Analysis of nitrogen implantation profiles in titanium and Ti–Nb alloys by glow discharge optical emission spectroscopy: nitrogen calibration

Abstract

In the analysis of nitrogen in Ti-based matrices by glow discharge emission spectroscopy (GDOES), the emission yield of the N I 149.262 nm line was found to depend on the sample composition, in particular, on the N/Ti ratio of the sample surface being sputtered. This was attributed to differences in the transport and redeposition of nitrogen in the GDOES discharge cell: if the surfaces surrounding the plasma consist largely of elemental Ti, the sticking coefficient of nitrogen on them is high and the number density of nitrogen in the volume of the plasma is reduced by adsorption on the walls more strongly than if these surfaces are partly or completely saturated with nitrogen. This leads to a decrease in emission yields of nitrogen lines and needs to be reflected in the analytical methodology. An analogous mechanism might be at play in the analysis of other gaseous elements as well.

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Introduction

Analysis of nitrogen in nitride coatings and nitrogen-enriched surface layers of some metals is a frequent task, reflecting the importance of such materials in science and technology. Important is the Ti–N system, and, in a broader perspective, various complex coatings in which titanium and nitrogen are present at high concentrations, see e.g. ref. 1 and 2. Different methods have been considered for the analysis of the Ti–N stoichiometry and attempts have been under way to develop the corresponding methodology for a long time.³ They involve energy- and wavelength dispersive electron microanalysis (EDS, WDS),^4,5 electron spectroscopies,^6–10 accelerator-based methods,^11,12 secondary-ion mass spectrometry (SIMS)¹³ and glow-discharge optical emission spectroscopy (GDOES).^8,14–19 The most common method of these, EDS/WDS, typically available in scanning electron microscopes, suffers from an overlap of titanium L- and nitrogen K-peaks⁵ and the same problem occurs in Auger electron spectroscopy: overlap of the Ti–L₃M₂₃N₂₃ (383 eV) and N–KL₂₃L₂₃ (381 eV) signals.⁷ This makes Ti–N analyses by these methods difficult. Moreover, EDS/WDS cannot be used for the analysis of ion-implanted materials because the depth distributions thereby produced are too shallow. Therefore, GDOES is a viable alternative for such materials.

GDOES is a relative method relying on calibration by bulk reference materials (RMs) with known compositions and sputter rates. For nitrogen calibrations, a popular class of such materials is the ‘Nitronic’-type stainless steels alloyed with nitrogen, for which good commercially available RMs are available, with nitrogen contents of up to ≈0.9 wt% N. For higher nitrogen concentrations, there is only one RM, a special cutting material called Coronite (JK 41-1N, the SWERIM Metals Res. Inst., Stockholm) with 6.9 wt% N, the composition of which corresponds to titanium nitride mixed with a high-speed steel with an addition of cobalt. In ref. 16, describing the comparison of GDOES and Rutherford Backscattering Spectroscopy (RBS) in the analysis of CrN_x coatings, a TiN coating with a stoichiometry claimed to be 1 : 1 (non-certified, ≈23 wt% N) was used as the high point in an essentially two-point linear nitrogen calibration, consisting of a bunch of points with low concentrations of nitrogen, below ≈0.6 wt%, and the TiN sample, with nothing in between. However, even this does not yield a universal solution, as it follows from the analyses described below. The main goal of this note is to describe GDOES analyses of N-implanted titanium and TiNb alloys and offer a plausible explanation of the nitrogen signal response in these matrices, with some more general consequences for the GDOES methodology.

Experimental

A set of Ti, Ti–25%Nb, Ti–55%Nb samples, ion implanted with nitrogen, were analysed by GDOES depth profiling. Their designations reflect the composition of the base material and the declared nitrogen fluence, e.g., Ti25Nb_3E17N means titanium with 25 wt% Nb, implanted with a fluence of 3.0 × 10¹⁷ nitrogen atoms per square centimeter. The Ti–Nb materials were prepared by powder metallurgy. Details of the metallurgical fabrication of TiNb alloys are described in our previous work.¹⁰ Prior to ion implantation, the samples were mechanically ground and polished to a mirror like finish.

