, H2

reduction. The amount of this type of nitrogen is indicated by [N]uNn ineq.(1).

I I . Nitrogen adsorbed at the nitride/matrix interface. As compared with nitrogen of type I, this nitrogen is less strongly bonded and can be removed by, for example, H2 reduction. All nitrogen of type

II contributes to the amount of excess nitrogen in eq. (1).

I I I . Nitrogen dissolved in the octahedral interstices of the ferrite matrix. The amount of nitrogen occupying these sites depends linearly on the nitriding potential and can be removed by, for example, H2 reduction. The amount of type III nitrogen exceeding

the equilibrium content in pure iron contributes to the amount of excess nitrogen (see eq. (1)).

2.1. Interfacial nitrogen

Transmission electron microscopy (TEM) of nitrided Fe-Ti (Jack 1976, Rickerby and Jack 1981, Rickerby et al. 1986), Fe-V (Pope et al.1973) and Fe-Cr (Phillips and Seybolt 1968) alloys showed that, in the initial

stages of nitriding, coherent platelets1 develop which are at most a

few atom layers thick (see Appendix A).

It is anticipated that nitrogen atoms of type II are adsorbed at the matrix/platelet interface. For the coherent-plate geometry two distinct sites for adsorption of excess nitrogen can be considered: edge sites at the rim and surface sites at the broad faces. There is no agreement in the literature with respect to the interfacial site preferred and its capacity for excess nitrogen uptake (cf. the debate on the most extensively studied Fe-Ti alloys: Jack 1976, Rickerby and Jack 1981, Rickerby et al. 1986, Foldeaki, Schwendemann and Kronmiiller 1986). This is undoubtedly partly due to the very indirect nature of the observations until now (such as mass change, internal friction and magnetic after-effect) providing the basis for a deduced atomistic description.

Obviously, the amount of nitrogen possibly associated with rim sites (Jack 1976) depends on the lateral size of the platelets. For the broad faces it can be argued that the nitrogen possibly adsorbed might be situated in interface-adjacent octahedral interstices, where it is coordinated by 5 Fe atoms and 1 M atom (Rickerby and Jack 1981, Rickerby et al. 1986). For monolayer discs this would lead to a maximal N (types l+ll)/M atom ratio of 3. However, the maximal values reported so far for nitrogen of types l+ll, as derived by extrapolation of the linear part of the absorption isotherm (Fig. 1), corresponds with atom

1 The initial stages of precipitation may alternatively be described as comprising a

substitutional-interstitial solute-atom cluster, analogous to Guinier-Preston zone formation (Jack 1975). For reasons discussed in Appendix A, the designation "coherent platelet" is preferred here. Whatever terminology is used, this does not, in principle, affect the interpretation given in this paper.

ratio N/M=2 (Podgurski and Davis 1981). This discrepancy could be ascribed to a platelet thickness in the experiments exceeding one monolayer (see also Section 4).

2.2. Interstitial nitrogen

If the nitriding potential, rN, exceeds a certain value, a linear

dependence on rN occurs for the absorption isotherm (region III; see also

below). The slope of the linear part can be conceived as an equilibrium constant K of

N H3^ Na +| H2 (2)

where K is defined in terms of concentrations and partial pressures. Thus, the amount of nitrogen dissolved in the matrix, [ N ^1, is given by

K . rN. A c c o r d i n g to c h e m i c a l t h e r m o d y n a m i c s it h o l d s :

K=Y"1exp{-pj.exp|- ^f\ where the (activity) coefficient y accounts for

non-ideal mixing behaviour and AH and AS are the enthalpy and entropy changes (also called reaction enthalpy and reaction entropy) for the dissolution of N by dissociation of NH3 and R and T denote the gas

constant and the absolute temperature. If y, AH and AS do not significantly depend on temperature in the temperature range investigated, In K depends linearly on 1/T (by the Van 't Hoff equation) which agrees with experimental results (Podgurski and Davis 1981, Rickerby and Jack 1981, Rickerby et al. 1986).

