High Pressure

in the broad sense, pressure that exceeds atmospheric pressure; in specific technical and scientific problems it is pressure that exceeds the value characteristic of a given problem. The subdivision of high pressure into high and superhigh pressure encountered in literature is equally arbitrary.

High pressure acting over a long period is called static; high pressure acting briefly is called instantaneous or dynamic high pressure.

In quiescent gases and liquids high pressure is hydrostatic: the only stresses that act on any free surface bordering on a compressed medium are normal stresses whose magnitude does not depend on the orientation of the surface and, to the accuracy of the pressure caused by the weight of the compressed medium, is identical throughout. Solids have finite shearing strength (in liquids the shearing strength is equal to zero when the loading is sufficiently slow); therefore, the stressed state of a solid is determined by both normal and tangential stresses (shear stresses). Upon compression of a solid medium a complicated system of mechanical stresses, which in the general case change from one point of the body to another, arises in it. The arithmetic mean of the normal stresses in the three perpendicular directions at a given point is called the mean pressure (the mean normal stress).

Shear stresses and a gradient in the mean pressure in a body that is being compressed introduce some uncertainty into the experimentally determined values of high pressure in a solid; in this case high pressure is said to be quasi-hydrostatic. The smaller the shear stress in comparison with the mean normal stress, the closer the quasi-hydrostatic high pressure will be to hydrostatic. The term “high pressure” is used to designate both hydrostatic and quasi-hydrostatic pressure.

In physics the kilobar is usually used as the unit of high pressure (1 kbar = 10⁸ newtons per sq m [N/m²], or 1,019.7 kilograms-force per sq cm [kgf/cm²]).

In nature static high pressure exists primarily because of the force of gravitation. The gravitational field of the earth creates in rocks a static pressure that changes from atmospheric pressure in surface layers up to ∼ 3.5 x 10³kbar at the center of the planet. Most of the earth is under static high pressure and temperatures that are sufficiently high to change the physical and chemical properties of minerals and the mineral composition of rocks (Figure 1). The static high pressure at the center of the sun is ∼ 10⁷kbar, and at the center of white dwarf stars it is assumed to be 10¹⁰—10¹²kbar.

Under natural conditions dynamic high pressure arises during explosions, the fall of meteorites, volcanic activity, and tectonic movements.

In technology, pressure of up to 3 kbar was produced during the combustion of powder in firearms as early as the 13th or 14th century. Static high pressure of the same order was attained only in the second half of the 19th century, by using pumps and presses.

Methods of generating high pressure have been greatly improved in the 20th century, especially as a result of the work of P. W. Bridgman. Research at high pressures was undertaken on an especially broad scale after World War II. In the USSR the Institute of High-Pressure Physics of the Academy of Sciences is the center for research on static high pressure.

By the end of the 1960’s, as a result of the development of high-pressure equipment based on the progress of machine building and metallurgy, as well as on advances in the development and use of explosives, static pressures as high as ∼ 2 x 10³ kbar and dynamic pressures of up to 10⁴ kbar

Figure 1. Boundaries of domains of existence of certain minerals. Names of the high-pressure phases are above the lines; names of the low-pressure phases are below the lines. M is the Moho (Mohorovicic discontinuity) beneath the continents.

(Figure 2) had been produced; in underground explosions pressures as high as ∼ 3 x 10⁴ kbar were attained.

Figure 2. Experimentally attained range of pressures and temperatures: (I) industrial pressing, (II) hydrothermal processes, (III) hydrostatic pressures (in gases and liquids). (IV) range of pressures attained by 1950 (Bridgman). (V) static pressures (up to 200 kbar) at high temperatures (by 1970). (VI) static pressures (up to 300 kbar) at extremely low temperatures, (VII) pressures generated by shock waves (up to ∼10⁴ kbar at temperatures of over 3000°C), (VIII) static pressures (up to ∼500 kbar) at room temperature

The sphere of application of high pressure is very broad. In combination with high temperature, high pressures are used in metallurgy (for rolling, forging, stamping, and hot forming), in ceramics production, and in the synthesis and processing of polymers. At high pressures substances are synthesized and chemical reactions are conducted that are difficult or impossible under other conditions, including the synthesis of ammonia (up to 1 kbar, 400°C), the synthesis of methyl alcohol (up to 0.5 kbar, 375° C), and the hydrogenation of coal (up to 0.7 kbar, 500° C). The hydrothermal synthesis of large and perfect quartz crystals (approximately 1 kbar, several hundred degrees), which are used as raw material for optical products and piezoelectric sensors, is of great industrial importance.

