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Shock wave compression of condensed matter

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Shock wave compression of condensed matter

1. 1. Chapter 1 Introduction to Shock Wave Physics of Condensed Matter 1.1 Introduction The scientiﬁc ﬁeld of shock wave physics uses information from a number of sub-ﬁelds, such as hydrodynamics, continuum mechanics, thermodynamics, electrodynamics, and quantum mechanics. Information is presented from these sub-ﬁelds, as needed. The reader is responsible for background reading in these sub-ﬁelds for further understanding. 1.2 General Assumptions Unless otherwise stated one-dimensional (1-D) plane shock waves in a continuum ﬂuid will be assumed. Solids will be treated in a separate chapter. Addressing ﬂuids allows the basic physics and hydrodynamics to be illustrated simply. Plane geometry is selected, because cylindrical and spherical waves have a natural geometric attenuation term, which makes the treatment more difﬁcult. In 1-D plane continuum mechanics state parameters such as pressure P, temperature T, and particle velocity u are the same across the entire planar wave front. In other words, at a given x the state parameters are the same for all (y, z) points. The wave propagates only in the + x or À x direction. Only isotropic solids under dynamic loading are treated in this primer book. It is assumed that no external energy source exists. Unless noted, it is assumed that the shocked material is in thermodynamic equilibrium. This implies time is not part of the material’s constitutive relationship. In other words, all material processes in shock waves occur almost instantaneously relative to nanosecond times. Therefore, continuum mechanics and thermodynamic treatments are valid. In fact, material science models and treatments are generally valid for shocked material where equilibrium exists. However, material time dependence and strain rate issues have to be dealt with in some speciﬁc materials. J.W. Forbes, Shock Wave Compression of Condensed Matter, Shock Wave and High Pressure Phenomena, DOI 10.1007/978-3-642-32535-9_1, # Springer-Verlag Berlin Heidelberg 2012 1
2. 2. When equilibrium is not achieved in all parameters (stress, volume, temperature, pressure), then a time-dependent material and hydrodynamic ﬂow treatment is required. Time dependent material properties will be discussed near the end of the book. The 1-D differential conservation equations for mass, momentum, and energy are derived early in the book to use in showing the uniqueness and simplicity of steady shock wave conservation laws and the wave front rise-time signiﬁcance. Knowing a shock wave is steady deﬁnes the linear P-v compression path without knowing the physical mechanisms, which is not scientiﬁcally satisfying, so efforts continue on revealing these physical mechanisms. 1.3 Brief History of Shock Field in the United States of America Twenty-one papers [1] on shock waves in condensed matter were presented at the 1947 American Physical Society meeting in Washington, DC. A majority of these papers were on the properties of shock waves in water and were presented by Navy scientists including Sigmund Jacobs. Cornell University scientists Hans Bethe, J. G. Kirkwood and S. Brinkley presented theoretical shock wave papers at this meeting. However, the shock wave ﬁeld did not gain acceptance as a scientiﬁc discipline until the mid 1950s after the publication of a paper by Bancroft, Petersen and Minshall [2] from Los Alamos on the phase transformation in iron under shock compression. They observed when iron was shocked above 130 kbar (say 200 kbar) that three shock waves propagated through the iron. The ﬁrst was the elastic shock about 12 kbar, the second was at 130 kbar, which they suggested was due to the phase transformation in iron seen in static work of Bridgman [3], and the third one a plastic shock taking the material to its ﬁnal stress. Bridgman’s reported transition pressure was higher than 130 kbar, but it was conﬁrmed later that the phase transition stress actually was the stress measured for the second shock wave. Accurate determination of transition pressures of rapid negative volume phase transformations allowed the shock wave ﬁeld to accurately determine a high pressure calibration scale. Nobel prize winner and pioneer of high pressure static physics P. Bridgman claimed that this transition did not occur at 130 kbar in his static press [4]. He also reasoned that there just was not enough time for this transformation to occur in shock waves. This comment was based on his static work where it took many hours and sometimes days before iron transformed. The shock wave people also were not sure why the transformation occurred so fast. They suggested that the shear forces in shock waves may dramatically increase the rate of transformation. Bridgman decided to check the pressure scale he was using and found it was incorrect. He then performed an experiment with increased force to his compression cell and found that the transition occurred but took days. Bridgman then conducted an experiment where he added shear stresses to his iron sample at pressures exceeding 130 kbar. To his surprise the iron transformation occurred within seconds. He was then convinced that the shock data was correct. However, the physical mechanism for 2 1 Introduction to Shock Wave Physics of Condensed Matter