1 In the sequel [N]a is taken as a fractional quantity of the matrix. For the small amounts of

alloying element considered usually (a few %) the difference between [N]a taken as a

fractional quantity of the specimen (cf. eq. (1)) and [N]a taken as a fractional quantity of

A prerequisite for the above interpretation is a stable precipitate/matrix configuration during investigation of this linear part of the absorption isotherm. If, for example, coarsening of the platelets occurs during the experiment, the capacity for adsorption of nitrogen of type II diminishes, primarily because the precipitate/ matrix interfacial area decreases. Consequently, a linear part of the absorption isotherm can not be expected. Isoconfigurationality can be achieved by subjecting the alloy considered to an appropriate prenitriding treatment: nitriding at a relatively high nitriding potential at or above the highest temperature of the temperature range employed for determination of the absorption isotherms afterwards.

Then, extrapolation of the linear parts of all absorption isotherms obtained, leads to a common M/N ratio at the ordinate for rN=0. This

ratio corresponds with the total amount of type I and type II nitrogen (see data of Podgurski and Davis (1981)). If an appropriate prenitriding treatment has not been performed, a linear part in the absorption isotherm is not observed indeed (see data of Jack (1976)).

It has been claimed (Rickerby and Jack 1981, Rickerby et al. 1986) that a linear part of the absorption isotherm is due to nitrogen occupation of a range of thermodynamically distinct environments (e.g. interfacial sites, type II nitrogen, and interstitial sites, type Ill-nitrogen) in a fixed ratio depending on temperature and M concentration. However, this interpretation can neither explain a linear dependence of In K on j - nor the occurrence of a common M/N ratio at rN=0 (obtained by

extrapolation; see above).

For the Fe-M alloys considered where minute, coherent nitride particles develop, the enhanced lattice solubility, corresponding to excess nitrogen of type III will be ascribed to an average lattice dilation of the matrix as a consequence of volume misfit in the

precipitate/matrix composite (see section 3). An interpretation on such a basis has been indicated earlier by Li (1978) and Podgurski and Davis (1981). This proposed interpretation of enhanced lattice solubility has been questioned (Rickerby et al. 1986). According to the opinion of the present authors, the objections raised by Rickerby et al. (1986) do not hold. For a discussion, see Appendix B.

As a final remark it is noted that for Fe-M alloys where small, coherent nitride particles do not develop, minor amounts of excess nitrogen can be absorbed by dislocations (in their cores as well as in their enveloping strain fields) (Podgurski, Oriani and Davis 1969; Wriedt and Darken 1965).

3. Quantitative description of excess nitrogen

The presence of misfitting second-phase particles can lead to elastic distortions in the surrounding matrix. Eshelby (1956) has developed a theory to describe the elastic distortions brought about by point imperfections in a matrix. This model will be adopted in the present paper for the case of small inclusions in a matrix. The original application of the model to point imperfections in a matrix , has its limitations (Eshelby 1956, Christian 1975): electronic interactions are not considered in the mechanical model. However, this restriction is less significant for the present case of inclusions composed of a number of atoms.

Consider a spherical particle of phase B and a continuous matrix A containing a cavity. The misfit parameter, e, is defined as:

o o rB "rA

rA

where rB and rA are the radii of the free, undeformed particle B and the

empty unstrained cavity, respectively. On hypothetically introducing particle B into the cavity, the assembly thus formed is allowed to relax in its self-stressed state in order to minimize its mechanical strain energy: an equilibrium state of stress develops.

If the matrix is conceived as an infinite, unbounded elastic continuum, it can be shown that only shear strains occur in the matrix and, consequently, no dilation of the matrix takes place. However, it is essential to recognize that, in general, the assembly is of finite dimensions. Then, an image strain field has to be superimposed on that corresponding with the infinite assembly, such that the external surface is free of traction. As a result, a net fractional volume change of the matrix. AVA/VA, occurs. For a volume fraction YB of B particles

(YB is defined for the unstressed condition), AVA/VA for elastically

isotropic materials is given by (Eshelby 1956, Christian 1975, Mittemeijer, Mourik and Keijser 1981):

AVA GA e o

-vf-^tf^" <

4

»

where C=3KB/(3KB + 4GA) and G and K represent shear and bulk modulus,

respectively. This predicted dilation of a matrix containing misfitting second-phase particles corresponds to a net change of the (average) lattice parameter of the matrix, aA: AVA/VA = 3 AaA/aA. Recent X-ray

diffraction data provide experimental evidence for the existence of this effect (Mittemeijer et al. 1981, Mittemeijer and Gent 1984; see also Appendix B).