Interest in high-pressure physics and chemistry is stimulated by the requirements of modern technology for materials with special properties (especially abrasive and semiconductor materials), as well as by the need for the development of advanced methods of metalworking. Many trends in high-pressure research are determined by the interests of solid-state theory and geophysics, whose development is related to the acquisition of new experimental data on the properties of substances upon compression to states of high density.

The artificial production of diamond (above 50 kbar and 1400° C) and the synthesis of borazon (above 40 kbar and 1400° C), which is close to diamond in hardness, as well as the production of dense crystalline modifications of silica (Si0₂)—coesite (from 35 kbar and 750° C upward) and stishovite (from 90 kbar and 600° C upward)—which are of great interest to geophysics and mineralogy, are among the best known achievements of high-pressure physics and chemistry in the field of static pressures in the second half of the 20th century. The peaceful and military uses of explosions and the investigation of the change in density and phase transitions in a number of substances at pressures and temperatures beyond the means of static high pressure are in the field of dynamic high pressure.

Behavior of substances at high pressures. The compression of a substance (an increase in its density) is the immediate result of the action of high pressure. At high pressures the direction of physical and chemical processes that leads to a reduction in the volume of all interacting substances (if their mass is conserved—the Le Chatelier-Braun principle) becomes favorable in terms of energy consumption.

High pressure also affects the rate (kinetics) of physical and chemical processes; it may either accelerate or retard them. The acceleration of certain chemical reactions is observed, for example, in gases (because of the increased frequency of collisions between molecules as a result of the increased density); deceleration may be found in certain phase transformations in alloys (because of a decline in the rate of diffusion and in the equilibrium concentration of vacancies). Therefore, under high pressure many processes of practical importance are conducted at high temperatures, increasing the mobility of the particles and thus accelerating the attainment of a state of equilibrium.

When a substance undergoes compression, the forces of pressure acting on it from without perform mechanical work, thus increasing the energy of the body—the internal energy if no heat exchange occurs with the environment (an isoen-tropic process accompanied by heating of the body), or the free energy if the temperature of the compressed body does not change (an isothermal process). In practice, processes of static compression, in which the temperature of the body may be considered constant, are often classified as isothermal. If the temperature of a body increases as a result of compression, higher pressure is developed in it than during isothermal compression (for identical initial conditions and an identical compression ratio—that is, relative density).

In gases pressure is of thermal origin; it is related to the transfer of the momentum of molecules in a constant state of thermal motion (upon collisions). In condensed phases (liquids or solids) distinction is made between the elastic and the thermal components of high pressure. The former, called cold pressure (p_c), is related to the elastic interaction of particles when the volume of the body is reduced; the latter, to their thermal motion caused by the increased temperature during compression. For static compression the thermal component is much smaller than the elastic, and for compression in a strong shock wave both components are comparable in magnitude and their sum is called hot pressure (p_n).

The reduction of the interatomic (intermolecular) distances upon compression ultimately leads to the deformation of molecules and of the outer electron shells of the atoms and to a change in the nature of interatomic interactions, which inevitably affects the physical and chemical properties of the substance. For example, upon static compression within the limits of several kbar or several dozen kbar, the conditions of mutual solubility of gases change; the density of gases is comparable to the density of liquids, and the liquids solidify (at room temperature and at a pressure of up to 30–50 kbar); many crystalline substances undergo transformations, resulting in the development of new crystalline forms (polymorphic transformations); and transitions of solid dielectrics and semiconductors to the metallic state are observed.

