A thermal model for laser interaction with thick dielectric film on metallic substrate: Application to Ca-P layer on Ti alloy

Article abstract of DOI:10.1016/j.jallcom.2009.07.162

Ca-P coatings on Ti-6Al-4V substrates were synthesized using a direct pulsed Nd:YAG laser writing technique. The phase and morphological evolutions within the coatings as a function of laser processing parameters were evaluated using X-ray diffraction and

Full text of DOI:10.1016/j.jallcom.2009.07.162

Journal of Alloys and Compounds 487 (2009) 499–503
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jallcom
A thermal model for laser interaction with thick dielectric film on metallic
substrate: Application to Ca–P layer on Ti alloy
Sameer R. Paital, Narendra B. Dahotre∗
Laboratory for Laser Materials Synthesis and Fabrication, Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 11 July 2009
Received in revised form 21 July 2009
Accepted 25 July 2009
Available online 5 August 2009
Ca–P coatings on Ti–6Al–4V substrates were synthesized using a direct pulsed Nd:YAG laser writing
technique. The phase and morphological evolutions within the coatings as a function of laser processing
parameters were evaluated using X-ray diffraction and scanning electron microscopy techniques. A three
dimensional modeling based on COMSOL’sTM Multiphysics was adopted to understand the temperature
evolution and corresponding cooling rate as a function of laser processing parameters. The temperature
evolutions and cooling rate estimated from the model, satisfactorily explained the variation in phases
and melt depth with varying pulse frequency of the laser beam.
Keywords:
Laser
Thermal model
Calcium phosphate tribasic
Bioceramics
© 2009 Elsevier B.V. All rights reserved.
Phase transformations
1. Introduction
certain drawbacks such as poor adherence of the coating to the
substrate material, lack of uniformity in the coating and absence of
Titanium-based alloys owing to their excellent mechanical
properties, corrosion resistance and biocompatibility are most
commonly used for load bearing implant applications, such as hip
joint prosthesis, knee joint prosthesis and dental implants. How-
ever, these bioinert materials when placed inside a human body
elicit minimal interaction with the surrounding tissues and thereby
induce the formation of a fibrous capsule at the interface [1,2].
Hence, to improve the reaction between the implant and surround-
ing tissue, bioresorbable materials such as tricalcium phosphate
(␣-TCP, Ca3(PO4)2) [2] and bioactive materials such as hydrox-
yapatite [Ca10(OH)2(PO4)6] (HA) [3], calcium phosphate tribasic
[Ca5(OH)(PO4)3] [4], and bioglass [5] are most commonly used as
coatings on Ti-based alloys. These bioceramics react with the sur-
rounding tissue and thereby provide a strong chemical bonding
between the implant and the remodeling bone. Further, coatings of
these bioceramics on Ti-based alloys provide the appropriate sur-
face chemistry for tissue compatibility without altering the bulk
mechanical properties of the material.
textures or topographical cues [12,13]. Hence, in the present work, a
laser-based direct writing technique to synthesize Ca–P coatings on
titanium alloys is introduced. In this approach, by proper selection
of laser processing parameters both the precursor (calcium phos-
phate tribasic) and a part of the substrate material (Ti–6Al–4V) can
undergo rapid melting and thereby a chemical and microstructural
bonding can be achieved at the interface. Further, by control-
ling the pulse frequency, the input laser energy and thereby the
phase and morphological evolutions within the coatings can also
be modulated. Finally, a three dimensional thermal model based
on COMSOL’sTM Multiphysics is adopted to understand the phase
transformations with varying laser processing parameters.
2. Materials and methods
Ti–6Al–4V substrate coupons (100 mm × 50 mm × 3 mm) cut from the rolled
sheets were polished using 30 ␮m grit SiC emery paper followed by rinsing with
acetone. Calcium phosphate tribasic (Ca5(OH)(PO4)3) powder (Fisher Scientific, USA)
was used as the precursor material. This precursor powder had a spherical morphol-
ogy with a unimodal distribution in the range of 10–30 ␮m. The precursor was mixed
in a water-based organic solvent LISI W 15853 (Warren Paint and Color Company,
Nashville, TN, USA) and sprayed onto the substrate coupons using an air pressurized
spray gun. This green body was air dried to remove the moisture and a uniform thick-
ness of 40 ␮m was maintained for all precoating precursor deposits. The samples
were then scanned using a 400 W average power, JK701 model pulsed Nd:YAG laser
to obtain the coating. The additional details related to the laser processing technique
are available in the previously published article [4]. The processing parameters used
for the above process are listed in Table 1.
