D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
142
Determination of Surface Hardness of Ti -based Alloys via Laser Induced
Breakdown Spectroscopy (LIBS)
*O. Aied Nassef and A. Hassan GalmedD. F. Mohamed, National Institute of Laser Enhanced Sciences (NILES), Cairo University, Egypt
Received: 4/10/2016 Accepted: 10/12/2016
ABSTRACT
Laser Induced Breakdown Spectroscopy (LIBS) is a well-known
spectrochemical elemental analysis technique, which has been exploited to
determine the surface hardness of a metallic alloy such as titanium-based alloy
samples (Ti-6Al-4V). It is shown that there is a direct proportionality relation
between the ionic to atomic spectral lines intensity ratios and the surface hardness
values measured mechanically via Vickers hardness test for the Ti-based alloy
samples. In the present study, the proportionality relation has been demonstrated
adopting different ionic and atomic spectral lines ratios from the corresponding
LIBS spectra.
Additionally, the laser induced plasma parameters, namely the electron
density and the plasma excitation temperature have been estimated as a function of
the surface hardness of the adopted alloy samples. The obtained direct
proportionality between the plasma temperature and the samples surface hardness
has been interpreted in view of the increased collisions in the plasma plume due to
the strong repulsive forces for harder targets. On the other hand, such high
repulsive force leads to fast expansion of the laser induced plasma plume and
consequently to a decrease in the electron number density in agreement with the
inverse proportionality obtained between the surface hardness and the electron
density.
The results obtained in the present work demonstrate the potential of using
LIBS in metallurgical and industrial applications for the direct determination of
different alloys surface hardness, saving time and cost adopted by conventional
techniques.
INTRODUCTION
Metal alloys are considered one of the most important materials used in many industrial,
medical, military, art and other applications. Their physical and mechanical properties determine the
applications in which they can be used. For example, especial aluminum alloys, are used in aviation
and missile industry, and also steel alloys are used in cars manufacturing (1).Titanium alloys are
utilized in many industrial applications such as aerospace, marine, chemical processing, connecting
rods in internal combustion engines, as well as in military aircraft and turbines. Moreover, they are
used in the medical field such as surgical implants (bones and teeth). Many metal alloys are
distinguished by superior combination of properties such as low densities that lead to very good
strength to weight ratios allowing lighter and stronger structures, high corrosion and erosion resistance
in many environments and high temperature applications (2,3). Thus, making use of a certain metal
alloy depends on its overall properties and on the easiness of its production.
The non-ferrous alloys can be classified according to their base element such as aluminum,
magnesium, copper, titanium, refractory metals, noble metals and miscellaneous alloys such as those
having nickel, lead, tin, and zinc as base metals. However, they can also be classified according to
their specific characteristics. Ti - 6Al - 4V alloy is stronger than the commercially utilized pure
The Egyptian
Society of Nuclear
Sciences and
Applications
ISSN 1110-0451 (ESNSA) Web site: esnsa-eg.com
Arab Journal of Nuclear Sciences and Applications
Vol 50, 4, (142-155) 2017
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
143
titanium (cp Ti). Both has the same stiffness and thermal properties, but the thermal conductivity of Ti
- 6Al - 4V is 60 % lower than that of the cp Ti (4). Titanium alloys have a low density, a high strength,
a very high melting point, ease of machining, a high corrosion resistance in diverse atmospheres and
wear out properties. The main limitation of their applications is the titanium chemical reactivity at
high temperatures (1); however they are still the most used alloys in biomedical applications among all
nonferrous alloys (5).