When the density of a substance becomes ten times or more greater than the density of solids under normal conditions, which corresponds to a pressure of ∼ 10¹² kbar, the dependence of the density ρ on the “cold” pressure approaches a limiting form and proves identical for all substances: p^5/3 ∼p_c. In principle, at such high pressures the nuclei of fully ionized atoms may converge and, after crossing the potential barrier, enter into nuclear reactions.

At sufficiently high pressures but at temperatures lower than the degeneration temperature, the substance passes into a degenerate state, in which the energy and pressure do not depend on temperature.

Certain properties of gases, liquids, and solids in an experimentally attainable range of high pressures are described below. At pressures of 30–50 kbar substances are studied in all states of aggregation, and at higher pressures the solid is the main object of physical research.

Figure 3. Dependence of relative density (δ — p/po) of gaseous nitrogen on pressure p, where p_t is the density at 1 atm and 0°C

Figure 4. Dependence of relative volume of fluid on pressure

The physical properties of an individual substance in the solid state may be divided into three main groups. The first group includes the properties related to so-called phenomena at the molecular level—the motion of atoms (molecules), point defects in crystals, and dislocations. Diffusion, phase transitions, breaking under the effect of mechanical loads, and a number of other physical properties of solids are determined by these phenomena. Properties defined by the character of the principal (nonexcited) state of the crystal— that is, by the distribution of the atoms, the average distance between them, and vibrations of the crystal lattice at a temperature of absolute zero (elasticity, compressibility, the electrical conductivity of metals, and ferromagnetism—belong to the second group. In the third group are properties connected primarily with the type of elementary excitations that occur in a solid—the quasi-particles (phonons, excitons, and others) and their interaction (for example, the dependence of compressibility, electrical conductivity, and magnetic effects on the temperature, magnetic field, electromagnetic radiation, and other external parameters). The theoretical description of this last group of properties is possible only for bodies whose temperature is close to absolute zero; therefore experiments at high pressures and extremely low temperatures are of great importance. The microscopic theory of the effect of high pressure on the first two groups of properties is inadequately developed, but a vast amount of experimental material exists.

Figure 5. Dependence of relative volume of solids on pressure

Figure 6. Change in density of certain metals upon shock compression

The dependence on pressure of the volume (density) of substances in the gaseous, liquid, and solid states is shown in Figures 3 to 6. After the high pressure is lifted, the initial volume of the gases, liquids, and solids (which have no pores or impurities) is restored. The property of bodies of changing their volume reversibly under pressure is called compressibility or bulk elasticity. Compressibility is due to the effect of interatomic forces and therefore is the most important characteristic of a substance. Gases have the highest compressibility. The density of gases at room temperature under a pressure of 10 kbar increases by a factor of hundreds, the density of liquids by an average of 20–30 percent, and the density of solids by 0.5–2 percent. As pressure rises, compressibility falls—the curves in the graphs become more sloping. At 30–50 kbar the compressibility of most liquids studied differs by no more than 10 percent and, at not very high temperatures, approaches the compressibility of the solid phase. Substances with the strongest interatomic bonds (for example, diamond or the refractory metals iridium and rhenium) are the least compressible (see Figures 5 and 6). At the highest dynamic pressure attained (approximately 3 x 10⁴ kbar), the density of iron and lead increases by 150 and 230 percent, respectively. Simple substances (the chemical elements), which have larger atomic volume, also have greater compressibility. The atomic volume is a periodic function of the

Figure 7. Dependence of atomic volume V of elements (in units of cm³/g-atom) on the atomic number Z: (a) under normal conditions, (b) at pressure of 1 Mbar, (c) computed data for 10 Mbar

atomic number Z of the element. Therefore, as the pressure rises, the periodicity of the dependence of the atomic volume (and of the compressibility) on Z smooths out (Figure 7), reflecting a change in the structure of the outer electron shells of the atoms and attesting to a change in the physical and chemical properties of elements under high pressure.

