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Damage in aluminum, zinc and tin from a nanosecond electric pulse discharge
Materials Science and Engineering, 64 (1984) 247-254
D a m a g e in Discharge
247
Aluminum, Zinc and Tin f r o m a N a n o s e c o n d E l e c t r i c P u l s e
C. G. WAKADE, NARENDRA B. DAHOTRE and K. MUKHERJEE Department of Metallurgy, Mechanics and Materials Science, Michigan State University, East Lansing, M148824-1226 (U.S.A.)
(Received October 18, 1983; in revised form December 6, 1983)
SUMMARY Microstructural effects associated with an electrical pulse discharge o f 36 ns duration on aluminum, zinc and tin samples have been investigated. These experiments were conducted in air as well as in a pure N2 atmosphere. The effects o f spark gap distance, operating potential and discharge gas pressure were studied. A linear relationship between the crater diameter and the operating potential or discharge gas pressure was observed. Adjacent to the damage site, plastic deformation in the form o f slip as well as a concentric ripple pattern was observed. These latter effects are similar to the deformation behavior associated with damage from a short duration laser pulse.
1. INTRODUCTION Changes in the properties of surface and subsurfaces of metallic materials due to a high energy electric pulse discharge have been the subject of several publications [1-4]. The nature of the damage produced by electrical discharges depends on the type of spark source and the nature of the electrodes as well as on the experimental conditions under which the spark source is operated. Holler [5] has reported compositional changes in alloyed cathodes due to multiple discharges lasting for seconds. A similar compositional change has also been reported by Basharov et al. [1] for discharges of microsecond duration. To date, there exists very little information regarding the microstructurai changes associated with such pulse discharges. If a properly impedance-matched high voltage discharge is used, then a large a m o u n t of energy is released, which causes rapid melting 0025-5416/84/$3.00
and subsequent resolidification of a thin surface layer. The a m o u n t of melting depends on experimental conditions such as the energy input, the spark gap, the nature of the ionization gas etc. as well as on the thermophysical properties of the sample. Apart from the gross microstructural changes such as the melting and crater formation, microscopic defects such as dislocations and point defects are also produced in the vicinity of the damage site. In the present study, microstructural effects due to spark discharge on three low melting pure metals, aluminum, zinc and tin, were investigated. 2. EXPERIMENTAL PROCEDURE Electrical sparks of 36 ns duration were obtained in a spark chamber by discharging a charged cable. A nanosecond pulser (Microwave Associates Inc.) was used for this purpose. The anode, in all cases, was a tungsten needle about 40 pm in diameter, and the material to be studied was used as the cathode. High purity (99.999%) aluminum, zinc and tin were investigated in this study. The applied voltage between the electrodes could be varied from about 500 to 3000 V. The spark gap setting could be adjusted accurately by a micrometer mechanism as shown schematically in Fig. 1. The spark gap was varied from 25 to 200 pm. The specimens were annealed to remove any possible residual stresses prior to metallographic preparation and final electropolishing. 3. RESULTS AND DISCUSSION Figure 2 shows a typical microcrater produced on tin specimens by a 2 kV spark dis@ Elsevier Sequoia/Printed in The Netherlands
248 -
~ Gas chamber~
Gas inlet - - ~ . ~ Inlet valve
II
l I
*~to nanosecond pulser
Discharge
cable
ressure gauge ~gas outlet Outlet valve
Tungsten needle -Specimen Stage with micrometer to adjust spark gap
Fig. 1. Schematic diagram showing the experimental set-up for electric pulse discharge.
Fig. 2. (a) Photomicrograph of microcrater produced in a tin specimen in air (applied voltage, 2 kV; spark
gap, 50 p_m); (b) magnified view of the grain boundary shown in (a) by an arrow.