Nitrogen implantation was performed using a Tecvac 221 ion implanter.¹⁹ Nitrogen ions were implanted at an accelerating voltage of 90 kV. The ion beam current I_i was measured using a Faraday cup. The ion distribution in the ion beam was 15% for atomic ions and 85% for molecular ions (measured by mass spectrometry by Tecvac Ltd company²⁰). The total charge of ions, Q, was determined by integrating the ion current values using the trapezoidal method. The fluence of implanted nitrogen I_F (i.e. the number of nitrogen atoms implanted during the implantation period per area unit) was determined according to the relation:

where k_t is the tooling factor (the distance ratio between the Faraday cup and the sample position from the ion source, k_t = 0.97), k_A expresses the abundance of nitrogen atoms implanted into the titanium target (k_A = 7/4), S is the area of the Faraday cup (0.86 cm²) and q is the elementary charge (q = 1.602 × 10⁻¹⁹ C).

GDOES analyses were made using a GDA750HR spectrometer (Spectruma Analytik GmbH, Germany). The emission lines used were Ti I 399.864 nm, Nb II 316.340 nm, and N I 149.262 nm. Besides these elements, carbon and hydrogen were also analysed, using the lines C I 165.701 nm and H I 121.467 nm, respectively. The measurements were performed with a 2.5 mm internal diameter anode, in a dc argon discharge, at 850 V and 15 mA. This corresponds to a working pressure of a few hPa. Sputter rate-corrected calibrations^15,21 were established for the elements under study. In this approach, the intensity I_λ(E),M of a line λ(E) of element E in the matrix (sample) M is supposed to follow the relation

I_λ(E),M = R_λ(E)c_E,Mq_M + b_λ(E) (2)

where c_E,M is the concentration of element E in the matrix M, q_M is the sputter rate of that matrix, and R_λ(E) and b_λ(E) are calibration constants; the former is called the emission yield of the line λ(E), and the latter is the background intensity at the wavelength λ(E). The resulting calibration functions of Ti, Nb and N are shown in Fig. 1.‡ Unlike the other lines, the titanium line used here exhibits a non-linear intensity response as a function of (c·q), as discussed, e.g., in ref. 22. Eqn (2) would not describe its response correctly and a quadratic approximation with an additional calibration parameter, a_λ(Ti), was used instead:

a_λ(Ti)I_λ(Ti),M² + I_λ(Ti),M = R_λ(Ti)c_Ti,Mq_M + b_λ(Ti) (3)

Fig. 1 Calibration curves of Ti, Nb and N. In the plots, abscissa denotes the respective signal intensity. On the ordinate, each magenta point denotes the concentration of the element, c, in the respective sample. Red points denote the respective (c·q) product, while the red and magenta points belonging to the same sample are connected by a vertical turquoise line. The calibration curve is defined by the red points. The calibration function of N depicted here is defined by the steel samples. The sputter rate (sputter factor) of TiN, q_TiN, was calculated based on the Ti calibration, (a), so that the respective (c·q) point, blue, lies on the Ti calibration curve established by the other Ti-containing samples.

Carbon calibration was set up using reference materials of steels and cast iron, calibration of hydrogen was based on the TiH₂ layer on Ti^23,24 and pure titanium. The calibration function of nitrogen, Fig. 1c and d was established based on reference samples of steels, with the highest nitrogen concentration of 0.896 wt%, in the sample NSC4-C (MBH Analytical Ltd, UK), see Fig. 1c. The point corresponding to TiN does not fit this calibration function and was excluded from its calculation. The same applies to the points corresponding to Coronite and the Ti_3.1E17N sample. This discrepancy is discussed below. The sputter rate q_TiN of the TiN sample was calculated¹⁵ using the Ti calibration, established with the other Ti-containing samples with known sputter rates and pure Fe as a blank sample, see Fig. 1a. In the calibration measurements, the intensities were recorded after letting the discharge run for a while to stabilize (30 seconds).

In depth profile analyses of the N-implanted samples, signal intensities were collected as functions of the sputtering time, t, and raw data (intensities-versus-time) were converted into quantitative depth profiles (concentrations-versus-depth) by a common GDOES quantification procedure:¹⁵ first, for every point t of the depth profile, the c_E,M(t)q_M(t) products were calculated for Ti, N, Nb, H, and C, based on the recorded intensities I_λ(E),M(t) and the respective calibrations, eqn (2) or (3). The instantaneous sputter rate q_M(t) was then calculated using the fact that, at every point of the depth profile, the sum of the concentrations of the mentioned elements is equal to 100%:

With q_M(t) already known, the sample composition as a function of time was established from the c_E,M(t)q_M(t) products. The conversion of the time scale into depth proceeds as follows: provided that the concentrations and sputter rates are in mass units, the mass of the sample sputtered off within the time interval dt is

dm = ρ_M·πr²·dh = q_M(t)dt (5)

where ρ_M is the density of the sample material and r is the anode radius, i.e., the radius of the analyzed spot. The depth h(t) as a function of the sputtering time was then established by integrating eqn (5):

The density of the matrix ρ_M(τ) may vary, as the composition of the sample varies with depth. For the calculation of h(t) using eqn (6), the sample density was treated as follows: in the Ti–N system, the density of pure Ti is ρ_Ti = 4.51 g cm³ and the density of TiN is ρ_TiN = 5.40 g cm⁻³. The density of a matrix consisting of titanium with nitrogen at a concentration c_N [at%] was then taken as the weighted average of ρ_Ti and ρ_TiN:

ρ_M(t) = [2c_N(t)ρ_TiN + (100 − 2c_N(t))ρ_Ti]/100 (7)

Concerning the TiNb alloys, the densities of Ti25Nb and Ti55Nb are 5.09 and 6.10 g cm⁻³, respectively. The density of the TiNb matrix with nitrogen was treated analogically as in the Ti–N case, except that, instead of ρ_Ti, the appropriate ρ_TiNb density was used, and for the corresponding (Ti, Nb)N nitride, a value that was 20% higher was taken, in analogy with titanium without Nb, as ρ_TiN/ρ_Ti = 1.20. The absolute sputter rate of pure Ti under the given discharge conditions was 38 nm s⁻¹. It was established as described in ref. 15, based on the Fe-3313 thickness standard (Kocour, Chicago, IL, USA) and confirmed by depth measurements of the erosion crater after a given sputtering time, using a scanning profilometer (DEKTAK XT, Bruker Corp.). The total amount of nitrogen in the N-implanted samples, [N atoms cm⁻²], was calculated by integration of the respective nitrogen depth profiles§. When doing that, the first several points of the depth profile (up to ≈1 s), with higher intensities of C, H, and N, were not included, as they largely reflect the desorption of atmospheric gases from the walls of the spectral source and the sample surface upon the discharge startup, rather than the implanted nitrogen.

The actual amount of implanted nitrogen in the Ti_3.1E17N sample was confirmed by Rutherford Backscattering Spectrometry (RBS). The RBS spectra were acquired using a 3.75 MeV helium ion beam. The backscattered helium ions were detected using an Ultra-Ortec PIPS detector positioned at a laboratory scattering angle of 170° in the Cornell geometry. The ion current during RBS measurements was approximately 5 nA. To mitigate sample degradation by the analysis ion beam, multiple RBS spectra were collected at different beam spots. The final spectrum represents the sum of these individual spectra. Elemental concentrations were determined using SIMNRA software²⁵ applying the relevant non-Rutherford cross-sections.

The mentioned sample was also analysed by another complementary method, SIMS, to confirm its agreement with the corresponding GDOES depth profile. The SIMS analysis was performed using an IMS 7f SIMS instrument (Cameca SAS, France). It was operated in positive primary ion (10 keV impact energy, 100 nA ion current, O₂⁺ species, scanned area 150 µm)/positive secondary ion (¹⁴N⁺, ⁴⁸Ti⁺) mode at a mass resolution of 1200. The depth scale was calibrated using a DEKTAK XT stylus profilometer (Bruker Corp.) and the assumption of a constant sputter rate¶. The concentration scale was calibrated using the indirect method mentioned below.