Many quantitative hardness measurement techniques, such as Rockwell, Brinell, Knoop and
Vickers hardness tests, were designed over the years. They provide arbitrary hardness values, not a
fundamental property of the materials. Their hardness measurement values are relative and especial
consideration must be taken when comparing values determined by different techniques. In 2006,
Laser Induced Breakdown Spectroscopy (LIBS) technique has been successfully used to determine the
surface hardness of various solid samples which have different degree of humidity such as concrete
samples (6). Also Abdel Salam et al. (7) used LIBS technique to measure the surface hardness of
calcified tissues. It has been demonstrated that there are a remarkable correlation between the surface
hardness of solid samples and the intensity ratio of ionic to atomic emission spectral lines from the
plasma. In calcified tissues, the intensity ratios of CaII / CaI and MgII / MgI gave a direct correlation
with the samples surface hardness of different types, namely, enamel of human teeth, shells and egg
shells. The results of such measurements reflected that the repulsive force of the laser induced shock
waves is clearly dependent on the surface hardness of the samples. In 2008, Double Pulse Laser
Induced Breakdown Spectroscopy (DPLIBS) method showed that the highest ratio of MgII 280.26 nm
/ MgI 285.22 nm corresponds well with the enamel position in tooth hardness monitoring(8). Abdel
Salam et al. successfully demonstrated a simple method for the qualitative and quantitative estimation
of ferrous metallic alloys surface hardness. The ratio of ZrII/ZrI is found to be proportional to the
target material hardness, depending on the material composition (9). In 2011, the LIBS was applied to
analyze bio ceramic samples (10), the relationship between sample hardness and LIBS plasma
properties was investigated, in comparison with the conventional Vickers hardness measurements.
In this work, we introduce a detailed study of the hardness determination for a non-ferrous
alloy; titanium based alloy samples, Ti-6Al-4V using LIBS technique. This study enabled us to
construct the calibration curves which correlate the surface hardness values of each type of the alloys
which have been measured mechanically and the spectroscopic data (ionic to atomic spectral emission
intensities). Also, an investigation of the physical parameters of the Ti-6Al-4V alloy plasma (electron
density and plasma excitation temperature) is presented.
I. Samples
The standard samples utilized in the present study were mainly titanium based alloys (Ti-6Al-
4V). Their composition is 6% aluminum, 4% vanadium, 0.25% (maximum) iron, 0.2% (maximum)
oxygen, and the remainder is titanium. Table 1 lists the alloy samples used with the corresponding
mechanically measured Vicker’s hardness number (VHN).
Table (1): The Ti-6Al-4V samples with their respective Vicker’s hardness number (VHN)
Ti-6Al-4V VHN
Sample 1 2400
Sample 2 1100
Sample 3 950
Sample 4 900
Sample 5 775
Sample 6 650
II. Experiment
A typical LIBS setup has been used in the present work. This experimental setup utilizes an
Nd:YAG laser (Brio-Quantel, France) delivering 5 ns laser pulses. The maximum energy of each pulse
was 50 mJ at a wavelength of 532 nm as our excitation source. Laser light is focused by a 10-cm focal
length quartz lens onto the surface of the sample. The target was mounted on an X-Y micrometric
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
144
translational stage. The focused laser pulses of energy of 22 mJ/pulse and a repetition rate of 10 Hz
provide an irradiance of 2.99 × 1011 W/cm2 onto the surface of the Ti-6Al-4V alloy samples. An
oscilloscope coupled to photodiode and Notch filter are used to cut the laser signal and obtain the
integrated light signal of the plasma in each run. The plasma optical emission was collected by a
quartz optical fiber with a diameter of 600 m held at a distance of 2 cm above the plasma at an angle
of 30o with respect to the target surface. The collected plasma emission is then fed via the optical fiber
to the echelle spectrometer (Mechelle 7500, Multichannel, Sweden) coupled to the ICCD camera
(DiCAM PRO-PCO, Computer optics, Germany) for dispersion and detection. The obtained spectra
are displayed and stored on a personal computer for further processing and analysis adopting
GRAM/32 commercial software. All measurements have been performed in air at atmospheric
pressure.
