influence of process temperature on phase formation … · aisi 420 martensitic stainless steel...

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INFLUENCE OF PROCESS TEMPERATURE ON PHASE FORMATION IN PLASMA NITRIDED AISI 420 STEEL C.J. Scheuer a,b , F.I. Zanetti a , R.P. Cardoso a , S.F. Brunatto a a Plasma Assisted Manufacturing Technology & Powder Metallurgy Group, Departamento de Engenharia Mecânica, UFPR, 81531990, Curitiba, PR, Brazil b Colégio Técnico Industrial de Santa Maria, UFSM, 97105-900, Santa Maria, RS, Brazil AISI 420 martensitic stainless steel samples were dc-plasma nitrided aiming to study the relationship between treatment temperature and the phases formed. Treatments were carried out applying a gas mixture composed by 70% N2 + 20% H2 + 10% Ar, for fixed time of 4 h, and at temperatures ranging from 200 to 600° C. The treated samples were characterized by optical microscopy, X-ray diffraction and hardness measurements (surface and profile). At extra-lowtemperatures conditions (200 and 250 °C), it was observed only the formation of N- expanded martensite phase (N). For low temperatures (300 to 400 °C), it was verified the occurrence of N and -Fe2-3N phases. Chromium nitrides phase (CrN and Cr2N), start to precipitate at 450 °C, with increased precipitation intensity with temperature rise. From 500 °C, besides the already mentioned phases, the occurrence of '-Fe4N iron nitride was remarked. Surface hardness values shows an increasing with temperature growth from 200 to 450 °C, decreasing for 500 °C, and stabilizing to 550 and 600 °C, which was credited to chromium nitride precipitation occurrence. Profile hardness measurements indicated a planar nitriding interface grown for samples treated at high temperatures (above 450 °C), and a diffuse profile for low-temperature nitrided samples (below 400 °C), pointing out the existence of dissimilar diffusion mechanism for low and high temperatures nitriding. Finally, the nitriding layer growth as a function of treatment temperature follows the Arrhenius law, with activation energies of 64 and 119 kJ mol 1 for low and high temperatures, respectively. Keywords: plasma nitriding, nitriding kinetics, diffusion mechanism, martensitic stainless steel, nitrogen expanded martensite. INTRODUCTION Plasma-assisted nitriding techniques are well-established surface engineering processes for improving surface properties of martensitic stainless steel (MSS) [1-47]. Plasma nitrided techniques like direct current d.c. [1-36], plasma immersion ion implantation PI 3 [36-43], active screen plasma nitriding ASPN [44-46], and radio frequency r.f. [47], have been successfully applied for this purpose. To increase mechanical and tribological properties of MSS, plasma nitriding was initially carried out in high temperature conditions (HTPN) [1-3,5,9,10,13,23-29,37,43], leading to a drop in corrosion resistance due to chromium nitride (CrN and Cr2N) formation at temperatures above 450 °C. To solve this problem, MSS plasma nitriding was therefore carried out at temperatures below to 400 °C (LTPN) [2,4,6-12,14- 22,24,25,29-31,33-36,38-48], making possible to produce hardened surfaces with 22º CBECiMat - Congresso Brasileiro de Engenharia e Ciência dos Materiais 06 a 10 de Novembro de 2016, Natal, RN, Brasil 10138

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Page 1: INFLUENCE OF PROCESS TEMPERATURE ON PHASE FORMATION … · AISI 420 martensitic stainless steel samples were dc-plasma nitrided aiming to study the relationship between treatment

INFLUENCE OF PROCESS TEMPERATURE ON PHASE FORMATION IN

PLASMA NITRIDED AISI 420 STEEL

C.J. Scheuera,b, F.I. Zanettia, R.P. Cardosoa, S.F. Brunattoa

a Plasma Assisted Manufacturing Technology & Powder Metallurgy Group, Departamento de

Engenharia Mecânica, UFPR, 81531‐990, Curitiba, PR, Brazil b Colégio Técnico Industrial de Santa Maria, UFSM, 97105-900, Santa Maria, RS, Brazil

AISI 420 martensitic stainless steel samples were dc-plasma nitrided aiming to

study the relationship between treatment temperature and the phases formed.

