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Structural changes in Mg alloy induced by plasma immersion ion implantation of Ag
Acta Materialia 52 (2004) 4329–4335 www.actamat-journals.com
Structural changes in Mg alloy induced by plasma immersion ion implantation of Ag L. Kutsenko a, D. Fuks a, A. Kiv a,*, L. Burlaka a, M. Talianker a, O. Monteiro b, I. Brown b a
Department of Materials Engineering, Ben-Gurion University of the Negev, Ben-Gurion Boulevard, POB 653 Beer-Sheva 84105, Israel b Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Received 9 May 2004; received in revised form 24 May 2004; accepted 28 May 2004 Available online 24 June 2004
Abstract Formation of intermetallic compounds within the Mg matrix as a result of implantation of Ag by plasma immersion ion implantation technology was investigated. Transmission electron-microscopy studies of the implanted samples revealed the appearance of nanoparticles of binary phase Mg–Ag. A model based on the classical mechanisms of propagation of accelerated ions through the metal matrix was suggested for the explanation of the experimental observations. Ab initio calculations of the electronic sub-systems proved to be helpful in providing theoretical prediction of the structural changes, which may be induced in the implanted system. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Implantation; Ab initio electron theory; Transmission electron microscopy; Magnesium alloy
1. Introduction Plasma immersion ion implantation (PIII) is a newly developed technology for the surface treatment of materials covering an important field at the forefront of materials science [1–3]. In PIII the target material is immersed in plasma, which contains low energy ions of the species to be implanted. Repetitively pulsed high negative voltage is applied to the samples, thus stimulating implantation of ions into the surface of the object. For the case when metal plasma is employed, metal ions condense on the material surface as a film in the time period between the high voltage pulses during the course of the PIII process. Ions accelerated by the high voltage bias pulse impact the deposited metal atoms producing recoil implantation. This affects the depth profile of the PIII process, making it different from the usual gauss-
*
Corresponding author. Tel.: +972-864-614-63; fax: +972-864-793-
50. E-mail address: [email protected] (A. Kiv).
ian-like shape. By varying the ratio of pulse-on time (during which implantation occurs) to pulse-off time (during which deposition occurs) the shape of the implantation profile can be tailored, providing new interesting options for surface engineering. Although numerous topics related to the technological aspects of PIII and its practical applications have received extensive study, very little has been done with regard to developing a theoretical basis for understanding the physical phenomena responsible for the structural changes caused in the material by PIII treatment. The existing theoretical models of ion implantation mainly deal with the penetration behavior of ions and with the stopping phenomena, rather than with the effects resulting in the formation of new phases in the implanted material [4]. From the point of view of radiation physics, two basic competing mechanisms are involved in the process of energy loss by the ion moving through the material: firstly, collisions of implanted ions with free and bound electrons, and secondly, collisions with the atomic nuclei. Assuming that these events occur independently,
1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.05.049
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L. Kutsenko et al. / Acta Materialia 52 (2004) 4329–4335
an expression for the energy lost by an ion per unit distance can be written as [5] dE ¼ N jSn ðEÞ þ Se ðEÞj; ð1Þ dx where N is the atomic density of the target atoms, and Sn and Se are the cross-sections for electronic and nuclear stopping, respectively. Specifically, in the case of PIII treatment the ion energy is relatively low, and therefore the condition Se Sn should be satisfied [5]. This means that during the PIII process the implanted ions lose their energy primarily via nuclear collisions, giving rise to elastic displacement of the atoms in the crystal lattice accompanied by formation of lattice defects [6]. If the ion energy is not sufficient to produce lattice defects, nuclear collisions would generate only large atomic oscillations. The region of such intense oscillations may be considered as a thermal spike, which causes local melting of the material within the microscopic volume [4–6]. It seems that the concept of thermal spikes might be useful for the explanation of structural and chemical transformations occurring in PIII implanted layers. In the present paper an attempt has been made to develop a theoretical basis for understanding the mechanisms leading to microstructural changes in the PIII treated material. The experimental observations obtained from the Mg-alloy implanted with Ag are discussed in terms of a thermal spike approach. Additionally, calculations based on first-principle methods were also carried out. The results show that analysis of the electronic states of non-equilibrium atomic configurations formed throughout PIII processing may be helpful to provide theoretical predictions of the stability of the structures induced.