3. 3. the transition was not understood, which is still true today. This highly publicized controversy launched the shock ﬁeld as a true sub-ﬁeld of high pressure science. The well developed experimental and theoretical science was presented to the physics community at large in the 1958 paper by Los Alamos scientists Rice, Walsh, and McQueen [5]. The experiments were based on a precisely controlled high explosive technology [6]. A review of many shock wave subjects is presented in High-Pressure Shock Compression of Solids [7], eds. Asay and Shahinpoor, Springer-Verlag, 1993. For more details of the history of shock wave physics in the United States, read J. W. Taylor [8], R. A. Graham [4] and J. W. Forbes [1]. 1.4 Practical Value of Shock Field Material equations of state and material constitutive relationships require informa- tion from mechanics, static compression, yield surfaces, shock wave data, etc. The information obtained from shock wave experiments and theory are limited to high strain rates. Information not dependent on strain rates can come from many sources other than shock wave experiments. However, there are some unique things that come from shock wave experiments, such as the very high pressure thermodynamic P-v curve called a Hugoniot, which is relatable to other thermodynamic paths such as isotherms and isentropes. Accuracy of 1-D plane experiments is very good, resulting in P-v data with typical accuracy of Æ 3 %. Stresses greater than 10 Mbar with good accuracy are achievable (three times greater than pressures at the earth’s core). This data is clearly important to material scientists, theorists, geophysicists and astrophysicists. Such data provides a test of accuracy of molecu- lar potentials over large compressions and helps to determine the physical state and chemical makeup of the earth’s core. New experimental techniques are becoming available for the study of materials at extreme states where materials become plasmas. An excellent review [9] was recently done on this ﬁeld known as High- Energy-Density Physics. This new extreme states technical ﬁeld offers a window into stellar processes, approaches to obtain fusion as an energy source, and world security by understanding nuclear weapons without testing. Shock wave studies can easily and accurately detect rapid negative volume phase transitions, which has allowed a high pressure standard for static work to be developed. This data is used by condensed matter physicists and material engineers to make metastable materials such as the production of industrial small diamonds, due to very fast temperature quench rates. It is also the basis for understanding explosive detonation waves, which will be treated in some detail in this book. The pressure scale used for static high pressure work was not well developed in the 1950s. With shock wave data, an accurate pressure scale was developed up to tens of Mbar. This was a very important contribution to high pressure science. The establishment of this pressure scale was done by measuring phase transformation 1.4 Practical Value of Shock Field 3
4. 4. stress levels on different shocked materials. To calibrate a static piston press for measuring pressure, the materials known to undergo phase transformations in the shock work were compressed until they transformed in the static press. The changes in volume or compression were measured as a function of piston displacement assuming no deformation of the press parts. This allowed making a calibration curve of pressure versus piston displacement for their particular apparatus. How- ever, at high pressures the piston and sample cell in a static press change volume and diameter in unknown amounts above yield strengths so calculating pressure as force applied over original area of piston was not accurate. Following the shock wave transition pressures of a number of materials, the static calibration was done for each press by ﬁnding the displacement that the transition occurred at and mapping out a speciﬁc displacement versus pressure relationship for each static press. More recently Raman shifts versus stress in ruby and other crystals have been accurately measured as a function of stress [7]. This allows a small ruby chip to be inserted in the cell ﬁlled with ﬂuid material surrounding the test sample. Measure- ment of the ruby’s shift in Raman spectra gives accurate pressure in the ﬂuid of the cell. This is widely used in the small diamond anvil static pressure cells. 