Results

It was found that, not only is the nitrogen intensity response for TiN incompatible with the calibration curve based on nitrogen-alloyed steels, but, as described above, nitrogen calibration based on steels is not good for the N-implanted samples, either: the thereby obtained total nitrogen content does not correspond to the declared nitrogen fluences. The problem obviously lies in the nitrogen calibration, namely in the emission yield of the nitrogen line used, R_N. To cope with this situation, in the first step, the data interpretation procedure was reversed, i.e., a selected N-implanted sample, Ti_3E17N (pure titanium implanted with nitrogen at 3.0 × 10¹⁷ at. cm⁻²), was taken as a reference, and the emission yield R_N was set so that the integrated quantified nitrogen depth profile yielded the ‘correct’ total amount of nitrogen, equal to the declared fluence in that ‘reference’ sample. This approach can be called an ‘indirect calibration’. The resulting depth profile of the sample Ti_3E17N, quantified with this emission yield R_N, is shown in Fig. 2. Its correctness was verified by the RBS method on a very similar sample, N-implanted titanium at a fluence of 3.1 × 10¹⁷ at. cm⁻², see above in the “Experimental” section. Further analyses showed that this ‘indirect calibration’ works reasonably well for the samples implanted with low fluences, and, also, the shape of nitrogen depth profiles in such samples was found to be close to Gaussian depth distributions, typical of ion implantation.^19,26 However, at higher fluences, saturation of the nitrogen concentration in the implanted layer takes place, i.e., the depth profile of nitrogen becomes flattened in the vicinity of the maximum, see Fig. 3, and the total nitrogen amount in the implanted layer does not further increase with increasing fluence. Much more realistic results for samples implanted with high nitrogen fluences were obtained by using the emission yield R_N derived from the intensity response of the TiN sample, as depicted in the nitrogen calibration in Fig. 1c. This can be demonstrated by the plots in Fig. 3 and 4. The three values of the emission yield of nitrogen mentioned above, i.e., R_N(steels), R_N(Ti_3E17N) and R_N(TiN) are 432, 233 and 703 mV/wt%, respectively||. They differ quite significantly, which violates the basic GDOES paradigm, i.e., that emission yields are virtually independent of the matrix under study**.

Fig. 2 Depth profile of sample Ti_3E17N. The quantification was performed with R_N = 233 mV/wt%, according to the declared fluence of 3.0 × 10¹⁷ at. cm⁻² (an ‘indirect calibration’). Ordinate: atomic concentrations of Ti, N, Nb, C, and H. Multiplicative scaling factors specified in the caption were applied, to match the concentration range displayed. They are indicated in the legend, after asterisk (*) at the symbol of each element. The black dashed line represents the calculated sputter rate, q_l, in nm s⁻¹. Realistic data reflecting the implantation profile start after the local minimum of N at ≈10 nm. The beginning of the depth profile reflects gas desorption at the discharge startup and/or prospective contamination of the sample surface.

Fig. 3 Depth profiles of samples Ti25Nb_3E17N (a) and Ti25Nb_6E17N (b), as quantified using R_N = 233 mV/wt% (an ‘indirect calibration’ based on the sample Ti_3E17N). The resulting nitrogen concentration in the latter sample (Ti25Nb_6E17N) is unrealistically high and that profile is not correct. Note that in the plots, concentrations are given in atomic percent, while the designation Ti25Nb means 25% weight percent of niobium.

Fig. 4 (a) Depth profile of sample Ti25Nb_12E17N, quantified with R_N = 233 mV/wt%, (unrealistic, incorrect). (b) Depth profile of the same sample, with the quantification derived from the intensity response of stoichiometric TiN, with R_N = 703 mV/wt%.

To complete the results concerning the present series of samples, there are three more features worth mentioning:

1. At extremely high nitrogen fluences, a distinct separate layer is formed at the interface between the implanted layer on the top and the base metal, with a markedly lower nitrogen concentration, and a stoichiometry approaching (Ti, Nb)₂N. See Fig. 5.

Fig. 5 Depth profile of sample Ti55Nb_24E17N, with the quantification derived from the intensity response of stoichiometric TiN, with R_N = 703 mV/wt%. Similar to before, Ti55Nb means 55 wt% niobium.

2. At the Ti–Nb samples, the region just beneath the implanted layer is enriched with hydrogen and carbon: see the depth profiles in Fig. 3–5. Hydrogen is known to affect GDOES intensities of some other elements to some extent.^24,27 In the present analyses, no ‘hydrogen corrections’ of the Ti, N and Nb signals were made. The TiH₂ sample used for hydrogen calibration was not certified and the resulting concentrations of H, as shown in Fig. 3–5, might be slightly overestimated.

3. At the Ti–Nb samples, niobium behaves similarly to titanium, i.e., the Nb/Ti ratio remains virtually constant throughout the whole depth profile. Only in the (Ti, Nb)₂N layer at the interface, formed at the highest nitrogen fluences and mentioned above under point 1, is the Nb/Ti ratio slightly higher than in the base metal, by about ≈10%.