The LIBS experiment for hardness measurements was performed by acquiring fifteen LIBS
spectra of each alloy sample, where five spectra are saved at three different positions on the sample’s
surface. At the same time of acquiring the LIBS spectra, the total integrated plasma, collected by the
fast photo-detector, is also saved via the oscilloscope for each sample at each position. The
identification of the different elements of each sample is initially carried out using each averaged
spectrum. The choice of the suitable spectral lines that are used in the analysis is defined in terms of
intensity, no self-absorption and no interference with other spectral lines. Normalization of the LIBS
spectra to the area under the peak of the oscilloscope’s wave form is performed individually for each
position, then averaged for the three different positions. Construction of the calibration curves, that
relate the TiII/TiI ratios of the specified lines and the corresponding mechanically measured values of
the hardness (VHN), is presented.
III. RESULTS AND DISCUSSION
The LIBS technique was exploited to measure the surface hardness of the Ti-6Al-4V alloy
using five ionic to atomic spectral lines ratios. The results of these tests will be discussed in the
following sections. A typical LIBS spectrum of Ti-6Al-4V alloy is shown in figure (1). It is clear from
this figure that the spectrum is highly crowded with spectral lines (atomic and ionic spectral lines) of
the elements contained in the alloy sample especially the titanium spectral lines. The study of the
surface hardness of these samples requires proper selection of well resolved and intense spectral lines
as shown in figure 2 (some zoomed segments of the spectrum).
250 300 350 400 450 500 550 600
0
200
400
600
800
1000
1200
1400
1600
Inte
nsit
y(a.
u.)
( nm )
Fig (1): Typical LIBS spectrum for Ti-6Al-4V alloy acquired under the adopted
experimental conditions
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
145
316 317294 295
0
200
400
416 417406398 400 444 445390308 309
Ti II
316.85 nm
Ti I
294.82 nm
Ti II
416.36
Ti I
406.02 nm
Ti I
398.97 nm
(nm)
Ti II
444.38 nm
Inte
nsity
(a.u
.) Al II
390.06
Al I
308.2 nm
Al I
309.3 nm
Fig. (2): Ti-6Al-4V alloy spectral lines used in the data analysis
III.1.a Ti II 316.36 nm/Ti I 294.82 nm for Ti-6Al -4V alloy
The obtained LIBS spectra of Ti-6Al-4V alloy samples of different surface hardness have been
used to plot the relation between the intensity ratios of titanium ionic to atomic spectral lines and the
corresponding mechanically measured Vickers Hardness Number (VHN). The ionic and atomic
spectral lines Ti II 316.85 nm and Ti I 294.82 nm were obtained as a result of focusing the second
harmonic Nd-YAG laser of wavelength 532 nm, are shown in figure( 3).
294 295 315 316 317 318
0
100
200
300
400
500
600(a)
316.85 nm
Ti II
294.82 nm
Ti I
VHN 2400
Inte
nsi
ty (
a.u
.)
(nm)294 315 316 317 318
0
100
200
(b)
VHN 1100
294.82 nm
Ti I
316.85 nm
Ti II
Inte
nsi
ty (
a.u
.)
(nm)
294 295 296 315 316 317 318
0
100
200
(c)
294.82
Ti I 316.85 nm
Ti II
VHN 950
Inte
nsi
ty (
a.u
.)
(nm)
294 295 315 316 317 318
0
50
100
150
200
(d)
VHN 900
316.85 nm
Ti II
294.82
Ti I
Inte
nsi
ty (
a.u
.)
(nm)
Fig. (3): Titanium ionic and atomic spectral lines used in the LIBS data analysis of the
alloy surface hardness of the four samples used
[
T
y
p
e
a
q
u
o
t
e
f
r
o
m
t
h
e
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
146
From here on, Figure (a) refers to results of raw intensity data while figure (b) presents the
results normalized to the total integrated emission from the plasma plume. Figure (4) shows the ratios
of the above mentioned ionic to atomic spectral lines intensities as a function of VHN where figure
(4.a) is plotted for the raw data and figure (4.b) illustrates the data normalized to the total plasma
emission.
