Marc Nikolussi

Andreas Leineweber

Eric Jan Mittemeijer

Nitrogen diffusion through cementite layers

Keywords: carbides, diffusion, nitrides, thermodynamics cementite, nitrocarburising, activation energy cementite, nitrogen diffusion, activation energy, nitrocarburising, nitriding

published or not. The documents may come

Introduction

The corrosion and wear resistances of iron-based workpieces as well as the fatigue endurance can be improved pronouncedly by thermochemical heat treatments such as nitriding and nitrocarburising which are of great technological importance [START_REF] Unterweiser | Source Book on Nitriding[END_REF][START_REF] Liedtke | Wärmebehandlung von Eisenwerkstoffen -Nitrieren und Nitrocarburieren[END_REF].

Gaseous nitriding and gaseous nitrocarburising are usually performed at temperatures between 773 K and 853 K. Thus, the process temperature is located below the binary/ternary eutectoid temperature of the Fe-N/Fe-N-C solid solution [START_REF] Massalski | Binary Alloy Phase Diagrams[END_REF][START_REF] Du | [END_REF]. The nitriding/nitrocarburising gas atmosphere provides nitrogen or nitrogen and carbon, which are taken up by the surface-region of the iron-based workpieces [START_REF] Knerr | ASM Handbook[END_REF].

The incorporation of nitrogen or nitrogen and carbon results in (i) the formation of a compound layer (several 10 µm thick) and/or (ii) the formation of a diffusion zone (several 100 µm thick). The compound layer is responsible for a considerable enhancement of the corrosion and wear resistance. Depending on the treatment temperature, the pressure and the composition of the gas atmosphere, the compound layer can consist of different phases.

Typically γ'-Fe 4 N 1-y and ε-Fe 3 (N,C) 1+x are constituents of the compound layer [START_REF] Colijn | [END_REF] but also cementite can occur in the compound layer [7,8]. The diffusion zone is responsible for a considerable enhancement of the fatigue endurance [9]. Nitrogen or nitrogen and carbon are dissolved (at the treatment temperature) as solid solution in the octahedral interstices of the iron bcc-lattice.

It was shown recently that, under certain conditions, also pure, massive cementite layers can form on the ferrite substrate [8]. These cementite layers have been investigated in detail with respect to their homogeneous cementite-phase microstructure, with respect to conditions for occurrence of additional (carbo)nitride phases and the corresponding phase equilibria as well as with respect to selected mechanical properties [8,10,11,12,13,14].

In the presence of cementite compound layers it turns out that the nitrogen (and carbon) diffusion into the substrate is strongly decelerated; cementite acts as a diffusion barrier for nitrogen [15] and carbon [16]. Nonetheless, although nitrogen transport through cementite is decelerated, it is shown in this paper that a certain time-dependent amount of nitrogen is transported through the cementite into the ferrite substrate, leading to an increase of the nitrogen content in (and the hardness of) the ferrite substrate. The solubility of nitrogen in the ferrite is much higher than for carbon at the temperatures of interest (783 K -843 K), e.g. values of 0.29 at.-% for nitrogen vs. ≈ 0.012 at.-% for carbon at 823 K are found in Ref. [START_REF] Kunze | Nitrogen and Carbon in Iron and Steel[END_REF].

Furthermore, most of the carbon incorporated in the solid is used to build up the cementite layer, whereas nitrogen passes through the cementite layer to be dissolved in the ferrite.

The present work focuses on the diffusion of nitrogen through cementite. Hardnessdepth profile measurements in the ferrite substrate are used to determine the nitrogen concentration-depth profiles. A model is proposed that enables the simulation of such nitrogen concentration-depth profiles. On this basis, for the first time, information about the diffusivity of nitrogen through cementite, including the corresponding activation energy of nitrogen diffusion in cementite, is obtained.

Experimental

Specimen preparation and gaseous nitriding/nitrocarburising

Two differently produced types of specimens were investigated in this study: "Thick-plate" specimens for nitrocarburising experiments were produced by cold-rolling a ferrite cast rod (Alfa Aesar, 99.98 wt.-% Fe) on both sides to a thickness of 1 mm. From the resulting coldrolled sheet, rectangular pieces (20 mm × 25 mm) were cut, ground, polished (final stage 1 µm diamond suspension) and cleaned ultrasonically in ethanol. "Thin-plate" specimens for nitriding experiments were produced by cutting from a 10 cm × 10 cm iron sheet (Alfa Aesar, 99.98 wt.-% Fe) of 0.1 mm thickness rectangular pieces of 20 mm × 25 mm which were ground, polished (final stage 1 µm diamond suspension) and cleaned ultrasonically in ethanol.

In order to remove the cold deformation both types of specimens were, prior to gaseous The nitriding/nitrocarburising facility had to ensure the desired gas environment and the desired temperature during treatment. Moreover, it was necessary to quench the specimens after treatment in order to retain the microstructure as at the treatment temperature. Thus, the nitriding/nitrocarburising facility was composed of a vertical quartz-tube furnace which was at its end equipped with a water (flushed with N 2 ) container for quenching the specimens to room temperature. Using a quartz fibre, which, to realise quenching, can mechanically be destroyed after the nitriding/nitrocarburising treatment, the specimens prepared as described above were positioned in the middle of the quartz-tube furnace where the process temperature (controlled within ± 1 K) prevailed.

Two types of treatments were conducted in the present work: (i) Nitrocarburising experiments to study nitrogen diffusion through growing cementite layers, and (ii) nitriding experiments to prepare specimens of homogeneous nitrogen content and without compound layer. For these experiments, ammonia (99.999 vol.-%) as nitrogen supply, carbon monoxide (99.97 vol.-%) as carbon supply, hydrogen (99.999 vol.-%), and nitrogen (99.999 vol.-%), as inert gas, were employed. Each gas flux was controlled by a separate mass-flow controller.

An overall linear flow rate of 13.5 mm s -1 (calculated for the gas volume at room temperature) through the quartz retort (diameter 28 mm) was maintained. Such a flow rate ensures that ammonia dissociation, which would change the composition of the gas atmosphere, can be neglected.

For gaseous nitrocarburising the gas atmosphere was composed of 13 vol.-% NH 3 , 58 vol.-% H 2 (nitriding potential 1 r N = 0.3 atm -1/2 ), 20 vol.-% CO and 9 vol.-% N 2 (as inert gas). The experiments were performed at T = 783 K, 823 K and 843 K, for treatment times of 0.5 h, 2 h, 6 h, 14 h, 24 h and 48 h, leading always to massive cementite layers on ferrite substrates [8,10] (cf. Fig. 1). For these experiments "thick-plate" specimens with a thickness of 1 mm, produced as described above, were used. In fact, the 783 K and 843 K specimens are among those used in Ref. [10] to analyse the cementite-layer growth kinetics at the corresponding temperatures.

Gaseous nitriding experiments were performed at 823 K using different NH 3 /H 2containing gas atmospheres yielding different nitriding potentials 1 (cf. Table 1). The applied experimental conditions ensured the formation of compound-layer free specimens in accordance with the Lehrer diagram [19]. Gaseous nitriding was performed for 42 h in order that the ferrite substrates were saturated with interstitial nitrogen with respect to the nitriding gas atmosphere. For these experiments "thin-plate" specimens with a thickness of 0.1 mm, produced as described above, were used.

Microstructural and hardness analysis

The specimens after both the nitriding and the nitrocarburising experiments were cut into four pieces, used for optical microscopy, hardness measurements, carrier-gas hot extraction and X-ray diffraction (XRD), respectively.

For optical microscopy of and hardness measurements on specimen cross sections, the nitrocarburised specimens were covered with an electrodeposited protective nickel layer using a Watts bath [START_REF] Colijn | [END_REF][START_REF] Chatterjee-Fischer | Wärmebehandlung von Eisenwerkstoffen[END_REF] at 333 K. The protective nickel layer avoids mechanical damage at the surface of the metallographic cross sections and guarantees the required sharpness at the sample surface in the cross sections. All specimens (nitriding and nitrocarburising experiments) were embedded using a Struers LaboPress 3. Embedding was performed with 15 of NH 3 /H 2 /CO/N 2 is (hypothetically) infinite [8] although an "effective" carburising potential acts at the specimen surface [10]. -6 -ml Polyfast (Buehler GmbH), a load of 15 kN, an annealing time of 5 min at 453 K and a cooling time of 3 min down to room temperature. After embedding, the specimens were ground, polished (final stage 1 µm diamond suspension) and etched using 1 vol.-% Nital containing 0.1 vol.-% HCl [START_REF] Wells | [END_REF]. In order to differentiate between the massive cementite layer and the ferrite substrate, the cross-sectional specimens were stained using either (i) an alkaline potassium permanganate solution (1 g NaOH, 1 g KOH and 4 g KMnO 4 per 100 ml distilled water) at 328 K [8,[START_REF] Petzow | Metallographic Etching[END_REF] of which the effect is similar to that of a Murakami solution [START_REF] Colijn | [END_REF][START_REF] Petzow | Metallographic Etching[END_REF] or (ii) an alkaline sodium picrate solution (25 g NaOH and 2 g picric acid per 75 ml distilled water) at room temperature [START_REF] Petzow | Metallographic Etching[END_REF]. In both cases the massive cementite layer gets, due to its high carbon content, severely stained. The ferrite substrate remains unstained and can therefore easily be distinguished from the cementite layer upon optical microscopy (Zeiss Axiophot microscope). By this type of staining it is also possible to differentiate between different nitride, carbonitride and carbide phases (also supported by electron back-scatter diffraction) in the compound layers, see e.g. Ref. 11, indicating that in the present work indeed were of pure cementite.