2. Experimental and computational details The commercial magnesium alloy WE 54 of composition Mg–5.1wt%Y–3.3wt%Rare Earth–0.4wt%Zr (manufactured by Magnesium Electron Company, UK) was used as a target for the implantation experiments, and Ag was chosen as the implanted species. Initially the alloy was in T6 condition obtained as a result of conventional age-hardening treatment. Thin foil specimens for transmission electron microscopy (TEM) were cut using an electric spark erosion machine and ground to a thickness of 0.1 mm before final ion beam thinning. Then specimens suitable for TEM were subjected to implantation of Ag (from both sides), applying metal plasma immersion ion implantation and deposition (Mepiiid) technology. The metal plasma was produced by a small, repetitively pulsed vacuum arc plasma gun operated at a pulse length of 5 ms and repetition rate 1 Hz and with arc current about 300 A. It is known that along with the
metal plasma that is generated, a flux of macroscopic droplets (re-solidified cathode debris) of size in the range 0.1–10 lm is also produced [7]; this solid particulate contamination was removed using a curved magnetic duct (bent solenoid of magnetic field strength a few hundred gauss) which stops line-of-sight transmission of macroparticles while allowing the transport of plasma [8]. The overall plasma formation system thus consists of the repetitively pulsed plasma gun in conjunction with a 90° magnetic filter. Implantation ion energy was controlled by repetitively pulse biasing the substrate. The pulse duration was 5 ls and the duty cycle 50%. We point out that silver atoms deposited on the substrate surface during the bias-off part of the cycle are subsequently implanted by knock-on (recoil) collisions with energetic silver ions belonging to the next bias-on part of the cycle; a 50% duty cycle is adequate to ensure that essentially all silver is implanted, with no remaining surface layer. The absence of a deposited layer of silver was also confirmed by TEM investigations. The implanted specimen was checked in TEM before and after cleaning its surface by argon glow discharge in EMITECH K-350 system. No discernible difference in the microstructure of the specimen was found, thus indicating that all structural characteristics obtained through TEM study can be considered as a bulk effect. Note also that the pulse biasing is applied, and is relevant, only for that time for which the vacuum arc metal plasma is produced, i.e., for 5 ms pulses once per second, and the ‘‘macroscopic’’ duty cycle for which the pulse biasing is applied is 50% of 5 ms per second, or 0.25%. Thus the mean power input to the sample by ion bombardment is modest and the substrate mean temperature rise is small (the substrate is clamped to a heavy metal holder). A simple estimate indicates an expected mean temperature of about 30–40 °C. The mean ion energy is Ei ¼ qV , where q is the mean ion charge state of the vacuum-arc-produced metal plasma, and V is the bias voltage. The mean ion charge state for the Ag plasma as used here is 2.1 and the ion energy was in the range 2.5–5.0 keV. The total retained dose was about 1017 1018 cm2 . The uniformity of dose across the substrate was about 10–20%. Ab initio calculations were carried out using linear muffin-tin orbital (LMTO) method of one-electron theory in the atomic sphere approximation (ASA) [9–14]. The important feature of this approach is the use of volume- and energy-independent structure constants, and employing the parameters containing the information about one-electron potential. These quantities completely specify the energy-band structure of given material. The approach is valid for closely packed crystalline solids, giving a physically simple description of the energy-band formation.
L. Kutsenko et al. / Acta Materialia 52 (2004) 4329–4335
The computer program BGFM, which was used for calculations, takes into account multipole corrections to ASA and employs coherent potential approximation (CPA) [14] for calculations of disordered system. This code was chosen as a fast scheme for direct calculation of the electronic structure of the atomic system. With self-consistently obtained bands the program calculates the total energies of the system. Core electrons are frozen after initial atomic calculations. The exchange-correlation effects are considered according to Vosko et al. [15]. The individual atomic sphere radii are set equal to the radius of the average atomic Wigner–Seitz sphere. The uncertainty of the absolute values of the energy gaps was reduced by use of a special extended k-point basis. For the total energy calculations the convergence criterion was chosen as 0.001 mRy. Additional details describing the program can be found in [14].
3. Results and discussion 3.1. TEM observations Comparison of TEM micrographs taken from the alloy before and after implantation of Ag (Fig. 1(a) and (b)) reveals that fine nano-particles, about 10–12 nm in size, homogeneously form in the interior of the a-Mg matrix grains as a result of Mepiid treatment. Qualitative X-ray energy dispersive microprobe analysis has indicated that the particles contained Ag and Mg. The vast bulk of these particles were positively identified by electron diffraction and dark-field tech An example nique as a cubic AgMg phase (a ¼ 3:314 A). of the electron diffraction diffraction pattern indexed in terms of cubic unit cell of AgMg phase is shown in Fig. 2(a), and corresponding bright-dark field pair of images of AgMg nano-particles are shown in Fig. 2(b) and (c).
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3.2. The mechanism of phase formation It may at first seem surprising that nano-precipitates of the second phase appear as a result of ion implantation. Considering the implanted material as a supersaturated solid solution of Ag in Mg matrix, one might suppose that the precipitation reaction should evolve through a conventional diffusion mechanism. However, as it was noted in Section 2, the specimen temperature under implantation does not exceed 30–40 °C, hence macroscopic migration of the atomic species in the material is insignificant for forming a nucleus of a new phase and can be ignored. It is clear, therefore, that another mechanism, not based on the concept of longrange diffusion, has to be used for understanding the precipitation effect observed in the implanted material. An approach based on ideas of the theory of propagation of fast particles through the solid seems to be more appropriate. Following this theory we may assume that specific regions of high thermal excitation, so-called thermal spikes [6,16], will be generated as a result of penetration of plasma ions into the metal matrix in the course of PIII processing. If the spatial spread of the temperature within the thermal spike zone obeys the equation of thermal conductivity, it can be written: T ðr; tÞ ¼ T0 þ
Q ð4pÞ
3=2
1 cd ðDtÞ
3=2
er
2 =4Dt
ð2Þ
where T ðr; tÞ is the temperature within the spike as a function of time t and distance r from the center of the spike, Q is the value of the heat energy in the center of the spike at t ¼ 0, D is the coefficient of thermal conductivity, and c and d denote the heat capacity and the material density, respectively. Bearing in mind that the so-called displacement energy needed for removing Mg atom from its lattice site by elastic collision is about 10 eV [16], and near dislocations, grain boundaries and other imperfections this energy decreases to 5 eV, we
Fig. 1. Transmission electron micrographs showing the WE54 alloy before (a) and after (b) implantation of Ag ions.