1000 1500 2000 25000.5
1.0
1.5
2.0
2.5
3.0 (a)R = 70
I (
Ti
II )
/ I
( T
i I )
VHN (Hardness)
1000 1500 2000 25000.5
1.0
1.5
2.0
2.5
3.0
(b)R = 96
I (
Ti
II )
/ I
( T
i I
) n
orm
ali
zed
VHN (Hardness)
Fig. (4): The intensity ratio of Ti II 316.85 nm/Ti I 294.82 nm versus the Vickers Hardness Number
(VHN) for Ti-6Al-4V alloy samples (a) raw data of line intensities (b) line intensities
normalized to the plasma total emission
It is clear that the ratio of the intensities of the ionic to atomic spectral lines of Ti- 6Al-4V
alloy(Ti II 316.85 nm/Ti I 294.84 nm) is directly proportional to the corresponding VHN values. This
is because the harder the surface, the stronger the repulsive force of the laser induced shock wave.
This leads to an increase of the collisions between the constituents of the plasma plume and
consequently, increases appreciably the ionic species on the account of the neutral one.
It is also shown that the calibration curve when the line intensities are normalized to the plasma
total emission (Fig.4.b) gives the best results for ionic titanium line at 316.85 nm to neutral line at
294.82 nm intensity ratio which corresponds to the best line regression value (R= 96).
III.1.b Ti II 416.36 nm/Ti I 294.82 nm for Ti-6Al -4V Alloy
Figure (5) illustrates a zoomed part of the LIBS spectrum obtained for the Ti-6Al-4V alloy
samples (a, b, c and d). The spectral lines (Ti II at 416.36 nm and Ti I at 294.82 nm) shown in this
figure are used in verifying the calibration curves which relates the mechanically measured VHN of
the alloy with ionic to atomic spectral lines intensity ratios.
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
147
294 295 415 416 417
0
100
200
300
400
500(a)
416.36 nm
Ti II294.82 nm
Ti I
VHN 2400
Inte
nsi
ty (
a.u
.)
(nm)
294 415 416 417
0
100
200
(b)VHN 1100
294.82 nm
Ti I
416.36 nm
Ti II
Inte
nsi
ty (
a.u
.)
(nm)
294 295 296 415 416 417
0
50
100
150
(c)
294.82 nm
Ti I 416.36 nm
Ti II
VHN 950
Inte
nsi
ty (
a.u
.)
(nm)
294 295 415 416 417
0
50
100
150
(d)
294.82 nm
Ti I
416.36 nm
Ti II
VHN 775
Inte
nsi
ty (
a.u
.)
(nm)
Fig. (5): Titanium atomic and ionic spectral lines used in LIBS data analysis of the alloy surface
hardness of the four samples used
The ratios of the above mentioned ionic to atomic spectral lines intensities are plotted as a
function of VHN in figure 6. Here also, the raw data are plotted in figure (6.a) and the data normalized
to the total plasma emission are shown in figure (6.b).
1000 1500 2000 25000.5
1.0
1.5
2.0
(a)R = 95
I (
Ti
II )
/ I
( T
i I
)
VHN (Hardness)1000 1500 2000 2500
0.5
1.0
1.5
2.0
(b)R = 94
I (
Ti
II )
/ I
( T
i I
) n
orm
ali
zed
VHN (Hardness)
Fig. (6): The intensity ratio of Ti II 416.36 nm / Ti I 294.82 nm versus the Vickers Hardness Number
(VHN) for Ti-6Al-4V alloy samples (a) raw data of line intensities (b) line intensities
normalized to the plasma total emission
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
148
It is clear that the best results for the calibration curve is obtained for the non-normalized line
intensities when the intensity ratios of the ionic titanium line at 416.36 nm to the neutral line at 294.82
nm are used.