charge in air. Surrounding the m ol t en crater a wavy deform at i on pattern is seen. The spacing of the wavy d e f o r m a t i o n zone near the microcrater is larger than those at a larger radial distance f r o m the center of the damaged spot. It is interesting to n o t e that the continuity of these bands is n o t disrupted by the grain boundaries, as shown in Figs. 2(a) and 2(b). A similar wavy plastic d e f o r m a t i o n around a damage spot from a pulsed laser has been report ed [6-9]. Some researchers [6, 7, 9, 10] have tried to explain this deform at i on mode by invoking interference of the incident and the reflected laser beams. However, in the present case there is no possibility of such interference since the source of energy is not a coherent p h o t o n energy. The alternative explanation, as suggested by Mukherjee et al. [ 11 ], thus seems to be more appropriate in our present case. The mechanism suggested by t h e m is as follows. When a large a m o u n t of energy is deposited on the surface of a substrate in a very short time (e.g. nanoseconds), a very rapid temperature rise occurs and the volume of the material, within the irradiated or affected region, tends to expand. However, the adjacent lattice cannot relax at a rate commensurate with the rate of increase in temperature. Thus, the local energy radiates out in the form of an elastic shock wave. If the stored elastic energy in the shock front is greater than the plastic yielding energy, then the material undergoes a permanent plastic deformation. The undulations are then the nodes of the propagating wave. This t ype of d e f o r m a t i o n in a crystalline material also implies a non-conservative motion of dislocations. Figure 3 shows that together with this wavy deform at i on process there is also some crystallographic slip. The relative amounts of slip and wavy deform at i on appear to be a function of the energy input. At lower input energies, more slip and less wavy deformation are observed. Figure 4 shows a symmetric sixfold slip pattern around the spark discharge crater in single-crystal aluminum, confirming the shock-induced plastic deform at i on associated with such an interaction. A shock wave can also be postulated in terms of a very rapid boiling of the material and the consequent recoil energy of the escaping atoms. Only at very high energy inputs, when a h o t plasma can form, can a shock wave of the latter t y p e result. At low or m oderat e energies
249
Fig. 3. Photomicrograph of a microcrater produced in tin in air (applied voltage, 2 kV; spark gap, 76 pm).
Fig. 4. Optical micrograph showing symmetric sixfold slip pattern around the microcrater produced in an aluminum single-crystal surface in an N 2 atmosphere (applied voltage, 3 kV; N 2 pressure, 0.2 MPa; spark gap, 200 pro).
250 the thermal effect is most probably the shock formation mechanism, as discussed earlier. It has been shown that lattice defects such as dislocations and vacancies are created in the volume of material adjacent to damage from a pulsed laser [12, 13]. Because of this relatively high defect density, these regions appear to become chemically active [12]. Evidence of such an enhancement of chemical activity is manifested by increased oxidation and tarnishing of an annular region concentric with the crater for electrodeposited copper irradiated by a pulsed laser [14]. A similar phenomenon is also observed in our present investigation. In our aluminum single crystals, a marked tendency to heavy oxidation was observed. Initially these crystals were electropolished before the spark damage. Immediately after the spark damage, the sample surfaces were examined by optical as well as scanning electron microscopy. Figure 5(a) is
Fig. 5. Optical micrographs of a microcrater produced in an aluminum single crystal in an N2 atmosphere (applied voltage, 3 kV; N2 pressure, 0.2 MPa; spark gap, 200 pro): (a) immediately after the damage had been produced; (b) after around 30 days.
an opticalmicrograph of such discharge craters in aluminum immediately after the discharge in a pure N2 atmosphere. Figure 5(b) shows the same craters after the sample had been stored for about 30 days. Extensive crack-like features are apparent in this micrograph. Also noticeable are fringe-type surface distortion contours adjacent to these craters. These surface cracks and the oxidized layer were examined further. Figure 6 is a scanning electron micrograph of a single crater at a higher magnification. The thickness of the oxidized layer adjacent to the crater and the cracks in this layer are clearly demonstrated. Tentatively it could be concluded that enhanced oxidation occurs around the crater via lattice defects. It must also be recognized that the base material has a substantial amount of residual stresses due to non-uniform deformation associated with the thermal expansion of the heated zone. If these residual stresses relax during or after the oxide layer is formed, then cracking of the relatively brittle oxide layer is a possibility. However, further detailed experiments are necessary to explain this unique cracking phenomenon. The crater morphology (especially the diameter of the damage spot) was found to be dependent (a) on the applied discharge voltage and (b) for a fixed voltage and spark gap on the discharge gas and gas pressure. Thus, during our present investigation these parameters were systematically varied within the limits of our experimental set-up. The variation in the average crater diameter with applied voltage (for a fixed spark gap and a fixed discharge gas) was found to be linear for the material studied. Figure 7 shows a plot of average crater diameter D v e r s u s applied voltage in the discharge medium of air. These experimental data points can be fitted by a set of least-squares straight lines. F u r t h e r studies were conducted on single crystals of pure aluminum in which the applied voltage and the spark gap were kept constant and a variable N2 pressure was used in the spark chamber. Figure 8 shows a plot of average crater diameter v e r s u s the N2 overpressure. Because of the experimental limitations, it was possible to attain a m a x i m u m pressure of only about 0.2 MPa. Within this pressure range the crater diameter appears to be a linear function of the gas pressure, as shown in Fig. 8. These two observed linear
251
Fig. 6. Scanning electron micrograph of a microcrater p r o d u c e d in an a l u m i n u m single crystal in an N 2 atmosphere, showing radial cracks in the oxide layer around the microcrater (applied voltage, 3 kV; N2 pressure, 0.2 MPa; spark gap, 200 #m).