As mentioned, the total amount of nitrogen in the N-rich layer of the samples was established by the integration of the respective depth profiles, quantified as described above, with R_N depending on the nitrogen fluence: R_N = 233 mV/wt% for the ‘lower’ N fluences, ≤3.0 × 10¹⁷ at. cm⁻², and R_N = 703 mV/wt% for the ‘higher’ fluences, >6.0 × 10¹⁷ at. cm⁻². The results are shown in Table 1 and are also plotted in Fig. 6. The fluence of 6.0 × 10¹⁷ at. cm⁻² lies in the ‘intermediate’ region between the ‘low’ and the ‘high’ fluences and quantification with neither of the two mentioned R_N values yields an acceptable total amount of nitrogen. Hence, the values in the parentheses in Table 1 were calculated as the average of the two figures resulting from the quantification with either R_N value. It should be noted that the three valid digits in the numbers in Table 1 do not imply anything about the level of accuracy of those results: the estimated relative uncertainty of the reference value indicated by the superscript ‘a’, for sample Ti_3E17N, is several percent, and, consequently, so would also be a possible systematic bias of the results for the other ‘lower-fluence’ samples, because they are linked to that reference value via the emission yield R_N.

Table 1 Total amount of nitrogen in the N-implanted samples of Ti and the Ti25Nb and Ti55Nb alloys as obtained from integrated GDOES depth profiles, quantified using an appropriate value of R_N (see the text). The first column shows the declared nitrogen fluence

N fluence [10^17 at. cm^−2]	N in Ti [10^17 at. cm^−2]	N in Ti25Nb [10^17 at. cm^−2]	N in Ti55Nb [10^17 at. cm^−2]
a Reference value for low fluences of up to 3.0 × 10^17 at. cm^−2 N.
1.0	0.87	0.81	1.21
3.0	3.00^a	3.11	3.36
6.0	(5.1)	(4.8)
9.0	4.65	5.41	5.26
12	5.97	6.37	5.07
18	4.80
24		5.06	4.60

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Fig. 6 Total amount of nitrogen in the N-implanted samples resulting from the GDOES depth profiles as a function of the declared nitrogen fluence. The dashed line represents the identity function, y = x.

Discussion

Eqn (2) means that, except for a low spectral background, b_λ(E), the emission intensities of the lines of an element are proportional to the product c_E,Mq_M. The rationale behind this is that the intensity I_λ(E),M is proportional to the number density n^vol_E of the atoms of element E in the volume of the glow discharge plasma, which is controlled by the dynamic equilibrium between the source flux of the atoms of element E entering the plasma due to sputtering, Φ_E(in),

Φ_E(in) ∝ c_Eq_M (8)

and the sink flux, Φ_E(out), of atoms of element E leaving the plasma and being redeposited on the anode wall (see Fig. 7). This flux is proportional to the impingement flux of element E, which itself is proportional to the number density n^adj_E next to the anode wall³⁶ and a proportionality constant ξ_E called the sticking coefficient²⁸ of element E:

where v̄_E is the average velocity of the atoms of element E in the plasma and the superscript ‘adj’ means that eqn (9) concerns the region (a thin layer) adjacent to the anode wall. The sticking coefficient expresses the probability that an atom of element E hitting the wall gets trapped. The transport of the analyte within the discharge cell is described by the diffusion equation, with boundary conditions defined by the source and sink fluxes, Φ_E(in) and Φ_E(out). Its solution is the number density distribution of the analyte, n_E(r, z), in the discharge cell. For the Grimm-type cell geometry, the diffusion equation was solved both analytically³⁷ and numerically by computer modelling,³⁴ see Fig. 7. The task here is to assess how the analyte number density in the plasma (and consequently the emission intensity I_E) depends on the fundamental parameters mentioned, in particular, the sticking coefficient ξ_E.

Fig. 7 The geometry of the Grimm-type GDOES discharge cell. The level lines illustrate a typical number density distribution in the plasma, n_E [atoms cm⁻³], of an element (Cu) sputtered from the sample. Adapted with permission from ref. 34, Copyright (1998) Elsevier.

At the steady state, the source and sink fluxes of the analyte atoms, integrated over the respective surfaces of the cell, are equal:

Φ_E(in) = Φ_E(out) = Φ_E, (10)

and the analyte transport within the cell can be approximately described in analogy with the equivalent electrical circuit depicted in Fig. 8.

Fig. 8 Analyte transport and redeposition in the discharge cell: an equivalent circuit. In this analogy, the current i corresponds to the flux of element E in the plasma, Φ_E, the voltages U_v and U_a correspond to the number densities n^vol_E and n^adj_E, respectively, resistor R_D corresponds to l/D_E, see eqn (12) and resistor R_ξ, corresponds to 4/(ξ_Ev̄_E), see eqn (9).