III.1.c Ti II 316.85 nm/Ti I 406.02 nm for Ti-6Al-4V Alloy
Irradiating the titanium alloy samples by a focused 532 nm Nd-YAG laser enabled the
attainment of different pair of ionic and atomic titanium spectral lines Ti II 316.85 nm and Ti I 406.02
nm. These are used for the spectroscopic estimation of the surface hardness of Ti-6Al-4V alloy are
shown in figure 7(a,b,c and d).
315 316 405 406 407
0
100
200
300
400
500
600
700
800
(a)
316.85 nm
Ti II
406.02 nm
Ti I
VHN 2400
In
ten
sit
y (
a.u
.)
(nm)
315 316 317 405 406 407
0
50
100
150
200
(b)
316.85 nm
Ti II
406.02 nm
Ti I
VHN 950
Inte
nsi
ty (
a.u
.)
(nm)
315 316 405 406 4070
50
100
150
200
(c)VHN 900
406.02 nm
Ti I
316.85 nm
Ti II
Inte
nsi
ty (
a.u
.)
(nm)
315 316 405 406 407
0
50
100
150
200(d)
406.02 nm
Ti I
VHN 775
Inte
nsi
ty (
a.u
.)
(nm)
Fig. (7): Titanium ionic and atomic spectral lines used in LIBS data analysis to estimate the alloy
sample surface hardness of the four samples used
The ratios of the spectral lines obtained from Figure (7) are plotted as a function of the VHN
values and shown in Fig.8 where figure 8.a represent the raw data and figure (8.b) shows the
normalized data normalized to the total plasma emission.
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
149
1000 1500 2000 2500
0.2
0.4
0.6
0.8
1.0
1.2
1.4 (a)R = 86 I
( T
i II
) /
I (
Ti
I )
VHN (Hardness)
1000 1500 2000 2500
0.2
0.4
0.6
0.8
1.0
1.2
1.4 (b)R = 89
I (
Ti I
I )
/ I (
Ti I
) n
orm
aliz
ed
VHN (Hardness)
It is shown that the calibration curve obtained in Fig.(8 a) and b shows almost acceptable
results for the considered spectral line intensity ratio (TiII 316.85 nm / TiI 406.02 nm). III.1.d Ti II 416.36 nm/Ti I 406.02 nm for Ti -6Al -4V Alloy
The ionic and atomic spectral lines Ti II 416.36 nm and Ti I 406.02 nm emitted from the plasma
plume of Ti-6Al-4V alloy after irradiating the sample surface by a focused 532 nm Nd-YAG laser
with irradiance 2.99 × 10 11 W/cm 2 are shown in Fig.( 9).
405 406 415 416 417
0
200
(a)
406.02 nm
Ti I
416.36 nm
Ti II
VHN 1100
Inte
nsit
y (a
.u.)
(nm)
405 406 407 415 416 417
0
50
100
150
200
250
(b)
406.02 nm
Ti I
416.36 nm
Ti II
VHN 950
Inte
nsi
ty (
a.u
.)
(nm)
405 406 415 416 4170
50
100
150
200
(c)VHN 900
416.36 nm
Ti II
406.02 nm
Ti I
Inte
nsi
ty (
a.u
.)
(nm)
405 406 407 415 416 417
0
50
100
150
200
250
300
350
400
(d)
416.36 nm
Ti II406.02 nm
Ti I
VHN 650
Inte
nsi
ty (
a.u
.)
(nm)
The ratios of the ionic and atomic spectral lines Ti II 416.36 nm and Ti I 406.02 nm are plotted
as a function of VHN and shown in figure (10). Figure (10.a) is devoted to the raw intensities data
while the data normalized to the total plasma emission is shown in Fig. (10.b).