The several coating techniques that can be used to achieve Ca–P
coatings on Ti-based alloys are plasma spray deposition [6], pulsed
laser physical vapor deposition [7], ion beam assisted deposition
[8], magnetron sputtering [9], sol–gel-based coatings [10] and elec-
trodeposition [11]. Most of the above coatings however suffer from
∗
Corresponding author. Tel.: +1 865 974 3609; fax: +1 865 974 4115.
E-mail address: ndahotre@utk.edu (N.B. Dahotre).
Phase evolutions within the coatings were studied using a Philips Norelco X-ray
diffractometer (XRD) with Cu-K␣ radiation of wavelength 1.5418 Å. The system was
0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2009.07.162

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S.R. Paital, N.B. Dahotre / Journal of Alloys and Compounds 487 (2009) 499–503
Table 1
Laser parameters used for the experiment.
Pulse duration
Energy of a single pulse (e)
Pulse frequency
Input laser energy (E)
Laser scan speed
0.5 ms
4 J
10, 20, 30, 40 Hz
4, 7.92, 10.48, 13.8 J
36 cm/min
Focus position
Laser spot diameter on the surface
Pulse shape
0.8 mm above the surface of the sample
900 ␮m
Rectangular
operated at 20 kV and 10 mA in a 2ꢀ range of 20–100◦ using a step size of 0.02◦
and count time of 1 s. The observations for microstructure evolution and depth of
heat-affected zone due to laser direct writing were conducted across the cross-
section of samples. The samples were chosen from the center of the coated plate and
were sectioned using a low speed diamond cutter (Buehler) so as to have at least
three overlapping laser tracks. The samples in cross-section were then prepared by
polishing with emery papers of grit sizes ranging from 200 to 1000 ␮m in succession
followed by disc polishing with colloidal silica of 0.3 and 0.05 ␮m to get a mirror
finished surface. The polished samples were then cleaned with acetone and etched
with 5 vol% HF, 3 vol% HNO3, and 92 vol% H2O for 10–20 s by immersion etching
to reveal the microstructural features. A Jeol scanning electron microscope (SEM)
coupled with EDS (energy dispersive spectrometer) was used to characterize for the
microstructural and elemental analysis at different locations of the coatings.
A three dimensional thermal model based on COMSOL’sTM Multiphysics was
adopted in the present work to predict thermal parameters (temperature evolu-
tion and cooling rate) which in turn influence the phase evolutions within the
coatings. The composite nature of the material system (coating + substrate), temper-
ature dependent thermophysical properties, conduction, convection and radiation
dependent heat transfer during laser processing were taken into account. Apart from
this, various other assumptions and dimensions of the geometry considered in the
present work are based on the earlier work by the group [14]. The residence time
(time required to travel the diameter of the beam), the on and off period during each
residence time and the peak power (input power density in W/m2) during the laser
on periods were employed for thermal analysis. The residence time (t) of the laser
beam for a pulsed Nd:YAG laser can be calculated as per the following equation:
Fig. 1. XRD patterns of the samples processed at varying laser pulse frequency of
(a) 10 Hz, (b) 20 Hz, (c) 30 Hz and (d) 40 Hz.
Here, ˛ is the thermal diffusivity and is equal to K/ꢁCp, K is the thermal conduc-
tivity, Cp is the specific heat, and ꢁ is the density (precursor = 3156 kg/m3 [16] and
substrate = 4420 kg/m3 [17]) of the material. At time t = 0 the initial temperature
T = T0 = 298 K was used in the model. For improved accuracy of temperature and
cooling rate evolution, variations in specific heat and thermal conductivity of the
material as a function of temperature were incorporated into the model [16,18].