75 175
E
150 .< 7, 50
~:L125 u~
~I00
,,~
~ 25
75
0.05 so
I I 0.10 0,15 PRESSURE (MPa)
I 0.20
0.25
Fig. 8. Average crater diameter v s . N 2 overpressure for a l u m i n u m single-crystal specimens (spark gap, 200 pro; applied voltage, 3 kV): - - , experimental results; - - - , calculated values.
25
I
1
,
I
2
,
I
3
APPLIED VOLTAGE (Y)
Fig. 7. Average crater d i a m e t e r v s . applied voltage relationship for a l u m i n u m (e), zinc (x) and tin (A) for a constant spark gap o f 25 pm.
behaviors, i.e. voltage versus D and gas pressure versus D , will be discussed next. The sparking potential is a function of the gas pressure P multiplied by the spark gap
252
distance d [15]. An analytical expression for the sparking potential is given by
Spd
V~ =
(1)
ln{Apd/ln(1/7)}
where V~ is the sparking potential, A and B are constants depending on the gas (ref. 16, p. 149) (for nitrogen, A = 9.34 and B = 375.01) and ~ is the number of electrons emitted from a given metal per impacting positive ion of a given gas (ref. 16, p. 159). For N2 and aluminum, ~, is 0.10 (ref. 16, p. 159). Using these quantities and eqn. (1) the sparking potentials for various values of pd and for a constant spark gap of 200 pm are calculated. Figure 9 shows a plot of breakdown voltage versus pd used in our experiments. This shows an approximately linear behavior. Since the crater formation is essentially a thermal process involving melting and perhaps some evaporation, a rough heat and energy balance calculation can now be performed. In the first approximation, we can assume that the entire electrical discharge energy is converted to an a m o u n t Q of heat. Then we can write Tmp
the mass evaporation and T~t, Tmp and Tbp are the room temperature, the melting temperature and the boiling temperature respectively. The mass of the material can be expressed in terms of density p and volume v of the metal in the molten zone. In order to calculate the volume of metal in this zone, we assume that the damage has a hemispherical shape. Since the damage zone is controlled by the thermal destruction, a temperature rise greater than or at least equal to the boiling point can be assumed. This high temperature is achieved in a skin depth L, which is given by the following equation [17] : L -- (ato) 112
(3)
where a is the thermal diffusivity and to is the pulse duration. A schematic representation of the spark damage is shown in Fig. 10 where R is the radius of a hypothetical spherical volume and r is the radius of damage as measured on the surface. The volume of spark damage is equivalent to the volume VL of a spherical segment of height L, where R-L
VL = 3 7rR3
-
f
-
Tbp
Q = m ( Cp d T + m f Trt
Try2 dx
(4)
o
Cp d T + m AHf
Tmp
+ c~m AHv
(2)
where m is the mass of the molten metal, Cp is the specific heat at constant pressure, AHf is the enthalpy of fusion, AHv is the enthalpy of vaporization, ~ is a fraction corresponding to
When y is expressed in terms of x using the equation of a circle, the integration is performed and R is eliminated, the equation may be written as 7r
7r
VL = - L 3 + - Lr 2 6 2
(5)
I
225C lI
\\
, , !