Hardness measurements (micro-Vickers) were performed with a Leica VMHT MOT microhardness indenter using a load of 25 gf (≅ 0.245 N) for 10 s. Hardness-depth profile measurements in the ferrite substrates were performed for all specimens of the nitrocarburising experiments. Hardness indents were set in the ferrite substrate at selected distances from the interface cementite/ferrite until the middle of the specimen was reached.

The exact distance values of the hardness indents from the interface cementite/ferrite were determined by optical microscopy using the software "analySIS" (Soft Imaging System GmbH). For each specific distance value from the interface cementite/ferrite five hardness measurements were made; the average value was taken as the local hardness and the standard deviation was taken as indication of the experimental error. For all specimens of the nitriding experiments, which should have -due to the small specimen thickness and due to the long In order to relate the hardness of the ferrite substrate with its nitrogen content, values for both quantities were determined for a couple of specimens with homogeneous nitrogen contents in the ferrite (see section 3). The nitrogen contents of all the nitrided specimens (compound-layer free) were determined by carrier-gas hot extraction. The same procedure was applied to specimens, which were nitrocarburised at 823 K with a treatment time of 6 h, 14 h, 24 h and 48 h, since these specimens do not exhibit a nitrogen concentration (hardness) gradient across the ferrite substrate in the cross section (cf. Fig. 2b). Prior to nitrogen-content determination by carrier-gas hot extraction on the nitrocarburised specimens, the massive cementite layer was removed by grinding so that only the nitrogen-enriched substrate was analysed. After completion of the grinding procedure, it was checked by X-ray diffraction whether the entire cementite layer had been removed.

To additionally verify the presence or absence of a (cementite) compound layer and of the possible presence of other nitride and carbonitride phases, phase identification was carried out by X-ray diffractometry. A PANalytical X'Pert Multi-Purpose Diffractometer, which was equipped with a graphite monochromator in the diffracted beam, was used. The diffractometer was operated with CoKα radiation in Bragg-Brentano geometry. Each specimen was rotated around its surface normal during the measurements to achieve better crystallite statistics.

Experimental results and evaluation: hardness measurements and nitrogencontent determination

Each nitrocarburising experiment performed at 783 K, 823 K and 843 K led to the formation of a massive cementite layer on the ferrite substrates (cf. Fig. 1) [8,10]. The cementite layers exhibit a characteristic microstructure (partially rough ferrite-cementite interface) and a -8 -specific orientation relationship with the ferrite substrate [12]. After cross-sectional metallographic preparation, hardness-depth profile measurements were performed in the ferrite substrate (cf. Figs. 2a -2c).

In order to transform hardness-depth profiles into nitrogen concentration-depth profiles (cf. Figs. 2a -2c), the dependence of hardness on nitrogen content in ferrite has to be known.

Such a dependence was obtained on the basis of the results for hardness and nitrogen content in homogeneously nitrided/nitrocarburised ferrite given in Table 1 and shown in Fig. 3.

α-Fe N C mh b = + , (1)
where

α-Fe N C
denotes the nitrogen concentration in the ferrite substrate, and h its hardness.

Least-squares fitting of a straight line to the experimental data in Fig. 3 yielded the following values for m (slope of the straight line in Fig. 3) and b (part cut from the ordinate):

( ) 3

Modelling nitrogen concentration-depth profile development 4.1 General assumptions

The experimentally determined nitrogen concentration-depth profiles will be simulated to analyse, on the basis of comparison with the experimentally determined nitrogen concentration-depth profiles, the diffusivity of nitrogen through cementite.

Consider a laterally infinitely extended iron plate of finite thickness. Nitrogen can enter this plate from both sides; a symmetrical (with respect to the centre plane of the plate) nitrogen concentration-depth profile is built up.

The process of gaseous nitrocarburising can be subdivided into four different steps: (i) diffusion of ammonia from the gas phase to the surface of the specimen, (ii) dissociation of ammonia at the surface, (iii) nitrogen diffusion through the growing cementite layer of timedependent thickness, (iv) nitrogen diffusion within ferrite (after having diffused through the cementite layer) from the interface cementite/ferrite to the core of the specimen. Ad (i): In the present experiments the gas-flow through the quartz-tube furnace is large; the gas composition at the sample surface can be taken constant for a constant treatment temperature [10]. Ad (ii): Already after very short treatment time dissociation of ammonia at the surface of the specimen is not rate determining for the nitrogen uptake; instead nitrogen diffusion through the growing cementite layer is rate-determining (in contrast with the case of nitriding pure ferrite [START_REF] Rozendaal | [END_REF]). The conditions indicated under ad (i) and ad (ii) imply that local equilibrium prevails at the interface of the gas atmosphere and the specimen. Furthermore, local equilibrium is assumed to hold at the interface cementite/ferrite, which in the present context in particular implies that there is no chemical-potential gradient for nitrogen at that interface.

Nitrogen diffusion within ferrite is governed by Fick's second law ( ) ( ) There are no reliable data about the N content in cementite (it is even unclear whether the concentration difference in Eq. ( 3) should be positive or negative). However, test calculations with nitrogen contents in cementite ranging from 0 at.% to 0.5 at. % indicate thatgiven the known growth rate of cementitethe nitrogen consumption or release due to the growing cementite (at the cost of ferrite with a nitrogen content of α-Fe N,interface

-11 - α-Fe 2 α-Fe N N 2 α-Fe N C C t x D ∂ ∂ ∂ ∂ = , (2)
3 3 3 α-Fe 3 N 3 Fe C Fe C Fe C -Fe N N N,interface N,interface 0 0 Fe C Fe C α-Fe N N,interface N,interface 0 x x C x x dS J J C C dt dS D C C dt α α α = = ∂ ∂ = = + - = - + - , (3)

C

) is negligible compared to the overall nitrogen flux through the cementite layer.

Nitrogen enters the ferrite substrate at both sides. Hence, a symmetrical nitrogen concentration-depth profile results and no net flux of nitrogen through the middle of the sample occurs, leading to the second boundary condition

α-Fe N = 0 C x x Z ∂ ∂ = , (4)
where x = Z denotes the position of the centre plane.

Before nitrogen can pass the interface cementite/ferrite and can diffuse through ferrite, it must be transported through the cementite layer. Nitrogen diffusion through cementite is provoked by a gradient of the chemical potential of nitrogen across the cementite layer (cf.

Fig. 4)

( ) Fe C 3 N , x p T F µ ∂ ∂ = - , ( 5
)
where F is the thermodynamic force, ( ) ( ) )

3 3 3 3 3 Fe C Fe C 3 3 N N 3 3 3 Fe C Fe C Fe C Fe C Fe C N N N N N Fe C Fe C Fe C N N N , , C x x p T p T J v C M FC M C D µ ∂ ∂ ∂ ∂ = = = - = - , (6)
Fe C 3 N 3 3 Fe C 3 N ln Fe C Fe C N N ln 1 C D M RT γ ∂ ∂ = + , (7)
where ( )

Fe C 3 N Fe C 3 N ln ln 1 C γ ∂ ∂ +
is the thermodynamic factor, with 3 Fe C N γ as the activity coefficient of nitrogen in cementite. The solubility of nitrogen in cementite is extremely small, e.g. for 1593 K a solubility of about 0.064 at.-% was reported [START_REF] Kagawa | [END_REF]. Due to this extremely limited solubility, Henry's law [START_REF] Atkins | Physikalische Chemie[END_REF][START_REF] Wedler | Lehrbuch der physikalischen Chemie[END_REF] is assumed for nitrogen in cementite. Consequently, the thermodynamic factor equals one and Eq. (6b) can be given as

( ) *,Fe C Fe C Fe C 3 3 3 N N,surface N,interface 3 Fe C 3 Fe C N D C C S J - = , (9) where 3
Fe C S is the cementite-layer thickness.