An increase in the density and a decrease in the compressibility of a substance at high pressure lead to an increase in the velocity of elastic waves (the speed of sound) by several percent in metals and ionic crystals and severalfold in gases. At a dynamic high pressure of several thousand kbar the

Figure 8. Dependence of viscosity of liquids on pressure at room temperature

velocity of elastic waves in metals is approximately doubled. As the density of gases and liquids increases, their viscosity rises. In contrast to most other properties, the dependence of viscosity on pressure has a positive derivative: as the high pressure consistently increases by a certain amount, the rise in viscosity increases (Figure 8).

In crystals, high pressure has plasticity: upon uniaxial tension (compression), destruction generally occurs after greater deformation than at atmospheric pressure. The type of fracture of low-plasticity metals under high pressure changes from brittle to elastic, and the density also increases somewhat. This is due to the fact that high pressure contributes to the healing of structural defects, such as microscopic cracks, in the process of the plastic deformation of crystalline bodies. During shear at high pressure in metals and ionic crystals increased shearing strength is observed as the pressure increases (for instance, in NaCl by approximately 230 percent in the interval from 10 to 50 kbar); softening, loss of continuity, and other phenomena are observed in rock and glass.

An abrupt change in physical properties, such as density (Figure 9) or electrical resistance (Figure 10), is observed in solids during phase transitions at high pressure (polymorphic transformations or melting).

Of the two crystalline modifications of a given substance, the modification that is stable at a higher pressure has the greater density. The difference in the density of two modifications may run as high as 30–40 percent but is less in most cases. In contrast to density, the electrical resistance of metals during polymorphous transitions may either decrease or increase. The jumps in the electrical resistance of certain metals (for example, bismuth and barium; see Figure 10) during polymorphic transitions are used to calibrate high-pressure equipment. When high pressure is reduced the reverse transformation usually occurs, and the substance returns to the less dense modification. It has been established by the method of X-ray structural analysis that structures

Figure 9. Change in the volume (density) of certain elements during polymorphic transitions. The magnitude of the vertical step on each curve corresponds to the change in volume during the transition.

Figure 10. Change in relative electrical resistance of metals undergoing polymorphic transitions at high pressures. The 0–2.0 scale is for Bi and Pb; the 0–5 scale is for Ba and Fe; the 0–100 scale is for Rb, Ca, and Cs.

that are known for other elements and compounds under normal conditions are generally formed at high pressure. Many polymorphic transformations occur during simultaneous exposure to high pressures and temperatures. In these cases the denser modification can often be retained under normal conditions by using high-pressure hardening. For this purpose first the temperature and then the pressure is sharply reduced (the latter is reduced to atmospheric pressure). In particular, hardening is used in the synthesis of diamond, borazon, and many minerals.

So-called phase diagrams, which depict the regions of stability of crystalline modifications and the melting range of individual substances (Figure 11), are constructed on the basis of experimental data on the pressure of phase transitions at various temperatures. The melting point (T_m) of most substances increases with pressure (Figure 12). For NaCl and Kcl, which at atmospheric pressure melt at a temperature of about 800° C, melting has been observed during dynamic compression at 3200° C (540 kbar) and 3500° C (330 kbar). respectively. The rise of the melting point with increasing pressure is extremely great in organic substances. For example, in benzene at atmospheric pressure T_m = 5° C, and at 11 kbar T_m =200° C. So-called anomalous substances—for example, water, bismuth, gallium, germanium, and silicon—are known in which T_m in a certain high-pressure interval declines as pressure increases, since the liquid phase of these substances is denser than the corresponding crystalline modification. After polymorphous transition, with the formation of a denser crystalline modification, the shape of the melting curve of these substances becomes normal (for example, above 2 kbar for water, and above ∼18 kbar for bismuth).

Figure 11. Phase diagram for iron. The domains of the crystal modifications of iron (α, δ, γ, and e) and the structure of the corresponding lattice cells are shown.