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Fig. 2. (a) Electron diffraction pattern taken from the area of specimen containing AgMg nano-particles formed within a-Mg matrix of the WE54 alloy by Mepiiid processing. The reflections related to AgMg phase are indexed. (b) Bright field. (c) Dark Field TEM micrographs of AgMg particles taken in (1 1 1) reflection.
may estimate that the energy Q for thermal oscillations should not exceed the value of 5 eV – otherwise the lattice atoms will be removed from their sites. Therefore, the value Q ¼ 3 eV would seem to be reasonable. Taking for the Mg matrix the values, c ¼ 1.02 kJ/(kg K), D 103 cm2 /s and density d ¼ 1:74 g/cm3 , we can calculate the temperature profiles T ðrÞ associated with the spike for different time intervals. From these profiles, the average size of the spike region, its time dependence and effective temperature can be readily estimated, as shown in Table 1. Table 1 shows that the occurrence of a spike gives rise to a temperature increase over a region of size about it can also be seen that the lifetime of the 100–200 A; spike is approximately 1010 –109 s, which corresponds to the time required for 30–300 atomic oscillations. Now a qualitative explanation of the formation of second phase particles within the implanted matrix can be given as follows: a liquid nano-size droplet of Mg–Ag melt forms as a result of excitation of the spike; the droplet quickly cools and at the end of the spike lifetime it may be considered as a metastable supercooled liquid within which 30–300 oscillations have occurred. These oscillations seem to be sufficient to displace atoms of Mg and Ag towards their new positions in a new intermetallic structure, which is formed during solidification. Table 1 Parameters estimated for thermal spikes in Mg r (A)
t (s) 11
2.5 10 5 1011 1010 1.5 1010 2 1010 109
15 20 30 40 50 100
T (K) 1500 1000 500 450 350 300
r is the effective radius of the region for the corresponding temperature.
3.3. Ab initio studies In this section we demonstrate the effectiveness of an Ab initio approach for analysis of Mg–Ag system obtained by implantation of Ag atoms into the Mg-matrix. The calculations were carried out for two following states of the system: (a) Initial, or starting state, which corresponds to the atomic configuration arising as a result of penetration of Ag-atoms into the Mg-target during the PIII processing. The system is considered as a rigid hcp lattice of Mg atoms mixed with a controlled amount of Ag atoms substituting for Mg atoms. Such a system is non-equilibrium one and its electronic subsystem is in an excited state. (b) Relaxed state, corresponding to a new atomic configuration, which may be adopted by the implanted system due to the relaxation process. Such configuration can be found through the simulation of the atomic displacements, causing transition of the system to a new non-stable equilibrium state characterized by the relative energy minimum. For both conditions, (a) and (b), the self-consistent values of the total system energy, Etinit and Etrelax , respectively, were determined over a wide range of Ag concentrations. CPA LMTO–ASA computation procedure [13,14,17] was used for this purpose. Also, the total and partial densities of the electronic states (DOS) were calculated for different concentrations of Ag in the Mg matrix. The energy Etinit was computed for the non-relaxed rigid Mg lattice with randomly distributed Ag atoms that substitute for Mg. Etrelax energy was obtained by minimization procedure, in which the lattice parameter of the implanted matrix was varied to find the minimal total energy of the system with respect to the volume X of the calculation cell. Such minimization procedure can
L. Kutsenko et al. / Acta Materialia 52 (2004) 4329–4335
be considered as equivalent to solving the equation of state ðoEtot =oXÞS ¼ p; when the temperature is equal to zero and the external pressure p ¼ 0. The values of the difference DE ¼ Etrelax Einit were then determined for the wide range of Ag content, as summarized in Fig. 3 presenting a plot DE vs. Ag concentration. Considering DE as a ’’relaxation energy’’ showing how the initial non-equilibrium state is far from the relaxed state, it was reasonable to assume that there should be some correlation between the value DE calculated for a specific Ag concentration and the possibility of formation a stable Mg–Ag compound with the same Ag content. It should be noted that both energies, Etinit and Etrelax , are related to the states, which, in fact, are not stable and do not exist in reality. Nevertheless, when comparing the behavior of DE (see Fig. 3) with the experimental data collected in Table 2 presenting some stable phases reported elsewhere [18] for the Mg–Ag system, it may be seen that abrupt changes of the value DE occur when the atomic concentrations of Ag in the implanted material are close to stochiometric compositions of stable phases (the AgMg and Ag17 Mg54 phases, in our example). This interesting result implies that ab inito calculations performed for the disordered implanted system may yield useful energy characteristics of the relaxation processes. These characteristics, such as difference DE ¼ Etrelax Einit , can be then employed to give a reasonable forecast which concentrations of the implanted element favor formation of a stable compounds in the implanted matrix. It is also instructive to analyze the behavior of DOS characteristics of the Mg–Ag system when different amounts of Ag are implanted into Mg-matrix. The system now is considered to be in its initial non-equilibrium state, and the total and partial DOSes are calculated for different concentrations of Ag atoms (within 0–75 at.% range). Examples of computations of total DOSes for pure Mg, Mg + 0.1 at.%Ag and