The equation used to model the balance between the absorbed laser energy and
radiation loss at the surface is given as:
ꢃ
ꢄ
∂T(x, t)
∂x
∂T(y, t)
∂y
∂T(0, t)
∂z
−K
+
+
= ıAI − εꢂ[T(x, y, 0, t)4 − T04
]
(9)
D
ı = 1 for 0 ≤ t ≤ ton
t =
(1)
V
ı = 0 for t > ton
Here, D is the laser beam diameter on the surface and V is the laser scan speed. The
total on time (ton) and off time (toff) of the laser beam within the residence time is
therefore given as:
Here, A is the absorptivity of the material and is taken as 0.1 [14,19], ε is the emmi-
sivity of the material, and ꢂ is the Stefan–Boltzmann constant. The emmisivity of
calcium phosphate tribasic when exposed to 1064 nm wavelength laser beam is not
available in the open literature. Hence, in the present model only the absorptivity
was considered and attempts are being made for in situ emmisivity measurements
under laser processing conditions similar to the ones employed in the present study
and they will be incorporated in future calculations.
f × w × D
ton
=
(2)
(3)
V
toff = t − ton
Here, f is the laser frequency and w is the pulse duration of laser beam. The input
power density or the intensity (I) of the laser beam used in the model was calculated
as per the following equation:
The convection at the bottom surface of the sample during laser processing was
also incorporated into the model and is given by the following equation:
ꢃ
ꢄ
∂T(x, t)
∂x
∂T(y, t)
∂y
∂T(L, t)
∂z
−K
+
+
= h[T(x, y, L, t) − T0]
(10)
D × E × f
I =
(4)
V × ˚ × w
Here, h is the convective heat transfer coefficient (W/m2 K), incorporated as func-
tion of temperature [20], and L the thickness of sample (0.04 mm for the precursor,
Ca–P + 3 mm for the substrate, Ti–6Al–4V). The solutions of the above three equa-
tions were obtained by using the heat transfer module of COMSOL’sTM Multiphysics
package, and the results were discussed in later part of the paper.
Here, E is the input energy and ˚ the cross-sectional area of the laser beam. As,
with increasing pulse frequency, the number of pulses within the residence time of
the laser beam increases, the input energy E of the laser beam contributed by these
pulses is given by the following equation [15]:
ꢀ
ꢂ
N
d
ꢁ
D − (n − 1)b
E =
e
(5)
3. Results and discussions
D
n
Here, Nd is the total number of pulses that can be obtained dividing the total on
time of the laser beam (Table 2) by the pulse duration of laser beam, n corresponds
to each of these pulses and is taken as n = 1, 2, 3, . . . Nd and e is the energy from a
single pulse. The distance traveled by the laser between two successive pulses is b
and calculated as follows:
As the interaction of the laser beam with the precursor and
substrate material is an energy intensive process the precursor
Ca5(OH)(PO4)3 is not expected to be retained and hence X-ray
diffraction studies were carried out to observe the change in phases.
The overlap of XRD patterns of the coatings processed at vary-
ing laser frequencies are represented in Fig. 1. It can be observed
(Fig. 1a–c) that there is no change in the types of phases evolved
when the pulse frequency is varied from 10 to 30 Hz and ␣-TCP,
TiO2, Ti, CaTiO3, and Al are the major phases within the coatings.
Nevertheless, additional phases such as CaO and Al2O3 along with
the above phases are observed (Fig. 1d) as the laser pulse fre-
quency is increased to 40 Hz. From the peak intensities it can be
realized that, although the phase constituents within the coatings
are same for 10, 20 and 30 Hz there is a variation in the amounts of
these phases with varying pulse frequency. The relative amounts of
b = (1 − X) × D
(6)
Here, X is the spot overlap of the laser beam and can be calculated from the following
equation:
V
X = 1 −
(7)
fD
The Fourier’s second law of heat transfer (Eq. (8)) in COMSOL’sTM heat transfer
mode was used to model the energy transfer from the laser beam to the precursor
during coating:
ꢃ
ꢄ
∂T(x, y, z, t)
∂2T(x, t)
∂x2
∂2T(y, t)
∂y2
∂2T(z, t)
∂z2
= ˛
+
+
(8)
∂t

S.R. Paital, N.B. Dahotre / Journal of Alloys and Compounds 487 (2009) 499–503
501
Fig. 2. Relative phase fractions as a function of laser pulse frequency.
phases of interest with regard to bio-application (␣-TCP, TiO2, and,
CaTiO3) were semi-quantitatively calculated as per the following
equation [21]:
Ii
%I =
× 100
(11)
ꢅ
Fig. 3. Temperature evolution as a function of depth for samples processed at vary-
ing laser pulse frequency and the inset showing the cooling rate for all laser pulse
frequencies.
