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Modification of titanium by high power electron beams
Surface and Coatings Technology 114 (1999) 143–147
Modification of titanium by high power electron beams V. Lavrentiev a, *, C. Hammerl b, B. Renner b, M. Zeitler b, B. Rauschenbach b, N. Gaponenko a,c, Yu. Lonin a,c, A. Pisanenko a a SIMPLEX, Institute of Applied Physics, Kirova Str. 36/11, 244030 Sumy, Ukraine b Universita¨t Augsburg, Institut fu¨r Physik, Memminger Str. 6, D-86135 Augsburg, Germany c Kharkov Physical Technical Institute, Akademicheskaya Str. 1, 310108 Kharkov, Ukraine Received 12 October 1998; accepted 24 January 1999
Abstract Irradiation of titanium was performed with high power electron beams. The electron energy was 800 keV, the pulse duration was 10 ns and energy density injected into the sample by one pulse was 20 J cm−2. Hardness measurements of irradiated samples permit the detection of two different modified layers. The hardness of these two layers depends on the pulse number. The states of stress and the grain size in irradiated samples were determined by X-ray diffraction. XRD shows the presence of the high pressure v phase in titanium after power electron beam exposure. The explanation of the results is based on stress waves, which arise due to such exposures. The observed hardening of irradiated titanium is a result of an intensive process of twinning produced by shear stress waves. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Electron beam; Titanium; Stress; Phase; Twinning
1. Introduction In previous work it has been shown that high power electron beams (HPEB) can be used successfully for the modification of various materials [1–3]. The features of energy dissipation during interaction of the fast electrons with the target atoms permit the creation of deep modified layers [1,2]. The depth of the modified layer and the peculiarities of modification are defined by the irradiation parameters such as electron energy, power density and pulse length. The creation of deep layers in metals may lead to an improvement of important material properties. The results from a study of hardening and stress formation in titanium after HPEB processing with a pulse duration in the nanosecond regime are presented.
2. Experimental procedures Polycrystalline titanium foils (99.98 mass%) with a thickness of 0.3 mm and a size of 15×15 mm2 were used as a target. The initial grain size was 1–3 mm. The irradiation of the samples was performed by a pulse electron accelerator with an acceleration voltage of * Corresponding author. Fax: +380 542 223760. E-mail address: [email protected] ( V. Lavrentiev)
800 kV, a beam current of 10 kA and a pulse duration of 10 ns on half of the voltage pulse height. The working pressure was about 10−3 Pa. To prevent the influence of the residual vacuum impurities on the modification process, an aluminium foil with a thickness of 50 mm was mounted in front of the surface of the titanium sample. The samples were exposed to one and five pulses. The study of the phase composition and the stress states of the irradiated samples was undertaken by X-ray diffraction ( XRD). Using the wavelength of Cu Ka the 2h interval was chosen from 30° up to 90° with a step size of 0.02°. The microhardness measurements were performed using a MICROMET-II device with various loads from 10 to 1000 gf. The value of the microhardness for each load was determined as an average value of ten measurements. The depth of the indentation (x) for any load was calculated using the average size of the indentation diagonals (d) and the shape of the device diamond pyramid using the equation x=(d/2) tan 22°.
3. Experimental results 3.1. Hardness measurements In Fig. 1 the increase of the hardness H of the irradiated samples to the hardness H of the unirradiated o
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Fig. 1. Dependence of microhardness on the indentation depth for unirradiated and HPEB irradiated titanium samples.