The nitrogen concentrations in cementite at both interfaces (gas atmosphere/cementite and at the interface cementite/ferrite) will be expressed in terms of "corresponding" (see what follows) nitrogen concentrations in ferrite. For both, cementite and ferrite, Henry's law can be adopted. Therefore, for cementite and ferrite in (hypothetical) equilibrium with each other and, possibly additionally, with the same outer gas atmosphere, the concentrations of nitrogen in cementite, The above consideration implies that Eq. ( 9) can be written as

*,Fe C α-Fe α-Fe 3 N,eq N,interface N 3 Fe C 3 ( ) Fe C N D C C S J ϕ - = , (11)
The cementite-layer thickness where k denotes the parabolic growth constant for cementite and 0 S a (hypothetical) initial cementite-layer thickness at t = 0 (see discussion in Ref. [8]). Combining Eqs. ( 11) and ( 12)

leads to *,Fe C α-Fe α-Fe 3 N,eq N,interface N 3 2 1/ 2 0 ( ) Fe C N ( ) D C C kt S J ϕ - + = .

Simulation of nitrogen concentration-depth profiles; numerical procedure

For the simulation of the nitrogen concentration-depth profiles, Fick's first and second law have to be solved subject to the boundary conditions given by Eqs. ( 3) and ( 4). This can be done numerically on the basis of the method after Crank and Nicolson [START_REF] Rozendaal | [END_REF][START_REF] Crank | The Mathematics of Diffusion[END_REF] using the implicit finite-difference method. For that purpose the nitrogen concentration profile within ferrite was calculated for equidistant grid points in space (distance ∆x) (cf. Fig. 4) at different time steps (see what follows in section 5). Details of the numerical procedure are described in supplementary material published together with the online version.

Results of the simulation

The simulation was performed with M = 100 grid points (up to the middle of the specimen)

and different time steps. The increment of time was increased by 0.5 % after each generation of a nitrogen concentration profile [START_REF] Rozendaal | [END_REF], recognising the decrease of the nitrogenconcentration gradients with time, in order to reduce calculation time. Doing this, the

condition 3 *,Fe C N 2 1 2 ( ) D t r x ∆ = ≤ ∆
has to be fulfilled [START_REF] Crank | The Mathematics of Diffusion[END_REF], where t ∆ denotes the increment of the time and x ∆ denotes the grid-point distance. The simulation was started at the respective treatment temperatures on the basis of the nitrogen concentration-depth profile determined after 6 h, since for smaller treatment times the diffusion geometry and mechanism is incompatible with the model (see section 6.2). The following parameters were known: (i) the diffusion coefficient of nitrogen in ferrite, which was calculated for the respective treatment temperature according to Ref. [START_REF] Weller | [END_REF] (cf.

Table 2) and (ii) the cementite-layer thickness, which was determined experimentally. Hence, the fitting parameters were: the equilibrium nitrogen concentration in ferrite, 2 and Fig. 5.

Table 2:

Results of the simulation of nitrogen concentration-depth profiles. The equilibrium nitrogen concentration in ferrite, and the product of the partition coefficient and the (tracer-)diffusion coefficient of nitrogen through cementite were refined by matching of the simulated data and the experimental data by least-squares fitting. Furthermore, the diffusion coefficient of nitrogen in ferrite has been given according to Ref. [START_REF] Weller | [END_REF].

Concluding discussion

Hardness/concentration-depth profiles

The hardness of the ferrite substrates increases linearly with the nitrogen concentration. Upon embedding (cf. section 2), which has to be considered as a heat treatment, the nitrogen in the ferrite forms (semi-)coherent α''-Fe 16 N 2 precipitates [30][31][32][33][34], which are responsible for the hardness increase as measured at room temperature. In order to guarantee comparability of the hardness measurements, the embedding has to be performed in a reproducible way. Therefore, a special standard embedding procedure was developed, which has been described in section 2.

In the course of relating the ferrite hardness with the nitrogen content in the ferrite, the effect of present carbon was neglected. The amount of carbon which can be dissolved in ferrite at 823 K is more than twenty times smaller than the amount of nitrogen (see introduction). Already because of this recognition it is expected that a much smaller hardening effect due to carbides in ferrite is expected than due to nitrides. Indeed, for carbon in ferrite an increase of Vickers hardness of at maximum of 15 HV was observed in Ref. [35],

which is much less than the maximum increase of 100 HV observed for nitrogen in ferrite (cf.

Figure 3). Moreover, in Ref. [35] the solid solution treatment prior to the age hardening was performed at temperatures as high 973 K, which certainly led to dissolution of more carbon in the ferrite than in the present experiments conducted at ≤ 843 K. Thus the (maximum possible) hardening effect due to carbon in ferrite in the present work is expected to be even smaller than 15 HV. Further, the data points in Figure 3 do not differ systematically from the common straight line, independently of whether the points originate from a nitrocarburised specimen (containing some carbon in the ferrite) or from purely nitrided specimen (containing no carbon in the ferrite), confirming that the hardness depends practically only on the nitrogen content in the ferrite.

Moreover, it must be noted that the calibration line shown in Fig. 3 was determined on the basis of experiments performed at 823 K. This calibration line was also applied to the data obtained at 783 K and 843. The true relation between hardness and nitrogen content at 783 K and 843 K may differ slightly from that pertaining at 823 K. This may be the origin of the slightly negative nitrogen-concentration values in the ferrite substrate for some data points at very short treatment times (0.5 h and 2 h) at 783 K (cf. Fig. 2a).

The data obtained for the nitrogen concentration-depth profiles at the three different considered treatment temperatures indicate pronounced nitrogen concentration gradients in the ferrite matrix at short treatment times as 0.5 h and 2 h; the concentration gradients level off with increasing treatment time. The development of the nitrogen concentration-depth profile in the ferrite substrate is dominated by two processes: (i) nitrogen transport through the cementite layer via diffusion. The cementite-layer thickness increases as a function of the treatment time (according to a modified parabolic growth law [8,10]). Therefore, the nitrogen flux trough cementite decreases with increasing treatment time. (ii) The inward-diffusion of -20 -nitrogen into the ferrite substrate remains relatively fast. From (i) and (ii) it is concluded that the initially large nitrogen concentration gradient in the ferrite substrate decreases with time, as observed.

Simulation of nitrogen concentration-depth profiles

In the present work, nitrogen concentration-depth profiles in the ferrite substrate with a growing cementite layer at the surface were simulated. In the literature [START_REF] Rozendaal | [END_REF] such an approach was already applied for the calculation of nitrogen concentration-depth profiles of compoundlayer free ferrite specimens. In that case local equilibrium between gas atmosphere and the surface of the specimen was not immediately established. Therefore, nitrogen absorption and/or ammonia dissociation and nitrogen transfer through the surface contributed significantly to the process kinetics. In fact, nitrogen transfer through the cementite layer in the present case and nitrogen transfer through the surface in case of nitriding ferrite without compound layer at the surface (Ref. [START_REF] Rozendaal | [END_REF]) can be conceived as analogues. However, different dependences on

( ) α-Fe α-Fe N,eq N,interface C C -
occur in both cases: In Ref. [START_REF] Rozendaal | [END_REF]: S , is introduced.

( ) surf α-Fe α-Fe N N,eq N,interface
Treatment times of 0.5 h and 2 h were not considered in the simulation procedure. In the early stage of cementite formation (t < 6 h), cementite-layer growth proceeded faster than as predicted by the developed model. This can be explained as follows: (i) in the early stage of cementite formation an incompletely closed cementite layer is present [8,10]. Nitrogen diffusion from the surface of the specimen into ferrite proceeds directly, i.e. bypassing density; for data demonstrating grain-boundary diffusion in cementite, see Ref. [12]. Due to such a 'bypass/short-circuit' mechanism, nitrogen can be transported relatively fast through the cementite layer in the early stage of cementite formation 5 . Therefore, treatment times < 6 h were not used in the data evaluation on the basis of the model developed in section 4.1.

Literature data for the equilibrium nitrogen concentration in ferrite vary considerably: e.g. the values reported in Ref. [36] are distinctly lower than the values reported in Ref. [START_REF] Kunze | Nitrogen and Carbon in Iron and Steel[END_REF].

The values of α-Fe N,eq C obtained in the present work are generally larger than those compatible with the data from Refs. [START_REF] Kunze | Nitrogen and Carbon in Iron and Steel[END_REF] and [36]. These differences can be understood recognising that the nitrogen concentration in the ferrite substrate, α-Fe N,eq C , as determined in the present work, pertains to the (hypothetical) equilibrium of ferrite with the present nitrocarburising gas atmosphere. In reality such an equilibrium cannot occur: for such high nitrogen concentrations, solubility limits for nitrogen in ferrite in equilibrium with iron (carbo-)nitrides are surpassed, and formation of γ'-Fe 4 N below 833 K or of ε-Fe 3 (N,C) 1+x above 843 K [11] occurs. Indeed, in the present work, treatment times >> 48 h at 853 K occasionally led to the formation of these (carbo-)nitride phases at the cementite/ferrite interface.

According to the knowledge of the present authors, diffusion data of nitrogen in cementite have not been reported, before. The values obtained for the product of the partition coefficient and the (tracer-)diffusion coefficient of nitrogen through cementite are considerably lower than values for the diffusion coefficients of nitrogen in ferrite [START_REF] Weller | [END_REF]37] (cf.