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Table 2 Stable phases in the Mg–Ag system Phases
Pearson symbol
Composition at.% Ag (%)
Space group
(Ag) a Ag3 Mg a0 AgMg b Ag17 Mg54 e0 Ag7:96 Mg25:04 e Ag9 Mg37 c (Mg) d
cF4 cP4 cP2 oI142 cF264 hP92 hP2
70.7–100 75 34.6–64.5 21.2–24.1 21.2–24.1 19.6 0–8.9
Fm3m Pm3m Pm3m Immm Fm3 P 63 P 63 =mmm
Mg + 40 at.%Ag are presented as plots in Figs. 4 and 5. It is not surprising that the small increase of Ag content in Mg matrix has no marked effect on the total DOS (compare DOS for pure Mg and for Mg + 0.1 at.%Ag), while significant increase in the number of states in total DOS occurs for the concentration of 40 at.%Ag (see Fig. 5). It is interesting, however, to understand which electron states contribute to this increase. The explanation can be found by considering the partial densities of Ag d-electrons. Fig. 6 shows the results of calculations of partial DOS of Ag d-electrons for two compositions: Mg + 0.1 at.%Ag and Mg + 40 at.%Ag. A comparison of concentration dependence of total DOS and partial density of d-states for the Mg–Ag sytem is presented in Fig. 7. It can be seen from Figs. 6 and 7 that the number of states of Ag d-electrons drops substantially when the concentration of the implanted Ag atoms increases from 0.1% to 40%. Besides, as it follows from Fig. 5, the dependence of total DOS on the Ag content is associated primarily with the deep electronic states, within the energy region of 0.15–0.45 Ry corresponding to the energy of Ag d-electrons. It can be surmised, therefore, that increase of the number of electronic states in total DOS occurs at the expense of d-states of Ag. It can be suggested, that, in fact, d-electrons of Ag promote more symmetrical and p states in the implanted Mg–Ag system. Increase in density of more symmetrical states may be advantageous for the formation of intermetallic
Fig. 3. The concentration dependence of the ‘‘relaxation energy’’ for Mg matrix implanted by Ag.
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Fig. 4. Total density of electronic states calculated for the pure Mg.
Fig. 5. Total density of electronic states calculated for Mg matrix implanted by 0.1 at.% Ag and 40 at.% Ag.
Fig. 6. Partial DOS for d-states of Ag implanted into Mg. Dashed line is for 0.1 at.% of Ag and solid line is for 40 at.% of Ag.
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Fig. 7. Comparison of concentration dependence of total DOS and partial density of Ag d-states for the Mg–Ag system.
phases with higher symmetry. This exactly corresponds to the general trends manifested in Table 2: structures with larger Ag content possess higher symmetry. 4. Conclusions (a) Implantation of Ag-ions into Mg alloy WE54 by Mepiiid technology results in occurrence of nanosize particles of compound AgMg under the surface of the specimen. (b) Basic concepts of classical theory of propagation of fast ions through the solid seem to be appropriate for qualitative understanding of the mechanism of formation of intermetallic nano-particles within the implanted matrix. The particles may appear as a result of solidification of nano-droplets of Mg–Ag melt, formed by thermal spikes generated in the course of penetration of implanted ions through the metal matrix. (c) Ab initio calculations may provide a profound, though qualitative, insight into the electronic structure of the implanted system and can be helpful for theoretical prediction of the essential structural changes induced by implantation. For the example of the Mg–Ag system it was shown that the parameter DðEÞ characterizing the energy difference between the initial ‘‘as-implanted’’ state of material and the non-stable equilibrium state attained during relaxation may serve as an indication of the possible formation of stable compounds at the given Ag concentration. Further, analysis of the changes in delectron states of Ag showed that d-electrons of Ag play an important role in the formation of intermetallic compounds in Mg–Ag alloy: their promotion to s and p states may be associated with the formation of intermetallic phases with higher symmetry.
Acknowledgements The authors acknowledge the support of this work by the Binational Scientific Foundation under Grant #2 000 122. L.K. and D.F. are thankful to Dr. A. Ruban for helpful discussions.
