Creating nanostars with buckyballs

Physics Letters A 377 (2013) 3304–3311

Contents lists available at ScienceDirect

Physics Letters A www.elsevier.com/locate/pla

Creating nanostars with buckyballs Young K. Bae ∗ Y.K. Bae Corporation, Tustin, CA 92780, United States

a r t i c l e

i n f o

Article history: Received 6 October 2013 Received in revised form 21 October 2013 Accepted 22 October 2013 Available online 25 October 2013 Communicated by V.M. Agranovich Keywords: Metastable innershell molecular state Warm dense matter Nanoparticle Soft X-ray Buckyball Superradiance

a b s t r a c t We report creating superradiant quantum nanoplasmas (nanostars) by impacting buckyballs at hypervelocities (v >100 km/s) in an innovative tabletop apparatus. The nanostars are estimated to have ∼10 TPa transient pressures and convert ∼35% of impact energy into soft-X-ray energy. The ultrahighefficiency conversion is proposed to result from Dicke Superradiance of Metastable Innershell Molecular State, originally discovered by the author and his colleagues in 1994. The usage of buckyballs and successful orders-of-magnitude scaling down of the apparatus size and complexity establish an innovative tabletop method for generating, studying, and utilizing matter in planetary or stellar interiors and open doors to numerous unprecedented applications. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Investigation and understanding of materials under extreme conditions, High Energy Density Materials, as in planetary or stellar interiors are crucial for advancing a wide range of scientific and technological fields, such as astrophysics [1,2], inertial confinement fusion, [1,2] X-ray lasers [3], material science [4–7] and biological science [7]. Recently, there have been extensive researches on Warm Dense Matter, which is a non-equilibrium state of matter between solid and plasma, and is too dense to be described by weakly coupled plasma physics, yet too energetic to be described by condensed matter physics [8]. Warm Dense Matter is expected in the cores of some large planets, in the inertial confinement fusion during the solid to plasma phase transition driven by laser pulses, and other systems that start as solids and are heated to become plasmas [8]. Recent theoretical studies have predicted High Energy Density Materials and Warm Dense Matter may have rich quantum manybody characteristics [4–6], including that metals may become insulators at high pressures [5,6,9]. Atomic quantum effects that result from innershell electron excitation and ionization have been theoretically studied for many of technologically important materials, such as aluminum, silicon, and iron [10,11]. For example, the theoretical Hugoniot curve of aluminum has two density maxima corresponding to full ionization effects of the L (pressure ∼30 Tpa or 300 Mbar) and K (pressure ∼400 TPa or 4 Gbar) electron shells

*

Tel.: +1 714 838 2881; fax: +1 714 665 8829. E-mail address: [email protected].

0375-9601/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2013.10.036

[10,11]. At shock pressures on the order of 10 TPa (100 Mbar or 1013 J/m3 ) aluminum would have 4 times of its normal density and an energy per atom greater than 260 eV, which is sufficient enough to excite or ionize the L-shell electrons. In addition to these atomic effects, the effects of crystalline or molecular states in such matter, of which optical transition energies are predicted to range from hundreds of eV to tens of keV, have also been theoretically investigated [4,5,9]. In their ab initio quantum calculations, Younger et al. [12] found that when an ensemble of He atoms are highly compressed, they may form tightly bound quasimolecular states. Winterberg [13] predicted an existence of quasimolecular states at pressures on the order of 10 TPa (100 Mbar) and super-intense X-ray radiations during their transition from atomic states to molecular states. In comparison with the extensive theoretical work, experimental observations of quantum effects in High Energy Density Material and Warm Dense Matter have been very scarce. Traditionally, the focuses of experimental works on High Energy Density Material and Warm Dense Matter have been on their thermodynamic properties, such as EOS (Equation of State) and Hugoniot curves. These materials have been produced and investigated with the use of ultra-large scale experimental setups, such as underground nuclear explosions [14,15], laser fusion facilities [16], z-machines [17] and X-ray Free-Electron Lasers (XFEL) [3,6,7]. However, a definitive experimental observation of the existence of the quantum effects that were predicted by the theoretical works has been prohibited by the large uncertainties in the experimental data [10,11,14]. The reason for this lack of progress results from the extreme complexity in the experimental setup and data interpretation, which obscured the manifestation of the quantum phenomena. Therefore,

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

non-destructive straightforward experimental methods, which are cable of producing these materials and permitting more detailed studies on their quantum characteristics, such as spectral characteristics, have been desired. To develop such non-destructive experimental methods, the author and his colleagues investigated the feasibility of generating and studying highly compressed matter by impacting various bio and water nanoparticle at hypervelocities (v ∼ 100 km/s) on various targets at the Brookhaven National Lab in the early 1990s [18, 19]. It was hypothesized that if the number of atoms in nanoparticles is large enough, the nanoparticle impact can generate strong shocks that can produce the highly compressed matter. One of the crucial questions was what the threshold number of atoms in the nanoparticles is to produce hydrodynamic shock characteristics. With number of atoms in nanoparticles greater than the threshold number, the pressure P s and the density ρs of the shocked target material in a one-dimensional strong shock produced by the nanoparticle particle impact at a velocity v can be approximated by [18,20]:

Ps =

ρS =

4 3

ρP v 2,

(γ + 1) ρT , (γ − 1)