For the development of alloying-element nitrides in iron-based alloys, the misfit parameter e is positive and, accordingly, the matrix lattice dilation is positive too (see eq. (4)). Therefore, the capacity of the

(widening) ferrite lattice to absorb nitrogen atoms at interstitial sites is enhanced on precipitating nitrides. This discussion can be considered as a geometrical rationale for excess solute, leading to an upper limit for the amount of excess solute in the ferrite matrix (see section 4.5.).

The t h e r m o d y n a m i c a l approach to excess solute proceeds via the effect of stress on the chemical potential (Li et al. 1966), as follows. The dilation of the matrix as given by eq. (4) is associated with the presence of an internally evoked (for precipitation induced) hydrostatic

AVA

stress component oA=KA.-rr—. It is well known that an externally applied

" A

pressure affects the lattice solubility of an interstitial solute in a solid metal (Swalin 1972). At constant temperature, T, it holds for the chemical potential, \i\, of the interstitial solute: du.|= RT.d(lna|)= Vj.dcjj, where R is the gas constant and a{ and V| denote the activity and

partial molar volume of the interstitial solute, respectively. On integration, it is obtained:

a (CTA-°Aef) Vj

-^=exp{ ^ }

ai

ref

'where at the temperature considered, a; indicates the activity of the interstitial solute for a specific reference state (yet to be defined; see

ref

section 4.1.) with hydrostatic pressure, aA . If, for the Fe-M alloys ref

considered, Henry's law holds for the nitrogen activity, the ratio aN/aN

is independent of the nitriding potential, and then eq. (5) can equally well be expressed as (see also below eq. (2)):

K yref (°A-°Ae) VN

W* = —

exp

{

}

(5a)

isotherms of the Fe-M alloys investigated and the reference alloy, respectively. Realizing that for all Fe-M alloys considered the excess

nitrogen is dissolved in a pure ferrite matrix (all M is precipitated), it will be assumed that the ratio of activity coefficients Yref/y can be

taken equal to one. From eq. (5) it follows immediately that, if the average hydrostatic stress is positive as a consequence of a positive misfit parameter (see above), enhanced lattice solubility can be expected. Eq. (5) prescribes to what extent the geometrically possible capacity for excess solute is utilized. It is important to realize that the actually occurring increase of the lattice parameter of the matrix according to eq. (4), does npj. correspond with the actual amount of solute absorbed (e.g. by application of Vegard's law; see section 4.6.).

In the above treatment, isotropic distortion of the ferrite matrix has been assumed. The nitrides in the alloys treated on this basis in section 4 (Fe-Ti, Fe-V, Fe-Cr) develop as coherent platelets along {100}a.F e

(Phillips and Seybolt 1968, Pope et al. 1973, Kirkwood, Atasoy and Keown 1974, Jack 1975, Atasoy 1976, Jack 1976, Kirkwood and Thomas 1976, Rickerby and Jack 1981). Such platelets introduce a local tetragonal distortion (cf. section 5). However, a homogeneous distribution over the three habit planes of {100}a.F e type can be

expected within each grain and, although ferrite shows anisotropic elastic behaviour, an isotropic overall distortion results due to the cubic crystal symmetry of ferrite. Therefore, the radii in eq. (3) can be replaced by the cubic root of the moiar volumes (see below).

In the absence of nitrogen atoms adsorbed at the nitride/matrix i n t e r f a c e (type II nitrogen) the misfit parameter, e, is straightforwardly obtained as