sample (DH=H−H ) is shown as a function of the o indentation depth. This plot reveals a distinction of the modified layer in two different hardened regions. The first region (subsurface region) extends from 0 up to 10 mm in depth and the second region (underlayer) is detected from 10 to 20 mm. The variation of the hardness depth profile with increasing HPEB pulse number is displayed. Thus, the increase of the pulse number from 1 to 5 leads to an increase in the microhardness of the subsurface region. The hardness maximum in the underlayer region (indicated in Fig. 1 by vertical lines) is slightly shifted towards the sample surface by increasing the pulse number. 3.2. XRD study A detailed analysis of XRD diffractograms of unirradiated and irradiated samples shows some differences in the peak positions and peak shapes. The shifting in the peak positions reveals the presence of macrostress (stress of the first type) in the modified layer. This can be seen in Fig. 2, where the (011) titanium peak of different treated samples is presented. The (011) peaks were also used for the calculation of the macrostress by [4]:
A B
s =E x
d−d d
0 ,
(1)
0 where d and d is the spacing of the planes parallel to o the sample surface for the irradiated and unirradiated sample, respectively and E is the Young’s modulus (E =120 GPa). The data of the macrostress calculation Ti applied for HPEB irradiated samples obtained using Eq. (1) are presented in Table 1. The value of macrostress obtained by analysing the (011) titanium peak correlates with the depth of X-ray penetration in the subsurface region of titanium after HPEB irradiation. Therefore the compressive macrostress induced by one pulse is reduced by the increase of four further pulses.
Fig. 2. XRD diffractogram for unirradiated and HPEB irradiated titanium samples showing the Ti (011) peak. The vertical lines indicate the peak positions for unirradiated and irradiated samples Table 1 The values of macrostress (s) in the subsurface region of titanium after irradiation by HPEB with various numbers of pulses (n) n
Compressive stress s (MPa)
1 5
260 52
For the determination of the average structure size
p and the microstresses s (stresses of the second i type) by XRD peak broadening, Wilson’s method was used [5]. For this method, the variance W for different 2h intervals D(2h) of (011) XRD titanium peaks was calculated and the values of p and s were determined i with use of l W = +4 e2 tan2 h (D2h), (2) 2h 2p2 p cos h 0 0 where h is the gravitation centre position of XRD o peak, e2 is the average value of the square of the microstrain and l is the wavelength [5]. The data of microstresses and substructure size in the subsurface region of the HPEB irradiated titanium samples are presented in Table 2. As shown, the values of p and s vary with the pulse number. The XRD data of a the i sample irradiated with five pulses show a small peak of Table 2 Microstress (s ), average strain e21/2 and average size p of the i substructure in the subsurface region of titanium irradiated by HPEB with various numbers of pulses (n) n
s (MPa) i
e21/2 (×10−3)
p (nm)
1 5
250 395
2.075 3.288
27 81
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145
Fig. 3. XRD peaks corresponding to the high pressure v phase in titanium after HPEB irradiation by one pulse and five pulses.
Fig. 5. Time evolution of temperature in layer A of titanium due to HPEB exposure.
the v-Ti phase at 60.67° (Fig. 3, bottom section), which confirms an irradiation-induced phase transformation, whereas an irradiation with one pulse (Fig. 3, top section) shows no effect on the phase composition.
surface of the titanium sample. The profile of the electron energy loss is similar to the temperature profile in the first moment of the exposure. The heating of the sample by the high power pulse is concentrated in the layer located 20–30 mm of the surface, which further on is called the layer A (Fig. 4). The thickness of this layer is determined by the rate of the electron energy loss in the material in the region between the sample surface and layer A as well as the pulse duration. Under the experimental conditions mentioned above, the thickness of the layer A does not exceed 5 mm [2]. In Fig. 5 the temperature evolution over time at the beginning of the electron beam exposure is presented as calculated from the thermal conductivity equation [6 ]. As Fig. 5 shows, the temperature maximum significantly exceeds the temperature of the a-Tib-Ti phase transformation. The heating rate is found to be 1011–1012 K s−1. Such a nonequilibrium condition in a solid leads to the formation of stress waves that start their propagation from the heated layer A. The start amplitude of the compressive component of these waves can be estimated from the maximum elastic stress formed nearest of the layer A. In this case the thermoelastic strain e nearest of the T layer A is estimated as
4. Discussion When fast electrons penetrate into a material they lose energy as a result of inelastic interactions with electrons of the target atoms. During this process, the depth distribution profile of the electron energy loss is well described by an Gaussian function [1]. The penetration depth of the fast electrons depends on the electron energy and the target material. The range of electrons with an energy of 800 keV in titanium is more than 120 mm [1,2]. The location of the aluminium foil with a thickness of 50 mm in front of the titanium surface shifts the maximum in electron energy loss towards the titanium surface. Therefore, according to our estimations, the maximum of the electron energy loss in these experiments locates in the depth of 20–30 mm from the free
e =a DT, (3) T where a is the coefficient of the thermal expansion, DT is the change in temperature induced by electron beam exposure. Thus the compressive stress is s=Ea DT.