200C
-T
I /
_.__-_<_i
\ L--.~
j
~ 175G (Cathode)
i
~ 1250 10
I
1
15
20
pd ( T ~
I 25 Gin)
I 30
Fig. 9. T h e sparking potential vs. p d r e l a t i o n s h i p .
i=i
~ r
'
___, x
Fig. 10. Schematic representation o f a m o l t e n c r a t e r as a s e c t i o n o f an imaginary sphere.
253
Hence the equation for total heat involved in spark discharge is
+
~- '1.2
Z
++
Lr 2
././'/"
1.3
Trnp Q = p
1.5 'I.4-
at 1.1 at
1.0
Trt
./
0.9
Tbp
k
+ | Cp dT + AHf +. AHv)
(6)
i
J
0.8--
N
0.7--
9 0.6--
Tmp
On the assumption that during the spark discharge the total electrical energy is converted to heat energy, the equation can be written
0.5
0
I
I
I
I
I
0.5 1.0 1.5 2.0 2.5 APPLIED VOLTAGE {kY)
] 3.0
3.5
Fig. 11. T h e i o n i z a t i o n c u r r e n t I vs. applied voltage V.
as Tmp
V~It = p
L 3 + ~ Lr
Cp dT + 4. C O N C L U S I O N S
~t
~p
+ f Cp d T + AH~ + ~ AHv)
(7)
Tmp
where Vs is the sparking potential, I is the ionization current and t is the pulse duration. Using this equation, theoretical values of the crater diameter at different N2 pressures were calculated. Since the mass loss due to evaporation was found to be very small, we assume that ~ ~ 0. In Fig. 8 the N 2 gas pressure versus the theoretically calculated crater diameter relationship is shown by a broken line. In spite of the approximations involved in this calculation, the agreement between the calculated and experimental results is reasonable. As shown in Fig. 11, within the experimental range the ionization current I varies linearly with the applied voltage V; hence eqn. (7) also can be written as follows: Tmp
T~t rbp +f CpdT+AH,+o~AHv)
(8)
Tmp
where R ' is the resistance in the circuit at a fixed spark gap. This equation predicts a relationship between the applied voltage and the crater radius, and thus the average crater diameter can also be calculated provided that R' and c~ are measured experimentally.
(1) Microcraters produced b y high energy, short duration (36 ns) electrical discharge on aluminum, zinc and tin are similar in nature to those produced by a pulsed laser. A concentric wavy surface deformation, similar to that reported for damage from a pulsed laser, was observed. (2) Distinct crystallographic slip was also observed adjacent to the damage spot. The relative amounts of wavy surface deformation and slip marking were found to be a function of input energy. At lower energy inputs, predominantly a slip-type deformation is observed. (3) This experiment suggests a high density of point and/or line defects in the volume adjacent to the discharge spot. An unusual amount of oxidation is observed within a thin volume in a relatively short period of time. This effect was most pronounced in aluminum samples. (4) An approximately linear relationship between the crater diameter and the ionizing gas pressure is observed for a fixed spark gap and potential, and an approximately linear relationship between the crater diameter and the applied potential for a fixed spark gap and ionizing gas pressure was also observed.
REFERENCES 1 R. Basharov, E. N. Gavrilovskaya, O. A. Malkin a n d E. S. T r e k h o v , S o y . P h y s . - - T e c h . P h y s . , 1 0 (10) (1966) 1428.
254 2 R. Basharov, E. N. Gavrilovskaya, O. A. Malkin and E. S. Trekhov, Soy. Phys. -- Tech. Phys., 12 (10) (1968) 1383. 3 V. V. Kantsel', T. S. Kurakina, V. S. Potokin, V. I. Rakhovskii and L. G. Tkachev, Soy. Phys. -Tech. Phys., 13 (6) (1968) 814. 4 Yu. D. Korolev, V. A. Kuz'min and G. A. Mesyats, Soy. Phys. -- Tech. Phys., 25 (4) (1980) 418. 5 P. Holler, Spectrochim. Acta, PartB, 23 (1967) 1. 6 C. T. Walters, Appl. Phys. Lett., 25 (12) (1974) 696. 7 N. R. Isenor, Appl. Phys. Lett., 31 (3) (1977) 148. 8 G. N. Maracas, G. L. Harris, C. A. Lee and R. A. McFarlane, Appl. Phys. Lett., 33 (5) (1978) 453. 9 H. J. Leamy, G. A. Rozgonyi and T. T. Sheng, Appl. Phys. Lett., 32 (9) (1978) 535. 10 A. K. Jain, V. N. Kulkarni, D. K. Sood and J. S.