In the discharge cell, the transport of the sputtered material proceeds by diffusion and the number density n_E in the plasma follows the first Fick's law:

Φ_E(z, r) = −D_E∇n_E(z, r) (11)

where D_E is the diffusion coefficient of element E in the plasma and ∇n_E is the gradient of n_E. Integrating this over all possible diffusion paths and the plasma volume, we can writewhere n^vol_E is the number density of element E in the volume of the plasma and l is a characteristic diffusion length, related to the anode radius. Unlike in the preceding sections, c_Eq_M is considered here in atomic units instead of mass units, so that the flux Φ_E is equal to c_Eq_M. The quantities l and n^vol_E may seem to be defined somewhat vaguely, but what is important is that eqn (11) holds also on the microscopic level, for every point in the plasma and every bit of a diffusion line; hence, the integration is justified, and n^vol_E represents some kind of averaged number density of element E in the glowing region.

Combining eqn (9)–(12), we get

Consequently, the emission yield R_λ(E) depends on the diffusivity and the sticking coefficient of element E as follows:

Substituting realistic parameters of the process, i.e., T = 800 K,³⁹ p(Ar) = 5.3 hPa and l = 1 mm for a 2.5 mm-diameter anode, the proportionality relation, eqn (14), for atomic nitrogen becomes

and, if a substantial degree of nitrogen recombination occurs in the plasma, an analogous relation for molecular nitrogen emission will be

where the first term on the right side represents diffusion in the volume and the second term refers to redeposition (entrapment rate) on the walls. This means that, for both atomic and molecular nitrogen, relative contributions of the diffusion in the cell and the wall entrapment rate to the emission yield R_λ(N) are comparable, although, for ξ_N → 1, the former would be greater. For ξ_N < 1, the relative importance of the entrapment rate rises, and the emission yield also goes up. Background data for eqn (14)–(16) are given in Table 2. The table also contains data for titanium. In most studies dealing with computer modelling of discharges, it is assumed that, for metals and other non-gaseous species, the entrapment rate on the walls virtually does not depend on the composition of the redeposited material and ξ_E → 1, because the temperature of the anode is relatively low. Emission yields are then controlled solely by diffusion, in accordance with ref. 42.

Table 2 Underlying data for eqn (14)–(16). Diffusion coefficients (column 5) were calculated based on the diffusivity of molecular nitrogen in argon at T = 293 K and the atmospheric pressure, D = 0.19 cm² s⁻¹,⁴¹ and the following proportionality relations: D ∝ T^1.75/p, D ∝ 1/σ, and D ∝ 1/√M_X–Ar,³⁶ where σ is the respective collision cross section with argon and M_X–Ar is the reduced atomic (molecular) mass of the X–Ar couple, X being the species under study. The collision cross sections come from the literature,^a see column 4. The figures refer to the experimental parameters mentioned in the text (T = 800 K, p = 5.3 hPa, and l = 1 mm)

	Mr	MX–Ar	σX in Ar [10^−20 m^2]	DX in Ar [cm^2 s^−1]	v̄X [m s^−1]	l/DX in Ar [10^−4 cm^−1 s]	4/v̄X [10^−4 cm^−1 s]
a Experimental collisional cross sections of N in Ar and N2 in Ar greatly differ from the values calculated using the commonly reported collisional diameters.
N	14	10.4	221 (ref. 40)	383	1096	2.6	0.36
N2	28	16.5	320 (ref. 40)	210	775	4.8	0.52
Ti	47.9	21.8	200 (ref. 38)	292	592	3.4	0.68