(vMNn) - (VJ

where the terms in brackets are the molar volumes of equilibrium compound MNn (only type I nitrogen) and oc-Fe, respectively. However,

from the discussion in section 2 it appears that the B particle in the present study is composed of MNX molecules; the particle incorporates n

nitrogen atoms to build up the stoichiometrical equilibrium compound M Nn (type I nitrogen) and (x-n) nitrogen atoms per MNX molecule bonded

to the coherent faces of the particle (type II nitrogen). Such a particle, containing both types of nitrogen, should be regarded as an entity which acts as the misfitting B particle in the calculation of the enhanced lattice solubility (excess nitrogen of type III). Then, a misfit parameter defined according to eq. (6a) can not be applied. For the assessment of the misfit parameter relevant to the MNX particles, the lattice of the

coherent MNn nitride can be conceived as extended by adsorption of the

(x-n) nitrogen atoms (type II nitrogen). Thus, the misfit parameter is taken as

[ VMNn+ ( x - n ) f VM N n]1 / 3- ( V °a)1 / 3

This misfit parameter can be interpreted as follows: the void left in the specimen by taking out a Fe atom on the matrix lattice is replaced by a "MNX molecule" on the MNn lattice. The parameter f describes the

extent to which the full misfit due to the building out of the lattice of the MNn particle is experienced; two values of f will be considered in

the calculations in section 4: f = 0.5 and f = 1.0.

Owing to the ill-defined nature of the misfit parameter in the presence of nitrogen atoms adsorbed at the nitride/matrix interface, it is realized that in the absence of adsorbed nitrogen atoms the best agreement between predictions from the strain model and experimental results can be expected. This is demonstrated by application of the

strain model to understand anomalous lattice parameter values (Mittemeijer and Gent, 1984) and by results on excess nitrogen (see section 4).

Further, because of their extremely small thickness of the order of one atomic layer the MNX platelets are considered as incompressible

(C = 1 in eq. (4)). Then using eqs. (4) and (5) it is finally obtained:

[N]„ fƒ V VN rN r 4eG, 4eGa wp r e { i = e x

P{"RT [ ï ï ^

x -

° I l <

)

[rC*

0+e)

where [M] denotes the atomic fraction of M atoms (all M in nitride). In the above model (eqs. (6-8)) x need and should not be considered as a constant during nitriding. Morphological changes of the particles during nitriding can result in a decrease of particle/matrix interfacial area (coarsening), and, consequently, a decrease of the value for x can occur, while the particles can remain coherent with the matrix. A smaller value of x not only corresponds to a smaller amount of-interfacial excess nitrogen, but also leads to a smaller amount of

o excess nitrogen dissolved in the matrix through its effect on e and Y ^N

(see eqs. (6) and (8)).

Obviously, if ageing has progressed so far that the particle/matrix interface becomes incoherent, the total amount of excess nitrogen will decrease further, because (i) less favourable sites are available for

nitrogen adsorption at the interfaces (disrupted atomic arrangement) and because (ii) only a part of the volume misfit between particles and matrix will now be accommodated elastically, corresponding to a smaller value of hydrostatic stress ( aa) as compared to the fully

coherent condition.

In section 4, the present model will be applied to published excess-nitrogen data for a number of systems nitrided under various conditions.

4. Application to several binary iron-base alloys

4.1. Fe-Ti

Most data regarding excess nitrogen contents are available for nitrided Fe-Ti alloys (Podgurski and Davis 1981, Rickerby et al. 1986; data of Jack (1976) have been included in Rickerby et al. 1986). In both references titanium contents up to about 2.0 at% were employed and absorption isotherms were given for different temperatures. In (Podgurski and Davis 1981) prenitriding treatments were applied; this was normally not the case with the experiments reported in (Rickerby et al. 1986) (cf. section 2.2 herein).

The Fe-Ti alloy preparation procedure strongly influences the microstructure prior to nitriding and, consequently, the as-nitrided microstructures (cf. Földeaki, Rapp and Kronmiiller 1983). The effect of such variations, as well as other systematic differences in experimental conditions between the various studies (e.g. impurity levels of the materials used), on the amount of excess nitrogen is minimized by considering the excess nitrogen content in a certain alloy relative to that of a chosen reference alloy of the same study (cf. eqs.