Treatments were carried out applying a gas mixture composed by

70% N2 + 20% H2 + 10% Ar, for fixed time of 4 h, and at temperatures ranging from

200 to 600° C. The treated samples were characterized by optical microscopy, X-ray

diffraction and hardness measurements (surface and profile). At “extra-low”

temperatures conditions (200 and 250 °C), it was observed only the formation of N-

expanded martensite phase (’N). For low temperatures (300 to 400 °C), it was verified

the occurrence of ’N and -Fe2-3N phases. Chromium nitrides phase (CrN and Cr2N),

start to precipitate at 450 °C, with increased precipitation intensity with temperature

rise. From 500 °C, besides the already mentioned phases, the occurrence of '-Fe4N

iron nitride was remarked. Surface hardness values shows an increasing with

temperature growth from 200 to 450 °C, decreasing for 500 °C, and stabilizing to 550

and 600 °C, which was credited to chromium nitride precipitation occurrence. Profile

hardness measurements indicated a planar nitriding interface grown for samples

treated at high temperatures (above 450 °C), and a diffuse profile for low-temperature

nitrided samples (below 400 °C), pointing out the existence of dissimilar diffusion

mechanism for low and high temperatures nitriding. Finally, the nitriding layer growth

as a function of treatment temperature follows the Arrhenius law, with activation

energies of 64 and 119 kJ mol−1 for low and high temperatures, respectively.

Keywords: plasma nitriding, nitriding kinetics, diffusion mechanism, martensitic

stainless steel, nitrogen expanded martensite.

INTRODUCTION

Plasma-assisted nitriding techniques are well-established surface engineering

processes for improving surface properties of martensitic stainless steel (MSS) [1-47].

Plasma nitrided techniques like direct current – d.c. [1-36], plasma immersion ion

implantation – PI3 [36-43], active screen plasma nitriding – ASPN [44-46], and radio

frequency – r.f. [47], have been successfully applied for this purpose.

To increase mechanical and tribological properties of MSS, plasma nitriding was

initially carried out in high temperature conditions (HTPN) [1-3,5,9,10,13,23-29,37,43],

leading to a drop in corrosion resistance due to chromium nitride (CrN and Cr2N)

formation at temperatures above 450 °C. To solve this problem, MSS plasma nitriding

was therefore carried out at temperatures below to 400 °C (LTPN) [2,4,6-12,14-

22,24,25,29-31,33-36,38-48], making possible to produce hardened surfaces with

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improved corrosion resistance compared to the untreated MSS. This treatment

temperature is high enough to activate nitrogen interstitial atom diffusion, and low to

avoid chromium substitutional atom diffusion, keeping unaltered the chromium content

in solid solution [17]. Under these conditions, the nitrogen surface alloying promotes a

supersaturation of tetragonal body-centered (tbc) cell interstices of the original

martensitic matrix, promoting the formation of the phase named by Kim et al. [47] as

nitrogen expanded martensite (’N).

Therefore, an understanding of the nitriding parameters effect on nitrided layer

structure and on nitrogen diffusion mechanism through the tbc structure is important for

MSS treatment optimization. Among the process parameters, the treatment temperature

is the main factor controlling the nitrogen diffusion during plasma nitriding. The

choosing of suitable treatment temperature allows obtaining the best performance of the

treated material under corrosion, wear and fatigue request, as well as determining

minimum process duration, which is an important economic factor.

Concerning the nitriding temperature influence on materials surface

features/performance, a hardened compound layer (-Fe2-3N, -Fe4N and CrN phases)

constitutes the surface microstructure of HTPN martensitic stainless steels [3,5,7,8,13,

23,28,31,35,42,44,46]. According some authors [1,2,21], for high temperature and long

times nitriding, the resultant intense nitride precipitation causes the treated layer

embrittlement, becoming worse the tribological properties. Similarly, these treatment

conditions promotes the nitrided layer sensitization, reducing the corrosion resistance of

treated surface [4,9,10,12,29,38,41,43]. In contrast, for LTPN conditions a precipitation

free N-expanded martensite layer with an improved wear [2,6,9,11,18,21,30], fatigue

[11] and corrosion [4,9,10,12,18,29,38,41,43] resistance is formed.