(1) (2)

where ρ P and ρ T are normal densities of projectiles and targets, and γ is the adiabatic index. For example, these equations predict that at v ∼ 100 km/s, large water nanoparticles can generate shock pressures exceeding 10 TPa (100 Mbar). If the threshold number of atoms in the nanoparticles is smaller than 1000, a principal advantage of using nanoparticles for generating such high pressure shocks for producing High Energy Density Material and Warm Dense Matter is in that they can be readily charged and accelerated to such hypervelocities greater than 100 km/s with the use of compact accelerator technologies, perhaps similar to that of dental X-ray generators. In our study at Brookhaven National Lab [18,19], the author and his colleagues proved the feasibility of generating the 10 TPa (100 Mbar) shocks and discovered anomalous signals, when the nanoparticles were directly impacted on and detected by Si particle detectors with windows sufficiently thick enough to block the penetration of the nanoparticles completely. With the use of the anomalous signals as functions of nanoparticle kinetic energy, the amounts of energy deposition through thin films were measured [18,19]. In these experiments, it was observed that the energy deposition of nanoparticles was very different from that of atoms. The deposited energy of individual atoms was flat over the investigated impact velocity range, on the other hand that of nanoparticles was proportional to v 2 as in Eq. (1). The observed v-square dependence of the energy deposition was used to prove the feasibility that the nanoparticles can be used to generate strong shocks [18]. The amount of the energy density in the thin film deposited by the nanoparticle impact was measured to be on the order of 1013 J/m3 , which is equivalent a pressure of 10 TPa (100 Mbar), in qualitative agreement with the pressure obtained with Eq. (1) [18]. However, the nature and production mechanism of the anomalous signals had been unresolved over 14 years [18,19]. In 2008, inspired by the theoretical proposition by Winterberg [13], the author reanalyzed the BNL data and concluded the anomalous signals resulted from soft X-ray photons from the optical decay of Metastable Innershell Molecular State in highly compressed matter generated by the nanoparticle impact [20]. By reinterpreting the Brookhaven National Lab data, the author found that the photon energy from the optical decay was in the range of 75–100 eV for Si targets. One surprising aspect of the discovery was that the conversion efficiency of the nanoparticle kinetic energy to photon energy was as high as ∼38% [20].

3305

Such a high energy conversion efficiency indicates that the overall optical decay process of Metastable Innershell Molecular State in the nanoplasma is faster than non-radiative decay processes, which are typically orders of magnitude faster than the former in non-compressed solids. Since the size of the impact generated nanoplasmas are typically smaller than or on the order of the wavelength of radiation involved, the author proposed [20] that the Dicke Superradiance [21] mechanism speeds up the radiative process by orders of magnitude and permits efficient optical probing of the transient states in the time scale of tens of fs. We report here creating the superradiant quantum nanoplasmas, which are defined here as nanostars, by impacting buckyball ions (C+ 60 ) on Al at hypervelocities (v > 100 km/s) in an innovative tabletop apparatus. The nanostars are estimated to have ∼10 TPa (100 Mbar) transient pressures and measured to convert ∼35% of impact kinetic energy into soft-X-ray energy, which is similar to the one observed (∼38%) at Brookhaven National Lab for Si. The present paper reports experimental generation of Dicke Superradiance of Metastable Innershell Molecular State in highly compressed materials, such as High Energy Density Material or Warm Dense Matter, in a table-top non-destructive apparatus that is completely different from and orders of magnitude smaller than that at BNL [18,19]. 2. Metastable Innershell Molecular State The theoretical Hugoniot curves related to High Energy Density Material and Warm Dense Matter of many elements, such as aluminum, silicon, and iron, show quantum effects of inner-shell excitation and ionization near or above pressures of 100 Mbar (10 TPa) [10,11]. Intuitively, innershell electrons of these atoms can be modeled to the first order as the closed outershell electrons similar to that of rare gas atoms. It is now well established that when the closed outershell electrons of the rare gas atoms are excited or ionized, they can readily form transient molecules, excimers, with a pairing ground state atom. In this paper, the author proposes that Metastable Innershell Molecular State can be modeled as an analogue to the excimer state. A realistic theoretical picture of the Metastable Innershell Molecular State requires full blown ab initio calculations that can handle molecular orbits; however, the barriers to such ab initio calculations are formidable owing to the extreme computational difficulty in solving the relevant many-body problem [10–12]. Consequently, such quantum plasmas have been theoretically described by atoms with electronic structures in terms of statistical models, such as Thomas–Fermi model, Spherical Cells or Jellium of Charges. Many EOS models rely on the Thomas–Fermi (TF) model of dense matter [10,11]. These approaches provide only semi-classical descriptions of electrons, and are valid over a limited range of conditions. At intermediate shock pressures, when the material becomes electronically excited or partially ionized, the EOS depends on the precise quantum-mechanical state of the matter, i.e. on the electronic shell structure. Recently Pain applied a quantum self-consistent-field (QSCF) EOS model, in which potential energies and bound-electron wave functions are determined by solving Schroedinger equations with a self-consistent procedure in the density functional theory using a finite-temperature exchange-correlation potential [10,11]. Hugoniot curves of variety of materials were calculated and the results showed quantum innershell effects clearly. On the other hand, the effects of molecular orbitals of innershell electrons have been unincorporated into these models. The potential existence of tightly bound transient quasimolecular states, similar to Metastable Innershell Molecular State, in highly compressed plasma with relatively low ion temperatures was numerically investigated and predicted by Younger et al.