(5) and (7)). As reference alloys, Fe-Ti alloys were adopted containing a small amount of titanium (0.085 at% (Podgurski and Davis 1981) and 0.08 at% (Rickerby et al. 1986), respectively), and subjected to the same treatment as the alloys of higher titanium content of the same study.

ref

Experimental values for [N]a/[N]a were derived from slopes of the

linear parts of published absorption isotherms (region III) or derived from published data for the reaction enthalpy and reaction entropy (see eq. (5a) and below eq. (2)).

r e f

For calculation of theoretical [ N ]a/ [ N ]a values, values for x,

indicating the amount of nitrogen adsorbed at the nitride/matrix interface, are required. These can be obtained from linear extrapolation of the absorption isotherms in region III towards the ordinate at rN = 0

(see discussion in section 2). Since for nitriding Fe-Ti at 673 K and 773 K no absorption isotherms were provided by Rickerby et al. 1986, values of x for these cases were estimated as follows. For the nitriding experiments of Rickerby et al. (1986) at 773 K, x was taken as 1.93, which is the average value of x derived from absorption isotherms given by Podgurski and Davis (1981) for Fe-Ti alloys prenitrided at the same temperature. At 673 K the maximum Ti:N ratio obtained at a high nitrogen potential of rN = 0.51 a t n r1 / 2 conforms to 1:3 (Jack 1976,

Rickerby et al. 1986). Then, taking the slope of the absorption isotherm in region III from Fig. 9 in (Rickerby et al. 1986), an x value of 2.40 is obtained by extrapolation to rN = 0.

A survey of the values of x extracted from the experiments is presented in table 1. As implied by the presentation in table 1, for a certain temperature the x values do not depend on alloying-element content. Clearly, x decreases with increasing nitriding temperature. Also ageing of a specific matrix/platelet assembly at a temperature

Table 1. Average N:Ti ratios (x; incorporating both type I and type II nitrogen) as derived from published nitrogen-absorption data about the (pre)nitriding of Fe-Ti alloys at different temperatures (see text; T = 673 K and 858 K (Rickerby et al. 1986); T = 773 K and 873 K (Podgurski and Davis 1981)). Temperatures denoted with an asterisk indicate that the corresponding x values were obtained after hydrogen reduction treatments at 873 K for 24 h and for over 200 h of Fe-Ti alloys initially nitrided at 773 K. T ( K ) x 673 2.40 773 1.93 858 1.25 873* (24 h) 1.53 873* (>200 h) 1.16

well above the initial nitriding temperature is associated with a reduction in x, as follows from additional experiments presented in table 1. This behaviour of the amount of interfacial nitrogen atoms can fully be explained by a reduction of the total platelet/matrix interfacial area due to the occurrence of thicker platelets at higher nitriding temperatures and of coarsening of the platelets on ageing.

Further, the following data were used in the calculations. The partial molar volume of nitrogen in iron, VN, was deduced from the expansion

of the ferrite lattice due to nitrogen dissolution (Ferguson and Jack 1983) as 5.12 cm3.mole"1. The shear modulus, Ga, of the matrix was

taken as 81.6 GPa (Smithells 1976). From lattice-parameter data for Fe and TiN (Pearson 1968) the respective molar volumes V^ = 7.092 cm3.mor1 and VxiN=11.51 cm3.mol'1 were obtained.

In (Ma) 3.0 exp 2.0 1.0 n . a Ü

' A*

V

Fig.2.Comparison of predicted (abscissa) and experimental (ordinate) values for l n { [ N ]a/ [ N ] ^ ' } of different Fe-Ti alloys nitrided under various conditions:

a. f = 0.5; b. f = 1.0 (O: T = 773 K, x ~ 1.93;«: T = 773 K, x ~ 1.53;

<>: = 723 K, x ~ 1.93;B: T = 848 K, x ~ 1.53;V: T = 773 K, x=1.16;A: [ N ] ^ ' by interpolation (Podgurski and Davis 1 9 8 1 ) 0 T=673 K,x = 2.40;A: T = 773 K, x = 1.93;V: T = 858 K, x ~ 1.25 (Rickerby et al. 1986)).

Finally, the experimental and theoretical values for [ N ]a/ [ N ] ^e f

obtained as indicated above, can be compared (Fig. 2). Ideally, the experimental data should fall on the straight line with slope 1 passing through the origin in Fig. 2. In view of the experimental uncertainties (see below), this first attempt to reconcile quantitatively the amount of excess nitrogen occurring in nitrided Fe-Ti alloys with a simple model gives encouraging results. Discrepancies between experimental data and theoretical predictions can be discussed as follows.