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As suggested by relations eqn (14)–(16), the likely explanation of the observed nitrogen signal response in different matrices, i.e., R_N(Ti_3E17N) < R_N(steels) <R_N(TiN), consists in different sticking coefficients of nitrogen on the different materials redeposited on the anode. In particular, for samples implanted with lower fluences of N, the Ti/N ratio of the redeposited material is higher than in samples implanted with high fluences of N, and in the TiN sample. Moreover, redeposition occurs not only on the anode, but thermalized atoms hit the sample surface as well, and, if the sample surface consists at least partly of elemental Ti, nitrogen from the plasma can also be (temporarily) trapped there and eventually re-sputtered. Here the Ti enhancement of a TiN surface by preferential sputtering also comes into play††.²⁸ It is well known that nitrogen has a high affinity for titanium and undergoes chemisorption on a Ti surface, through Ti–N bonds, thereby increasing the sticking coefficient. This is what causes the well-known ‘gettering’ effect and is widely used in vacuum technology, e.g., in ion-sorption pumps. In contrast, if the surfaces surrounding the plasma are covered largely by TiN instead of Ti, the sticking coefficient of nitrogen, ξ_N, dramatically drops. This was clearly demonstrated, e.g., in reactive magnetron sputtering.^29–31 There is also a Ti–N phase with a higher N/Ti ratio, TiN₂;³² however, its formation was not confirmed here. Because emission yields in GDOES rise as the respective sticking coefficients drop, as follows from eqn (14), the empirically established relation R_N(Ti_3E17N) < R_N(TiN) can be explained by ξ_N(Ti) > ξ_N(TiN). The magnitude of the differences in R_N between Ti and TiN reported above under Results implies that the sticking coefficient ξ_N(TiN) on the anode should indeed be several times lower than ξ_N(Ti). It may well be, that the sticking coefficient of nitrogen in the analysis of N-alloyed steels, ξ_N(steel), is somewhere in between ξ_N(Ti) and ξ_N(TiN), which would plausibly explain the observed relation between emission yields of the mentioned nitrogen line in the analysis of those three matrices. Also, the fact that the total amounts of nitrogen resulting from the analysis, exceed the declared fluence in the Ti25Nb_3E17N and Ti55Nb_3E17N samples when the Ti_3E17N sample is taken as a reference, (see Table 1), suggests that the sticking coefficient for nitrogen in the TiNb alloys also depends on the titanium concentration, so that ξ_N(Ti55Nb) < ξ_N(Ti25Nb) < ξ_N(Ti). Obviously, using the Ti_3E17N sample as a reference is rather a virtue of necessity than a universal solution. However, for these ‘low fluence’ samples, the thereby obtained results are still much better than those obtained with TiN as a reference, in which case the discrepancy would not be 4% (Ti25Nb_3E17N) or 12% (Ti55Nb_3E17N) but the nitrogen results (c_Nq) would be biased by a factor of ≈2–3.

For completeness, there is one more aspect worth mentioning: while the response of TiN was measured after a 30 s long ‘preburn’ period, the whole depth profile of a N-implanted sample lasts only a few seconds (e.g., in sample Ti_3E17N, the first 1.4 s after the startup was not considered (outgassing of the anode), and, after another 1.3 s, the peak of the implanted profile was reached). Hence, temporal characteristics may also play a role. It appears that, except of sample heating and the changes in the sticking coefficient ξ_N, all the other transient processes in the plasma are too fast to affect the signal–time relationships mentioned here.³³

Conclusions

GDOES is a fast and affordable multi-element depth profiling method, suitable for the analysis of nitrogen in coatings and N-implanted materials. A central role in the analytical interpretation of line intensities in GDOES is played by the emission yields, R_E, expressing relative sensitivity of the emission line used for the given element. In the conventional approach, emission yields are considered independent of the matrix analysed. This applies to the analysis of metals and other non-gaseous elements with high sticking coefficients on the surfaces surrounding the plasma, ξ_E → 1. In the present work, it was found that this assumption does not hold for nitrogen analysis in N-implanted titanium and Ti–Nb alloys. Due to a much higher sticking coefficient of nitrogen on the Ti or Ti–Nb surface than on the surface of TiN_x or (Ti, Nb)N_x, the emission yield of the N I 149.262 nm line varies with the concentration of nitrogen in the matrix. This feature is not common in the analysis of other materials and quantification schemes implemented in commercial GDOES spectrometers must be used with caution in applications like this.

For Ti and Ti–Nb samples implanted with nitrogen at lower fluences, up to ≈3 × 10¹⁷ at. cm⁻², an implanted sample with a known fluence can be taken as a reference and the quantification of such depth profiles can be performed using the emission yield R_N established accordingly, so that the integrated depth profile of nitrogen yields the total amount of nitrogen, equal to the implanted fluence. At such fluences, the shape of nitrogen depth profiles is close to the Gaussian distribution of nitrogen with depth, typical of ion implantation profiles,¹⁹ with the maximum at several tens of nanometers below the surface. For very high nitrogen fluences, greater than ≈6 × 10¹⁷ at. cm⁻², quantification of the depth profiles can be performed with R_N derived from the intensity response of stoichiometric titanium nitride. At such fluences, saturation of the nitrogen concentration in the implanted layer takes place, at a level close to- or slightly above 50 at%, i.e., the depth profile of nitrogen becomes flattened in the vicinity of the maximum. Furthermore, the total amount of nitrogen in the implanted layer does not increase further with increasing fluence. At the highest fluences approaching 12–24 × 10¹⁷ at. cm⁻², a distinct separate layer is formed at the interface between the surface-near zone and the base metal, with a lower nitrogen concentration and a stoichiometry approaching (Ti,Nb)₂N. A similar behaviour was described four decades ago, with nitrogen implantation at very high fluences into pure titanium, resulting in the formation of the Ti₂N phase.³⁵