References [1] Brown IG. Rev Sci Instrum 1994;65(10):3061. [2] Mantese JV, Brown IG, Cheung NW, Collins GA. MRS Bulletin 1996;(August):8. [3] Anders A, Anders S, Brown IG, Dickinson MR, MacGill RA. J Vac Sci Technol 1994;B12:815. [4] Hirvonen JK. Ion implantation. New York: Academic Press; 1981. [5] Brice DK. In: Ion implantation range and energy deposition distributions, vol. 1. New York: Plenum; 1975. [6] Vavilov VS, Kiv AE, Niyazova OR. Mechanisms of defects formation and migration in semiconductors. Moscow: Nauka; 1981. [7] Anders S, Anders A, Brown IG. J Appl Phys 1994;75: 4895. [8] Brown IG, Anders A, Dickinson MR, MacGill RA, Monteiro OR. Surf Coat Technol 1999;112:271. [9] Skriver HL. The LMTO method. Berlin: Springer Series of SolidState Sciences; 1984. [10] Skriver HL, Rosegaard NM. Phys Rev B 1991;43:9538. [11] Skriver HL, Rosegaard NM. Phys Rev B 1992;46:7157. [12] Rosegaard NM, Skriver HL. Phys Rev B 1993;47:12865; Rosegaard NM, Skriver HL. Phys Rev B 1994;50:4848. [13] Abrikosov IA, Skriver HL. Phys Rev B 1993;47:16532. [14] Ruban AV, Skriver HL. Comput Mater Sci 1999;15:119. [15] Vosko SH, Wilk L, Nusair M. Canad J Phys 1980;58:1200. [16] Pranyavichus L, Dudonis Yu. Ion beam modification of solids. Vilnius: Mokslas; 1980. [17] Connoly JWD, Williams AR. Phys Rev B 1983;27:5169. [18] Kreiner G, Spiekermann S. Z Anorg Allg Chem 2001;677: 2460.
Structural changes in Mg alloy induced by plasma immersion ion implantation of Ag L. Kutsenko a, D. Fuks a, A. Kiv a,*, L. Burlaka a, M. Talianker a, O. Monteiro b, I. Brown b a
Department of Materials Engineering, Ben-Gurion University of the Negev, Ben-Gurion Boulevard, POB 653 Beer-Sheva 84105, Israel b Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Received 9 May 2004; received in revised form 24 May 2004; accepted 28 May 2004 Available online 24 June 2004
Abstract Formation of intermetallic compounds within the Mg matrix as a result of implantation of Ag by plasma immersion ion implantation technology was investigated. Transmission electron-microscopy studies of the implanted samples revealed the appearance of nanoparticles of binary phase Mg–Ag. A model based on the classical mechanisms of propagation of accelerated ions through the metal matrix was suggested for the explanation of the experimental observations. Ab initio calculations of the electronic sub-systems proved to be helpful in providing theoretical prediction of the structural changes, which may be induced in the implanted system. Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Implantation; Ab initio electron theory; Transmission electron microscopy; Magnesium alloy
1. Introduction Plasma immersion ion implantation (PIII) is a newly developed technology for the surface treatment of materials covering an important field at the forefront of materials science [1–3]. In PIII the target material is immersed in plasma, which contains low energy ions of the species to be implanted. Repetitively pulsed high negative voltage is applied to the samples, thus stimulating implantation of ions into the surface of the object. For the case when metal plasma is employed, metal ions condense on the material surface as a film in the time period between the high voltage pulses during the course of the PIII process. Ions accelerated by the high voltage bias pulse impact the deposited metal atoms producing recoil implantation. This affects the depth profile of the PIII process, making it different from the usual gauss-
*
Corresponding author. Tel.: +972-864-614-63; fax: +972-864-793-
50. E-mail address: [email protected] (A. Kiv).
ian-like shape. By varying the ratio of pulse-on time (during which implantation occurs) to pulse-off time (during which deposition occurs) the shape of the implantation profile can be tailored, providing new interesting options for surface engineering. Although numerous topics related to the technological aspects of PIII and its practical applications have received extensive study, very little has been done with regard to developing a theoretical basis for understanding the physical phenomena responsible for the structural changes caused in the material by PIII treatment. The existing theoretical models of ion implantation mainly deal with the penetration behavior of ions and with the stopping phenomena, rather than with the effects resulting in the formation of new phases in the implanted material [4]. From the point of view of radiation physics, two basic competing mechanisms are involved in the process of energy loss by the ion moving through the material: firstly, collisions of implanted ions with free and bound electrons, and secondly, collisions with the atomic nuclei. Assuming that these events occur independently,
1359-6454/$30.00 Ó 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.05.049
4330
L. Kutsenko et al. / Acta Materialia 52 (2004) 4329–4335
an expression for the energy lost by an ion per unit distance can be written as [5] dE ¼ N jSn ðEÞ þ Se ðEÞj; ð1Þ dx where N is the atomic density of the target atoms, and Sn and Se are the cross-sections for electronic and nuclear stopping, respectively. Specifically, in the case of PIII treatment the ion energy is relatively low, and therefore the condition Se Sn should be satisfied [5]. This means that during the PIII process the implanted ions lose their energy primarily via nuclear collisions, giving rise to elastic displacement of the atoms in the crystal lattice accompanied by formation of lattice defects [6]. If the ion energy is not sufficient to produce lattice defects, nuclear collisions would generate only large atomic oscillations. The region of such intense oscillations may be considered as a thermal spike, which causes local melting of the material within the microscopic volume [4–6]. It seems that the concept of thermal spikes might be useful for the explanation of structural and chemical transformations occurring in PIII implanted layers. In the present paper an attempt has been made to develop a theoretical basis for understanding the mechanisms leading to microstructural changes in the PIII treated material. The experimental observations obtained from the Mg-alloy implanted with Ag are discussed in terms of a thermal spike approach. Additionally, calculations based on first-principle methods were also carried out. The results show that analysis of the electronic states of non-equilibrium atomic configurations formed throughout PIII processing may be helpful to provide theoretical predictions of the stability of the structures induced.