First of all, the effect of experimental errors is considered. The error made in the determination of the slope of the absorption isotherm

ref

affects the experimental value of ln{[N]a/[N]a }. The vertical error bar

indicated in Fig. 2 corresponds with this experimental inaccuracy as derived from the published data (maximal and minimal estimates for the slopes of the absorption isotherms; Podgurski and Davis 1981). Further, inaccuracies inherent to the determination of x and [M] affect

ref

the predicted value for ln{[N]a/[N]a }. The horizontal error bar in Fig. 2

has been determined by straightforward calculus for an error in x of 0.1 at x = 1.5 and an error in [M] of 0.05 at% (for [M] = 2.0 at%). It can be concluded that the scatter of the data points in Fig. 2 may be largely due to the experimental inaccuracies.

It should be realized that the theoretical prediction is obtained after adoption of an expression of the misfit parameter. In particular for the Fe-Ti system the misfit parameter used (eq. (6b)) can only be considered as an approximation, since for this system the largest amounts of nitrogen atoms adsorbed at the nitride/matrix interface occur (as exhibited by x values > 1; cf. Table 1). In view of the experimental errors discussed above it is not considered worthwhile at present to propose a more evolved form of the misfit parameter, although it is recognized that best agreement seems to be obtained for

the extreme case of f = 1 (Fig. 2).

An other contribution to a systematic deviation can be due to the use of the elastic constants of pure iron for the matrix in the calculations, whereas the, at present unknown, elastic constants valid for the iron matrix of the strained assembly should have been applied (Sayers 1987; see also Mittemeijer et.al. 1981).

4.2. Fe-V

Nitrogen absorption isotherms for Fe-V alloys have not been published until now. Isolated data (nitrogen potentials and corresponding nitrogen contents; in fact points of absorption isotherms) have been presented by Pope et al. (1973) and Yang and Krawitz (1984) and are gathered in table 2.

For a direct theoretical prediction of the amount of excess nitrogen, the absorption isotherms have to be known in order to establish values of x by extrapolation. In the absence of such data, the procedure can be reversed: application of the model for quantitative description of excess nitrogen to the published data (table 2) leads to values of x. Applicability of the model can then be verified by investigating the consistency of the occurring values of x with respect to temperature and composition dependence (internal consistency) and type of alloying element (external consistency).

No reference Fe-V alloy is available, because neither x nor K (= slope in region III) is known for any Fe-V alloy. Therefore, pure iron was adopted as a reference (see eqs. 5 and 5a); [N^e = Kref.rN, where Kref is

the equilibrium constant for nitrogen absorption in pure iron according 9 2 7 0

to l n Kr e f= - ~Y~ + 10.27. with Kref expressed in w t % N . a t m1 / 2

(Podgurski and Knechtel 1969). The molar volume of VN amounts to

10.68 cm3.mole"1 (Pearson 1968); other numerical data were equal to

those applied in section 4 . 1 .

Before application of the model, the compatibility of the data from Pope et al. (1973) and Yang and Krawitz (1984) has to be discussed. It is clear from the absorption data presented for 843 K, that these results can not be reconciled simply (cf. table 2). This may be due to incorrect values taken for the amounts of V dissolved in the unnitrided alloys. After reduction in hydrogen at 843 K, the ratio N:V should equal

Table 2. Nitriding conditions (T and r^) and the total amount of nitrogen absorbed ([N]tol)

by different Fe-V alloys on nitriding.

[V] T rN [N]t o t Ref.

(at%) (K) (atm"1 / 2) (at%)

0.52 843 0.031 0.70 0.117 1.01 1.08 843 0.031 1.16 0.117 1.65 2.26 843 0.031 2.70 0.117 3.59 773 823 843 773 823 843 773 823 843 0.191 0.078 0.078 0.191 0.078 0.078 0.191 0.078 0.078 1.50 1.25 1.26 3.25 2.65 2.65 4.82 4.00 4.00 Pope et al. (1973) Yang and K r a w i t z (1984)