It was shown how the observed signal response of nitrogen depends on the number density n^vol_N of nitrogen atoms in the plasma. Not only is n^vol_N controlled by the flux of nitrogen atoms sputtered from the cathode and entering the plasma, proportional to (c_N·q), but it is also controlled by the transport of nitrogen in the plasma and its redeposition on the walls. These processes depend on the diffusivity of nitrogen in the plasma and the sticking coefficient of nitrogen on the walls and are described by relations eqn (13) and (14). The discussion of this topic presented here refines the somewhat simplistic treatment of n^vol_N in ref. 22. An analogous mechanism might be at play in the analysis of other gaseous elements as well.

Author contributions

Z. Weiss: conceptualization, GDOES analyses, interpretation of GDOES data, writing; V. Smola, M. Lebeda, and P. Vlčák: sample preparation and ion implantation experiments; J. Lorinčík: SIMS analyses; I. Elantyev: stylus profilometer measurements; P. Malinský: RBS analyses.

Conflicts of interest

There are no conflicts to declare.

Data availability

Data for this article, including bitmap versions of the Figures and the underlying depth profiles in csv format, are available at Zenodo at https://doi.org/10.5281/zenodo.18493405.

Acknowledgements

Ion implantation experiments were performed with the support of the Grant Agency of the Czech Technical University in Prague (grant No. SGS24/121/OHK2/3T/12) and the VVI CENAKVA Research Infrastructure (ID 90238, MEYS CR, 2023–2026). RBS analysis was carried out at the CANAM (Centre of Accelerators and Nuclear Analytical Methods) infrastructure LM 2015056. SIMS and stylus profilometry results were obtained using the CICRR infrastructure, which is financially supported by the Czech Ministry of Education, Youth and Sports – project LM2023041. GDOES analyses were funded by the Ferroic Multifunctionalities project, supported by the Ministry of Education, Youth, and Sports of the Czech Republic. Project No. CZ.02.01.01/00/22_008/0004591, co-funded by the European Union.

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Footnotes

† Presented at the 7th International Glow Discharge Spectroscopy Symposium (7th IGDSS), 19–22 April 2026, Antwerp, Belgium.

‡ In the plots in Fig. 1, sputter rates (originally expressed as sputtered mass per second) are treated as ‘sputter factors’, i.e., as dimensionless quantities relative to the sputter rate of pure iron under the same glow discharge conditions, q_M/q_Fe.

§ The total amount of an element E, if it is present solely in a surface layer, can also be established by integrating the quantity I_E(t)/R_E over the time interval from zero to the time at which the signal I_E(t) vanishes, i.e., without even knowing sample density as a function of depth or as a function of the sputtering time, ρ_M(h) or ρ_M(t).¹⁵

¶ Not only do the sputter rates in SIMS and GDOES differ in magnitude, but they are in fact different quantities: in GDOES it is the net sputter rate, affected by redeposition and self-sputtering,¹⁵ while in SIMS and other high vacuum methods using ion beams these phenomena do not occur.

|| Absolute values of R_λ(E) do not have fundamental significance, as they depend on the sensitivity setting of the respective analytical channel (light detector), which is instrument dependent. However, the ratios of emission yields of the same channel in the analysis of different matrices, as discussed here, bear some information about the physics taking place.

** This paradigm applies with good accuracy to commonly used ‘analytical’ lines of non-gaseous elements. However, this is not a universal rule and deviations from this calibration model exist, especially in the analysis of gaseous elements, e.g. oxygen.⁴³

†† Nitrogen has a slightly higher sputtering yield than titanium when TiN_x is sputtered. Therefore, a surface layer develops, a few monolayers thick, with a higher Ti concentration than in the material underneath, so that the Ti/N ratio in the resulting flux of sputtered atoms is the same as that below this modified surface layer.

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