Fig. (8): The intensity ratio of Ti II 316.85 nm / Ti I 406.02 nm versus the Vickers
Hardness Number (VHN) for Ti-6Al-4V alloy samples (a) raw data of line
intensities (b) line intensities normalized to the plasma total emission
Fig. (9): Titanium atomic and ionic spectral lines used in the LIBS data analysis of the
alloy surface hardness of the four samples used
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
150
600 800 1000 12000.4
0.5
0.6
0.7
0.8
0.9
1.0(a)
R = 99 I
( T
i II
) /
I (
Ti
I )
VHN (Hardness)
600 800 1000 12000.4
0.5
0.6
0.7
0.8
0.9
1.0
(b)R = 100
I (
Ti
II )
/ I
( T
i I
) n
orm
aliz
ed
VHN (Hardness)
From this figure, it is clear that both cases a and b give best results for ionic titanium line at 416.36 nm
to neutral line at 406.02 nm intensity ratio where both lines showed a good regression value.
III.1.e Ti II 444.38 nm/Ti I 398.97 nm for Ti -6Al -4V alloy
Fig. (11) refers to Ti II 444.38 nm and Ti I 398.97 nm spectral lines used to obtain the
calibration curves which relate the mechanical measured VHN of Ti-6Al-4V alloy samples with ionic
to atomic spectral lines ratio resulted by irradiating the titanium sample by 532 nm Nd-YAG laser
source. These are shown in Fig.(11 a, b, c and d)
398 399 400 443 444 445
0
500
1000
1500
2000
(a)
444.38 nm
Ti II
398.97 nm
TiI
VHN 2400
Inte
nsi
ty (
a.u
.)
nm
398 399 443 444 445
0
100
200
300
400
500
600
(b)VHN 1100
398.97 nm
TiI
444.38 nm
Ti II
Inte
nsi
ty (
a.u
.)
nm
398 399 400 443 444 445
0
100
200
300
400
500
600
(c)
444.38 nm
Ti II
398.97 nm
TiI
VHN 775
Inte
nsi
ty (
a.u
.)
nm
398 399 400 443 444 445
0
200
400
600
(d)398.97 nm
TiI
444.38 nm
Ti II
VHN 650
Inte
nsi
ty (
a.u
.)
nm
Fig. (10): The intensity ratio of Ti II 416.36 nm / Ti I 406.02 nm versus the Vickers
Hardness Number (VHN) for Ti-6Al-4V alloy samples (a) raw data of line
intensities (b) line intensities normalized to the plasma total emission
Fig. (11): Titanium atomic and ionic spectral lines used in LIBS data analysis of the alloy
surface hardness of the four samples used
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
151
The obtained ratios from the above mentioned ionic to atomic spectral lines intensities are
plotted against VHN and are shown in Fig.(12). Again, the raw data is presented in Fig (12.a) while
the data normalized to the total plasma emission is shown in Fig. (12.b).
1000 1500 2000 25000.4
0.5
0.6
0.7
(a)R = 99
I (
Ti
II )
/ I
( T
i I
)
VHN (Hardness)
1000 1500 2000 25000.4
0.5
0.6
0.7(b)R = 97
I (
Ti
II )
/ I
( T
i I
) n
orm
ali
zed
VHN (Hardness)
Fig. (12): The intensity ratio of Ti II 444.38 nm/Ti I 398.97 nm versus the Vickers Hardness
Number (VHN) for Ti-6Al-4V alloy samples (a) raw data of line intensities (b) line
intensities normalized to the plasma total emission
Following to the R value obtained in Fig. (12.a and b), the best results for ionic titanium line at
444.38 nm to neutral line at 398.97 nm intensity ratio is observed for the calibration curve obtained
when the line intensities are non-normalized.
III.2 Plasma Parameters
The determination of plasma parameters (electron density and plasma temperature) is essential
for the comprehension of the mechanisms underlying the LIBS technique. The local thermodynamic
equilibrium (LTE) approximation is often used for modeling the plasma. When the collisional
processes especially those involving electrons, are the dominating mechanism in plasma, such plasma
is referred to as collisional-dominant plasma (CDP).