Fig. 4. Scheme showing the formation of specific layers in titanium after HPEB exposure. S is the subsurface region, U is the underlayer and A is the heating layer A. T(x) is a qualitative plot of the temperature profile of the sample in the moment of exposure.
(4)
For an estimation of s we must consider that about 20% of the electron energy is lost in the aluminium foil and the subsurface region of titanium ( layers S and U, Fig. 4) [2]. For DT=2500 K, E =120 GPa and a= Ti 10−5 K−1 [7], s the calculated is 3 GPa. Consequently the direct phase transformation a-Tiv-Ti with a stress threshold of 2 GPa can take place [8,9]. Of course, it can also be assumed that an v phase formation by
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transformation of a-Tib-Tiv-Ti takes place. However this is less possible from the energetic point of view. The phase transformation a-Tib-Ti leads to a lower material density (r =4.507 g cm−3 and a r =4.350 g cm−3 [8]) and to an increase of the internal b energy due to the additional elastic strain e that can ph be estimated as r e = b =0.025. ph r a
(5)
The total compressive stress s=E(e +e ) must T ph therefore increase to 7.2 GPa in order to activate an a-Tib-Ti transformation. Such a high level of compressive stress will not be realised in the system. Moreover the temperature in the nearest region of the thin layer A may be not high enough for an a-Tib-Ti phase transformation. So, as a result of the HPEB irradiation, the v phase in titanium arises by a direct a-Tiv-Ti phase transformation. The time of this transformation must be compared with the duration of exposure; hence it may be realised by transformation of the martensitic type, only. The presence of the v phase in titanium samples after exposure confirms the conservation of high internal stresses in the nearest region of the layer A. This stress (macrostress) is formed as a result of a high concentration of point defects and its redistribution. The value of the macrostress depends on the point defect concentration [10]. The high level of the compressive stresses near layer A can be determined by a large concentration of nonequilibrium vacancies formed as a result of the high rate cooling process (see Fig. 4). In a first order approximation, the value of the concentration of nonequilibrium vacancies (Dc ) in layer A can be estimated v as Dc #e =0.025 [10]. Such a high level of the nonequiv T librium vacancies may be formed in metals as a consequence of the high power pulse exposure, e.g. during high power ion beam irradiation [11]. The processes of the redistribution of these nonequilibrium vacancies during irradiation and the point defects produced by the stress waves lead to a hardening of the underlayer U. As shown in [1,12], compressive and shear stress waves are formed as a result of such irradiation. In the case of these experiments the compressive and shear stress waves propagate from the heated layer A to both sides of the horizontal axis x (see Fig. 4). In our view the shear stress waves contribute primarily in the process of the production of structural defects in the subsurface region. Under the influence of shear stress waves, the screw dislocations begin to move and point defects are produced from the steps on the dislocation line. This process leads to an increase in the point defect concentration and results in the formation of macrostresses and some hardening [13]. However, the base hardening of the titanium subsurface region is caused by twinning
processes [14] that take place during high rate pulse loading [15]. The twinning under the conditions of HPEB irradiation leads to a nanocrystalline structure (see Table 2). The increase in the substructure average size p and the value of the microstresses s with higher i HPEB pulse numbers is caused by the growth of twins appearing after the exposure to the first pulse, because the energy of the shear stress wave is too low for further twinning of the newly formed nanocrystalline grains. The growth of twins leads to a higher twinning dislocation density along the twin boundaries [15] and therefore to a higher value