Table 2) and iron nitrides [38][39][40][41] at similar treatment temperatures. The role of the cementite layer as diffusion barrier for nitrogen can be illustrated by assuming that the cementite layer would instead consist of ferrite. In that case, in Eq. ( 11) The activation energy of nitrogen diffusion through cementite (here determined as 65 ± 2 kJ/mol) is relatively low as compared to real or "apparent" activation energies for carbon diffusion through cementite which are in the range of 110 -185 kJ/mol [10,[42][43][44], and for nitrogen diffusion in iron nitrides, which are in the range of 92 -144 kJ/mol [40,41,45]. The activation energy for nitrogen diffusion in cementite appears to be as low as the activation energy for nitrogen (or carbon) diffusion in ferrite, which is about 78 -79 kJ/mol [START_REF] Weller | [END_REF]37].

One possibility is that ϕ, although very small, depends significantly on temperature and thus affects the activation energy value determined. Another possibility is that the low activation energy for 3 *,Fe C N D may hint at nitrogen transport favourably occurring via cementite grain boundaries; preferred diffusion of carbon along grain boundaries in cementite was reported very recently [12]. A role of defects (which later-on heal out) has indeed already been discussed above for the initial fast stage of nitrogen transport through cementite (see paragraph 2 of the present section 6.2), but it is imaginable that still later nitrogen diffusion along remaining grain boundaries (or other extended defects) may contribute to the occurring nitrogen flux through cementite. As long as the grain-boundary density remains constant, the grain boundaries' contribution to the nitrogen transport will lead to same kinetic equations as derived in section 4, and the obtained diffusion coefficient becomes an "effective" diffusion coefficient and the activation energy is an "effective" activation energy [START_REF] Philibert | Atom movements, diffusion and mass transport in solids[END_REF].

Conclusions

  , recrystallised at 973 K for 2 h under a reductive hydrogen flow of 200 ml min -1 , polished (final stage 1 µm diamond suspension) and cleaned ultrasonically in ethanol.

  a homogeneous nitrogen content, 10 hardness measurements were made across the cross-sectional specimen; their average value and their standard deviation was calculated.

  b = -0.354 ± 0.02 at.-%. On this basis, the experimentally determined hardness-depth profiles can be transformed into nitrogen concentration-depth profiles (cf. Figs.2a -2c). This was done for all considered treatment temperatures (783 K, 823 K and 843 K) and treatment times. Such quantitative information on the nitrogen concentration in ferrite cannot be obtained by other techniques. Whereas e.g. carrier-gas hot extraction can only provide an average nitrogen concentration across the whole specimen (instead of a location-resolved nitrogen concentration), the sensitivity of electron probe microanalysis (EPMA) is too low for the presently determined nitrogen concentrations.

  where α-Fe N D is the diffusion coefficient of nitrogen in ferrite (taken as concentration independent), α-Fe N C the nitrogen concentration at depth x (measured from the interface cementite/ferrite 2 ) and t the time of diffusion. The flux of nitrogen through cementite at the interface cementite/ferrite, from the flux of nitrogen into ferrite at this interface -Fe N 0 x J α = by a term considering the amount of N consumed by the moving interface cementite/ferrite due to the concentration difference at the interface:

  x = 0 denotes the location coordinate which represents the interface cementite/ferrite.

µ

  the chemical potential of nitrogen in cementite and x the location coordinate, T the treatment temperature and p the pressure.

C

  is the nitrogen concentration in cementite. The diffusion coefficient of nitrogen in cementite can be expressed by (

D

  is the (tracer-)diffusion coefficient of nitrogen in cementite. Thus, profile of nitrogen across cementite is assumed in Eq. (6b). The concentration difference of nitrogen across the cementite layer is given by the difference of the nitrogen concentration in cementite at the interface gas atmosphere/cementite, concentration in cementite at the interface cementite/ferrite,

C , are in equilibrium related by 3 3.

 3 For the chemical potential of nitrogen in cementite it holds that chemical potential of nitrogen in ferrite it holds that α-Fe 0 α-Fe α-Fe N Assuming for both, cementite and ferrite, the same reference state and Henry's law (constant activity coefficient of nitrogen), the mole fractions of nitrogen in cementite and ferrite in equilibrium with each other are related by a partition ϕ is the partition coefficient. Hence, the nitrogen concentration in ferrite at the cementite/ferrite interface in (real, local) equilibrium with cementite at the same interface will come to a halt if the nitrogen concentration in the ferrite corresponds to the nitrogen concentration which would prevail in ferrite in (hypothetical) equilibrium with the gas atmosphere, α-Fe N,eq C . Hence, the concentration of nitrogen in cementite at the surface in (real, local) equilibrium with the gas atmosphere,

S.

  has been determined experimentally for the present samples. The layer thickness could be described for each temperature by adopting a modified parabolic growth law[8,10] It will be assumed that for the minute range of nitrogen concentration in cementite ϕ does not depend on nitrogen concentration.

3 *.

 3 the partition coefficient and the (tracer-)diffusion coefficient of nitrogen in cementite, Values for these parameters were determined (for each considered treatment temperature) by minimising the sum of the squared differences of simulated and experimental nitrogen concentrations for all treatment times simultaneously (cf. Figs.2a -2c).The results obtained for

4 ⋅ 3 *

 43 10 -12 1.3 ⋅ 10 -11 1.8 ⋅ 10 -11 Adopting an Arrhenius-type temperature dependence for the (tracer-)diffusion coefficient of nitrogen in cementite and taken the partition coefficient ϕ as temperature independent, a plot of the logarithm of T should yield a straight line. This is observed indeed; see Fig. 5. The slope of the straight line obtained equals Q R -, with Q as the activation energy of nitrogen diffusion in cementite and R as the gas constant. It follows: Q = 65 ± 2 kJ/mol.

cementite 4 .

 4 (ii) Further, just after the formation of a closed cementite layer, short-circuit diffusion of nitrogen through thin and defect-rich parts of the cementite layer occurs. In this stage of cementite formation, cementite is expected to exhibit a relatively high grain-boundary

3 * 5 A

 35 N D . Hence, the nitrogen flux through the (cementite) surface layer, similar explanation was used for the observed enhanced initial growth rate during carbon-diffusion controlled cementite-layer growth on ferrite[8,10]. e. a factor of about 2500 -3000 (cf. Table2). This clearly demonstrates the diffusion-barrier behaviour of the cementite layer for nitrogen, which then could be due in particular to the very low solubility of nitrogen in cementite, leading to very small values of ϕ; further, the pre-exponential factors contained in

  profile measurements provide a suitable method to quantitatively determine nitrogen-concentration depth profiles in ferrite (maximal nitrogen content: ≈ 0.4 at.-%) after well-defined thermal post-treatment on the basis of a calibration. The relation between hardness and nitrogen content was found to be linear.(ii)Massive cementite layers with a time-dependent thickness can be generated on ferrite substrates by gaseous nitrocarburising at 783 K, 813 K and 843 K. The nitrogen concentration-depth profile in the ferrite substrate underneath the growing cementite layer can be simulated on the basis of a developed model using the implicit finite-difference method, yielding values for the diffusivity of nitrogen through cementite.(iii) The effective activation energy of nitrogen diffusion through cementite is about as large as the activation energy of nitrogen diffusion in ferrite. This may hint at nitrogen grain-boundary diffusion as dominant transport mechanism of nitrogen through cementite. The cementite layer acts as a diffusion barrier for nitrogen in particular because of the very low solubility of nitrogen in cementite.

F

Figure 1 :

 1 Figure 1: Optical micrograph (cross-sectional view; bright field) of a massive cementite layer

Figure 2 :

 2 Figure 2: Experimentally determined hardness-depth profiles in the ferrite substrate with a

Figure 3 :

 3 Figure 3: Calibration line: Nitrogen concentration (determined by carrier-gas hot extraction;

Figure 4 :

 4 Figure 4: Schematic drawing of a cementite layer on a ferrite substrate (cross-sectional view).

Figure 5 : 3 *

 53 Figure 5: Arrhenius plot: natural logarithm of the product of the partition coefficient and the

Table 1 :

 1 The experimentally determined (average) hardness values and (average) nitrogen contents (results from carrier-gas extraction) of all nitrided specimens. Composition (NH 3 and H 2 contents and corresponding nitriding potential) of the nitriding gas atmosphere, yielding compound-layer free specimens, have been indicated. The experiments were performed for 42 h at 823 K leading to a homogeneous solid solution of interstitial nitrogen in the ferrite substrate. The hardness of pure iron without any nitrogen dissolved determined in this work equals 100 ± 2 HV. Similar results obtained for some selected (see text) nitrocarburising experiments at 823 K have been given as well.

	nitriding experiments

It follows that a linear dependence exists between nitrogen content and hardness of the ferrite substrate:

  Nikolussi, S. Shang, T. Gressmann, A. Leineweber, E. J. Mittemeijer, Y. Wang and Z.-K. Liu: Scr. Mat., 2008, vol. 59, 814-817.

	o r F o r [14] M. F o r F o r
	P P P P
	e e e e
	e r e r e r e r
	R R R R
	e e e e
	v i e v i e v i e v i e
	w w w w
	O n l O n l O n l O n l
	y y y y
	-25 --27 -

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

The cementite layer is thin compared to the ferrite substrate at all considered treatment times and the cementite layer grows much slower than the extent of the nitrogen concentration-depth profile in the substrate. Therefore, the consumption of a part of the ferrite upon formation of the cementite is neglected in the modelling of the diffusion of nitrogen in ferrite.