3306

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

[12]. They performed a set of ab initio quantum calculations of the electronic structure of a nine-atom helium plasma over wide ranges of temperature and density. The results of the calculations revealed a potential presence of tightly bound quasimolecular states in high-density quantum plasmas, even at electron temperatures high enough to ionize fully the component atoms. They found that such quasimolecular quantum states gradually disappear as the electron temperature increases. The nature and optical or quantum properties of such excited states, however, were uninvestigated. Overall, Younger et al. demonstrated the possibility of forming transient molecular states with closed-shell electrons in ab initio calculations for the first time for frozen or slow moving ion systems that can be approximated with the Born–Oppenheimer approximation [12]. More recently, Winterberg [13] predicted that if atoms in a matter are put under a high pressure in excess of 10 TPa (100 Mbar), they can form transient molecular states. Further, Winterberg [13] predicted that the formation of the transient molecular state can emit intense X-rays. Winterberg further intuitively predicted that the X-ray energy, δ E, can be approximately estimated by [13],

log10 (δ E ) ∼ = 1.3 × 10−2 Z − 1.4

(3)

where Z is the sum of the nuclear charge for both components of the molecule. More recently, the author proposed that Metastable Innershell Molecular State and the associated intense soft X-ray radiation [5, 6] can be more readily produced in electronically “cold” compression in nanoparticles hypervelocity (v > 100 km/s) impact [20]. If Metastable Innershell Molecular State exists, it would decay into the lower orbit via radiative and non-radiative processes. The optical decay formed by heavy element atoms can be fast enough to compete with other non-radiative decay channels, however, the optical decay of Metastable Innershell Molecular State formed by light element atoms, such as aluminum atoms, may not be fast enough to compete with other non-radiative decay channels. The radiative lifetime, τrad , is approximately given by [20]

τrad ≈

4.5 × 10−8 λ2 n

,

(4)

where λ is the wavelength of the radiation in μm and n is the index of refraction. For example, if the Metastable Innershell Molecular State of light elements, such as aluminum, emits X-ray photons with an energy of 100 eV, λ = 1.2 × 10−2 μm, τrad = 6.5 × 10−12 s, which is much longer than the ion–electron thermalization time scale and other non-radiative decay lifetimes of tens of fs [20]. Therefore, in normal circumstances light element Metastable Innershell Molecular State is expected to decay primarily via nonradiative channels, and the conversion efficiency of the excited energy to the optical energy would be very low. However, the author proposed that in the hypervelocity impact of nanoparticles the rate of optical decay of Metastable Innershell Molecular State can be increased by orders of magnitude via Dicke Superradiance mechanism [20,21], if the size of shock compressed zone is smaller than that the wavelength of the associated radiation. Originally, in 1954 R.H. Dicke [21] predicted that if N quantum oscillators are prepared in inverted but incoherent fashion and all contained in a volume small compared to the emission wavelength cubed, the quantum oscillators would all be coupled together through their overlapping radiation fields [21]. In Dicke Superradiance, the radiation will be emitted in a burst with duration of τrad / N [20,21]. For example, in a 0.1 keV photon radiation decay of impact generated quantum nanoplasmas with 100 oscillators (N ∼ 100) with an isolated individual radiative decay lifetime, τrad = 6.5 × 10−12 s, the Dicke Superradiance drastically decrease

the radiative decay lifetime to ∼ τrad / N ∼ 6.5 × 10−14 s, which is comparable with the collision time and non-radiative decay time, and much shorter than ion–electron thermalization times. Therefore, during the nanoparticle collision the radiative process can be a dominant decay process of the proposed Metastable Innershell Molecular State due to Dicke Superradiance [20,21]. Very recently, such shortening of radiative lifetime of atoms due to Dicke Superradiance in nanoparticle impact has been directly observed in gold nanoparticle impact experiments that investigated UV radiation from the impacted target [22]. In their experiment, Fernandez-Lima et al. observed radiative decays of electronically excited CsI target as a function of the nanoparticle size. The lifetime of the excited state produced by atomic gold ion and small gold cluster impacts followed individual oscillator behavior with exponential decay (T ∼7–8 ns), however, the time spectra of the optical decay of the excited state followed more Gaussian behavior with the width smaller than 1 ns that probably was limited by the instrumental time resolution [22]. Such an accelerated non-exponential optical decay provides an evidence of direct observation of Dicke Superradiance in nanoparticle impact, which supports the feasibility of Metastable Innershell Molecular State superradiance proposed by the author [20]. The exact theoretical model of Metastable Innershell Molecular State has yet to be developed. In this paper, the author proposes an intuitive model in which Metastable Innershell Molecular State is described as an excimer-like molecule formed by an innershell excited/ionized atom and a ground state atom in highly compressed strongly coupled quantum plasma environment with low electron temperatures as in Warm Dense Matter. In atmospheric pressure environment, electronic excitation/ionization of rare gas atoms with closed electronic shells can generate transient molecules, excimers formed by outershell electron excitation/ionization, which can typically radiate from a temporarily bound metastable molecular state (an excimer state) to free repulsive states [23]. In terms of molecular processes, the formation of excimers requires frequent third-body interaction that can quench free atomic states into temporary bound molecular states, excimer states. In typical rare gas excimer formation with binding energies on the order of eV, the collision frequency of the third bodies is high enough in atmospheric pressure environment. On the other hand, excimer-like transient molecular states formed by innershell electrons, Metastable Innershell Molecular State, with binding energies on the order of or greater than 100 eV, the third body collision frequency should be orders of magnitude higher, thus Metastable Innershell Molecular State formation requires high densities and pressures that can only be produced by strong shock compression. Table 1 summarizes the comparison between characteristics of Metastable Innershell Molecular State radiation and that of excimer radiation [23]. Most importantly, Metastable Innershell Molecular State radiation can be generated virtually by all elements in the periodic table, while excimer radiation can only be generated by closed outer-shell elements, such as rare gas elements. Therefore, Metastable Innershell Molecular State radiation is predicted to cover a much wider range of photons from Extreme-Ultraviolet to X-ray photons than that are accessible with the exiting state-ofthe-art X-ray generation technologies. Specifically, a schematic diagram of the Metastable Innershell Molecular State radiation mechanism based on the excimer model is illustrated in Fig. 1. In this diagram, two innershell atomic states are denoted by Am+ and Bn+ , in which the numbers of outershell electrons in the atoms are m and n respectively. During compression at pressures high enough to overlap innershell electrons (on the order of 100 Mbar, or 10 TPa), one of innershell can be excited to (Am+ )∗ in the vicinity of Bn+ , both of which are surrounded by other innershell atoms and outershell electrons. The innershell excitation results presumably from a hybrid process of