As demonstrated above, there are many published studies (with different

achievement goals) on plasma nitriding of martensitic stainless steel. According the

bibliographic survey carried out, the studied treatment temperatures covers the range

between 300 to 566°C for d.c. plasma nitrided technique. In this work, considering that

the temperature is the main process parameter controlling the nitrogen diffusion during

nitriding treatment, a study on the microstructural characteristics and hardness of

AISI 420 martensitic stainless steel samples treated under temperatures between 200 to

600 °C at 4 h are reported. The influence of nitrided layers phase constituents, as a

result of applied treatment temperature, on the nitrogen diffusion mechanism and

kinetics were also analyzed and discussed.

EXPERIMENTAL PROCEDURE

Cylindrical samples of 10 mm in height and 9.5 mm in diameter were cut from

an AISI 420 steel commercial rod (composition obtained by X-ray fluorescence, in

wt.%: 0.17% C, 0.70% Mn, 0.50% Si, 12.2% Cr, 0.23% P, 0.03% S, and Fe balance).

Samples were austenitized at 1050 °C for 0.5 h and air-cooled. After heat treatment,

samples were ground using SiC sandpaper from 120 to 1200 grade and polished using

1 μm Al2O3 abrasive suspension. Finally, samples were alcohol cleaned in ultrasonic

bath, dried in a heated airflow, and then introduced into the discharge chamber.

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Nitriding treatments were carried out in a conventional plasma apparatus, which

is illustrated and described in detail on [17]. Samples were placed on the cathode of this

system, which was negatively biased at 600 V. Prior to nitriding treatments, specimens

were plasma sputter-cleaned in a gas mixture of 80% H2+20% Ar, under a pressure of

400 Pa, at 300 °C for 0.5 h, aiming to remove the native surface oxide layer. Plasma

nitriding treatments were carried out using a gas mixture composed of

70% N2 + 20% H2 + 10% Ar, in volume. The total gas flow rate and pressure were fixed

at 3.34 × 10−6 Nm3s−1 and 400 Pa, respectively. Samples were nitrided at 200, 250, 300,

350, 400, 450, 500, 550 and 600 °C, for a constant treatment time of 4 h. After

treatment, the nitrided samples were cooled under continuous Ar-H2 flow.

After nitriding treated samples were cross-sectioned and prepared for

microstructural analysis by conventional metallographic procedure. After polishing, the

samples were etched using Vilella’s reagent. Samples were analyzed by an Olympus

BX51M optical microscope, and the thickness of the observed nitrided layers was

determined by taking the mean of ten measurements using optical microscopy images.

The identification of the phases present in the nitrided layers was carried out by X­ray

diffractometry (XRD) technique, using a Shimadzu XDR7000 X­ray diffractometer

with a Cu Kα X­ray tube in the Bragg-Brentano configuration. Surface and profile

hardness measurements were obtained using a Shimadzu Micro Hardness Tester

HMV­2T, applying a load of 10 gf for a peak-load contact of 15 s.

RESULTS AND DISCUSSION

The cross-section optical micrographs of AISI 420 martensitic stainless steel

samples plasma nitrided at 4 h for temperatures ranging from 200 to 600 °C are

presented in Figure 1. For LTPN samples (below to 400 °C), a white-aspect nitrided

layer can be observed on samples surface, and no sharp interface between this and the

martensite bulk is noted. The used chemical reagent did not attack the materials surface

region, whereas the bulk was etched. This results show that the nitrided layer presents a

higher resistance to Vilella’s reagent etchant when compared to the MSS substrate. In

contrast, for HTPN samples (from 450 °C), dark-aspect nitrided layers are noticed,

indicating the occurrence of treated surface sensitization (which will be confirmed by

the XRD patterns showed following). Likewise, for the HTPN conditions, two different

surface regions can be distinguished previously the unnitrided bulk: a dark near surface

precipitation zone, followed by a white one. Finally, an incipient sensitization along the

grain boundaries close to the surface is observed for samples nitrided at 400 °C,

evidencing that Cr nitride precipitation starts at this temperature for 4 h treatment.

It is important to mention that, from the best knowledge of the author, there is

not available work reporting the ’N phase formation for temperatures below to 300 °C.

Therefore, this result opens up a new perspective to the MSS d.c. low-temperature

plasma assisted treatment subject: the possibility of obtained the ’N in “extra-low”

temperatures plasma nitriding (ELTPN). In this regard, a further study is required in

order to investigate the characteristics and properties of 'N phase obtained under these

conditions.