José Luis Romero

Sabine Mücke

Julio Pérez
email: julio.perez@uab.es

A male destroying an egg in a cooperative breeding attempt in Lesser Spotted Woodpecker Dendrocopos minor

Keywords: Cooperative breeding, Lesser Spotted Woodpecker, Picoides minor, egg destruction

A cooperative breeding case was found in Lesser Spotted Woodpecker (LSW) in which a male and three different females were involved. For the first time contributions of each member of the cooperative breeding team were quantified during nest excavation and incubation in LSW. During daytime, the nest was mainly occupied by the male during the final excavation phase, nest guarding and egg laying. Aggressive interactions were recorded between two of these females during nest excavation, egg laying and incubation. The male was recorded destroying an egg presumably laid by the dominant female. The highest contribution during daytime incubation was by the dominant female (39%), followed by the male (34%) and a second female (27%). The third female had a very small contribution at any stage. A picture of the male removing the egg was analyzed to estimate the egg maximum width, ruling out a possible runt egg.

Motivations behind the behaviour of the male destroying the egg remained unclear.

Introduction

The mating system of Lesser Spotted Woodpecker (LSW) has been previously described by Wiktander et al. (2000), [START_REF] Höntsch | Autokölogie einer bestandsbedrohten Vogelart im hessischen Vordertaunus[END_REF] and [START_REF] Rossmanith | Breeding biology, mating system and population dynamics of the Lesser Spotted Woodpecker (Picoides minor)[END_REF] as mainly monogamous but exhibiting certain tendency to social multi-nest polygamy (Wiktander, 2000;[START_REF] Rossmanith | Sex-related parental care strategies in the lesser spotted woodpecker Picoides minor: of flexible mothers and dependable fathers[END_REF]. Recently, during a study of a colour-marked population of Lesser Spotted Woodpecker (LSW) in NE Spain two cases of cooperative breeding were reported, in which two females and a male were rearing the brood in the years 2005and 2006[START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. These cases appeared in a poplar plantation in which standing dead trees were selectively logged in high percentage (about 85%). These researchers suggested that selective logging could be understood as an (anthropogenic) ecological constraint, which could force the cooperation of the birds because of a lack of suitable nesting trees [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. Among European woodpeckers regular cooperative breeders are not known, and, as far as we know, only two cases of cooperative breeding attempts have been described (besides the cases reported in LSW), (i) a male helper has been described for the Middle Spotted Woodpecker (Dendrocopos medius, Pasinelli 1993, cited in Pasinelli 2003) and (ii) a female helper Grey-headed Woodpecker (Picus canus, [START_REF] Südbeck | Grauspecht-Weibchen Picus canus als Helfer an der Bruthöhle[END_REF].

In the last case, the reasons why this cooperative breeding attempt appeared were associated also to ecological constraints [START_REF] Südbeck | Grauspecht-Weibchen Picus canus als Helfer an der Bruthöhle[END_REF].

On the other hand, different cooperative breeding strategies in birds have been described based on the relative direct contribution of genes by the same-gender individuals in the breeding unit (also known as reproductive skew, [START_REF] Vehrencamp | Evolutionary routes to joint-female nesting in birds[END_REF].

When one only individual contributes genes while the others provide care, one usually uses the term helpers-at-the-nest system (also known as high skew), on the contrary when same-gender individuals have a direct contribution of genes, the term used is joint-nesting system (i.e. low skew, [START_REF] Vehrencamp | Evolutionary routes to joint-female nesting in birds[END_REF].

We would like to briefly report a new cooperative breeding case in LSW, in which three different females and a male were involved in the breeding attempt.

Methods

The study area is located between Barcelona and Girona (NE Spain, coordinates 41º 46'N 2º 41'E) and covered a surface of about 150 km 2 . The LSW territories are found basically in poplar (Populus x canadiensis) plantations. A more detailed description of the study area can be found elsewhere [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. The specific territory where the cooperative breeding attempts appeared is also a poplar plantation, named Can Rieró. Eighty five percent of standing dead trees in this territory was logged (summer and autumn 2004). In addition, in summer 2006 about 75% of the poplar plantation was completely logged, i.e. the remaining forest surface in Can Rieró was less than 3 ha.

The individuals in the study area were marked with colour rings since 2000 following the methodology described in [START_REF] Wiktander | Reproduction and survival in the Lesser Spotted Woodpecker. Effects of life history, mating system and age[END_REF], for details see also [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. The territories were visited periodically at least once per week from September to June. When nests were accessible (i.e. at a height lower than 8 m) a hole was cut to ring nestlings.

Results and discussion

Description of the cooperative breeding case (all dates in this section refer to 2007)

A non-ringed male (M, see table 1 for a description of each individual) was discovered in the Can Rieró Forest on 25 April excavating a nesting cavity from the inside. Later the same day the male was observed copulating with a ringed female (female A, FA) on a branch of the tree where the nesting cavity was being excavated. After the copulation the male and FA disappeared and a second female (female B, FB) was observed excavating inside the same cavity. On 27 April the male was observed excavating the nesting cavity and copulating with FA on a thin branch close to the cavity, in the same tree. After the copulation FA entered into the cavity and spent there nine minutes, then the male arrived to the cavity and FA flew off from it. The male entered inside the cavity and seconds later he was sticking the head out of the nest with an egg in its bill (see figure 1). After few seconds the male flew off and came back after several seconds without the egg, he entered in the nesting cavity again and continued with the excavation. Later in the morning also FB was observed inside the cavity, excavating (find a short sequence of pictures in the "Electronic supplementary material", figure I.A-H). That morning, each time FA was inside the cavity and FB was arriving to the nest, FA did not allow FB to enter. FB was only able to enter in the cavity for nest excavation when the male was inside. Sometimes FA was chasing FB to avoid her entrance inside the cavity. Similar behaviour was observed during several days. On 1 May in addition to the male, FA and FB, a third female (female D, FD) was observed entering inside the cavity. At the end of the incubation period FA disappeared and we failed, up to day, to relocate the bird. Nevertheless, none of the members of the cooperative breeding team, including the male, were calling insistently as it is a common reaction when a member of a (regular) monogamous pair disappeared due for instance to predation (own unpublished data). After hatching, mainly the male and FB were feeding nestlings, although we had several observations in which FD was also contributing. On 3 June the first chick was fledging. On 4 June still a nestling was inside the cavity fed by adults. A total of 44 hours of observation in 21 different days were used since 25 April until 4 June.

The nest was excavated in the main trunk of a dead Carolina Poplar (Populus x canadiensis) at a height of 10 m, with the nest entrance oriented to the east. The tree had a DBH of 30 cm.

Daytime contribution of the members of the cooperative breeding team in the different nesting stages

The daytime contribution of each member was quantified in the different breeding stages and results are presented in table 2. Male woodpeckers usually incubate and brood at night. For the purpose of comparison, however, we estimated the contribution of the members with daytime observations only. In the previously reported cooperative breeding cases in LSW poor information could be obtained for the early breeding stages (excavation, egg laying and incubation, [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. Therefore, this was the first time that the contribution of each team member in the early breeding stages was assessed (see table 2) for a cooperative breeding attempt in LSW. It is important to note that these two females (FA and FB) were already involved in a cooperative breeding case in 2005 [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF]. Also interesting that FA was involved in the three cooperative breeding cases (2005, 2006 and 2007). The dominant female (FA) was quite aggressive with FB during egg laying and incubation, this reduced the contribution of FB despite the latter insistently tried to cooperate. The contribution of FB was only possible if the male was in the cavity, given that no aggression was recorded between male and any of the females. The results of this behaviour are patent as presented in table 2, since FB contributed 6.1 and 26.5 % in the final excavation phase and during incubation, respectively, in contrast to the higher contribution of the dominant female FA (31.9 and 39.3 %, respectively). This would suggest that the gametic contribution of FA is important, as concluded by [START_REF] Mumme | Individual contributions to cooperative nest care in the Acorn Woodpecker[END_REF] in their detailed studies in the Acorn Woodpecker (Melanerpes formicivorus). The third female involved (FD) had a very small contribution at any stage, if different than zero then 3.2 and 3.0 % of contribution (see table 2) in the final excavation phase and during nestling feeding, respectively. Unfortunately, due to the disappearance of FA before egg hatching, and given the sporadic contribution of the third female involved (FD), we could not corroborate the trends previously reported during nestling feeding [START_REF] Romero | Two cooperative breeding cases in Lesser Spotted Woodpecker Dendrocopos minor[END_REF] in which the male showed a (compensatory) reduction in nestling feeding. The male contribution is about one third (34.2 %) during incubation, when the two females (FA and FB) were recorded actively cooperating. The male contribution to nestling feeding (54.3%) is close to the usual contribution of males in regular monogamous breeding pairs (i.e. 50%, Wiktander et al., 2000).