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

3307

Table 1 Comparison between characteristics of Metastable Innershell Molecular State radiation and excimer radiation.

Atoms involved Electrons involved Photon energy Observed linewidth (FWHM) Observed energy to photon conversion efficiency Radiation character

Metastable Innershell Molecular State radiation

Excimer radiation

Any kind of atoms Innershell electrons 100–100 keV ∼10% ∼40% Bound-free?

Rare gas or halide atoms Outershell electrons 5–10 eV ∼10% 10–40% Typically bound-free

Fig. 1. Excimer model of Metastable Innershell Molecular State (MIMS). When the innershell of one of atoms in the compressed region is excited, it behaves like a rare gas atom excited state. The collision between the innershell excited atom and other atoms in the ground state results in formation of Metastable Innershell Molecular State. Metastable Innershell Molecular State subsequently dissociates into two ground state atoms by emitting a soft X-ray photon. Because the final state is repulsive, the linewidth of the Metastable Innershell Molecular State radiation is expected to be large (FWHM>10%) as in rare gas excimer radiation.

collisional excitation and pressure excitation during compression. During the compression, the surrounding atoms and electrons can be a third body (X) that is necessary for forming Metastable Innershell Molecular State, (Am+ Bn+ )∗ by quenching excess continuum energy, as in:



Am +

∗

 ∗   + Bn+ + X → Am+ Bn+ + X.

(5)

This kind of innershell reaction to form Metastable Innershell Molecular State would not happen in low pressure (pressure 100 Mbar), because the probability of innershell excitation is extremely low in this low pressure range and because the lack of proximate third bodies that are crucial to quench the atomic states into compound molecular states. If the proposed excimerlike model is valid for Metastable Innershell Molecular State, the radiation energy of Metastable Innershell Molecular State, EMIMS , can be approximately given by:

EMIMS ∼ Eexcitation − Equenching − Ebound-free .

(6)

Typically in excimer radiation, Eexcitation Equenching and Eexcitation >Ebound-free . Thus, EMIMS ∼Eexcitation . For example, in aluminum, E2p-3s ∼100 eV, thus, EMIMS for aluminum should be on the order of 100 eV in consistent with the present observation. 3. Experimental The experimental results discovered by the author and his colleagues (Bae et al.) in 1994 at Brookhaven National Lab have not been confirmed independently [18,19]. Therefore, one of main purposes of the present work is to independently confirm the Brookhaven National Lab experimental observation with a different nanoparticle in a completely different experimental setup. In particular in the Brookhaven National Lab experiments, because the anomalous signals were generated by impacting nanoparticles directly on thin films or deadlayers/windows deposited directly on

Fig. 2. Schematic diagram of the experimental setup. The C+ 60 ions were generated by VUV photoionization of sublimated C60 nanoparticles from powder in a Knudsen cell. The VUV photons (∼10 eV) were generated by a Kr-line lamp. The ions were accelerated to the aluminum cathode and the impact generated X-ray photons, secondary ions, and secondary electrons. Three Si-photodiode detectors with thin film coatings were used for measuring the X-ray photon energy. The secondary electrons, which were generated from the impact region and accelerated to the detectors were deflected by permanent magnets, and the secondary ions were completely stopped in the thin films deposited on the detectors.

the particle detectors that detected the nanoparticles as well, there has been a question regarding whether the signals resulted from soft X-rays or some unknown particle energy amplification effects in the impact region. In the present experiments, the apparatus was designed and constructed such that the results can provide answers to the questions unambiguously. The schematic diagram of the present setup is shown in Fig. 2. The key differences between the Brookhaven National Lab setup and the present setup are provided in Table 2. The primary differences are in the species of nanoparticles and the characteristics and location of the soft X-ray detectors. Specifically, in the Brookhaven National Lab experiments, the produced X-ray was detected with particle detectors that were directly exposed to the nanoparticle beam on-axis. Thus, there remained a lingering question: whether the observed signals could result from energetic particles that were somehow produced in the shocked region and penetrated through the detector window, although all of such possibilities were systematically eliminated in the Brookhaven experiments [18,19]. To conclusively eliminate such possibilities of particle energy amplification mechanism, in the present setup, we have designed the experimental setup such that the impact generated soft X-rays were detected off-axis from the nanoparticle beam axis and the signals were analyzed using three Si photodiode detectors with selective energy response curves. Therefore, the present detection setup can confidently prove that the signals indeed result from soft X-rays. One of the primary goals of the present work was to demonstrate a nanoparticle impact soft-X-ray generator that is much more compact and simpler than that at Brookhaven National Lab. For this goal, the author concluded that C60 would be one of the best nanoparticles that can satisfy the requirements. Therefore, in this experiment, C60 was chosen as a projectile nanoparticle and

3308

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

Table 2 Comparison between experimental setups of the present work and Brookhaven National Lab work.