of hardness of the subsurface region after an exposure to five pulses (see Fig. 1). The increase of the microstress in this case is caused by the elastic interactions of the growing twins. The disappearing of the nonequilibrium vacancies in the twinning dislocations, which are formed after the first pulse leads to a reduction of the macrostresses (see Table 1). The formation of two layers with different hardness (subsurface region and underlayer) may be explained by the interaction of the emitted shear waves and the reflected ones from the sample surface [16 ]. The wavelength of the shear wave l is given by e l = e
S
m r
t,
(6)
where m is the shear modulus (for Ti m=45.6 GPa [7]), t is the pulse duration (here t=10−8 s) and r is the density. For titanium, a wavelength of the shear wave of 32 mm can be obtained [6 ]. Since the distance Dx between points with maximum amplitudes in the standing wave is equal to half of the wavelength, l /2=16 mm, can be determined, which correlates well e with the distance between the maxima of microhardness (see Fig. 1). So the development of large amplitudes of the shear waves as a result of the interaction of running and reflecting waves leads to intensive formation of structural defects and as a consequence, an increase in the hardness. The displacement of the deeper microhardness maximum towards the sample surface as a result of the increasing pulse number is caused by a point defect flux induced by the heating from the layer A.
5. Conclusions As a result of the HPEB irradiation of titanium, two maxima in the depth profile of microhardness are shown. These maxima correlate with two modified layers: a subsurface region (up to 10 mm in depth) and an underlayer (from 10 to 20 mm in depth). The dissipation of the fast electron energy leads to a heating of a deep layer A and therefore to the development of shear waves. The interaction of those emitted shear waves and waves, reflected by the sample surface, leads to high
V. Lavrentiev et al. / Surface and Coatings Technology 114 (1999) 143–147
amplitudes and therefore to intensive twinning and hardening. A point defect flux is caused by the heating of layer A and effects the formation of the underlayer. The high pressure v phase in titanium was observed and can be explained by a compressive stress near layer A. HPEB leads to a direct a-Tiv-Ti phase transformation.
Acknowledgement This research was supported by the DRL program of BMBF under project No UKR005-97.
References [1] J.M. Poate, G. Foti, D. Jacobson ( Eds.), Surface Modification and Alloying by Laser, Ion and Electron Beams, Plenum, New York, 1985.. [2] R. Mehnert, in: P. Misaelides ( Ed.), Kluwer, Dordrecht, 1995, p. 557. [3] E. D’Anna, G. Leggieri, A. Luches, Thin Solid Films 182 (1989) 215. [4] B.D. Cullity, Elements of X-Ray Diffraction, Addision-Wesley, Reading, MA, 1978. [5] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedures For
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Polycrystalline and Amorphous Materials, Wiley, New York, 1974. [6 ] Y. Hashimoto, M. Yatsuzuka, H. Uchida, T. Yamasaki, Proceedings of 11th International Conference on High Power Particle Beams, BEAMS’96, Prague, June 10–14 (1996) 848. [7] Metals Handbook, Properties and Selection: Nonferrous Alloy and Special-Purpose Materials, 10th edition, Vol. 2, ASM International, Metals Park, OH, 1990. [8] J.L. Murray ( Ed.), Phase Diagrams of Binary Titanium Alloys, ASM International, Metals Park, OH, 1990. [9] R.W. Cahn, E.J. Kramer, P. Haasen ( Eds.), Material Science and Technology, A Comprehensive Treatise, Vol. 5, Phase Transformations in Materials VCH, Weinheim, 1991, Vol. Ed. P. Haasen. [10] Ya.E. Geguzin, Diffusion Region, Nauka, Moscow, 1979. [11] V.I. Lavrent’ev, Phys. Solid State 36 (12) (1994) 1896. [12] S. Fassbender, B. Hoffman, W. Arnold, in: G.M. Crean, M. Locatelli, J. McGilp (Eds.), Proceedings of Symposium C on Acoustic, Thermal Wave and Optical Characterisation of Materials of the 1989 E-MRS Conference, Strasbourg, 30 May–2 June, 1989, North-Holland, Amsterdam, 1990, p. 37. [13] A.D. Damask, G.J. Dienes, Point Defects in Metals, Gordon and Breach, New York, 1963. [14] V.S. Boyko, R.I. Garber, A.M. Kossevich, Reversible Crystal Plasticity, American Institute of Physics, New York, 1994. [15] S. Leclercq, C. Nguy, P. Bensussan, in: J. Harding ( Ed.), Mechanical Properties of Materials at High Rates of Strain, 1989. Proceedings of the 4th International Conference on the Mechanical Properties of Materials at High Rates of Strain, Oxford, 19–22 March, Institute of Physics, Bristol, 1989, p. 299. Inst. Phys. Conf. Ser. 102: Session 6b. [16 ] A. Bedford, D.S. Drumheller, Introduction to Elastic Wave Propagation, Wiley, New York, 1994.