Uppal, J. Appl. Phys., 52 (7) (1981) 4882. 11 K. Mukherjee, T. M. Kim and W. T. Waiters, Bull. AIME Annu. Meet., Las Vegas, NV, in J. Met., 31 (1979) F19. 12 O. T. Inal and L. E. Murr, J. Appl. Phys., 49 (4) (1978) 2427. 13 D. M. Follstaedt and W. R. Wampler, Appl. Phys. Lett., 38 (3) (1981) 140. 14 K. Mukherjee, T. H. Kim and W. T. Waiters, in K. Mukherjee and J. Majumder (eds.), Lasers in Metallurgy, Metallurgical Society of AIME, Warrendale, PA, 1982, p. 137. 15 F. Paschen, Wiedemann Ann., 37 (1889) 69. 16 J. D. Cobine, Gaseous Conductors -- Theory and Engineering Applications, McGraw-Hill, New York, 1941. 17 A. V. Gorbunov, E. B. Leiko, E. M. Nadgorny and S. N. Valkovskii, Scr. Metall., 14 (1980) 417.
D a m a g e in Discharge
247
Aluminum, Zinc and Tin f r o m a N a n o s e c o n d E l e c t r i c P u l s e
C. G. WAKADE, NARENDRA B. DAHOTRE and K. MUKHERJEE Department of Metallurgy, Mechanics and Materials Science, Michigan State University, East Lansing, M148824-1226 (U.S.A.)
(Received October 18, 1983; in revised form December 6, 1983)
SUMMARY Microstructural effects associated with an electrical pulse discharge o f 36 ns duration on aluminum, zinc and tin samples have been investigated. These experiments were conducted in air as well as in a pure N2 atmosphere. The effects o f spark gap distance, operating potential and discharge gas pressure were studied. A linear relationship between the crater diameter and the operating potential or discharge gas pressure was observed. Adjacent to the damage site, plastic deformation in the form o f slip as well as a concentric ripple pattern was observed. These latter effects are similar to the deformation behavior associated with damage from a short duration laser pulse.
1. INTRODUCTION Changes in the properties of surface and subsurfaces of metallic materials due to a high energy electric pulse discharge have been the subject of several publications [1-4]. The nature of the damage produced by electrical discharges depends on the type of spark source and the nature of the electrodes as well as on the experimental conditions under which the spark source is operated. Holler [5] has reported compositional changes in alloyed cathodes due to multiple discharges lasting for seconds. A similar compositional change has also been reported by Basharov et al. [1] for discharges of microsecond duration. To date, there exists very little information regarding the microstructurai changes associated with such pulse discharges. If a properly impedance-matched high voltage discharge is used, then a large a m o u n t of energy is released, which causes rapid melting 0025-5416/84/$3.00
and subsequent resolidification of a thin surface layer. The a m o u n t of melting depends on experimental conditions such as the energy input, the spark gap, the nature of the ionization gas etc. as well as on the thermophysical properties of the sample. Apart from the gross microstructural changes such as the melting and crater formation, microscopic defects such as dislocations and point defects are also produced in the vicinity of the damage site. In the present study, microstructural effects due to spark discharge on three low melting pure metals, aluminum, zinc and tin, were investigated. 2. EXPERIMENTAL PROCEDURE Electrical sparks of 36 ns duration were obtained in a spark chamber by discharging a charged cable. A nanosecond pulser (Microwave Associates Inc.) was used for this purpose. The anode, in all cases, was a tungsten needle about 40 pm in diameter, and the material to be studied was used as the cathode. High purity (99.999%) aluminum, zinc and tin were investigated in this study. The applied voltage between the electrodes could be varied from about 500 to 3000 V. The spark gap setting could be adjusted accurately by a micrometer mechanism as shown schematically in Fig. 1. The spark gap was varied from 25 to 200 pm. The specimens were annealed to remove any possible residual stresses prior to metallographic preparation and final electropolishing. 3. RESULTS AND DISCUSSION Figure 2 shows a typical microcrater produced on tin specimens by a 2 kV spark dis@ Elsevier Sequoia/Printed in The Netherlands
248 -
~ Gas chamber~
Gas inlet - - ~ . ~ Inlet valve
II
l I
*~to nanosecond pulser
Discharge
cable
ressure gauge ~gas outlet Outlet valve
Tungsten needle -Specimen Stage with micrometer to adjust spark gap
Fig. 1. Schematic diagram showing the experimental set-up for electric pulse discharge.