2. Experimental and computational details The commercial magnesium alloy WE 54 of composition Mg–5.1wt%Y–3.3wt%Rare Earth–0.4wt%Zr (manufactured by Magnesium Electron Company, UK) was used as a target for the implantation experiments, and Ag was chosen as the implanted species. Initially the alloy was in T6 condition obtained as a result of conventional age-hardening treatment. Thin foil specimens for transmission electron microscopy (TEM) were cut using an electric spark erosion machine and ground to a thickness of 0.1 mm before final ion beam thinning. Then specimens suitable for TEM were subjected to implantation of Ag (from both sides), applying metal plasma immersion ion implantation and deposition (Mepiiid) technology. The metal plasma was produced by a small, repetitively pulsed vacuum arc plasma gun operated at a pulse length of 5 ms and repetition rate 1 Hz and with arc current about 300 A. It is known that along with the
metal plasma that is generated, a flux of macroscopic droplets (re-solidified cathode debris) of size in the range 0.1–10 lm is also produced [7]; this solid particulate contamination was removed using a curved magnetic duct (bent solenoid of magnetic field strength a few hundred gauss) which stops line-of-sight transmission of macroparticles while allowing the transport of plasma [8]. The overall plasma formation system thus consists of the repetitively pulsed plasma gun in conjunction with a 90° magnetic filter. Implantation ion energy was controlled by repetitively pulse biasing the substrate. The pulse duration was 5 ls and the duty cycle 50%. We point out that silver atoms deposited on the substrate surface during the bias-off part of the cycle are subsequently implanted by knock-on (recoil) collisions with energetic silver ions belonging to the next bias-on part of the cycle; a 50% duty cycle is adequate to ensure that essentially all silver is implanted, with no remaining surface layer. The absence of a deposited layer of silver was also confirmed by TEM investigations. The implanted specimen was checked in TEM before and after cleaning its surface by argon glow discharge in EMITECH K-350 system. No discernible difference in the microstructure of the specimen was found, thus indicating that all structural characteristics obtained through TEM study can be considered as a bulk effect. Note also that the pulse biasing is applied, and is relevant, only for that time for which the vacuum arc metal plasma is produced, i.e., for 5 ms pulses once per second, and the ‘‘macroscopic’’ duty cycle for which the pulse biasing is applied is 50% of 5 ms per second, or 0.25%. Thus the mean power input to the sample by ion bombardment is modest and the substrate mean temperature rise is small (the substrate is clamped to a heavy metal holder). A simple estimate indicates an expected mean temperature of about 30–40 °C. The mean ion energy is Ei ¼ qV , where q is the mean ion charge state of the vacuum-arc-produced metal plasma, and V is the bias voltage. The mean ion charge state for the Ag plasma as used here is 2.1 and the ion energy was in the range 2.5–5.0 keV. The total retained dose was about 1017 1018 cm2 . The uniformity of dose across the substrate was about 10–20%. Ab initio calculations were carried out using linear muffin-tin orbital (LMTO) method of one-electron theory in the atomic sphere approximation (ASA) [9–14]. The important feature of this approach is the use of volume- and energy-independent structure constants, and employing the parameters containing the information about one-electron potential. These quantities completely specify the energy-band structure of given material. The approach is valid for closely packed crystalline solids, giving a physically simple description of the energy-band formation.
L. Kutsenko et al. / Acta Materialia 52 (2004) 4329–4335
The computer program BGFM, which was used for calculations, takes into account multipole corrections to ASA and employs coherent potential approximation (CPA) [14] for calculations of disordered system. This code was chosen as a fast scheme for direct calculation of the electronic structure of the atomic system. With self-consistently obtained bands the program calculates the total energies of the system. Core electrons are frozen after initial atomic calculations. The exchange-correlation effects are considered according to Vosko et al. [15]. The individual atomic sphere radii are set equal to the radius of the average atomic Wigner–Seitz sphere. The uncertainty of the absolute values of the energy gaps was reduced by use of a special extended k-point basis. For the total energy calculations the convergence criterion was chosen as 0.001 mRy. Additional details describing the program can be found in [14].
3. Results and discussion 3.1. TEM observations Comparison of TEM micrographs taken from the alloy before and after implantation of Ag (Fig. 1(a) and (b)) reveals that fine nano-particles, about 10–12 nm in size, homogeneously form in the interior of the a-Mg matrix grains as a result of Mepiid treatment. Qualitative X-ray energy dispersive microprobe analysis has indicated that the particles contained Ag and Mg. The vast bulk of these particles were positively identified by electron diffraction and dark-field tech An example nique as a cubic AgMg phase (a ¼ 3:314 A). of the electron diffraction diffraction pattern indexed in terms of cubic unit cell of AgMg phase is shown in Fig. 2(a), and corresponding bright-dark field pair of images of AgMg nano-particles are shown in Fig. 2(b) and (c).