Figure 12. Dependence of melting point of metals on pressure

The electrical resistance of a number of metals decreases at high pressure (in cobalt, silver, and aluminum, by 15–20 percent at 100 kbar; see Figure 13). In qualitative terms this is due to the decrease in the amplitude of the vibrations of atoms in the crystal lattice and to the corresponding decline in the scattering of conduction electrons by the lattice. In alkaline and alkaline earth metals, as well as rare earths, the dependence of electrical resistance on high pressure is more complicated (see Figure 10) because of the change in the form of the Fermi surface and the overlapping of the energy bands of solids under pressure. In semiconductors and dielectrics the high electrical conductivity characteristic of metals appears at high pressures (because of the overlapping of the energy bands, the electrons pass from the so-called valence band to the conduction band). The change in the type of conductivity may be either gradual (as in iodine at 160–240 kbar) or abrupt (as in selenium at about 130 kbar). The tendency to pass into the metallic state is apparently common to all substances at sufficiently high pressures. For example, in sulfur the transition to the metallic state is observed at 200 kbar; for hydrogen the computed value of the high pressure at which metallic conductivity appears is ∼(1–2) x 10³ kbar; for lithium hydride ∼(25–30) x 10⁴ kbar; and for helium, ∼9 × 10⁴ kbar. The shifting of energy bands in a certain pressure range sometimes causes the reverse effect. For example, in the range from 20 to 30 kbar, metallic ytterbium behaves like a semiconductor, and as the pressure is further increased it undergoes a polymorphic transition, with the formation of a new metallic modification.

Figure 13. Dependence of relative electrical resistance R/R₀ of metals on pressure. The values of R/R₀ are plotted along the vertical axis (R₀ is electrical resistance at normal pressure; R is at high pressure).

The electron structure of solids at high pressure is also being studied by optical methods and methods that make use of a number of subtle physical effects. Studies of superconductivity also provide information on the electronic structure of metals and the interaction of electrons with phonons at high pressure. The temperature of transition of metals and alloys into the superconducting state under high pressure varies: it decreases in all nontransition metals (such as tin, indium, aluminum, cadmium, and zinc) and increases in a number of transition metals (niobium, vanadium, tantalum, lanthanum, and uranium) and some alloys. Some elements (silicon, germanium, tellurium, selenium, and phosphorus), which are not superconductors at atmospheric pressure,

Figure 14. Change in Curie temperature under pressure in various magnetic materials: (1) (MnZn)Fe₂ө0₄, (2) La_o.₇₅Sr_o,₊₂₅Mn0,. (3) Ni, (4) Ni-Cu alloy (67% Ni), (5) Alumel (94% Ni), (6) Cd, (7) Fe-Ni alloy (64% Fe), (8) Fe-Ni alloy (70% Fe)

have superconducting modifications at high pressure. The formation of such modifications in silicon, germanium, and tellurium, which are semiconductors under normal conditions, occurs at 120, 115, and 45 kbar, respectively. A shift in the temperature of transformation of a ferromagnetic into a paramagnetic (the Curie points; Figure 14) is among the best known magnetic effects of high pressure.

Methods of generating high pressure. Dynamic high pressure is produced by means of an explosion, a spark discharge, or a pulse change in a magnetic field, and especially by inertial methods—the deceleration by the body being compressed of another body moving with high velocity.

Upon abrupt and significant displacement of the surface of a body caused by one of these methods, a shock wave appears. Shock compression is accompanied by significant heating of the substance: the temperature _oof table salt and lead compressed to 1,000 kbar is ∼ 9 × 10^3° C and of copper and tungsten, 1500° and 750° C, respectively. When the pressure increases without limit the compression ratio ahead of the shock wave does not exceed some maximum value (5–7 for metals, depending on temperature). This is due to the increase in pressure, mainly caused by its “thermal” component. In isothermal and isoentropic processes this limitation is not present.

A pressure several dozen times greater than that attainable by static methods can be achieved by dynamic compression. However, the operating time of dynamic pressures is limited to thousandths of a second, whereas in the case of static pressure it can be maintained for hours and even days with predetermined temperature conditions.