Egg destruction

In cooperative breeding species when different females contribute genes often egg destruction has been described due to a competition among females to assure a high percent of contribution of their own genes in the brood [START_REF] Mumme | Reproductive competition in the communal Acorn Woodpecker: sisters destroy each other's eggs[END_REF]. This competition is also understood as a way to synchronize the brood between (among) females [START_REF] Mumme | Reproductive competition in the communal Acorn Woodpecker: sisters destroy each other's eggs[END_REF][START_REF] Mcrae | Family values: costs and benefits of communal nesting in the moorhen[END_REF]. In this type of breeding attempts an important production of runt eggs have been detected [START_REF] Koenig | The determination of runt eggs in birds[END_REF]. Runt eggs are abnormally small and do not hatch [START_REF] Koenig | The determination of runt eggs in birds[END_REF].

Natural examples of egg destruction by a breeder male in woodpeckers have been also described in the polygynandrous Acorn Woodpecker (Melanerpes formicivorus), although they are rare [START_REF] Koenig | Opportunities of parentage and nest destruction in polygynandrous acorn woodpeckers, Melanerpes formicivorus[END_REF]. Reasons for such behaviour are linked to reduced or no possibilities to parent the egg(s) destroyed (Prof. Walter D. Koenig, personal communication). In other bird species such as Common Moorhen (Gallinula chloropus), known to be predominantly monogamous but exhibiting cases of polyandry and polygyny as well as cooperative breeding with communal nesting [START_REF] Mcrae | Family values: costs and benefits of communal nesting in the moorhen[END_REF], the male may inhibit each female's ability to interfere with the other female's reproduction (i.e., egg destruction;[START_REF] Mcrae | Family values: costs and benefits of communal nesting in the moorhen[END_REF].

Possible explanations to understand the reasons why the male removed the egg could be postulated based on previous knowledge on Acorn Woodpecker (Melanerpes formicivorus) (Prof. Walter D. Koenig, personal communication): (i) the male removed the egg under circumstances in which he was denied to access to the breeder female he felt he was entitled to; (ii) the male observed the female copulating with another male;

(iii) the female came to join the nest late in the season; (iv) the male took over the nest from another male.

Since the male was inside the cavity before FA arrived and given she spent 9 minutes inside, the most likely female laying the egg is FA. In addition several copulations were observed between the male and FA (see previous sections), discarding therefore hypothesis (i). The assessment of the rest of hypothesis, (ii)-(iv) is certainly difficult, and additional information regarding previous relationships of the male with females A, B (and D) and possibly other LSW individuals, would have been required to fully understand the motivations for such complex behaviour.

On the other hand, we would like to investigate if the removed egg was a runt egg. With this purpose, a photo of the male removing the egg from the nesting cavity was analysed (see figure 1). The averaged length of the bill of LSW males for this subspecies (i.e. D. minor buturlini, own unpublished data: 15.9 0.4 mm, [13.9-19.6], n=18) was used to estimate the egg maximum width as 15.6 mm. Due to the angle in which the photo was taken, together with the position of the egg, only the egg maximum width can be estimated with certain precision. This eliminates the possibility to obtain an accurate estimation of the volume, given that the maximum length of the egg can not be known.

We compared the estimated value with the average maximum width of LSW eggs for (i) our own unpublished measurements of an abandoned nest (14.1 0.4 mm; n=5 of the same clutch) and (ii) with the average found elsewhere (15 mm, [13-16], n=100, [START_REF] Cramp | Handbook of the Birds of Europe and the Middle East and North Africa[END_REF]. Therefore, our estimation would indicate that the egg was a normal egg and not a runt one. Direct measurement of all eggs of the clutch, including the one removed, will have been the more reliable way to discard a possible runt egg, given that runt eggs are not always evident to separate from normal ones [START_REF] Koenig | The determination of runt eggs in birds[END_REF]. In fact, [START_REF] Koenig | The determination of runt eggs in birds[END_REF] studied the variations in egg dimensions in case of runt eggs but he used volume rather than absolute variations in dimensions as the best way to separate runt eggs from normal ones.

Zusammenfassung

Figure 1 .

 1 Figure 1. Male removing an egg from the nest, presumably laid by FA. Arrows indicate the length of the bill and the egg maximum width (white and black, respectively). Average bill length measured for D. minor buturlini was used to estimate the egg maximum width.

Acknowledgements

We would like to thank the direct support of this research by the Catalan institution Fundació Caixa de Catalunya (Area Territori i Paisatge). The authors would like to thank Dr. Martjan Lammertink (Cornell Laboratory of Ornithology, Cornell University, Ithaca, NY, USA) for advice and help with regards to the course of the research; Prof.

Walter D. Koenig (Cornell Laboratory of Ornithology, Cornell University, Ithaca, NY, USA) for discussion and valuable hypothesis regarding the possible reasons behind the behaviour of the male during the cooperative breeding case. We would like to acknowledge as well the help of Peter Südbeck, Hans Winkler, Ulf Wiktander, Hugo Robles, Eva Rossmanith, Jose Luis Copete, Marta Pascual, Francesc Macià, Raül Aymí, Sergi Ricart and Ramon Sanz. All of the manipulations of birds performed during this study comply with the current laws of the country in which they were performed.


MD Jana Godau
email: jana.godau@medizin.uni-tuebingen.de

Nike Spinnler

Anne-Kathrin Wevers

Claudia Trenkwalder

MD Daniela Berg

Poor effect of guideline based treatment of restless legs syndrome in clinical practice

Background: Numerous randomized controlled trials prove efficacy of dopaminergic and nondopaminergic drugs in the treatment of restless legs syndrome (RLS). In contrast, epidemiological data demonstrate generally insufficient RLS treatment in clinical practice.

Objective: To prospectively assess the success of RLS treatment in the clinical setting and to evaluate potential demographical factors and comorbidities that may influence the response to therapy.

Methods: 100 patients with idiopathic RLS (40% had never received RLS specific treatment before) were examined at baseline and after 12 months. Recommendations for therapy according to RLS treatment guidelines of the German Neurological Society were given at baseline. Primary measures for the success of therapy were reduction of RLS symptoms (IRLS) and improvement of quality of life (RLS-QoL).

Results: No statistically significant improvement of IRLS and RLS-QoL could be detected after 12 months, neither in initially untreated nor in pre-treated patients. Poor treatment success, regarding improvement of RLS symptoms, quality of life and number of RLS related physician contacts, was related to the presence of neuropsychiatric comorbidity, i.e. somatoform disorders (prevalence 41%), chronic pain (32%), anxiety (20%) and major depression (16%).

Conclusion:

Success of guideline conform treatment of RLS appears to be rather poor in clinical practice. Neuropsychiatric comorbidity may be a target for interventions to improve the overall outcome.

Introduction

With an age-dependent prevalence of about 10% in Germany, restless legs syndrome (RLS) is one of the most common neurological disorders [START_REF] Berger | Iron metabolism and the risk of restless legs syndrome in an elderly general population--the MEMO-Study[END_REF] . A number of randomized controlled trials have proven good efficacy and tolerability of various dopaminergic, opiod or antiepileptic drugs for the treatment of RLS symptoms (for current review see [START_REF] Trenkwalder | Treatment of restless legs syndrome: an evidence-based review and implications for clinical practice[END_REF] ). Contrasting these findings, a number of epidemiological studies demonstrate a generally insufficient treatment of RLS symptoms in clinical practice [START_REF] Tison | Epidemiology of restless legs syndrome in French adults: a nationwide survey: the INSTANT Study[END_REF][START_REF] Allen | Restless legs syndrome prevalence and impact: REST general population study[END_REF][START_REF] Kushida | Clinical presentation, diagnosis, and quality of life issues in restless legs syndrome[END_REF] . Beside the lack of the correct diagnosis, one explanation for these seemingly contradictory data might be that there are a number of comorbidities, regularly co-occuring in RLS, which may potentially impair treatment success, such as psychiatric disorders like depression or anxiety [START_REF] Sevim | Correlation of anxiety and depression symptoms in patients with restless legs syndrome: a population based survey[END_REF][START_REF] Winkelmann | Anxietas tibiarum". Depression and anxiety disorders in patients with restless legs syndrome[END_REF][START_REF] Lee | Restless legs syndrome is associated with DSM-IV major depressive disorder and panic disorder in the community[END_REF][START_REF] Ulfberg | Prevalence of restless legs syndrome among men aged 18 to 64 years: an association with somatic disease and neuropsychiatric symptoms[END_REF][START_REF] Ulfberg | Comorbidity in restless legs syndrome among a sample of Swedish adults[END_REF] , pain disorders like fibromyalgia [START_REF] Shaver | Women's health issues with fibromyalgia syndrome[END_REF][START_REF] Stehlik | Restless legs syndrome is common among female patients with fibromyalgia[END_REF] and migraine [START_REF] Borek | Phenomenology of dreams in Parkinson's disease[END_REF][START_REF] Sabayan | Possible joint origin of restless leg syndrome (RLS) and migraine[END_REF] , iron deficiency as measured by low serum ferritin levels 1, 15, 16 ; excessive daytime sleepiness [START_REF] Ulfberg | Prevalence of restless legs syndrome among men aged 18 to 64 years: an association with somatic disease and neuropsychiatric symptoms[END_REF] or cardiovascular disorders [START_REF] Walters | Review of the relationship of restless legs syndrome and periodic limb movements in sleep to hypertension, heart disease, and stroke[END_REF] . Although a number of studies have been performed to elucidate factors that may be associated with RLS, to date no prospective data is available assessing and weighting all these factors in the clinical setting with regard to their impact on disease severity, quality of life and treatment success.