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Figure 1. Cross-section optical micrographs of plasma nitrided AISI 420 martensitic stainless samples.

Figure 2 shows the influence of treatment temperature on nitriding layer

thickness (continuous grey line). It can be noticed that the layer thickness increases with

nitriding temperature, which may be attributed to the increase of interstitial elements

diffusivity with increasing treatment temperature [48]. This behaviour is expected for

thermally activated treatments controlled by atomic diffusion. It also appears that the

nitrided layers thicknesses grow up at a faster acceleration rate with temperature

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increasing beyond to 450 °C. This can be explained by the increment on activation

energy for nitrogen diffusion in high temperatures conditions, as discussed below.

Likewise, Figure 2 shows the Arrhenius plot of the nitrided layer thickness (red

dashed line). In this plot, the slope of the straight line gives the activation energy for the

diffusion process. The two-segment data linearity suggests that different nitrogen

diffusion mechanism occurs for low and high temperatures nitriding. As illustrated and

discussed by Cardoso [17], considering that the nitrogen transport during the nitriding

process can occurs by volume (lattice) diffusion and by high diffusivity paths (e.g. grain

boundaries and dislocations), the role of these diffusion mechanisms is related to the

treatment temperature. As diffusion by high diffusivity paths present lower activation

energy than volume diffusion, the contribution of high diffusivity paths is expected to

be remarkable principally at low-temperature. However, for high temperature the main

contribution comes from volume diffusion, given that at sufficient high temperatures,

defects annihilation and grain growth reducing the high diffusivity path density, and so

its relative contribution [17]. The related author showed that between these two extreme

cases it appears a temperature range where both diffusion mechanisms are significant,

being related to the transition range, between the LTPN and HTPN process (in this

work, it is believed that this range is between 400 to 450 °C). Finally, the calculated

activation energies for low and high temperatures nitriding of AISI 420 MSS were 64

and 119 kJ mol-1, being in accordance with the values previous showed by [5] and [32]

(125 and 136 kJ mol-1, respectively) for HTPN, and by [17] (60 kJ mol-1) for LTPN.

Figure 2. (Continuous grey line) evolution of nitride layer thickness with treatment temperature; and (red

dashed line) Arrhenius plot for the nitrided layer thickness. (QdH and QdL are the activation energy for

layer growth at high and low temperatures, respectively).

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Figure 3 shows the X-ray diffraction patterns of untreated (as-quenched) and

carburized samples. The untreated sample presents three peaks (within accomplished

scan interval) all attributed to the martensite phase (α′). After treatment, a gradual

change in the phase’s constituents of nitrided layer can be observed on the XRD data,

which are highly dependent on the treatment temperature. It is found that in extra-low

temperature conditions (200 and 250 °C) (Figure 3b), peaks of the substrate (martensite)

are observable together with the nitrogen expanded martensite supersaturated phase

(’N). As already widely discussed in the literature [4,6,9-11,13,14,16-22,28-30,32,38-

40,42-47], the ’N phase formation is evidenced by the enlargement and displacement

to lower angles of the original martensite peaks (the anisotropic diffusivity of interstitial

solute [52] and decreasing of stacking faults energy promoted by the presence of

nitrogen [53], are able to create elastic distortions on the crystalline lattice, whose effect

yields the broadening of the diffracted peaks). For such treatment conditions (extra-low

temperatures) the ’N peak is less evident and appears as an asymmetry of the ’ peak.

It was not verified the occurrence of peaks relating to the chromium nitride phases,

which was expected given the low diffusivity of chromium at these temperatures.

For low-temperatures conditions (300 to 400 °C) (Figure 3c), the higher nitrogen

diffusion (considering the greater diffusion coefficient) avoids the -Fe2-3N phase

formation and a further expansion of the original martensitic phase. It is worth to

emphasize that the peaks position of expanded martensite phases are continuously

changed according to the treatment temperature, being this change credited to the

increase in the retained nitrogen on octahedral sites of the tbc structure lattice [32].

According to Bragg’s law these results indicate that lattice parameter is increasing

gradually with the treatment temperature. It is important to mention that although it has

been observed an incipient sensitization for the sample treated at 400 °C (Figure 1), no

chromium nitride peak was observed on XRD pattern of this condition. Thus, it is

believed that the fraction of chromium nitrides precipitates is so small for this nitriding

condition, that the employed technique does not identifies their presence on nitrided

layer.