Modification of titanium by high power electron beams V. Lavrentiev a, *, C. Hammerl b, B. Renner b, M. Zeitler b, B. Rauschenbach b, N. Gaponenko a,c, Yu. Lonin a,c, A. Pisanenko a a SIMPLEX, Institute of Applied Physics, Kirova Str. 36/11, 244030 Sumy, Ukraine b Universita¨t Augsburg, Institut fu¨r Physik, Memminger Str. 6, D-86135 Augsburg, Germany c Kharkov Physical Technical Institute, Akademicheskaya Str. 1, 310108 Kharkov, Ukraine Received 12 October 1998; accepted 24 January 1999
Abstract Irradiation of titanium was performed with high power electron beams. The electron energy was 800 keV, the pulse duration was 10 ns and energy density injected into the sample by one pulse was 20 J cm−2. Hardness measurements of irradiated samples permit the detection of two different modified layers. The hardness of these two layers depends on the pulse number. The states of stress and the grain size in irradiated samples were determined by X-ray diffraction. XRD shows the presence of the high pressure v phase in titanium after power electron beam exposure. The explanation of the results is based on stress waves, which arise due to such exposures. The observed hardening of irradiated titanium is a result of an intensive process of twinning produced by shear stress waves. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Electron beam; Titanium; Stress; Phase; Twinning
1. Introduction In previous work it has been shown that high power electron beams (HPEB) can be used successfully for the modification of various materials [1–3]. The features of energy dissipation during interaction of the fast electrons with the target atoms permit the creation of deep modified layers [1,2]. The depth of the modified layer and the peculiarities of modification are defined by the irradiation parameters such as electron energy, power density and pulse length. The creation of deep layers in metals may lead to an improvement of important material properties. The results from a study of hardening and stress formation in titanium after HPEB processing with a pulse duration in the nanosecond regime are presented.
2. Experimental procedures Polycrystalline titanium foils (99.98 mass%) with a thickness of 0.3 mm and a size of 15×15 mm2 were used as a target. The initial grain size was 1–3 mm. The irradiation of the samples was performed by a pulse electron accelerator with an acceleration voltage of * Corresponding author. Fax: +380 542 223760. E-mail address: [email protected] ( V. Lavrentiev)
800 kV, a beam current of 10 kA and a pulse duration of 10 ns on half of the voltage pulse height. The working pressure was about 10−3 Pa. To prevent the influence of the residual vacuum impurities on the modification process, an aluminium foil with a thickness of 50 mm was mounted in front of the surface of the titanium sample. The samples were exposed to one and five pulses. The study of the phase composition and the stress states of the irradiated samples was undertaken by X-ray diffraction ( XRD). Using the wavelength of Cu Ka the 2h interval was chosen from 30° up to 90° with a step size of 0.02°. The microhardness measurements were performed using a MICROMET-II device with various loads from 10 to 1000 gf. The value of the microhardness for each load was determined as an average value of ten measurements. The depth of the indentation (x) for any load was calculated using the average size of the indentation diagonals (d) and the shape of the device diamond pyramid using the equation x=(d/2) tan 22°.