Here, we report the results of a 12-months prospective RLS benchmarking study aiming to assess (1) the effectiveness of guideline based RLS treatment on the improvement of RLS symptoms and quality of life apart from selected trial populations in a community based sample of 100 patients with idiopathic RLS and (2) to elucidate demographical factors and comorbidities which may influence the therapeutic outcome in the general clinical setting.

Patients and Methods

We included 100 consecutive patients with idiopathic RLS presenting for the first time in our outpatient department. Written informed consent was obtained from all patients, the study was approved by the local Ethics Committee. All patients had responded to a press article in the two main regional newspapers searching for participants in a one year observational study to assess the course of idiopathic RLS. In total, 186 subjects had responded to the article, however 86 were excluded either for not having RLS (n=13), for having symptomatic RLS (n=46) or for seeking advice but not wishing to participate in a study (n=27).

All patients underwent a structured interview assessing demographical factors, RLS and treatment related symptoms and comorbidity (see below), as well as a thorough clinical and neurological examination by a RLS experienced neurologist. RLS diagnosis was confirmed using the RLS diagnostic index (RLS-DI) [START_REF] Hogl | RLS assessment and sleep questionnaires in practice--lessons learned from Parkinson's disease[END_REF] . Severity of RLS symptoms was assessed using the International RLS Study Group Rating Scale (IRLS) [START_REF] Walters | Validation of the International Restless Legs Syndrome Study Group rating scale for restless legs syndrome[END_REF] , quality of life was measured applying the RLS Quality of Life Questionnaire (RLS-Qol) [START_REF] Abetz | Validation of the Restless Legs Syndrome Quality of Life questionnaire[END_REF] . Based on the RLS guidelines of the German Neurological Society recommendations for further treatment and follow-up were given to the patients and the treating primary care physician in written form (figure 1).

Patients were additionally educated about the background and course of the recommended treatment; expected improvements of RLS related symptoms and potential side effects in an open consultation of 30-60 minutes duration. After 12 months, a follow-up examination was performed including the same examinations as at baseline. Treatment and follow-up investigations between baseline and the 12 months follow up examination was performed as judged by the treating primary care physician.

Assessment of cormorbidities

In an open consultation all patients were asked for comorbidities. Additionally, diseases which are known to be related to RLS were directly asked for in a structured interview (see introduction). Major depression and anxiety disorder were diagnosed according to DSM-IV criteria, somatoform disorders based on the German version of the Patient Health Questionnaire (PHQ) [START_REF] Spitzer | Validation and utility of a self-report version of PRIME-MD: the PHQ primary care study. Primary Care Evaluation of Mental Disorders. Patient Health Questionnaire[END_REF] and chronic pain according to ICD-10 criteria. Excessive daytime sleepiness was diagnosed according to the the ICD-10 criteria for hypersomnia. Diagnosis of augmentation was based on the diagnostic criteria reported on the WASM consensus conference 2007 (Max-Planck-Criteria) [START_REF] Garcia-Borreguero | Diagnostic standards for dopaminergic augmentation of restless legs syndrome: report from a World Association of Sleep Medicine-International Restless Legs Syndrome Study Group consensus conference at the Max Planck Institute[END_REF] . Augmentation severity was assessed using the Augmentation severity rating scale (ASRS) [START_REF] Garcia-Borreguero | Validation of the Augmentation Severity Rating Scale (ASRS): a multicentric, prospective study with levodopa on restless legs syndrome[END_REF] , depressive symptoms were rated with Beck's depression inventory (BDI) [START_REF] Hautzinger | The Beck Depression Inventory in clinical practice[END_REF] , daytime sleepiness was assessed using Epworth Sleepiness Scale (ESS) [START_REF] Bloch | German version of the Epworth Sleepiness Scale[END_REF] .

Statistical analysis

For statistical analysis we used SPSS 17.0 (SPSS, Chicago, IL). As indicated in the introduction analysis was performed in two steps with regard to two different objectives.

(1) Primary outcome measures for analysis of treatment success after 12 months were changes on IRLS and RLS-Qol (in absolute values as well as in percentages). Paired t-test for IRLS and RLS-Qol was performed for the whole cohort, as well as separately for pre-treated and initially untreated patients.

(2)

In order to identify demographical and disease related factors which may influence the clinical outcome, principal component analysis was performed for data reduction of 25 variables including demographical factors, comorbidities, measures of baseline symptom severity and treatment complications (see supplementary material for details). Five main components were extracted which accounted for 82% of the total variance in all variables.

They are referred to as "age and somatic comorbidity", "neuropsychiatric comorbidity", "disease duration", "augmentation" and "baseline disease severity". Results were used as a basis for post-hoc subgroup analysis. Bonferoni correction for multiple comparisons was performed, results were assumed to be significant at p<0.05.

Results

Description of the cohort

An overview on demographics and outcome measures for the whole cohort as well as for the subgroups of pre-treated and untreated RLS patients is given in table 1. Comorbidities are listed in figure 2. At the time of the baseline examination 40% patients have never received RLS-specific treatment. Fourty-two per cent of the patients had a monotherapy, 18% had a combined therapy for RLS symptoms. Guideline based therapy could be found in 64% of all patients at baseline. More detailed information on the medication is given in table 2. In 14% of the patients, baseline control of RLS symptoms was classified as sufficient by the examining neurologist. In all patients guideline based recommendations for optimation of RLS medication were given.

(1) Clinical outcome

Treatment course

During the 12 months observational period, the mean number of physician contacts for RLS was 3.1 ± 4.2, 42% had been referred to a neurologist by the primary care physician and 12% had been further referred to a tertiary care facility. In the follow-up examination after 12 months, guideline based treatment was achieved in 71% of the cases. In only three of the other patients non-guideline based advice was given by the treating primary care physician, in all other cases the patients reported to explicitly not follow the guideline-based recommendations. Reasons for non-compliance were given as follows: intent to spare medication (n=6), extreme fear of deterioration of RLS symptoms when reducing levodopa or changing from levodopa to another drug (n=5), general lack of belief in Western medicine (n=4), being afraid of side effects after reading the package insert (n=4), being afraid of drug dependency (n=3), hope for spontaneous improvement of symptoms (n=2), no specific reason (n=2). Demographical data and baseline IRLS, RLS-QoL, ESS and BDI did not differ between compliant and non-compliant patients. 41.2% of the treated patients experienced side effects. 11.8% of the patients experienced more than one side effect. However, in 86.1% side effects were rated as mild and did not lead to any change of the medication. The following side effects were observed: augmentation (24%), sleepiness (14.7%), nausea (13.2%), dizziness (8.8%), nocturnal compulsive eating (7.4%), headache (5.9%), vivid dreams (2.9%), leg edema (2.9%) and erectile dysfunction (1.5%).

Treatment outcome

As shown in table 1, IRLS and RLS-QoL did not improve after 12 months, neither regarding the whole cohort, nor in the subgroups of pre-treated patients, untreated patients, patients in whom guideline based treatment was achieved or non-compliant patients (p=0.13-0.32).

Contrasting these findings, 91% of the patients receiving dopaminergic drugs, however, reported very good effectiveness of the applied drug in the reduction of the key RLS symptoms. Furthermore, treatment was rated satisfactory by the examiner in 40% of the cases, compared to 14% at baseline (p=0.002).

Regarding secondary outcome measures, ESS was unchanged after 12 months in the whole cohort (p=0.41) as well as in all subgroups (p=0.30-0.87). BDI improved significantly in the whole cohort (p=0.001), as well as in the subgroup of initially untreated patients (p=0.005), but not in any of the other subgroups (p=0.24-0.68).