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3.2. The mechanism of phase formation It may at first seem surprising that nano-precipitates of the second phase appear as a result of ion implantation. Considering the implanted material as a supersaturated solid solution of Ag in Mg matrix, one might suppose that the precipitation reaction should evolve through a conventional diffusion mechanism. However, as it was noted in Section 2, the specimen temperature under implantation does not exceed 30–40 °C, hence macroscopic migration of the atomic species in the material is insignificant for forming a nucleus of a new phase and can be ignored. It is clear, therefore, that another mechanism, not based on the concept of longrange diffusion, has to be used for understanding the precipitation effect observed in the implanted material. An approach based on ideas of the theory of propagation of fast particles through the solid seems to be more appropriate. Following this theory we may assume that specific regions of high thermal excitation, so-called thermal spikes [6,16], will be generated as a result of penetration of plasma ions into the metal matrix in the course of PIII processing. If the spatial spread of the temperature within the thermal spike zone obeys the equation of thermal conductivity, it can be written: T ðr; tÞ ¼ T0 þ
Q ð4pÞ
3=2
1 cd ðDtÞ
3=2
er
2 =4Dt
ð2Þ
where T ðr; tÞ is the temperature within the spike as a function of time t and distance r from the center of the spike, Q is the value of the heat energy in the center of the spike at t ¼ 0, D is the coefficient of thermal conductivity, and c and d denote the heat capacity and the material density, respectively. Bearing in mind that the so-called displacement energy needed for removing Mg atom from its lattice site by elastic collision is about 10 eV [16], and near dislocations, grain boundaries and other imperfections this energy decreases to 5 eV, we
Fig. 1. Transmission electron micrographs showing the WE54 alloy before (a) and after (b) implantation of Ag ions.
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Fig. 2. (a) Electron diffraction pattern taken from the area of specimen containing AgMg nano-particles formed within a-Mg matrix of the WE54 alloy by Mepiiid processing. The reflections related to AgMg phase are indexed. (b) Bright field. (c) Dark Field TEM micrographs of AgMg particles taken in (1 1 1) reflection.
may estimate that the energy Q for thermal oscillations should not exceed the value of 5 eV – otherwise the lattice atoms will be removed from their sites. Therefore, the value Q ¼ 3 eV would seem to be reasonable. Taking for the Mg matrix the values, c ¼ 1.02 kJ/(kg K), D 103 cm2 /s and density d ¼ 1:74 g/cm3 , we can calculate the temperature profiles T ðrÞ associated with the spike for different time intervals. From these profiles, the average size of the spike region, its time dependence and effective temperature can be readily estimated, as shown in Table 1. Table 1 shows that the occurrence of a spike gives rise to a temperature increase over a region of size about it can also be seen that the lifetime of the 100–200 A; spike is approximately 1010 –109 s, which corresponds to the time required for 30–300 atomic oscillations. Now a qualitative explanation of the formation of second phase particles within the implanted matrix can be given as follows: a liquid nano-size droplet of Mg–Ag melt forms as a result of excitation of the spike; the droplet quickly cools and at the end of the spike lifetime it may be considered as a metastable supercooled liquid within which 30–300 oscillations have occurred. These oscillations seem to be sufficient to displace atoms of Mg and Ag towards their new positions in a new intermetallic structure, which is formed during solidification. Table 1 Parameters estimated for thermal spikes in Mg r (A)
t (s) 11
2.5 10 5 1011 1010 1.5 1010 2 1010 109
15 20 30 40 50 100
T (K) 1500 1000 500 450 350 300
r is the effective radius of the region for the corresponding temperature.
3.3. Ab initio studies In this section we demonstrate the effectiveness of an Ab initio approach for analysis of Mg–Ag system obtained by implantation of Ag atoms into the Mg-matrix. The calculations were carried out for two following states of the system: (a) Initial, or starting state, which corresponds to the atomic configuration arising as a result of penetration of Ag-atoms into the Mg-target during the PIII processing. The system is considered as a rigid hcp lattice of Mg atoms mixed with a controlled amount of Ag atoms substituting for Mg atoms. Such a system is non-equilibrium one and its electronic subsystem is in an excited state. (b) Relaxed state, corresponding to a new atomic configuration, which may be adopted by the implanted system due to the relaxation process. Such configuration can be found through the simulation of the atomic displacements, causing transition of the system to a new non-stable equilibrium state characterized by the relative energy minimum. For both conditions, (a) and (b), the self-consistent values of the total system energy, Etinit and Etrelax , respectively, were determined over a wide range of Ag concentrations. CPA LMTO–ASA computation procedure [13,14,17] was used for this purpose. Also, the total and partial densities of the electronic states (DOS) were calculated for different concentrations of Ag in the Mg matrix. The energy Etinit was computed for the non-relaxed rigid Mg lattice with randomly distributed Ag atoms that substitute for Mg. Etrelax energy was obtained by minimization procedure, in which the lattice parameter of the implanted matrix was varied to find the minimal total energy of the system with respect to the volume X of the calculation cell. Such minimization procedure can