Fig. 2. (a) Photomicrograph of microcrater produced in a tin specimen in air (applied voltage, 2 kV; spark
gap, 50 p_m); (b) magnified view of the grain boundary shown in (a) by an arrow.
charge in air. Surrounding the m ol t en crater a wavy deform at i on pattern is seen. The spacing of the wavy d e f o r m a t i o n zone near the microcrater is larger than those at a larger radial distance f r o m the center of the damaged spot. It is interesting to n o t e that the continuity of these bands is n o t disrupted by the grain boundaries, as shown in Figs. 2(a) and 2(b). A similar wavy plastic d e f o r m a t i o n around a damage spot from a pulsed laser has been report ed [6-9]. Some researchers [6, 7, 9, 10] have tried to explain this deform at i on mode by invoking interference of the incident and the reflected laser beams. However, in the present case there is no possibility of such interference since the source of energy is not a coherent p h o t o n energy. The alternative explanation, as suggested by Mukherjee et al. [ 11 ], thus seems to be more appropriate in our present case. The mechanism suggested by t h e m is as follows. When a large a m o u n t of energy is deposited on the surface of a substrate in a very short time (e.g. nanoseconds), a very rapid temperature rise occurs and the volume of the material, within the irradiated or affected region, tends to expand. However, the adjacent lattice cannot relax at a rate commensurate with the rate of increase in temperature. Thus, the local energy radiates out in the form of an elastic shock wave. If the stored elastic energy in the shock front is greater than the plastic yielding energy, then the material undergoes a permanent plastic deformation. The undulations are then the nodes of the propagating wave. This t ype of d e f o r m a t i o n in a crystalline material also implies a non-conservative motion of dislocations. Figure 3 shows that together with this wavy deform at i on process there is also some crystallographic slip. The relative amounts of slip and wavy deform at i on appear to be a function of the energy input. At lower input energies, more slip and less wavy deformation are observed. Figure 4 shows a symmetric sixfold slip pattern around the spark discharge crater in single-crystal aluminum, confirming the shock-induced plastic deform at i on associated with such an interaction. A shock wave can also be postulated in terms of a very rapid boiling of the material and the consequent recoil energy of the escaping atoms. Only at very high energy inputs, when a h o t plasma can form, can a shock wave of the latter t y p e result. At low or m oderat e energies
249
Fig. 3. Photomicrograph of a microcrater produced in tin in air (applied voltage, 2 kV; spark gap, 76 pm).
Fig. 4. Optical micrograph showing symmetric sixfold slip pattern around the microcrater produced in an aluminum single-crystal surface in an N 2 atmosphere (applied voltage, 3 kV; N 2 pressure, 0.2 MPa; spark gap, 200 pro).
250 the thermal effect is most probably the shock formation mechanism, as discussed earlier. It has been shown that lattice defects such as dislocations and vacancies are created in the volume of material adjacent to damage from a pulsed laser [12, 13]. Because of this relatively high defect density, these regions appear to become chemically active [12]. Evidence of such an enhancement of chemical activity is manifested by increased oxidation and tarnishing of an annular region concentric with the crater for electrodeposited copper irradiated by a pulsed laser [14]. A similar phenomenon is also observed in our present investigation. In our aluminum single crystals, a marked tendency to heavy oxidation was observed. Initially these crystals were electropolished before the spark damage. Immediately after the spark damage, the sample surfaces were examined by optical as well as scanning electron microscopy. Figure 5(a) is
Fig. 5. Optical micrographs of a microcrater produced in an aluminum single crystal in an N2 atmosphere (applied voltage, 3 kV; N2 pressure, 0.2 MPa; spark gap, 200 pro): (a) immediately after the damage had been produced; (b) after around 30 days.