31Ii
Here, Ii is the integrated intensity of the phase in concern normal-
ized to the integrated intensity of the Ti peaks and
ꢅ
3Ii is the sum
1
of these integrated intensities for the three phases. The results as
illustrated in Fig. 2 show a decrease in the relative amounts of TiO2
and ␣-TCP phase and an increase in the relative amount of CaTiO3
phase with increasing pulse frequency. The kinetics and stability
of these phase transformations and the relative amounts of these
phases was understood from the temperature evolutions and cool-
ing rate estimations during processing of the composite system
(coating + substrate) made by using the thermal model as explained
in the earlier section.
The temperature evolutions as a function of depth for all laser
frequencies employed in the present work and corresponding
cooling rates during processing of the composite system are repre-
sented in Fig. 3. It can be observed (Fig. 3) that within the frequency
range of 10–30 Hz the temperatures at the surface (2100, 2680,
3688 K) and corresponding substrate-coating interface (1850, 2400,
3200 K) were high enough to melt the precursor calcium phosphate
tribasic (melting point of 1843 K [16]) and substrate Ti–6Al–4V
(melting point of 1800 K [18]) respectively. Hence, the dissociation
products (␣-TCP, TiO2, and CaTiO3,) are a result of direct interaction
between the calcium phosphate tribasic and the substrate and their
oxidation in the melt pool as per the following possible equations
[4,22,23]:
of the precursor (boiling point of 3500 K [16]) and substrate (boil-
ing point of 3315 K [18]) material. Hence a severe oxidation of
the substrate material has taken place resulting in the presence
of additional oxidation products such as Al2O3 as observed in the
XRD (Fig. 1). Although the temperature at surface reaches as high
as 3688 K for 30 Hz there is no presence of CaO (melting point of
2843 K and boiling point of 3171 K) [14] in the XRD (Fig. 1) unlike
its presence in 40 Hz pulsing. This is attributed to the fact that as
the cooling rates (inset in Fig. 3) for lower frequencies were rela-
tively lower (<9.25 × 106 K/s) compared to the cooling rate of 40 Hz
(11.4 × 106 K/s), there was enough time for most of CaO formed in
the melt pool to evaporate and remaining to involve in formation
of CaTiO3 as per reaction (4). On the contrary, the associated very
high cooling rate for 40 Hz pulsing resulted in solidifying some of
the CaO in the matrix along with formation of CaTiO3 through reac-
tion with CaO. Hence, there was an increase in the relative amount
of CaTiO3 phase and decrease in the TiO2 phase with increasing
laser pulse frequency (Fig. 2).
Microstructure and depth of melt zone across the cross-section
for the coated surfaces were observed using a SEM. Since, there was
no change in phase evolution for the samples processed at 10, 20,
and 30 Hz, for comparison purpose, microstructural evolution and
depth of melt zone across the cross-section were presented for only
the samples processed at 20 and 40 Hz (Fig. 4). For the sample pro-
cessed at 20 Hz the geometry of the textured topography is clearly
visible and the depth of melt is approximately 220 ␮m (Fig. 4a).
A higher magnification SEM image of the coating area, presented
as an inset in Fig. 4a clearly demonstrated the rapid solidification
of the precursor material to form dendrite like structures. The EDS
spectra obtained from a random location in this area indicated the
strong presence of Ca, P, Ti, Al, V and O peaks (inset in Fig. 4a). The
presence of Ti, Al and V atoms within the coating was due to the
fact that a certain amount of dilution has taken place as a part of the
substrate material was also melted during this process. Further, as
2[Ca5(OH)(PO4)3] + TiO2 → CaTiO3 + 3␣-TCP + H2O(g) ↑
␣-TCP + TiO2 → CaTiO3 + ␣-Ca2P2O7
(1)
(2)
(3)
␣-Ca2P2O7 + Ti → CaTiO3 + CaO + P2O3(g) ↑
Once CaO is formed, it can easily react with TiO2 to form CaTiO3
as per the following equation:
CaO + TiO2 → CaTiO3
(4)
Further, as the laser pulse frequency is increased to 40 Hz the
temperature at the surface (4800 K) and at substrate coating inter-
face (4150 K) was sufficient enough to evaporate a major portion
Table 2
Variations in total on time, total off time, melt depth and experimental laser fluence with varying pulse frequency and the theoretical fluence for evaporation of calcium
phosphate tribasic.