A crucial parameter for the establishment of LTE conditions in the CD plasma is its electron
density (ne), since a necessary conditions for the LTE is given by McWhirter criterion (11):
ne (cm-3) ≥ 1.4 × 1014 (kT)1/2 ΔE3 (1)
Where T (in eV) is the plasma temperature and ΔE (in eV) is the energy difference between the upper
and lower levels of the transitions.
III.2.a Determination of the Electron Density
The electron density has been calculated from Hα line at 656.72 nm using LIBS++ software. The
lower limit of Hα is 1.7 × 1017 cm-3, which verifies the LTE criterion. Hydrogen emission is always
present in the LIBS spectra taken in ambient air because of water vapor of the natural humidity of the
air.
The use of the Hα line for the measurement of the electron density has the definite advantage of
providing a result which is not affected by self-absorption, unless the sample itself would contain high
levels of hydrogen. Moreover, the linear Stark effect acting on hydrogen lines results in a large
broadening, which reduces the relative uncertainty of the measurement is compared to the case of lines
emitted by other elements. Figure (13) shows an exponential decrease between electron density and
Vickers hardness number (VHN) for five Ti-6Al-4V alloy samples with 2400, 1100, 950, 775 and 650
VHN.
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
152
500 1000 1500 2000 2500-100
0
100
200
300
400
500
600
700
Ele
ctro
n de
nsit
y *1
017 (c
m-3 )
VHN (Hardness )
The electron density is decreased by increasing the surface hardness of the metal alloy due to
the increase in the repulsion force of laser induced shock wave. These results in plasma plume
expansion which in turn lowering the number of electrons per unit volume, hence the electron density
decreases.
III.2.b Determination of the Plasma Temperature
If the LTE is verified in the plasma, the population density of atomic states is described well by
a Boltzmann distribution and the ionization states are populated according to Saha- Boltzmann
equilibrium equation. According to these requirements, the plasma temperature deduced from the
Boltzmann plot method is an important parameter for determining the elemental composition.
In fact, in LTE approximation, the emission intensity of the emitting line is related to the total
density by the Boltzmann law:
Ln [λ Іi / gi Ai] = Ln (N/ZT) i - Ei / k Tex (2)
where the spectroscopic constants: gi, λ and Ai are the ith level degeneracy, the wavelength and the
transition probability, respectively. These relevant spectroscopic constants are tabulated in Table (2), Іi
is the emission intensity of the emitting line; N is the number of atoms or ions, Z (T) is the partition
function of the emitting species, which depends on plasma temperature Tex and k is the Boltzmann
constant. By plotting the left hand side versus Ei the slope of the obtained line is (-1/kT).Therefore, the
plasma temperature can be obtained without knowing the values of N, the total number density, and
Z(T), the partition function.
The special conditions required for thermometric purposes should consider the following; lines
in close spectral proximity, reasonably intense, of known transition probability and with different
upper energy levels. The emission lines of Ti (I) have been used to determine electron temperature
under the condition of local thermodynamic equilibrium (LTE). According to these requirements, the
Ti (I) lines selected to determine the plasma temperature are listed in Table (2) with their required
parameters using the spectra normalized to 461.72 nm atomic titanium line.
Table (2): Spectroscopic data for the wavelengths that was used in the estimation of plasma
temperature for Ti-6Al-4V alloy(11):
(nm) E (eV) Ai gi
263.242 4.71 2.7*10-1 5
295.680 4.20 1.8*10-1 5
372.457 4.83 9.1*10-1 9
375.364 3.32 8.2*10-2 5
398.248 3.11 4.5*10-2 5
418.612 4.46 2.1*10-1 9
441.728 4.69 3.6*10-1 9
Fig. (13): Electron density versus Vickers Hardness Number (VHN) for Ti-6Al-4V alloy
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
153
The wavelengths listed in Table (2) with their corresponding spectroscopic data were
substituted in equation (2) to calculate the plasma excitation temperature for each sample The
Boltzmann plots for Ti-6Al-4V alloy samples with 1100, 950, 900, 775 and 650 VHN, are shown in
Fig. (14 a-e).