(2) Predicitive factors

As shown above neither initial treatment status nor compliance affected the therapeutic outcome. For assessment of other predictors of treatment success correlation analysis with regard to demographic factors, comorbidities, medication and side effects was performed including the whole cohort. No single factor was related to the improvement of IRLS or RLS-QoL after 12 months (p=0.19-0.78). Principal component analysis for data reduction resulted in the extraction of five principal components as described above which were not correlated to each other. From these five principal components only "neuropsychiatric comorbidity" was related to the therapeutic outcome. Higher factor scores on this component are coherent with a higher number of different psychiatric and psychosomatic symptoms.

Based on these data, in a posthoc analysis we compared patients affected by neuropsychiatric comorbidity (NP+; n=64) and those free of neuropsychiatric comorbidity (NP-; n=36). There was no difference between both groups regarding demographical data (p=0.13-0.58) and baseline IRLS, RLS-QoL, ESS and BDI (p=0.08-0.58; table 1). During the 12 months observational period, NP+ patients had significantly more physician contacts for RLS than NP-patients (p<0.001) and were more often referred to specialists (p=0.003). After 12 months, the NP-showed no improvements on IRLS (paired t-test; p=0.35) and RLS-QoL (p=0.43), whereas the NP-group improved on both scales (p=0.005 and 0.008, respectively, see also figure 3). Neither group showed improvement on the BDI or ESS (p=0.13-0.69).

Discussion

This 12-months benchmarking study was set out to evaluate success of guideline based RLS treatment in the clinical setting and further to illuminate factors which may influence the therapeutic outcome. Surprisingly, in this large cohort of 100 patients with idiopathic RLS neither symptom severity nor quality of life improved after 12 months of guideline based RLS treatment. This finding contrasts evidence from pharmacological studies demonstrating efficacy of various dopaminergic and non-dopaminergic drugs in the reduction of RLS symptoms and in the improvement of quality of life. 2 However, it is line with data from large population based studies showing that in the general population RLS is rarely diagnosed and often insufficiently treated. [START_REF] Tison | Epidemiology of restless legs syndrome in French adults: a nationwide survey: the INSTANT Study[END_REF][START_REF] Allen | Restless legs syndrome prevalence and impact: REST general population study[END_REF][START_REF] Kushida | Clinical presentation, diagnosis, and quality of life issues in restless legs syndrome[END_REF] It has been stated that awareness and training of the treating physicians may be one of the most important issues to explain this apparent discrepancy. This is, however, not supported by our data demonstrating that (1) treatment according to the current therapy guidelines was achieved in 64% (baseline) and 71% (follow-up) of the patients, that (2) the vast majority of the patients not receiving guideline-based treatment was non-compliant despite good clinical advice by different physicians and that (3) compliance had no significant impact on the treatment outcome, anyway. Also demographical factors such as age, gender, age at symptom onset and disease duration as well as somatic comorbidities, specific drugs and side effects could be excluded as main causes for the poor treatment outcome in this cohort. Finally, even patients who received RLS medication for the first time did not significantly improve regarding RLS symptoms and quality of life. However, it needs to be considered that the expected striking effect of initiation of drug treatment may have not been displayed in our study because of the relatively long observational interval of 12 months. This emphasizes the need for long-term controlled studies to assess effectiveness of drug therapies in RLS.

According to our data, neuropsychiatric comorbidity is a major issue in the management of RLS patients. Neuropsychiatric comorbidity including anxiety, depression, chronic pain and various somatoform disorders is common in idiopathic RLS, affecting 64% of the patients in our cohort. As shown in figure 3, only a minority of these patients achieved improvement of RLS symptoms or quality of life, compared to about 80% of RLS patients without apparent neuropsychiatric comorbidity. Furthermore, neuropsychiatric comorbidity was the main predictor for a high number of RLS related physician contacts during the observational period. One reason for both, the poor outcome on objective scales and the high number of RLS related physician contacts may be that patients may not be capable to differentiate the key RLS symptoms from accompanying neuropsychiatric symptoms such as chronic pain and depression. These, however, obviously do cause a high degree of suffering, which is not expected to change during RLS treatment, but might still be reflected in the symptom severity and quality of life scales. This assumption is supported by the finding that despite the poor outcome on the scales, still 91% of all patients reported excellent effectiveness of their RLS drugs. This interaction between neuropsychiatric comorbidity and improvement of RLS symptoms may also explain the contrasting results between pharmacological and epidemiological studies discussed above, since patients with predominant neuropsychiatric comorbidity were generally excluded from pharmacological trials. However, even when regarding only RLS patients without apparent neuropsychiatric comorbidity, the outcome in our study still appears poor with a mean improvement of IRLS of only 4.5 points and 3.8 points on RLS-QoL, although the majority did benefit from therapy.

Limitations

One may argue that the cohort examined in this study is a cohort of a tertiary referral center and might therefore be more severely affected by RLS and more difficult to treat than idiopathic RLS patients in the general population. However, to overcome this we recruited the patients from the general population via newspaper articles and did not include patients who had been referred to our clinic for diagnosis and treatment. Moreover, baseline symptom severity as measured by IRLS, RLS-QoL and distribution of age, sex and disease duration are in line with the description in population based cross-sectional studies, suggesting that our cohort does represent a normal cohort of idiopathic RLS patients. [START_REF] Winkelmann | Clinical characteristics and frequency of the hereditary restless legs syndrome in a population of 300 patients[END_REF] One may further argue that the cohort we examined was mixed regarding medication, what may bias the treatment outcome. From clinical experience, the greatest differences in the outcome would have been expected between pre-treated and initially untreated patients. The cohort examined is large enough to allow for differentiation of these two groups (n=60 vs. n=40, respectively); no differences in treatment success could be found comparing both groups. Moreover, this study was designed to monitor and quantify the treatment success in guideline based RLS treatment. All drugs applied according to the guidelines have already shown efficacy in the reduction of RLS symptoms. The decision on a specific drug in clinical practice is individual and complex as it takes into account a number of factors such as expected side effects, comorbidity, concomitant medication, timely distribution of symptoms or even patient's preference. Although this may cause some bias in the evaluation of treatment success, and the present study therefore does not fulfil the criteria normally applied to pharmacological trials regarding inter-individual comparability of the data, the rather large sample size (n=100) in this cohort should ensure that data is not biased to one specific drug.

Finally, as described above there is no evidence in our data for a drug-specific positive or negative effect on the treatment success.

Conclusion

The findings in this RLS benchmarking study demonstrate for the first time that the success of RLS therapy in the clinical setting stays far behind the efficacy of drug therapy in pharmacological trials, although the medication seems to work equally well (91% excellent responses). Neuropsychiatric comorbidity including depression, anxiety, chronic pain and somatoform disorders seems to be a promising target for improvement of RLS treatment in clinical practice, since it does not only affect the majority of patients (64% in our cohort), but also appears to be the main predictor for frequent physician contacts and for poor treatment success most likely due to interfering neuropsychiatric symptoms. Therefore, careful consideration should be given to the diagnosis and treatment of neuropsychiatric comorbidities along with RLS in clinical practice. Future long term and controlled studies will have to address if and how supportive treatment strategies such as psychotherapy and behavioural treatment either as single or as add-on therapy may contribute to the success of RLS therapy. 27

Figure 1 .

 1 Figure 1. Guideline based therapy of idiopathic RLS according to the guidelines of the

Figure 2 .

 2 Figure 2. Comorbidities in percentage of the whole cohort at baseline.

Figure 3 .

 3 Figure 3. Impact of neuropsychiatric disease on treatment success.

Table 1 . Overview on the clinical data of baseline (BL) and follow-up (FU).

 1

	NP-: Subgroup of patients free of neuropsychiatric comorbidity, NP+ : subgroup of patients with
	neuropsychiatric comorbidities

Table 2 . Medication at baseline and follow-up.

 2

			Baseline	12 months Follow-Up
		N	Dose/day	N	Dose/day
	Untreated	40	n.a.	21	n.a.
	Levodopa	42	50-1200 mg	36	50-1000 mg
	Pramipexol	7	0,18 -1,4 mg	24	0,09-2,1 mg
	Ropinirol	4	2-4 mg	16	0,25-5 mg
	Rotigotine	1	4 mg	12	1-6 mg
	Cabergoline	4	2-4 mg	0	n.a.
	Tilidin	2	100-150 mg	2	100-200 mg
	Gabapentin	6	600-1800 mg	6	1200-1800 mg
	In accordance with guidelines		64%		71%

JG, NS and AKW have nothing to disclose. CT has received honoraria for lectures or clinical advice from Boehringer Ingelheim, GSK, UCB, Novartis and Solvay. DB has received honoraria for lectures from UCB, GSK, TEVA and Lundbeck and for serving on scientific advisory boards for Novartis, UCB, GSK and TEVA. DB has received grants from the Michael J. Fox Foundation, the BMBF, Janssen Pharmaceuticals, TEVA Pharma GmbH and the German Parkinson's disease Association.

Contributions

JG and DB designed the study. JG, NS and AKW were responsible for data acquisition and analysis. All authors contributed to the interpretation of the data. JG wrote up the manuscript, all authors contributed to the revision of the manuscript. DB supervised the study.