At high temperatures condition (from 450 °C), the increasing chromium mobility

induces precipitation of chromium nitride phases. As observed in (Figure 3d) at 450 °C,

besides the aforementioned phases, there is the occurrence of CrN, Cr2N (confirming

the sensitization occurrence indicated in Figure 1) and '-Fe4N compounds. With

increasing treatment temperature (500 to 600 °C), the ’N peaks disappear (phase

decomposition as a consequence of Cr nitride formation, consuming nitrogen of the

expanded phase), giving rise to a XRD patterns constituted only by iron (-Fe2-3N and

'-Fe4N) and chromium (CrN and Cr2N) nitride phases. According Wang et al. [30],

from 450 °C the equilibrium limit solubility of nitrogen in martensitic structure is overly

exceeded and then Cr nitride precipitation occurs. In such treatments conditions (above

450 °C) the formation of stable CrN and Cr2N phases is favored owing its more

negative enthalpy formation, and the great chromium mobility allowing segregation

from the martensitic matrix and precipitating as Cr and Fe nitrides [38,43]

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Figure 3. X-ray diffraction patterns for untreated and plasma nitrided AISI 420 stainless steel samples.

The evolution of the surface hardness as a function of the nitrided temperature is

presented in Figure 4. Measurements were performed on the nitrided surface (samples

top) and untreated (samples bottom). The slight hardness increase verified for the

sample treated at 200 to 300 °C is probably due to the small thickness of the nitrided

layer (indentation penetration depth on the order or higher than the layer thickness), as a

result of the low thermal activation, and the relative low nitrogen diffusivity. The

highest hardness values were obtained for samples nitrided at 450 °C. The surface

hardness increase with respect to the bulk material, in this case, would be related to the

increase of the nitrided layer thickness and the nitrogen addition into solid solution at

the martensite lattice, allied to the presence of ε-Fe2-3N phase in the treated layer. On

the other hand, the hardness decrease evidenced from 500 °C would be directly related

to the strong chromium nitride precipitation, which would reduce the nitrogen content in

solid solution and, consequently, the nitrogen expanded martensite (α′N) hardness. It is

an evidence that the α′N has an important contribution to the final surface hardness of

the treated surface [6,9,11,16,17,20,24,30,44,32,47]. Furthermore, a decrease of the

sample bottom hardness was verified, which is a direct result of substrate

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overtempering. Finally, by confronting the sample top and bottom hardness values, it

can be verified a steady increase on treated samples hardness with temperature

increasing from 200 to 450 °C (about 5 to 80%, respectively), and stabilizing the

hardness increasing around 75% for samples nitrided from 500 to 600 °C. These results

showed that the nitriding strengthening overcomes the tempering softening effect,

evidencing the effectiveness of the plasma nitriding treatment of AISI 420 steel.

Figure 4. Hardness of untreated (non-exposed to the plasma) and nitrided (exposed to the plasma) surface

of AISI 420 martensitic stainless steel samples.

The microhardness-depth profiles for nitrided samples are presented in Figure 5.

Firstly, it appears that the hardening depth increases with nitriding temperature. This

result can be attributed to the increase in diffusivity of interstitial elements with

increasing treatment temperature [48]. Likewise, it can be noted that the hardness of

samples surface region increases for nitriding temperatures up to 450 °C and, on the

other hand, reduces and stabilizes at values around 1270 to 1370 HV for samples treated

at 500 to 600 °C. This behaviour is similar to that seen in Figure 4 for surface hardness

results, and the explanation is the same presented above (equivalent result was reported

by [3,7,9,10], being also justified by intense chromium nitrides precipitation). The

chromium nitride precipitation consumes nitrogen from the 'N phase, and

consequently, the martensite lattice nitrogen-expansion is decreased. As the

precipitation is dependent on treatment temperature and the nitrogen content along the

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concentration gradient, it can be expected a stronger precipitation next to the surface, as

can be seen in Figure 1. As expected, the lower hardness values and the smaller

hardening depth for samples treated at 200 to 300 °C are in agreement with the smaller

nitrogen diffusivity. An difference on hardness profile for low and high temperature

plasma nitriding can be considered: for LTPN condition (up to 400 °C) the

microhardness of nitrided layer reduces gradually with depth until reaches the bulk

hardness; in contrast, for HTPN condition (from 450 °C), a well-defined planar

interface between the nitrided layer and the bulk is observed, after a maximum hardness

horizontal plateau. This result confirms the different diffusion mechanism for the nitride

layer growth at low and high nitriding temperature condition, as previously discussed

for Figure 2.

