We examine the Lindemann melting law at different pressures using the vibrational density of stat... more We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter δL (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of δL with pressure is non-negligible: δL is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for δL, these values are about 0.067(±0.002) and 0.084(±0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of δL suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.
An accurate EOS for polystyrene foam is necessary for analysis of numerous experiments in shock c... more An accurate EOS for polystyrene foam is necessary for analysis of numerous experiments in shock compression, inertial confinement fusion, and astrophysics. Plastic to gas ratios vary between various samples of foam, according to the density and cell-size of the foam. A matrix of compositions has been investigated, allowing prediction of foam response as a function of the plastic-to-air ratio. The EOS code CHEETAH allows participation of the air in the decomposition reaction of the foam, Differences between air-filled, nitrogen-blown, and CO2-blown foams are investigated, to estimate the importance of allowing air to react with plastic products during decomposition. Results differ somewhat from the conventional EOS, which are generated from values for plastic extrapolated to low densities.
ABSTRACT The plastic-bonded explosive PBX-9502 undergoes unusual hysteretic thermal expansion, or... more ABSTRACT The plastic-bonded explosive PBX-9502 undergoes unusual hysteretic thermal expansion, or ``ratchet growth'' as a consequence of the uniaxial thermal expansion of the graphitic structure of the major component, TATB explosive. Upon thermal cycling, the density of the material can be reduced by as much as 9%, resulting in a distinct increase in the shock sensitivity of the solid. Run distances to detonation have been measured in thermally expanded samples of PBX-9502, using embedded particle velocity gauges and shock tracker gauges. Uniaxial shocks were generated using a light gas gun, to provide a repeatable stimulus for initiation of detonation. We have applied a porosity model to adjust standard Pop plot data to the reduced density of our samples, to investigate whether the sensitivity of the PBX 9502 increases ideally with the decreasing density, or whether the microscopically non-uniform expansion that occurs during ``ratchet growth'' leads to abnormal sensitivity, possibly as a result of cracking or debonding from the binder, as observed in micrographs of the sample.
ABSTRACT Mechanical desensitisation of explosives (e.g. by a preshock) has important technologica... more ABSTRACT Mechanical desensitisation of explosives (e.g. by a preshock) has important technological consequences for safety and performance. Many widely-used reactive flow models are not capable of reproducing the desensitisation observed in experiments such as double-shock particle velocity profiles. Improved models are under development, where we intend to incorporate enough flexibility to reproduce experimentally observed shock desensitisation while retaining plausible and computationally practical physical models for the equations of state (unreacted, partially-reacted and products), equilibration processes and reaction rate.
ABSTRACT An equation of state (EOS) for unreacted nitromethane, CH3NO2 provides the accurate temp... more ABSTRACT An equation of state (EOS) for unreacted nitromethane, CH3NO2 provides the accurate temperatures required to support a temperature dependent reaction rate within a reactive flow model. A quasiharmonic form based on the Gru¨neisen equations of state was used, normalised to shock wave data but with a more rigorous treatment of thermal modes. We use reactive flow models that include temperature as well as mechanical state to investigate shock initiation in nitromethane. Temperatures predicted by the model for various off-Hugoniot states in reactive configurations show reasonable agreement with data from experimental measurements reported by several different workers, using different diagnostic methods. A thermochemical model was used for the reaction products, and Arrhenius reaction parameters reported in the literature reproduced reported reactive behavior of nitromethane.
Shock waves were induced in single crystals of beryllium, by direct illumination using the TRIDEN... more Shock waves were induced in single crystals of beryllium, by direct illumination using the TRIDENT laser at Los Alamos. The velocity history at the surface was measured using a line-imaging VISAR, and transient X-ray diffraction (TXD) records were obtained with a plasma backlighter and X-ray streak cameras. At lower pressures, the VISAR records exhibited an elastic precursor followed by a plastic wave and spall. At higher pressure, the velocity records showed a two-wave structure suggesting a phase change, then at the highest pressure a single broad wave suggesting a shock directly into the high pressure phase. The rocking curves of the crystals were typically about 2 degrees wide, so analysis of the TXD records is complicated by the relatively large amount of blurring. However, the Bragg record of the shocked 0002 peak clearly indicates a smaller lattice parameter at higher pressure. In the shots where polymorphism seemed to appear in the VISAR record, additional lines appeared in the Bragg record, and new lines also appeared within the field of view of the Laue camera. These results are consistent with a new quantum mechanical equation of state for beryllium, which suggests that the hexagonal to body-centered cubic transition occurs at ~40 GPa on the principal Hugoniot.
Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with... more Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.
Design calculations are presented for a pulsed neutron source comprising polychromatic protons ac... more Design calculations are presented for a pulsed neutron source comprising polychromatic protons accelerated from a metal foil by a short-pulse laser, and a LiF converter in which (p,n) reactions occur. Although the proton pulse is directional, neutrons are predicted to be emitted relatively isotropically. The neutron spectrum was predicted to be similar to the proton spectrum, but with more neutrons of low energy in the opposite direction to the incident protons. The angular dependence of spectrum and intensity was predicted. The (p,n) reactions generate unstable nuclei which decay predominantly by positron emission to the original Li and ¹F isotopes. For the initial planned experiments using a converter 1mm thick, we predict that 0.1% of the protons will undergo a (p,n) reaction, producing 10 neutrons. Ignoring the unreacted protons, neutrons, and prompt gamma emission as excited nuclear states decay, residual positron radioactivity (and production of pairs of 511 keV annihilation photons) is initially 4.2MBq decaying with a half-life of 17.22 s for 6 mins (¹Ne decays), then 135Bq decaying with a half-life of 53.22 days (Be decays).
The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were i... more The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were investigated based on classical nucleation theory and undercooling experiments, molecular dynamics ͑MD͒ simulations, and dynamic experiments. The highest ͑or lowest͒ temperature T c achievable in a superheated solid ͑or an undercooled liquid͒ depends on a dimensionless nucleation barrier parameter  and the heating ͑or cooling͒ rate Q.  depends on the material: ϵ16␥ sl 3 /(3kT m ⌬H m 2 ) where ␥ sl is the solid-liquid interfacial energy, ⌬H m the heat of fusion, T m the melting temperature, and k Boltzmann's constant. The systematics of maximum superheating and undercooling were established phenomenologically as ϭ(A 0 Ϫb log 10 Q) c (1Ϫ c ) 2 where c ϭT c /T m , A 0 ϭ59.4, bϭ2.33, and Q is normalized by 1 K/s. For a number of elements and compounds,  varies in the range 0.2-8.2, corresponding to maximum superheating c of 1.06 -1.35 and 1.08 -1.43 at Q ϳ1 and 10 12 K/s, respectively. Such systematics predict that a liquid with certain  cannot crystallize at cooling rates higher than a critical value and that the smallest c achievable is 1/3. MD simulations (Q ϳ10 12 K/s) at ambient and high pressures were conducted on close-packed bulk metals with Sutton-Chen many-body potentials. The maximum superheating and undercooling resolved from single-and two-phase simulations are consistent with the c --Q systematics for the maximum superheating and undercooling. The systematics are also in accord with previous MD melting simulations on other materials ͑e.g., silica, Ta and ⑀-Fe͒ described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the c --Q systematics are supported by simulations at the level of interatomic interactions. The heating rate is crucial to achieving significant superheating experimentally. We demonstrate that the amount of superheating achieved in dynamic experiments (Qϳ10 12 K/s), such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.
Design calculations are presented for a pulsed neutron source comprising polychromatic protons ac... more Design calculations are presented for a pulsed neutron source comprising polychromatic protons accelerated from a metal foil by a short-pulse laser, and a LiF converter in which (p,n) reactions occur. Although the proton pulse is directional, neutrons are predicted to be emitted relatively isotropically. The neutron spectrum was predicted to be similar to the proton spectrum, but with more neutrons of low energy in the opposite direction to the incident protons. The angular dependence of spectrum and intensity was predicted. The (p,n) reactions generate unstable nuclei which decay predominantly by positron emission to the original Li and ¹F isotopes. For the initial planned experiments using a converter 1mm thick, we predict that 0.1% of the protons will undergo a (p,n) reaction, producing 10 neutrons. Ignoring the unreacted protons, neutrons, and prompt gamma emission as excited nuclear states decay, residual positron radioactivity (and production of pairs of 511 keV annihilation photons) is initially 4.2MBq decaying with a half-life of 17.22 s for 6 mins (¹Ne decays), then 135Bq decaying with a half-life of 53.22 days (Be decays).