an opticalmicrograph of such discharge craters in aluminum immediately after the discharge in a pure N2 atmosphere. Figure 5(b) shows the same craters after the sample had been stored for about 30 days. Extensive crack-like features are apparent in this micrograph. Also noticeable are fringe-type surface distortion contours adjacent to these craters. These surface cracks and the oxidized layer were examined further. Figure 6 is a scanning electron micrograph of a single crater at a higher magnification. The thickness of the oxidized layer adjacent to the crater and the cracks in this layer are clearly demonstrated. Tentatively it could be concluded that enhanced oxidation occurs around the crater via lattice defects. It must also be recognized that the base material has a substantial amount of residual stresses due to non-uniform deformation associated with the thermal expansion of the heated zone. If these residual stresses relax during or after the oxide layer is formed, then cracking of the relatively brittle oxide layer is a possibility. However, further detailed experiments are necessary to explain this unique cracking phenomenon. The crater morphology (especially the diameter of the damage spot) was found to be dependent (a) on the applied discharge voltage and (b) for a fixed voltage and spark gap on the discharge gas and gas pressure. Thus, during our present investigation these parameters were systematically varied within the limits of our experimental set-up. The variation in the average crater diameter with applied voltage (for a fixed spark gap and a fixed discharge gas) was found to be linear for the material studied. Figure 7 shows a plot of average crater diameter D v e r s u s applied voltage in the discharge medium of air. These experimental data points can be fitted by a set of least-squares straight lines. F u r t h e r studies were conducted on single crystals of pure aluminum in which the applied voltage and the spark gap were kept constant and a variable N2 pressure was used in the spark chamber. Figure 8 shows a plot of average crater diameter v e r s u s the N2 overpressure. Because of the experimental limitations, it was possible to attain a m a x i m u m pressure of only about 0.2 MPa. Within this pressure range the crater diameter appears to be a linear function of the gas pressure, as shown in Fig. 8. These two observed linear
251
Fig. 6. Scanning electron micrograph of a microcrater p r o d u c e d in an a l u m i n u m single crystal in an N 2 atmosphere, showing radial cracks in the oxide layer around the microcrater (applied voltage, 3 kV; N2 pressure, 0.2 MPa; spark gap, 200 #m).
75 175
E
150 .< 7, 50
~:L125 u~
~I00
,,~
~ 25
75
0.05 so
I I 0.10 0,15 PRESSURE (MPa)
I 0.20
0.25
Fig. 8. Average crater diameter v s . N 2 overpressure for a l u m i n u m single-crystal specimens (spark gap, 200 pro; applied voltage, 3 kV): - - , experimental results; - - - , calculated values.
25
I
1
,
I
2
,
I
3
APPLIED VOLTAGE (Y)
Fig. 7. Average crater d i a m e t e r v s . applied voltage relationship for a l u m i n u m (e), zinc (x) and tin (A) for a constant spark gap o f 25 pm.
behaviors, i.e. voltage versus D and gas pressure versus D , will be discussed next. The sparking potential is a function of the gas pressure P multiplied by the spark gap
252
distance d [15]. An analytical expression for the sparking potential is given by
Spd
V~ =
(1)
ln{Apd/ln(1/7)}
where V~ is the sparking potential, A and B are constants depending on the gas (ref. 16, p. 149) (for nitrogen, A = 9.34 and B = 375.01) and ~ is the number of electrons emitted from a given metal per impacting positive ion of a given gas (ref. 16, p. 159). For N2 and aluminum, ~, is 0.10 (ref. 16, p. 159). Using these quantities and eqn. (1) the sparking potentials for various values of pd and for a constant spark gap of 200 pm are calculated. Figure 9 shows a plot of breakdown voltage versus pd used in our experiments. This shows an approximately linear behavior. Since the crater formation is essentially a thermal process involving melting and perhaps some evaporation, a rough heat and energy balance calculation can now be performed. In the first approximation, we can assume that the entire electrical discharge energy is converted to an a m o u n t Q of heat. Then we can write Tmp
the mass evaporation and T~t, Tmp and Tbp are the room temperature, the melting temperature and the boiling temperature respectively. The mass of the material can be expressed in terms of density p and volume v of the metal in the molten zone. In order to calculate the volume of metal in this zone, we assume that the damage has a hemispherical shape. Since the damage zone is controlled by the thermal destruction, a temperature rise greater than or at least equal to the boiling point can be assumed. This high temperature is achieved in a skin depth L, which is given by the following equation [17] : L -- (ato) 112
(3)
where a is the thermal diffusivity and to is the pulse duration. A schematic representation of the spark damage is shown in Fig. 10 where R is the radius of a hypothetical spherical volume and r is the radius of damage as measured on the surface. The volume of spark damage is equivalent to the volume VL of a spherical segment of height L, where R-L
VL = 3 7rR3
-
f
-
Tbp
Q = m ( Cp d T + m f Trt
Try2 dx
(4)
o
Cp d T + m AHf
Tmp
+ c~m AHv
(2)
where m is the mass of the molten metal, Cp is the specific heat at constant pressure, AHf is the enthalpy of fusion, AHv is the enthalpy of vaporization, ~ is a fraction corresponding to
When y is expressed in terms of x using the equation of a circle, the integration is performed and R is eliminated, the equation may be written as 7r
7r
VL = - L 3 + - Lr 2 6 2
(5)
I
225C lI
\\
, , !