Nanoparticles Ionization mechanism System size Acceleration voltages Targets X-Ray detectors Target detector integration

Present experiment

Bae et al. experiment in 1994

C60 Photoionization Desktop Up to 100 kV Solid aluminum Off-Axis Si photodiode Separated

H(H2 O)n+ , multiply charged biomolecules (albumin, cytochrome-c etc.) Discharge and electrospray ionization Building Up to 1000 kV Aluminum thin film or B-doped silicon On-Axis Si particle detector Combined

Fig. 3. The theoretical upper bound of shock pressures that can be generated by C60 impact based on Eq. (1) as a function of acceleration voltage (in kV).

the reasons for the choice are given below. The water nanoparticle impact experiment that probed the effect of size (the number of molecules) by the author and his colleague at Brookhaven National Lab [19] showed that the onset of the hydrodynamic shock behavior begins near the size of ∼50. More specifically, the author and his colleagues performed [19] an experiment in which the response of the passivated solid state detector to the impact water nanoparticle ions with (H2 O) N H+ with N from 1 to 1500 was systematically investigated at a fixed acceleration energy of 500 keV [19]. The detector signals obtained with water nanoparticles with 1 < N < 10 followed the theoretical curves calculated for the impact of individual atoms on the sensitive part of the detector through the window (a non-reactive region to radiation or particles) [19]. Based on the individual atomic impact model, the atoms in the nanoparticles with N > 30 should be completely stopped by the window, however, signals persisted with N > 30 and flattened over 50 < N < 300 as in Fig. 2 of Ref. [19]. In the previous paper [20], by reinterpreting the data presented in Ref. [18] and Ref. [19], the author showed that the signals with N > 50 resulted from intense soft X-ray photons that cannot be generated by the impact of individual atoms in the nanoparticles, but can be generated by the proposed collective optical decay of Metastable Innershell Molecular State in shock-generated nanoplasmas. Thus, any nanoparticles that consist of more than ∼50 atoms (heavy atoms) can be used for inducing the desired hydrodynamic nano-shocks, and therefore C60 has sufficient numbers of atoms (greater than 50) to induce hydrodynamic shock behavior [19]. Indeed, the prediction that C60 at impact velocities on the order of 100 km/s can induce strong shocks is supported by recent molecular dynamics simulations, in which C60 impacts on Ag [24]. The upper-bound shock pressure that can be generated by C60 ion impact can be estimated by Eq. (1), and is shown as a function of acceleration voltage in Fig. 3. Based on this estimation, the required C60 acceleration voltage for generating 10 TPa (100 Mbar) shock compression is at least ∼17 kV. The advantages of C60 over

other bio and water nanoparticles in generating the nanostars, thus intense soft X-rays are: (1) C60 can be readily sublimated from an off-the-shelf high purity C60 powder, thus its generation does not require ultra-large pumping systems, such as roots blowers or other high capacity vacuums pumps that are required for generating bio and water nanoparticles as in Brookhaven National Lab works, (2) the unused C60 can be readily pumped by the vacuum chamber walls at room temperature, thus its pumping does not require additional large pumping systems, (3) the need for a mass spectrometer system is eliminated, if a soft ionization method, such as photoionization, is employed. Furthermore, the C60 has much smaller mass than the nanoparticles used in the Brookhaven National Lab experiments; the required acceleration voltage is considerably smaller. These advantages permit the reduction of the overall experimental apparatus size by orders of magnitude compared with that at Brookhaven National Lab and enable the design of a wide range of compact highly energy-efficient X-ray generators with the use of state-of-the-art particle acceleration techniques from electrostatic accelerators to explosive driven compressors. Specifically, C60 ions were generated by photoionizing sublimated C60 nanoparticles from a commercial off-the-shelf Knudsen cell that can be heated to 1000 ◦ C to sublimate 99.5% pure C60 powder. C60 at temperatures above 750 ◦ C is known to have extensive fragmentation, therefore, the operation temperature of the Knudsen cell in this work was set below 650 ◦ C. In the present experiment, photoionization was used for ionizing C60 to minimize fragmentation. Election impact ionization of C60 in gas or plasma environment has been extensively researched and was found to cause extensive fragmentation of C60 at the electron impact energies to induce sufficient ionization. Thus, Photoionization is used here instead to minimize the fragmentation. The photoionization threshold of C60 is ∼7.6 eV, and the photoionization cross section of C60 is about 1.5 × 10−16 cm2 at 10 eV and peaks at 1.5 × 10−15 cm2 at 22 eV [25]. To minimize the fragmentation, the photon energy should be as close as possible to the threshold energy of 7.6 eV. Because the photoionization cross section of C60 rapidly decreases as the photon energy becomes smaller towards the photoionization threshold, the reasonable required photon energy is ∼10 eV, which deposits only ∼2.4 eV of residual energy in C60 vibrational energy and kinetic energy of the photoelectron. The exact energy partition of these two main competing channels is unknown, however, in the photoionization process of atoms and molecules, typically, the major portion of excess energy above the photoionization threshold is partitioned to the kinetic energy of photoelectrons. Thus, the vibration energy is expected to be considerably smaller than 2 eV, and it is estimated that the fragmentation resulted from the photoionization process of C60 is negligible at photon energy of ∼10 eV. Here, the 10-eV photons were generated by a commercial off-the-shelf compact Krypton line lamp manufactured by Resonance Ltd, which has a magnesium–fluoride window and can generate on the order of 1015 photons/sec. The efficiency, Y , of photoionization can be estimated by