As discussed by [49-51], in the presence of substitutional alloying elements that

presenting a strong chemical affinity with nitrogen, the kinetics of nitrided layer grown

is not only proportional to nitrogen diffusion coefficient and treatment time, but should

be consider the thermodynamic interaction between nitrogen and nitride forming

elements (the chromium, in the case of this work). Thereby, Jung [51] showed that the

nitrogen concentration profile depends on content of the nitride forming element, being

that for an strong interaction type the compositional profile is flattened (similar to those

obtained for HTPN hardness profile on Figure 5); and for an intermediate interaction

type, the composition profile is decrescent (similar to those obtained for LTPN hardness

profile on Figure 5). Considering that for chromium contents higher than 9.0 wt.%, a

strong type nitrogen interaction is observed and, for lower levels, an intermediate

interaction occurs (thus, for AISI 420 MSS a strong interaction occurs between the Cr-

N system and a flattened nitrogen profile would be expected after plasma nitriding

treatment application). However, it was verified by Pinedo and Magnabosco [38] that

the nitrogen composition profile depends also of the treatment temperature: for HTPN

condition the profile follows the described features for strong type Cr-N interation;

however, to the LTPN conditions the nitrided layer formation are quite different.

According to authors, at these treatments temperatures conditions, the kinetic

predominated over the thermodynamic, and the nitrided layer growth mechanism is

modified. Under these circumstances, the chromium diffusivity through the material

structure is limited, which prevents that the thermodynamic Cr-N interaction factor can

prevail, and so the nitrided layer growth show an intermediate interaction behavior [38].

Thus, the hardness mechanism under HTPN conditions is the formation of a thin and

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continuous chromium nitride layer, whereas for LTPN the hardness mechanism occurs

due the iron nitride and ’N phase formation [38].

Considering the nitrided material surface performance, the gradually reduced

profile has advantages with respect to planar interface due the possibility of

delamination under sliding contact condition, as appointed by [1]. Ultimately, the

change of the bulk hardness is in agreement with that presented in Figure 4, for the

hardness of the untreated surface, confirming the different tempering effect verified for

each treatment temperature.

Figure 5. Microhardness profiles of plasma nitrided AISI 420 martensitic stainless steel samples.

CONCLUSION

A comprehensive study was carried out aiming to evaluate the relationship

between nitriding temperature and the phases formed on AISI 420 martensitic stainless

steel. The main conclusions of the work can be listed as follows:

A single nitrogen expanded martensite layer can be produced in extra-low

nitriding temperatures conditions (200 and 250 °C). At low-temperatures (300 to

400 °C) a layer composed by nitrogen expanded martensite and -Fe2-3N iron

carbide is obtained. For high temperature nitriding (450 to 600 °C), an intense

iron (-Fe2-3N and '-Fe4N) and chromium (Cr2N and CrN) nitrides occurs,

promoting the nitrided layer sensitization.

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Dissimilar diffusion mechanism prevailing according to the adopted nitriding

temperature: at extra-low and low temperatures conditions, the contribution of

high diffusivity paths on nitrogen diffusion is remarkable. For high temperature,

the main mechanism controlling the nitrogen transport is the volume diffusion.

Hardness increases with nitriding temperature increasing up to 450°C, undergoes

reduction to 500 °C, and remains continuous increasing up the temperature to

600 °C. At extra-low temperature conditions, surface hardening occurs by

nitrogen expanded martensite formation. For low-temperatures, hardening is due

the formation of a nitride layer composed by nitrogen expanded martensite and

iron nitride. At high temperature plasma nitriding the hardness reduction is

credited to chromium nitrides precipitation, and consequent impoverishment of

the nitrogen content in martensite matrix.

The hardening depth profiles is dependent on the predominant diffusion

mechanism. At low temperatures, a gradually reduced on hardness is observed

from surface to bulk. For high temperature, a well-defined planar interface

between a maximum hardness horizontal plateau and the bulk is verified.

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