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be considered as equivalent to solving the equation of state ðoEtot =oXÞS ¼ p; when the temperature is equal to zero and the external pressure p ¼ 0. The values of the difference DE ¼ Etrelax Einit were then determined for the wide range of Ag content, as summarized in Fig. 3 presenting a plot DE vs. Ag concentration. Considering DE as a ’’relaxation energy’’ showing how the initial non-equilibrium state is far from the relaxed state, it was reasonable to assume that there should be some correlation between the value DE calculated for a specific Ag concentration and the possibility of formation a stable Mg–Ag compound with the same Ag content. It should be noted that both energies, Etinit and Etrelax , are related to the states, which, in fact, are not stable and do not exist in reality. Nevertheless, when comparing the behavior of DE (see Fig. 3) with the experimental data collected in Table 2 presenting some stable phases reported elsewhere [18] for the Mg–Ag system, it may be seen that abrupt changes of the value DE occur when the atomic concentrations of Ag in the implanted material are close to stochiometric compositions of stable phases (the AgMg and Ag17 Mg54 phases, in our example). This interesting result implies that ab inito calculations performed for the disordered implanted system may yield useful energy characteristics of the relaxation processes. These characteristics, such as difference DE ¼ Etrelax Einit , can be then employed to give a reasonable forecast which concentrations of the implanted element favor formation of a stable compounds in the implanted matrix. It is also instructive to analyze the behavior of DOS characteristics of the Mg–Ag system when different amounts of Ag are implanted into Mg-matrix. The system now is considered to be in its initial non-equilibrium state, and the total and partial DOSes are calculated for different concentrations of Ag atoms (within 0–75 at.% range). Examples of computations of total DOSes for pure Mg, Mg + 0.1 at.%Ag and
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Table 2 Stable phases in the Mg–Ag system Phases
Pearson symbol
Composition at.% Ag (%)
Space group
(Ag) a Ag3 Mg a0 AgMg b Ag17 Mg54 e0 Ag7:96 Mg25:04 e Ag9 Mg37 c (Mg) d
cF4 cP4 cP2 oI142 cF264 hP92 hP2
70.7–100 75 34.6–64.5 21.2–24.1 21.2–24.1 19.6 0–8.9
Fm3m Pm3m Pm3m Immm Fm3 P 63 P 63 =mmm
Mg + 40 at.%Ag are presented as plots in Figs. 4 and 5. It is not surprising that the small increase of Ag content in Mg matrix has no marked effect on the total DOS (compare DOS for pure Mg and for Mg + 0.1 at.%Ag), while significant increase in the number of states in total DOS occurs for the concentration of 40 at.%Ag (see Fig. 5). It is interesting, however, to understand which electron states contribute to this increase. The explanation can be found by considering the partial densities of Ag d-electrons. Fig. 6 shows the results of calculations of partial DOS of Ag d-electrons for two compositions: Mg + 0.1 at.%Ag and Mg + 40 at.%Ag. A comparison of concentration dependence of total DOS and partial density of d-states for the Mg–Ag sytem is presented in Fig. 7. It can be seen from Figs. 6 and 7 that the number of states of Ag d-electrons drops substantially when the concentration of the implanted Ag atoms increases from 0.1% to 40%. Besides, as it follows from Fig. 5, the dependence of total DOS on the Ag content is associated primarily with the deep electronic states, within the energy region of 0.15–0.45 Ry corresponding to the energy of Ag d-electrons. It can be surmised, therefore, that increase of the number of electronic states in total DOS occurs at the expense of d-states of Ag. It can be suggested, that, in fact, d-electrons of Ag promote more symmetrical and p states in the implanted Mg–Ag system. Increase in density of more symmetrical states may be advantageous for the formation of intermetallic
Fig. 3. The concentration dependence of the ‘‘relaxation energy’’ for Mg matrix implanted by Ag.
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Fig. 4. Total density of electronic states calculated for the pure Mg.
Fig. 5. Total density of electronic states calculated for Mg matrix implanted by 0.1 at.% Ag and 40 at.% Ag.
Fig. 6. Partial DOS for d-states of Ag implanted into Mg. Dashed line is for 0.1 at.% of Ag and solid line is for 40 at.% of Ag.
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Fig. 7. Comparison of concentration dependence of total DOS and partial density of Ag d-states for the Mg–Ag system.
phases with higher symmetry. This exactly corresponds to the general trends manifested in Table 2: structures with larger Ag content possess higher symmetry. 4. Conclusions (a) Implantation of Ag-ions into Mg alloy WE54 by Mepiiid technology results in occurrence of nanosize particles of compound AgMg under the surface of the specimen. (b) Basic concepts of classical theory of propagation of fast ions through the solid seem to be appropriate for qualitative understanding of the mechanism of formation of intermetallic nano-particles within the implanted matrix. The particles may appear as a result of solidification of nano-droplets of Mg–Ag melt, formed by thermal spikes generated in the course of penetration of implanted ions through the metal matrix. (c) Ab initio calculations may provide a profound, though qualitative, insight into the electronic structure of the implanted system and can be helpful for theoretical prediction of the essential structural changes induced by implantation. For the example of the Mg–Ag system it was shown that the parameter DðEÞ characterizing the energy difference between the initial ‘‘as-implanted’’ state of material and the non-stable equilibrium state attained during relaxation may serve as an indication of the possible formation of stable compounds at the given Ag concentration. Further, analysis of the changes in delectron states of Ag showed that d-electrons of Ag play an important role in the formation of intermetallic compounds in Mg–Ag alloy: their promotion to s and p states may be associated with the formation of intermetallic phases with higher symmetry.
Acknowledgements The authors acknowledge the support of this work by the Binational Scientific Foundation under Grant #2 000 122. L.K. and D.F. are thankful to Dr. A. Ruban for helpful discussions.
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