Y ≈ nσ l

(7)

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

3309

Fig. 4. The quantum efficiencies of the three detectors used for detecting soft X-ray photons from Al Metastable Innershell Molecular State radiation decay induced by C60 impact.

where n is the C60 number density, σ is the photoionization cross section, and l is the interaction length between photon and C60 beams. For example, if n ∼ 1.5 × 1015 /cm3 , which corresponds to the Knudsen cell operation temperature of 650 ◦ C, and l is 2.5 cm, then Y is 0.56 or 56%. The soft X-ray photons generated by the C+ 60 impact were observed off-axis from the C60 ion beam axis with three thin film coated Si-photodiodes by Opto Diode Corp. for detecting photons with energies in the ranges of 40–73 eV (Detector A), 60–120 eV (Detector B), and 80–170 eV (Detector C), respectively as shown in Fig. 4. According to the manufacturer, their responses are absolute and linear over 12 decades. In our experiment, in addition to soft X-ray photons, the C60 impact on the target cathode generates secondary electrons and secondary ions. Therefore, the three Si-photodiodes would produce signals from the impingement of the electrons and ions as well. The secondary electrons have the same kinetic energy as the C60 ions at the detector front surface, thus can readily penetrate the thin films on the detectors by losing a small portion of their energy. Secondary negative ions also would have the same kinetic energy as C60 ions, but their ranges are shorter than the thicknesses of the thin films on detectors, thus they were completely stopped by the thin films. Therefore, the major noise contribution to the detector signals came from the secondary electrons. We have used arrays of rare-earth permanent magnets both located on the sides of the detectors and outside of the vacuum chamber to minimize the secondary electron noises. The magnetic field strength in front of the detectors produced by the magnets was about 800 G. According to the ion trajectory simulation (SIMION) results, with this magnetic field strength the electrons with kinetic energy less than 20 keV were completely deflected. The electrons with kinetic energies higher than 20 keV, however, were able to penetrate the magnetic field. Therefore, the main noise contribution to the detector at acceleration voltages above 20 kV resulted from the secondary electrons. 4. Results and discussion The Brookhaven National Lab water nanoparticle soft X-ray yield experimental data [19,20], which were interpreted and presented in Fig. 1 of Ref. [20], showed a possible existence of an activation energy to a metastable state, thus were curve fitted with the Arrhenius Equation:



H = H 0 exp −

Ea E



,

(8)

where H is the relative pulse height, H 0 is a constant, E a is the reaction threshold kinetic energy per water molecule, and E is

Fig. 5. Arrhenius plots of the signal recorded on Detector A and B. With 1/KE < 0.04 (KE > 25 keV), the data from three detectors (see Fig. 6) show almost identical behaviors, which resulted from the high energy secondary electron infiltration. With 1/KE > 0.04 (KE < 25 keV) the detector A and B data show responses from soft X-ray photons greater than the secondary electron noise, while the detector C data does not. See Fig. 6.

the impact kinetic energy per water molecule in the nanoparticles. Such Arrhenius behavior was interpreted to suggest an existence of a barrier to forming Metastable Innershell Molecular State. Similar to the Brookhaven National Lab data, the present data follow Arrhenius behavior (Eq. (8)) [20]. To visually show the fitting to Eq. (8), we plotted signals from the C+ 60 impact measured with the three detectors as a function of inverse kinetic energy (1/KE) in Fig. 5 (Detector A, B) and Fig. 6 (Detector C). With 1/KE < 0.04 (E > 25 keV), the data from all detectors show almost identical behaviors, which were determined to result from the high energy (E > 20 keV) secondary electron infiltration as mentioned in the previous section. With 1/KE > 0.04 (E < 25 keV), however, the detector A and B data (Fig. 5) show responses from soft X-ray photons greater than that of the secondary electron noise, while the detector C data (Fig. 6) do not. Thus, two competing processes for generating signals resulted in a sum of two Arrhenius equations, of which intensities become dominant in two different impact energy ranges. The intersections in Fig. 5, thus shows the transition from the soft X-ray signal dominant range to the secondary electron noise signal dominant range. Subtraction of the secondary electron noise signal from the total signal results in the signal only from soft X-ray photons, which follows the Eq. (8), as in the water nanoparticle data fitting to Eq. (8) [20]. The curve fitting of the present data to the Arrhenius equation (Eq. (8)) resulted in the activation energies of 0.09 keV/amu and 0.12 keV/amu for detectors A and B, respectively. Fig. 6b shows the

3310

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

Fig. 7. The four stages of superradiance generation by hypervelocity nanoparticle impact. Stage I: Pre-impact stage, where the aluminum is in the standard condition. Stage II: Impact compression produces pressure ionization with minimal electron heating in the C+ 60 impact zone. Stage III: The L-shell holes that survive decompression irreversibly form Metastable Innershell Molecular State [20] with L-shell holes in a nanostar. The excimer-like picture of Metastable Innershell Molecular State is not indicated in this figure. Stage IV: Most of the Metastable Innershell Molecular State collectively decay via Dicke Superradiance [21] in a time frame of tens of fs by emitting intense soft X-ray photons.