200C
-T
I /
_.__-_<_i
\ L--.~
j
~ 175G (Cathode)
i
~ 1250 10
I
1
15
20
pd ( T ~
I 25 Gin)
I 30
Fig. 9. T h e sparking potential vs. p d r e l a t i o n s h i p .
i=i
~ r
'
___, x
Fig. 10. Schematic representation o f a m o l t e n c r a t e r as a s e c t i o n o f an imaginary sphere.
253
Hence the equation for total heat involved in spark discharge is
+
~- '1.2
Z
++
Lr 2
././'/"
1.3
Trnp Q = p
1.5 'I.4-
at 1.1 at
1.0
Trt
./
0.9
Tbp
k
+ | Cp dT + AHf +. AHv)
(6)
i
J
0.8--
N
0.7--
9 0.6--
Tmp
On the assumption that during the spark discharge the total electrical energy is converted to heat energy, the equation can be written
0.5
0
I
I
I
I
I
0.5 1.0 1.5 2.0 2.5 APPLIED VOLTAGE {kY)
] 3.0
3.5
Fig. 11. T h e i o n i z a t i o n c u r r e n t I vs. applied voltage V.
as Tmp
V~It = p
L 3 + ~ Lr
Cp dT + 4. C O N C L U S I O N S
~t
~p
+ f Cp d T + AH~ + ~ AHv)
(7)
Tmp
where Vs is the sparking potential, I is the ionization current and t is the pulse duration. Using this equation, theoretical values of the crater diameter at different N2 pressures were calculated. Since the mass loss due to evaporation was found to be very small, we assume that ~ ~ 0. In Fig. 8 the N 2 gas pressure versus the theoretically calculated crater diameter relationship is shown by a broken line. In spite of the approximations involved in this calculation, the agreement between the calculated and experimental results is reasonable. As shown in Fig. 11, within the experimental range the ionization current I varies linearly with the applied voltage V; hence eqn. (7) also can be written as follows: Tmp
T~t rbp +f CpdT+AH,+o~AHv)
(8)
Tmp
where R ' is the resistance in the circuit at a fixed spark gap. This equation predicts a relationship between the applied voltage and the crater radius, and thus the average crater diameter can also be calculated provided that R' and c~ are measured experimentally.
(1) Microcraters produced b y high energy, short duration (36 ns) electrical discharge on aluminum, zinc and tin are similar in nature to those produced by a pulsed laser. A concentric wavy surface deformation, similar to that reported for damage from a pulsed laser, was observed. (2) Distinct crystallographic slip was also observed adjacent to the damage spot. The relative amounts of wavy surface deformation and slip marking were found to be a function of input energy. At lower energy inputs, predominantly a slip-type deformation is observed. (3) This experiment suggests a high density of point and/or line defects in the volume adjacent to the discharge spot. An unusual amount of oxidation is observed within a thin volume in a relatively short period of time. This effect was most pronounced in aluminum samples. (4) An approximately linear relationship between the crater diameter and the ionizing gas pressure is observed for a fixed spark gap and potential, and an approximately linear relationship between the crater diameter and the applied potential for a fixed spark gap and ionizing gas pressure was also observed.
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