Table 3. Optimum x values obtained from fitting eqs. (6b-8) to experimental data (Pope, et al. 1973) for Fe-V alloys nitrided at 843 K (rN = 0.117 atm"1'2). [V]

indicates the reported vanadium contents; [V*] denotes vanadium contents modified by imposing N:V = 1:1 after a hydrogen reduction treatment at 843 K subsequent to nitriding. [V] (at%) 0.52 1.08 2.26 t = 0.5 1.38 1.19 1.30 X f = 1.0 1.34 1.17 1.24 [ V ] (at%) 0.50 0.90 2.12 f = 0.5 1.43 1.43 1.38 X f = 1.0 1.39 1.38 1.31

1, corresponding to the equilibrium nitride. Varying values smaller than unity were reported by Pope et al. (1973), indicating that the effective vanadium contents for nitride formation are smaller than those reported. This can be due to the reported presence of carbon in the specimens concerned, possibly associated with the occurrence of vanadium carbides.

The model calculations for the data from Pope et al. (1973) are presented using the original data for V contents as well as corrected values to eliminate the above inconsistency (table 3). The model calculations for the data from Yang and Krawitz (1984) are shown in table 4. The x values derived from both sources for the same nitriding temperature are not identical, which can be due to:

(i) the V contents given by Yang and Krawitz (1984) may be in error (an error of ± 0.1 at% V was reported). In table 4 also results from the model calculations are presented as obtained by imposing the x values derived from the data from (Pope et al., 1973);

( i i ) overageing of Fe-V alloys occurs on nitriding (Yang and Krawitz, 1984), thereby underestimating the maximal amount of excess nitrogen to be absorbed (see section 4.3.).

Table 4. Optimum x values obtained from fitting eqs. (6b-8) to experimental data (Yang and Krawitz 1984; see table 2) for Fe-V alloys nitrided under different conditions. [V] indicates the reported vanadium contents; [V*] denotes vanadium contents used for determination of x by fitting (at 773 K and 823 K). These modified vanadium contents were obtained by taking x at 843 K equal to the average of the x values given in Table 3 for both [V] and [V*] and determining the vanadium content in eq. (8) that corresponds with enhanced lattice solubility in agreement with eq. (7).

f=0.5 f=1.0

[V] [V*] x x x [V*] x x x

(at%) (at%) T=773K T=823K T=843K (at%) T=773K T=823K T=843K

1.1 1.10 1.16 0 . 9 8 0.95 1.10 1.15 0.99 0.95 0.80 1.59 1.35 1.29 0.82 1.51 1.29 1.25 0.74 1.73 1.45 1.41 0.75 1.64 1.41 1.36 2.2 2.20 1.29 1.08 1.05 2.20 1.25 1.07 1.04 1.78 1.59 1.33 1.29 1.80 1.49 1.29 1.25 1.63 1.73 1.45 1.41 1.64 1.63 1.40 1.36 3.3 3.30 1.25 1.09 1.06 3.30 1.20 1.07 1.05 2.69 1.53 1.33 1.29 2 . 6 8 1.43 1.28 1..25 2 . 4 5 1.68 1.46 1.41 2 . 4 3 1.56 1.40 1.36

It follows from the results given in table 3, that the value of x for nitriding at 843 K does not depend significantly on alloying-element content if the modified vanadium contents are used. This unimposed result agrees with the finding for nitrided Fe-Ti alloys (section 4.1.). Further, whatever value for vanadium content is taken, all values for x presented in table 4 show the same trend: x decreases as the temperature increases, which also agrees with the results for nitrided Fe-Ti alloys and can be explained accordingly (see section 4.1.). The

numerical interpretation is only slightly dependent on the value of f selected (tables 3 and 4).

Comparing the values of x derived for nitrided Fe-Ti and Fe-V (tables 1, 3 and 4) it can be concluded that, at the same temperature, a smaller value of x is observed for nitrided Fe-V (see in particular the data at 773 K in tables 1 and 4). This is consistent with the discussion in section 5 where it is concluded that the interaction of titanium and

nitrogen is stronger than the interaction of vanadium and nitrogen.