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.02
3
4
5
6
7
8
(a)R = 97
B = -2.0776
T = 5585 K
Ln
( I i /
Aig
i )
E(eV)
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
2
3
4
5
6
7
8
(b)R = 97
B = - 2.4269
tex
= 4782 K
Ln
( I i /
Aig
i )
E(eV)
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
2
3
4
5
6
7
8
(c)R = 95
B = -2.4495
Tex
= 4737 K
Ln
( I i /
Aig
i )
E(eV)
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.02
3
4
5
6
7
8
(d)R = 98
B = -2.3471
Tex
= 4944 K
Ln
( I i /
Aig
i )
E(eV)
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.01
2
3
4
5
6
7
8
(e)R = 91.3
B = -2.54493
Tex
= 4560 k
Ln
( I i /
Aig i )
E(eV)
Fig. (14): Boltzmann plots for Ti-6Al-4V alloy sample with (a) 1100, (b) 950, (c) 900, (d) 775, and (e)
650 VHN
D. F. Mohamed, et al. Arab J. Nucl. Sci. Appl, Vol 50, 4, 142-155 (2017)
154
The linear relation between plasma temperature and hardness for the five Ti-6Al–4V alloy
samples using average spectrum of three spectra normalized to 461.72 nm atomic titanium lines is
shown in Fig.(15). It is noticed that he plasma temperature increases as the hardness of the metallic
alloy target increases. This increase is attributed to the increase of the collision force. This result is
found to be similar to that attained by Cowpe et al.10 when LIBS was applied to the analysis of bio
ceramics samples where they also demonstrated a linear relationship between sample surface hardness
and plasma temperature.
600 800 1000 1200 14004000
4200
4400
4600
4800
5000
5200
5400
5600
5800
6000
R = 76E
xci
tati
on
tem
per
atu
re (
K)
VHN (Hardness)
Fig. (15): The plasma temperature versus VHN (Hardness) for Ti-6Al-4V alloy
CONCLUSION
In this study, it has been proven that the LIBS technique is capable of assessing surface
hardness of different types of metal alloys. This was clearly demonstrated by the calibration curves
obtained for the Ti-6Al-4V alloy samples. The surface hardness of Ti-6Al-4V alloy has been estimated
adopting the ionic to atomic spectral lines intensity ratios of the lines obtained from the LIBS spectra,
namely (a) Ti II 316.85 nm/Ti I 294.82 nm, (b) Ti II 416.36 nm /Ti I 294.82 nm, (c) Ti II 316.85 nm
/Ti I 406.02 nm, (d) Ti II 416.36 nm/Ti I 406.02 nm and (e) Ti II 444.38 nm/Ti I 398.97 nm.
The tudy of the relation between plasma parameters (i.e. electron density and plasma excitation
temperature) and the metal alloy surface hardness revealed a direct relation between the laser-induced
plasma excitation temperature and the surface hardness of the relevant metal alloy. This direct
proportionality relationship was interpreted in view of the increase of collisions in the plasma plume
as a result of the increase of the repulsive force for harder surfaces. On the other hand, the increase in
the repulsive force and consequently in the plasma plume expansion led to an inverse relationship
between the electron density and the sample surface hardness.
In general, the obtained results demonstrate the feasibility of exploiting LIBS, which is well
known as a spectrochemical analytical technique, for fast and precise estimation of different metallic
alloys surface hardness. The fact that LIBS is a quasi-nondestructive technique makes its application
in industry and archaeology appealing, especially when mobile LIBS systems are used for in situ and
real time measurements.
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