3. Experimental results 3.1. Hardness measurements In Fig. 1 the increase of the hardness H of the irradiated samples to the hardness H of the unirradiated o
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Fig. 1. Dependence of microhardness on the indentation depth for unirradiated and HPEB irradiated titanium samples.
sample (DH=H−H ) is shown as a function of the o indentation depth. This plot reveals a distinction of the modified layer in two different hardened regions. The first region (subsurface region) extends from 0 up to 10 mm in depth and the second region (underlayer) is detected from 10 to 20 mm. The variation of the hardness depth profile with increasing HPEB pulse number is displayed. Thus, the increase of the pulse number from 1 to 5 leads to an increase in the microhardness of the subsurface region. The hardness maximum in the underlayer region (indicated in Fig. 1 by vertical lines) is slightly shifted towards the sample surface by increasing the pulse number. 3.2. XRD study A detailed analysis of XRD diffractograms of unirradiated and irradiated samples shows some differences in the peak positions and peak shapes. The shifting in the peak positions reveals the presence of macrostress (stress of the first type) in the modified layer. This can be seen in Fig. 2, where the (011) titanium peak of different treated samples is presented. The (011) peaks were also used for the calculation of the macrostress by [4]:
A B
s =E x
d−d d
0 ,
(1)
0 where d and d is the spacing of the planes parallel to o the sample surface for the irradiated and unirradiated sample, respectively and E is the Young’s modulus (E =120 GPa). The data of the macrostress calculation Ti applied for HPEB irradiated samples obtained using Eq. (1) are presented in Table 1. The value of macrostress obtained by analysing the (011) titanium peak correlates with the depth of X-ray penetration in the subsurface region of titanium after HPEB irradiation. Therefore the compressive macrostress induced by one pulse is reduced by the increase of four further pulses.
Fig. 2. XRD diffractogram for unirradiated and HPEB irradiated titanium samples showing the Ti (011) peak. The vertical lines indicate the peak positions for unirradiated and irradiated samples Table 1 The values of macrostress (s) in the subsurface region of titanium after irradiation by HPEB with various numbers of pulses (n) n
Compressive stress s (MPa)
1 5
260 52
For the determination of the average structure size
p and the microstresses s (stresses of the second i type) by XRD peak broadening, Wilson’s method was used [5]. For this method, the variance W for different 2h intervals D(2h) of (011) XRD titanium peaks was calculated and the values of p and s were determined i with use of l W = +4 e2 tan2 h (D2h), (2) 2h 2p2 p cos h 0 0 where h is the gravitation centre position of XRD o peak, e2 is the average value of the square of the microstrain and l is the wavelength [5]. The data of microstresses and substructure size in the subsurface region of the HPEB irradiated titanium samples are presented in Table 2. As shown, the values of p and s vary with the pulse number. The XRD data of a the i sample irradiated with five pulses show a small peak of Table 2 Microstress (s ), average strain e21/2 and average size p of the i substructure in the subsurface region of titanium irradiated by HPEB with various numbers of pulses (n) n
s (MPa) i
e21/2 (×10−3)
p (nm)
1 5
250 395
2.075 3.288
27 81
V. Lavrentiev et al. / Surface and Coatings Technology 114 (1999) 143–147
145
Fig. 3. XRD peaks corresponding to the high pressure v phase in titanium after HPEB irradiation by one pulse and five pulses.