4.3. Fe-Cr

The occurrence of excess nitrogen in nitrided Fe-Cr alloys has been reported in several references (Mortimer, Grieveson and Jack 1972, Mittemeijer, Rozendaal, Colijn, Schaaf and Furnée 1981, Hekker et al. 1985). Only the quantitative result from Hekker et al. (1985) can be employed for fitting of the proposed model. On nitriding Fe-Cr alloys the development of coherent CrN precipitates (continuous precipitation) is succeeded by a discontinuous precipitation starting in the near surface region of the specimens already at an early stage of nitriding. As a result of this ageing process, the (local) amount of excess nitrogen depends on treatment time. Consequently, an apparent (for thickness dependent) maximum is found for the total amount of excess nitrogen. Hekker et al. (1985) met this problem by nitriding Fe-Cr specimens of various thicknesses and determining the amount of excess nitrogen corresponding to a dispersion of coherent nitrides, by extrapolation of the apparent nitrogen maximum towards a specimen thickness equal to zero. In this way, only one point of a nitrogen absorption isotherm of Fe-Cr is obtained.

Proceeding analogously as for the nitrided Fe-V alloys, the model for quantitative description of excess nitrogen can be applied in order to derive a value for x. As a reference pure iron is applied for which the nitrogen solubility has been determined for exactly the same nitriding conditions as for the Fe-Cr alloy investigated (Hekker et al. 1985). The molar volume of CrN amounts to J 0 . 7 5 cm3.mole-1 (Pearson 1968); other

numerical data were equal to those applied in sections 4 . 1 . and 4.2. It is obtained: x = 1.0. Hence, the amount of nitrogen adsorbed at the nitride/matrix interface is neglibible for nitrided Fe-Cr. As compared to nitrided Fe-Ti and Fe-V a minimal value for x is consistent with the expected relatively weak interaction of chromium and nitrogen (see also section 5). A minimal value for x can also be expected in view of the rapid ageing/coarsening process occurring already during nitriding (see above and Hekker et al. 1985). This is also apparent from a comparison of nitride-platelet thicknesses in Fe-V and Fe-Cr alloys containing about the same amount of alloying element and nitrided under similar conditions (cf. Fig. 5 from Pope et al. (1973) and Fig. 2 from Mortimer et al. (1972)).

4.4. Fe-Mo

On nitriding Fe-Mo alloys, ageing phenomena in the first nitrided (outer) part of the specimen are even more pronounced than for Fe-Cr: a series of intermediate molybdenum-iron nitrides is passed through (Brenner and Goodman 1971, Driver, Unthank and Jack 1972, Driver and Papazian 1973, Wagner and Brenner 1978). Until now, no data have been reported which could be used for quantitative application of the strain model.

4.5. Maximal lattice solubility

The matrix-lattice dilation generated by misfitting second-phase particles (e.g. nitrides) provides a geometrical understanding for the occurrence of enhanced solubility of interstitials (e.g. nitrogen). This dilation, induced by the hydrostatic component of the image-stress field of finite bodies, is not a direct function of temperature (eq. (4)). The actually occurring amount of excess solute can be estimated applying the thermodynamics of stressed solids. The resulting formula for the amount of excess solute shows a direct dependence on temperature (eq.(5)). This interpretation indicates that thermo-dynamical conditions imposed on the system determine to what extent the geometrical capacity for excess solute is utilized (cf. section 3); for example, a change of temperature, keeping all other parameters, i.e. x, [M] and rN, constant, already causes a change of the quantity of

excess solute, while, to first-order approximation, the matrix dilation does not change. In the following a formula for the prediction of the maximal amount of excess solute will be proposed and a comparison will be made with experiment-based estimates for the largest possible amounts of excess nitrogen in the ferrite matrix of nitrided Fe-Ti alloys.

Literature data for the relation between lattice parameter aa and

nitrogen content of stress-free a-Fe indicate that Vegard's law is obeyed: Aaa/a° = p.[N]„ (for [N]a as the atom fraction of nitrogen,

P = 2.3 x 10"5 (Ferguson and Jack 1983)), where a° represents the

lattice parameter of pure a-Fe. Applying this relation in reverse to the strained ferrite lattice (lattice parameter change -> nitrogen content), the geometrically maximal estimate for enhanced lattice solubility, [N]™ax, is obtained by equating Aa/a° to the lattice dilation derived from