We examine the Lindemann melting law at different pressures using the vibrational density of stat... more We examine the Lindemann melting law at different pressures using the vibrational density of states (DOS), equilibrium melting curve, and Lindemann parameter δL (fractional root-mean-squared displacement, rmsd, at equilibrium melting) calculated independently from molecular dynamics simulations of the Lennard-Jones system. The DOS is obtained using spectra analysis of atomic velocities and accounts for anharmonicity. The increase of δL with pressure is non-negligible: δL is about 0.116 and 0.145 at ambient and extreme pressures, respectively. If the component of rmsd normal to a reflecting plane as in the Debye-Waller-factor-type measurements using x rays is adopted for δL, these values are about 0.067(±0.002) and 0.084(±0.003), and are comparable with experimental and calculated values for face-centered-cubic elements. We find that the Lindemann relation holds accurately at ambient and high pressures. The non-negligible pressure dependence of δL suggests that caution should be exerted in applying the Lindemann law to obtaining the high pressure melting curve anchored at ambient pressure.
An accurate EOS for polystyrene foam is necessary for analysis of numerous experiments in shock c... more An accurate EOS for polystyrene foam is necessary for analysis of numerous experiments in shock compression, inertial confinement fusion, and astrophysics. Plastic to gas ratios vary between various samples of foam, according to the density and cell-size of the foam. A matrix of compositions has been investigated, allowing prediction of foam response as a function of the plastic-to-air ratio. The EOS code CHEETAH allows participation of the air in the decomposition reaction of the foam, Differences between air-filled, nitrogen-blown, and CO2-blown foams are investigated, to estimate the importance of allowing air to react with plastic products during decomposition. Results differ somewhat from the conventional EOS, which are generated from values for plastic extrapolated to low densities.
ABSTRACT The plastic-bonded explosive PBX-9502 undergoes unusual hysteretic thermal expansion, or... more ABSTRACT The plastic-bonded explosive PBX-9502 undergoes unusual hysteretic thermal expansion, or ``ratchet growth'' as a consequence of the uniaxial thermal expansion of the graphitic structure of the major component, TATB explosive. Upon thermal cycling, the density of the material can be reduced by as much as 9%, resulting in a distinct increase in the shock sensitivity of the solid. Run distances to detonation have been measured in thermally expanded samples of PBX-9502, using embedded particle velocity gauges and shock tracker gauges. Uniaxial shocks were generated using a light gas gun, to provide a repeatable stimulus for initiation of detonation. We have applied a porosity model to adjust standard Pop plot data to the reduced density of our samples, to investigate whether the sensitivity of the PBX 9502 increases ideally with the decreasing density, or whether the microscopically non-uniform expansion that occurs during ``ratchet growth'' leads to abnormal sensitivity, possibly as a result of cracking or debonding from the binder, as observed in micrographs of the sample.
ABSTRACT Mechanical desensitisation of explosives (e.g. by a preshock) has important technologica... more ABSTRACT Mechanical desensitisation of explosives (e.g. by a preshock) has important technological consequences for safety and performance. Many widely-used reactive flow models are not capable of reproducing the desensitisation observed in experiments such as double-shock particle velocity profiles. Improved models are under development, where we intend to incorporate enough flexibility to reproduce experimentally observed shock desensitisation while retaining plausible and computationally practical physical models for the equations of state (unreacted, partially-reacted and products), equilibration processes and reaction rate.
ABSTRACT An equation of state (EOS) for unreacted nitromethane, CH3NO2 provides the accurate temp... more ABSTRACT An equation of state (EOS) for unreacted nitromethane, CH3NO2 provides the accurate temperatures required to support a temperature dependent reaction rate within a reactive flow model. A quasiharmonic form based on the Gru¨neisen equations of state was used, normalised to shock wave data but with a more rigorous treatment of thermal modes. We use reactive flow models that include temperature as well as mechanical state to investigate shock initiation in nitromethane. Temperatures predicted by the model for various off-Hugoniot states in reactive configurations show reasonable agreement with data from experimental measurements reported by several different workers, using different diagnostic methods. A thermochemical model was used for the reaction products, and Arrhenius reaction parameters reported in the literature reproduced reported reactive behavior of nitromethane.
Shock waves were induced in single crystals of beryllium, by direct illumination using the TRIDEN... more Shock waves were induced in single crystals of beryllium, by direct illumination using the TRIDENT laser at Los Alamos. The velocity history at the surface was measured using a line-imaging VISAR, and transient X-ray diffraction (TXD) records were obtained with a plasma backlighter and X-ray streak cameras. At lower pressures, the VISAR records exhibited an elastic precursor followed by a plastic wave and spall. At higher pressure, the velocity records showed a two-wave structure suggesting a phase change, then at the highest pressure a single broad wave suggesting a shock directly into the high pressure phase. The rocking curves of the crystals were typically about 2 degrees wide, so analysis of the TXD records is complicated by the relatively large amount of blurring. However, the Bragg record of the shocked 0002 peak clearly indicates a smaller lattice parameter at higher pressure. In the shots where polymorphism seemed to appear in the VISAR record, additional lines appeared in the Bragg record, and new lines also appeared within the field of view of the Laue camera. These results are consistent with a new quantum mechanical equation of state for beryllium, which suggests that the hexagonal to body-centered cubic transition occurs at ~40 GPa on the principal Hugoniot.
Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with... more Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.
Design calculations are presented for a pulsed neutron source comprising polychromatic protons ac... more Design calculations are presented for a pulsed neutron source comprising polychromatic protons accelerated from a metal foil by a short-pulse laser, and a LiF converter in which (p,n) reactions occur. Although the proton pulse is directional, neutrons are predicted to be emitted relatively isotropically. The neutron spectrum was predicted to be similar to the proton spectrum, but with more neutrons of low energy in the opposite direction to the incident protons. The angular dependence of spectrum and intensity was predicted. The (p,n) reactions generate unstable nuclei which decay predominantly by positron emission to the original Li and ¹F isotopes. For the initial planned experiments using a converter 1mm thick, we predict that 0.1% of the protons will undergo a (p,n) reaction, producing 10 neutrons. Ignoring the unreacted protons, neutrons, and prompt gamma emission as excited nuclear states decay, residual positron radioactivity (and production of pairs of 511 keV annihilation photons) is initially 4.2MBq decaying with a half-life of 17.22 s for 6 mins (¹Ne decays), then 135Bq decaying with a half-life of 53.22 days (Be decays).
The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were i... more The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were investigated based on classical nucleation theory and undercooling experiments, molecular dynamics ͑MD͒ simulations, and dynamic experiments. The highest ͑or lowest͒ temperature T c achievable in a superheated solid ͑or an undercooled liquid͒ depends on a dimensionless nucleation barrier parameter  and the heating ͑or cooling͒ rate Q.  depends on the material: ϵ16␥ sl 3 /(3kT m ⌬H m 2 ) where ␥ sl is the solid-liquid interfacial energy, ⌬H m the heat of fusion, T m the melting temperature, and k Boltzmann's constant. The systematics of maximum superheating and undercooling were established phenomenologically as ϭ(A 0 Ϫb log 10 Q) c (1Ϫ c ) 2 where c ϭT c /T m , A 0 ϭ59.4, bϭ2.33, and Q is normalized by 1 K/s. For a number of elements and compounds,  varies in the range 0.2-8.2, corresponding to maximum superheating c of 1.06 -1.35 and 1.08 -1.43 at Q ϳ1 and 10 12 K/s, respectively. Such systematics predict that a liquid with certain  cannot crystallize at cooling rates higher than a critical value and that the smallest c achievable is 1/3. MD simulations (Q ϳ10 12 K/s) at ambient and high pressures were conducted on close-packed bulk metals with Sutton-Chen many-body potentials. The maximum superheating and undercooling resolved from single-and two-phase simulations are consistent with the c --Q systematics for the maximum superheating and undercooling. The systematics are also in accord with previous MD melting simulations on other materials ͑e.g., silica, Ta and ⑀-Fe͒ described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the c --Q systematics are supported by simulations at the level of interatomic interactions. The heating rate is crucial to achieving significant superheating experimentally. We demonstrate that the amount of superheating achieved in dynamic experiments (Qϳ10 12 K/s), such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.
Design calculations are presented for a pulsed neutron source comprising polychromatic protons ac... more Design calculations are presented for a pulsed neutron source comprising polychromatic protons accelerated from a metal foil by a short-pulse laser, and a LiF converter in which (p,n) reactions occur. Although the proton pulse is directional, neutrons are predicted to be emitted relatively isotropically. The neutron spectrum was predicted to be similar to the proton spectrum, but with more neutrons of low energy in the opposite direction to the incident protons. The angular dependence of spectrum and intensity was predicted. The (p,n) reactions generate unstable nuclei which decay predominantly by positron emission to the original Li and ¹F isotopes. For the initial planned experiments using a converter 1mm thick, we predict that 0.1% of the protons will undergo a (p,n) reaction, producing 10 neutrons. Ignoring the unreacted protons, neutrons, and prompt gamma emission as excited nuclear states decay, residual positron radioactivity (and production of pairs of 511 keV annihilation photons) is initially 4.2MBq decaying with a half-life of 17.22 s for 6 mins (¹Ne decays), then 135Bq decaying with a half-life of 53.22 days (Be decays).
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