Fig. 5. Time evolution of temperature in layer A of titanium due to HPEB exposure.
the v-Ti phase at 60.67° (Fig. 3, bottom section), which confirms an irradiation-induced phase transformation, whereas an irradiation with one pulse (Fig. 3, top section) shows no effect on the phase composition.
surface of the titanium sample. The profile of the electron energy loss is similar to the temperature profile in the first moment of the exposure. The heating of the sample by the high power pulse is concentrated in the layer located 20–30 mm of the surface, which further on is called the layer A (Fig. 4). The thickness of this layer is determined by the rate of the electron energy loss in the material in the region between the sample surface and layer A as well as the pulse duration. Under the experimental conditions mentioned above, the thickness of the layer A does not exceed 5 mm [2]. In Fig. 5 the temperature evolution over time at the beginning of the electron beam exposure is presented as calculated from the thermal conductivity equation [6 ]. As Fig. 5 shows, the temperature maximum significantly exceeds the temperature of the a-Tib-Ti phase transformation. The heating rate is found to be 1011–1012 K s−1. Such a nonequilibrium condition in a solid leads to the formation of stress waves that start their propagation from the heated layer A. The start amplitude of the compressive component of these waves can be estimated from the maximum elastic stress formed nearest of the layer A. In this case the thermoelastic strain e nearest of the T layer A is estimated as
4. Discussion When fast electrons penetrate into a material they lose energy as a result of inelastic interactions with electrons of the target atoms. During this process, the depth distribution profile of the electron energy loss is well described by an Gaussian function [1]. The penetration depth of the fast electrons depends on the electron energy and the target material. The range of electrons with an energy of 800 keV in titanium is more than 120 mm [1,2]. The location of the aluminium foil with a thickness of 50 mm in front of the titanium surface shifts the maximum in electron energy loss towards the titanium surface. Therefore, according to our estimations, the maximum of the electron energy loss in these experiments locates in the depth of 20–30 mm from the free
e =a DT, (3) T where a is the coefficient of the thermal expansion, DT is the change in temperature induced by electron beam exposure. Thus the compressive stress is s=Ea DT.
Fig. 4. Scheme showing the formation of specific layers in titanium after HPEB exposure. S is the subsurface region, U is the underlayer and A is the heating layer A. T(x) is a qualitative plot of the temperature profile of the sample in the moment of exposure.
(4)
For an estimation of s we must consider that about 20% of the electron energy is lost in the aluminium foil and the subsurface region of titanium ( layers S and U, Fig. 4) [2]. For DT=2500 K, E =120 GPa and a= Ti 10−5 K−1 [7], s the calculated is 3 GPa. Consequently the direct phase transformation a-Tiv-Ti with a stress threshold of 2 GPa can take place [8,9]. Of course, it can also be assumed that an v phase formation by
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transformation of a-Tib-Tiv-Ti takes place. However this is less possible from the energetic point of view. The phase transformation a-Tib-Ti leads to a lower material density (r =4.507 g cm−3 and a r =4.350 g cm−3 [8]) and to an increase of the internal b energy due to the additional elastic strain e that can ph be estimated as r e = b =0.025. ph r a
(5)
The total compressive stress s=E(e +e ) must T ph therefore increase to 7.2 GPa in order to activate an a-Tib-Ti transformation. Such a high level of compressive stress will not be realised in the system. Moreover the temperature in the nearest region of the thin layer A may be not high enough for an a-Tib-Ti phase transformation. So, as a result of the HPEB irradiation, the v phase in titanium arises by a direct a-Tiv-Ti phase transformation. The time of this transformation must be compared with the duration of exposure; hence it may be realised by transformation of the martensitic type, only. The presence of the v phase in titanium samples after exposure confirms the conservation of high internal stresses in the nearest region of the layer A. This stress (macrostress) is formed as a result of a high concentration of point defects and its redistribution. The value of the macrostress depends on the point defect concentration [10]. The high level of the