Fig. 6. An Arrhenius plot of the signal recorded on Detector C and the quantum efficiencies of all detectors as functions of photon energy. The detector C shows the signal from the high energy secondary electron infiltration only indicating that the upper bound of the photon energy is ∼80 eV. Along with the quantum efficiencies, the soft X-ray emission data from the ultrahigh intensity soft X-ray photoionized aluminum at atmospheric pressure by Vinko et al. [7,27] with XFEL are also shown for comparison. However, the internal temporary pressure of the ionization region after ionization should be orders of magnitude higher than the atmospheric pressure.

quantum efficiencies of the three detectors. The analysis of the detector A signals (Fig. 5a) resulted in the conversion efficiency of the C+ 60 kinetic energy to photon energy 35%, which is similar to the Brookhaven National Lab result (∼38%) [18,19]. This similarity indicates a possible existence of an underlying unifying theory for the mechanism of the Metastable Innershell Molecular State soft X-ray generation. It should be noted that the proposed Metastable Innershell Molecular State (as also in Winterberg’s theory, Ref. [13]) production is related with the temporary shock pressure generated by nanoparticles. The pressure can be approximately related with the impact kinetic energy of the nanoparticles, which is given by Eq. (1). However, because we do not know the exact functional relationship between the shock pressure and the impact kinetic energy, thus, in this paper, we have used impact kinetic energy in the Arrhenius equation, Eq. (8). If Al Metastable Innershell Molecular State in this case consists of L shell holes, it will have a radiation energy close to the L shell hole radiation energy in compressed solid density, because Metastable Innershell Molecular State binding energy is expected to be smaller than that of the L shell hole energy. The radiative recombination of electrons from the valence band to the LIII or LII levels of solid aluminum [26] results in emission that ranges in energy from approximately 62 eV to ∼73 eV. Vinko et al.

measured such emission spectra from the plasma generated by intense L-shell photoionization with XFEL [7,27], If excimer-like model of Metastable Innershell Molecular State holds, the difference between the Metastable Innershell Molecular State energy and the electron excitation energy should be smaller than the former. Therefore, the Al Metastable Innershell Molecular State soft X-ray photon energy is predicted to be similar to that of the L level emissions. Fig. 6b also shows a graphical representation of their data [27], which can be fitted with the theoretical curve with 10 holes for 32 atoms (∼30% ionization). Such spectra can mainly be registered on the detectors A and B, and the responses of the two detectors would be roughly equal, which are similar to the data shown in Figs. 5–6. If the present proposition is valid, Metastable Innershell Molecular State radiation energy of any materials, could be similar to the radiation energy of the innershell hole of interest, and this hypothesis can be used for estimating Metastable Innershell Molecular State radiation energies of most of materials in the periodic table as in Eq. (6). Another interesting fact is that the width (∼ 10% FWHM) [19,20] of radiation observed with silicon targets in the Brookhaven National Lab data is similar to the L shell hole measured by Vinko et al. [27] of ∼15%. As mentioned in the previous section, the large bandwidth of the radiation may indicate the excimer-like characteristics of Metastable Innershell Molecular State. Fig. 7 illustrates proposed production and optical decay processes of Metastable Innershell Molecular State based on the excimer model of Metastable Innershell Molecular State. The author proposes that the hypervelocity C+ 60 impacts pressure-excite or pressure-ionize the L-shell electrons of aluminum during the initial inertial confinement time on the order of 10 fs. During this stage as shown in Stage II of Fig. 7 the continuum is lowered to the L-shell level resulting in extensive L-shell holes. Such pressure excitation/ionization effect was directly experimentally observed by Nantel et al. [28] in strongly coupled carbon plasma produced by 100-fs laser pulses. In their experiment, continuum lowering of as much as 40 eV was observed. In their work, the number of aluminum atoms in the impact region is estimated to be on the order of 100. For 25 keV impact, with a 35% energy conversion efficiency and a 70 eV photon energy, the number of emitted photons is estimated to be 125. Therefore, the number of L-shell holes should be greater than 125, and the portion of aluminum atoms with an L-shell hole may be close to 100%. The L-shell holes subsequently form excimer-like Metastable Innershell Molecular State during the decompression stage (Stage III)