Laser pulse frequency (Hz)
Total on time (␮s)
Total off time (ms)
Melt depth (␮m)
Experimental laser
Theoretical fluence for
fluence × 106 (J/kg)
evaporation × 106 (J/kg)
10
20
30
40
750
1500
2250
3000
149.250
148.500
147.750
147.000
300
6.6
17.7
37.0
85.1
220
140
80
4.5

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S.R. Paital, N.B. Dahotre / Journal of Alloys and Compounds 487 (2009) 499–503
of material can be calculated by the following equation:
ꢆ
ꢆ
T
T
v
m
Qtheoretical
=
(Cp dT) + ꢃHm
+
(Cp dT) + ꢃHv
(12)
298
T
m
Here, Cp is the specific heat of calcium phosphate tribasic and its
variation with temperature is taken as Cp = 201.68T0.245 J/kg K10
,
ꢃHm and ꢃHv are the latent heat of melting and latent heat
of vaporization for calcium phosphate tribasic and are taken as
15.5 kJ/mol [16], and 458.24 kJ/mol [16] respectively. With increase
in pulse frequency, the number of pulses within a single beam area
is increased and therefore the experimental energy Qexperimental
delivered per unit mass can be calculated as per the following
equation:
4E
Qexperimental
=
(13)
ꢁCa–PꢄD2l
Here, ꢁCa–P is the density of calcium phosphate tribasic (3156 kg/m3
[16]) and l the melt depth. The theoretical and experimental energy
obtained from these calculations and melt depths measured in the
cross-section are listed in Table 2. While the experimental laser
energies for the samples processed at 10, 20 and 30 Hz are higher
but less than an order of magnitude to that of the theoretical
energy, the experimental energy for the sample processed at 40 Hz
is approximately 2 orders of magnitude higher than the theoretical
energy. Hence, a predominant amount of precursor material likely
to have evaporated while processing at 40 Hz thereby resulting in
a reduced melt depth as stated earlier. Further, for the sample pro-
cessed at 40 Hz the total on time of the laser beam (Table 2) was
sufficiently long (3000 ␮s) as compared to the samples processed
at 10, 20 and 30 Hz, for formation of a stable plasma on the surface.
Such plasma is likely to block the incoming laser beam and further
reduce the melt depth. The presence of cracks (Fig. 4b) for the sam-
ple processed at 40 Hz might be due to the shock waves generated
at the interface as a result of the stable plasma plume.
4. Conclusions
From the model calculations it was observed that as the laser
pulse frequency is increased, the surface temperature and the cool-
ing rate increased. This in turn resulted in a reduction of the relative
phase amounts of ␣-TCP and TiO2 and an increase in CaTiO3 phase.
Further, with increasing pulse frequency the input energy needed
to vaporize a unit mass of material increases beyond the theoretical
energy. This in turn resulted in evaporation of precursor material at
higher laser frequencies (40 Hz). The stable plasma plume formed
on the surface at such higher laser frequencies is likely to decouple
the incoming laser beam and further reduce the melt depth.
Fig. 4. SEM image and the corresponding EDS spectra for the sample processed at
(a) 20 Hz and (b) 40 Hz.
the processing was carried out in an ambient atmosphere and tem-
perature developed at the surface was very high (>2500 K, Fig. 3),
a part of the precursor and substrate material may have oxidized
for the presence of O peak. For samples processed at 40 Hz, the sur-
face is less rough (Fig. 4b) compared to the sample processed at
20 Hz (Fig. 4a) and the depth of melt zone is approximately 80 ␮m
(Fig. 4b). The less surface roughness in 40 Hz sample is attributed to
the increased pulse overlap with increasing pulse frequency [24].
In addition EDS (inset in Fig. 4b) indicate that 40 Hz sample has
very weak peak of Ca and P from coated region. Such weak peaks
of Ca and P along with lower melt depth in 40 Hz sample compared
to 20 Hz sample even with higher input laser energy (Table 1) is
explained in the following section.
The correlation between melt depth and pulse frequency
strongly depends upon the input energy and corresponding ther-
mal parameters (temperature and cooling rate) and physical
conditions generated and prevailed during processing. Depending
upon the input energy, the temperature will rise to melt or vaporize
the material. Especially, during laser material processing, presence
of vapor over the surface of sample strongly influences the trans-
fer (coupling) of the incoming laser beam energy and accordingly
affects the chemical and physical nature of modified surface region.
The theoretical energy Qtheoretical required to vaporize a unit mass
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