Static high pressure is produced by mechanical or thermal means. The mechanical means include pumps and compressors, which force the substance being compressed (liquid or gas) into an enclosed area or flow system (designs of hydraulic compressors for a pressure of up to 16 kbar are known), and apparatus in which the mass of the compressed substance remains constant (or nearly constant) and the volume it occupies decreases under external forces. Units of the second type make it possible to produce the maximum static pressures (up to ∼ 2 × 10³ kbar). and their principle of operation is extremely simple: a large force, usually generated by a hydraulic press, is concentrated on a small area, on which the high pressure is developed (see Figure 15).

Figure 15. Diagrams of high-pressure apparatus: (a) “cylinder-piston” type, (b) Bridgman “anvil,” (c) device with conical plungers, (d) “anvils” submerged in a plastic medium compressed to a lower pressure, (e) and (f) “tetrahedral” and “cubic” devices (the plunger, which is facing the viewer, is not shown); the form of the body being compressed is shown separately. (1) plunger (piston), (2) high-pressure vessel, (3) sample being compressed, (4) medium transmitting pressure. The directions of action of forces are shown by the arrows.

In units based on the principle illustrated in Figure 15, a (the “cylinder-piston” type), high pressure is generated in the cylinder, into which the piston moves under an external force. In such units solids, liquids, and gases may be used to transmit the pressure. The range of applicability of units of the type depicted in Figure 15, a is limited by the strength of the material of pistons made of hard-facing alloys and is ∼50 kbar.

Pressure that exceeds the ultimate strength of structural materials is achieved by using a number of methods for strengthening the designs: (1) supporting the entire unit or the most heavily loaded members with a compressed plastic substance or fluid; (2) generating a system of compression stresses in the pistons by elastic deformation of the vessel, which in turn is secured by a set of rings that are pressed on from without; (3) reducing the stresses in the vessel walls by dividing them into sectors (multiple-plunger units, in which the movable plungers are at the same time the chamber walls; see Figure 15,b-f). A combination of methods (1) and (2) makes it possible to increase the pressure in units with cylindrical pistons to 70–100 kbar.

In units with conical or pyramidal plungers all three methods are used. High pressure is generated by two, three, four, six, or more plungers that interlock at an angle to the direction of the force. In these units lime, talc, boron, and other solids are used to transmit the pressure. In units of this type measurements have been made of optical absorption (through diamond plungers) at pressures of up to 160–170 kbar; of the Mössbauer effect, up to ∼250 kbar; and of compressibility (by the X-ray structural method) and electrical conductivity, up to 500 kbar. A static pressure of ∼2 × 10³kbar, at which irreversible changes in the density of glass have been studied, has been produced in two-stage multiplunger units.

In chambers with a solid compressible medium, high pressure is determined either by calculation (in chambers of the type shown in Figure 15,a) or by calibration (in more complex chambers). Calibration consists in establishing the dependence of pressure in the compressed medium on the force applied to the dies. For example, it may be performed on the basis of the jumps in electrical resistance that accompany polymorphic transitions in some metals. The problem of calibrating chambers has not yet been fully solved.

In a solid medium, temperatures of up to +1500°-3000° C in the fixed mode and higher temperatures in the pulse mode are attained\\by using internal electrical (resistance) heaters. To produce temperatures of ™196° to 400° C, external heaters and coolers are used, and in the case of lower temperatures, cryogenic equipment is used.

Optical studies are conducted through windows prepared from materials that are transparent in a certain part of the spectrum: diamond, sapphire, and sodium chloride in the optical band and diamond and beryllium in the X-ray region. In chambers of the type shown in Figure 15,b, X radiation and gamma radiation may also pass through gaps between the plungers.

In apparatus based on thermal methods, high pressure is generated either by increasing the pressure in the gases or liquids by heating them in a closed vessel (in some units a pressure of up to 30–40 kbar has been achieved in gases) or as a result of the expansion of “anomalous” liquids upon solidification. The body being compressed is surrounded with liquid, and after the liquid has been cooled until it solidifies in the closed area, a fixed high pressure is produced (in the case of water, for example, about 2 kbar).