compressive stresses near layer A can be determined by a large concentration of nonequilibrium vacancies formed as a result of the high rate cooling process (see Fig. 4). In a first order approximation, the value of the concentration of nonequilibrium vacancies (Dc ) in layer A can be estimated v as Dc #e =0.025 [10]. Such a high level of the nonequiv T librium vacancies may be formed in metals as a consequence of the high power pulse exposure, e.g. during high power ion beam irradiation [11]. The processes of the redistribution of these nonequilibrium vacancies during irradiation and the point defects produced by the stress waves lead to a hardening of the underlayer U. As shown in [1,12], compressive and shear stress waves are formed as a result of such irradiation. In the case of these experiments the compressive and shear stress waves propagate from the heated layer A to both sides of the horizontal axis x (see Fig. 4). In our view the shear stress waves contribute primarily in the process of the production of structural defects in the subsurface region. Under the influence of shear stress waves, the screw dislocations begin to move and point defects are produced from the steps on the dislocation line. This process leads to an increase in the point defect concentration and results in the formation of macrostresses and some hardening [13]. However, the base hardening of the titanium subsurface region is caused by twinning
processes [14] that take place during high rate pulse loading [15]. The twinning under the conditions of HPEB irradiation leads to a nanocrystalline structure (see Table 2). The increase in the substructure average size p and the value of the microstresses s with higher i HPEB pulse numbers is caused by the growth of twins appearing after the exposure to the first pulse, because the energy of the shear stress wave is too low for further twinning of the newly formed nanocrystalline grains. The growth of twins leads to a higher twinning dislocation density along the twin boundaries [15] and therefore to a higher value of hardness of the subsurface region after an exposure to five pulses (see Fig. 1). The increase of the microstress in this case is caused by the elastic interactions of the growing twins. The disappearing of the nonequilibrium vacancies in the twinning dislocations, which are formed after the first pulse leads to a reduction of the macrostresses (see Table 1). The formation of two layers with different hardness (subsurface region and underlayer) may be explained by the interaction of the emitted shear waves and the reflected ones from the sample surface [16 ]. The wavelength of the shear wave l is given by e l = e
S
m r
t,
(6)
where m is the shear modulus (for Ti m=45.6 GPa [7]), t is the pulse duration (here t=10−8 s) and r is the density. For titanium, a wavelength of the shear wave of 32 mm can be obtained [6 ]. Since the distance Dx between points with maximum amplitudes in the standing wave is equal to half of the wavelength, l /2=16 mm, can be determined, which correlates well e with the distance between the maxima of microhardness (see Fig. 1). So the development of large amplitudes of the shear waves as a result of the interaction of running and reflecting waves leads to intensive formation of structural defects and as a consequence, an increase in the hardness. The displacement of the deeper microhardness maximum towards the sample surface as a result of the increasing pulse number is caused by a point defect flux induced by the heating from the layer A.
5. Conclusions As a result of the HPEB irradiation of titanium, two maxima in the depth profile of microhardness are shown. These maxima correlate with two modified layers: a subsurface region (up to 10 mm in depth) and an underlayer (from 10 to 20 mm in depth). The dissipation of the fast electron energy leads to a heating of a deep layer A and therefore to the development of shear waves. The interaction of those emitted shear waves and waves, reflected by the sample surface, leads to high
V. Lavrentiev et al. / Surface and Coatings Technology 114 (1999) 143–147
amplitudes and therefore to intensive twinning and hardening. A point defect flux is caused by the heating of layer A and effects the formation of the underlayer. The high pressure v phase in titanium was observed and can be explained by a compressive stress near layer A. HPEB leads to a direct a-Tiv-Ti phase transformation.
Acknowledgement This research was supported by the DRL program of BMBF under project No UKR005-97.
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