1.5 Techniques for Producing 1-D Plane Shock Waves The original experiments (reviewed in Chap. 4) to produce 1-D plane shock waves in test materials used explosive shock driver systems. These experiments consisted of a detonator to initiate an explosive plane wave booster (PWB) that transmitted a strong detonation shock wave into a ﬂat disc of a driver explosive. The driver explosive with a characteristic pressure (C-J pressure) would have an inert buffer (usually metal) against it with the test samples on top of this buffer plate. The detonation shock wave from the PWB thus results in a strong plane 1-D shock wave being transmitted to the test sample. This technique is still used today for select high pressure experiments. Most of the shock wave equation of state data has been generated using such an explosive system. Note also that with proper design the metal buffer plate can become a ﬂying plate, which impacts samples set a distance above the plate. Only a small range of induced stresses is available for any one explosive design, which is a limitation. It is important to note that the physical scale of the produced planar shock wave in a test sample is a few centimeters in diameter for these explosive systems. To overcome the limited control of the range of stress available for experiments, ﬂat ended projectiles propelled by light gas guns or explosive powder driven guns were created. These are devices that accelerate ﬂat plates with sabots on the back into stationary test samples. The selection of impact velocity and therefore impact stress in the test sample is a continuum for the range of the guns capability. This has obvious advantages over the limited stress ranges of the explosive systems, espe- cially at lower stresses. Again the physical scale of the produced shock wave in a test sample is a few centimeters. 4 1 Introduction to Shock Wave Physics of Condensed Matter
5. 5. A high powered pulse laser can create large pressures in samples by ablating the surface of a material, causing a shock wave to be transmitted through it into a test sample. Since pressure/stress is a function of area, lasers can reach high stresses for small areas and short pulse widths. This is an emerging technique in the ﬁeld of shock wave physics since many experiments can be done on a table top in a research laboratory. To reach very extreme states large laser facilities are being used. There are issues of time and space scale that need to be addressed, and more on this will be given later in this book. 1.6 Dynamic Versus Static Compression Static and dynamic compression are not equivalent due to the high strain rate, viscous forces, energy scattering and shear forces in a 1-D plane shock wave. The strain rate in a steady shock wave is the highest strain rate possible for that material to have in an equilibrium situation. Shock waves compress materials in fractions of a microsecond putting energy directly into atoms and molecules. Shock waves also create defects in materials, which increases entropy. The physical mechanism has not been determined to date for energy scattering that keeps the shock compression path for steady waves on a linear P-v path called the Rayleigh line. It will be shown that just the condition of a wave being steady in a continuum media is all that is required for proving the shock P-v curve is along a straight line without knowing the physical mechanism. A major issue for shock physics is the inability to measure continuum tempera- ture in a shocked solid. So average temperatures are calculated from continuum thermodynamics. Clearly the static data is obtained at known or measurable temperatures. Another issue for shock waves is determining the physical mecha- nism for energy scattering and phase transitions. These issues will be addressed later in the book. 1.7 Select Areas of Shock Wave Research A broad range of topics make up shock wave research. They are broadly based around thermodynamic properties, experimental techniques for dynamic loading, Geophysics and Planetary Science, inelastic deformation, fracture and spall, continuum and multi scale modeling, ﬁrst principal and molecular dynamics calculations, phase transitions, physics and chemistry at high pressure, spectros- copy and optical studies, nanomaterials, and detonation of explosives. A good example of these areas is given in the Shock Compression of Condensed Matter proceedings of the American Physical Society’s Shock Compression of Condensed Matter Topical Group meetings proceedings that are listed in the references. A select list of references for speciﬁc subjects are given in this chapter’s references 1.7 Select Areas of Shock Wave Research 5