Y.K. Bae / Physics Letters A 377 (2013) 3304–3311

in presumably the highly compressed nanoplasma phase (Fig. 7). In the bulk aluminum plasma, the total lifetime of such an L-shell vacancy is dominated by the Auger decay, and is estimated to be on the order of 40 fs [29]. Thus, the lifetime of the aluminum L-shell Metastable Innershell Molecular State is estimated to be shorter than 40 fs. In the nanoparticle impact zone, because the wavelength of the soft X-ray photon (∼20 nm) is larger than the impact region (several nm), the entire community of the metastable molecules with L-shell holes decay collectively in a time scale of τ / N [20,21], where τ is the radiative lifetime of Metastable Innershell Molecular State, which should be similar to that of an L-shell hole (a few ps), and N is the number of Metastable Innershell Molecular State in the highly coupled quantum nanoplasmas (nanostars). Thus, the collective radiation of ∼100 Metastable Innershell Molecular State oscillators in the nanoplasmas is estimated to have a lifetime on the order of a few tens of fs, which is shorter than the Auger decay time [29]. This shortening of the radiative lifetime results in Dicke Superradiance [20,21] as illustrated in Stage IV of Fig. 7. The Metastable Innershell Molecular State photon energy approximately estimated in Bae et al.’s experiment [18–20] was in the range of ∼75–100 eV obtained with bio nanoparticles impacting on silicon, which is expected to have higher energy L-shells than aluminum. Therefore, Bae et al.’s data are in qualitative agreement with the present data. The upper bound of the present aluminum Metastable Innershell Molecular State photon energy is determined to be 80 eV based on the null results obtained with Detector C, which is smaller than the theoretically predicted value of 88 eV by Winterberg [13]. The studies on detailed spectral characteristics of the highly compressed quantum nanoplasmas (nanostars), which are expected to be functions of projectile and target materials and size of nanoparticles, are currently underway in the author’s lab using a soft X-ray spectrometer. 5. Conclusions The present paper reported demonstration of an innovative tabletop non-destructive experimental technique to create High Energy Density Material or Warm Dense Matter by impacting the ions of buckyballs (C60 ) on aluminum at velocities on the order of 100 km/s with estimated impact pressures on the order of 10 TPa (100 Mbar), and to diagnose them by observing the soft X-ray radiation from the impact. The present experimental setup is completely different experimental setup from that at Brookhaven National Lab, yet its results are in confirmation with the Brookhaven National Lab results obtained by the author and his colleagues [18, 19] and consistent with the interpretation in terms of Metastable Innershell Molecular State and Dicke Superradiance by the author in the previous paper [20]. The highly compressed quantum nanoplasmas created by the buckyball impact behaved like “nanostars” by emitting bursts of superradiant soft X-ray photons at a kinetic energy to photon energy conversion efficiency exceeding 35%. It is concluded here that the present results establish a new method that can efficiently cre-

3311

ate materials under “stellar” conditions in a nondestructive fashion and permit spectroscopic studies on their characteristics by exploiting hypervelocity nanoparticle impact. Furthermore, it is concluded that the innovative way of using buckyballs in the present method paves a pathway to its scaling up for generating soft Xray beams with unprecedented CW power greater than 1 kW or energy per pulse greater than 1 kJ with narrow line widths in compact devices. Therefore, if such scaling up is successful, the present method will open doors to new fields of science, such as the keV chemistry, and enable practical usage of “stellar” materials for a wide range of unprecedented applications in lithography, X-ray laser and inertial fusion, for example. Acknowledgements The author acknowledges the support and encouragement of Dr. William Wilson at the Defense Threat Reduction Agency, and the helpful discussions and suggestions of Dr. Douglas Tasker at LANL. Helpful discussions with Prof. Winterberg are also highly acknowledged. This work has been supported by the DTRA Contract HDTRA1-10-C-0088 and HDTRA1-12-C-0094. References [1] R. Davidson, Frontiers in High Energy Density Physics: The X-Games of Contemporary Science, National Academies Press, 2003. [2] Frontiers for Discovery in High Energy Density Physics. Prepared for National Science and Technology Council, Committee on Science by the Interagency Working Group on the Physics of the Universe, 2004. [3] N. Rohringer, et al., Nature (London) 481 (2012) 488. [4] C.J. Pickard, R.J. Needs, Nat. Mater. 9 (2010) 624. [5] Y.M. Ma, et al., Nature (London) 458 (2009) 182. [6] B. Nagler, et al., Nat. Phys. 5 (2009) 693. [7] S.M. Vinko, et al., Nature (London) 482 (2012) 59. [8] M. Koenig, et al., Plasma Phys. Control. Fusion 47 (2005) B441. [9] M. Gatti, I.V. Tokatly, A. Rubio, Phys. Rev. Lett. 104 (2010) 216404. [10] B.F. Rozsnyai, et al., Phys. Lett. A 291 (2001) 226. [11] J.C. Pain, Phys. Lett. A 362 (2007) 120–124. [12] S.M. Younger, A.K. Harrison, K. Fujima, D. Griswold, Phys. Rev. Lett. 61 (1988) 962. [13] F. Winterberg, J. Fusion Energy 7 (2008) 250. [14] I.V. Lomonosov, Laser Part. Beams 25 (2007) 567. [15] A.S. Vladimirov, N.P. Voloshin, V.N. Nogin, A.V. Petrovtsev, V.A. Simonenko, JETP Lett. 39 (1984) 85. [16] A. Taylor, et al., Science 315 (2007) 1092. [17] M.G. Haines, et al., Phys. Rev. Lett. 96 (2006) 075003. [18] Y.K. Bae, Y.Y. Chu, L. Friedman, Phys. Rev. A 51 (1995) R1742. [19] Y.K. Bae, et al., Nucl. Inst. Meth. Phys. Res. B 114 (1996) 185. [20] Y.K. Bae, Phys. Lett. A 372 (2008) 4865. [21] R.H. Dicke, Phys. Rev. 93 (1954) 99. [22] F.A. Fernandez-Lima, et al., Surf. Interface Anal. 43 (2011) 53. [23] J.B. Birks, Rep. Prog. Phys. 38 (1975) 903. [24] Z. Postawa, et al., J. Phys. Chem. B 108 (2004) 7831–7838. [25] J. De Vries, et al., Chem. Phys. Lett. 188 (1992) 159. [26] B.L. Henke, E.M. Gullikson, J.C. Davis, X-ray interactions: photoabsorption, scattering, transmission, and reflection at ED50-30,000 eV, ZD1-92, At. Data Nucl. Data Tables 54 (1993) 181. [27] S.M. Vinko, et al., Phys. Rev. Lett. 104 (2010) 225001. [28] M. Nantel, et al., Phys. Rev. Lett. 80 (1998) 4442. [29] C. Almbladh, A. Morales, G. Grossmann, Phys. Rev. B 39 (1989) 3489–3502.