Transition pressure

Heydemann P L M 1997 The Bi l-ll transition pressure measured with a dead-weight piston gauge J. Appi. Phys. 38 2640... 

The ability to control pressure in the laboratory environment is a powerful tool for investigating phase changes in materials. At high pressure, many solids will transfonn to denser crystal stmctures. The study of nanocrystals under high pressure, then, allows one to investigate the size dependence of the solid-solid phase transition pressures. Results from studies of both CdSe [219, 220, 221 and 222] and silicon nanocrystals [223] indicate that solid-solid phase transition pressures are elevated in smaller nanocrystals. 

Jones, O.E. and Graham, R.A., Shear Strength Effects on Phase Transition Pressures Determined from Shock Compression Experiments, in Accurate Characterization of the High Pressure Environment (edited by Lloyd, E.C., National Bureau of Standards Special Publication 326, US Government Printing Office, Washington, DC, 1971, pp. 229-242. 

Fig. 2.13. Transition pressures for fee iron alloys have been observed to depend strongly on the solute. The data shown represent one of the major eontributions of shoek-eompression seienee as reported by Los Alamos workers (after Duvall and Graham [77D01]).

The indicated transition pressure of 15 GPa is in agreement with the published data with shock-wave structure measurements on a 3% silicon-iron alloy, the nominal composition of Silectron. A mixed phase region from 15 to 22.5 GPa appears quite reasonable based on shock pressure-volume data. Thus, the direct measure of magnetization appears to offer a sensitive measure of characteristics of shock-induced, first-order phase transitions involving a change in magnetization. 

The room temperature transformation of the columbite phase to baddeleyite commences at 13-17 GPa 6, with transition pressure increasing linearly with temperature Direct transition from rutile to baddeleyite phase at room temperature and 12 GPa has also been reported 7. The baddeleyite phase undergoes further transition to an as yet undefined high-symmetry structure at 70-80 GPa. The most likely candidate for the high-pressure phase is fluorite, which is consistent with the general pattern of increasing Ti coordination number from 6 in rutile, to 7 in baddeleyite (a distorted fluorite structure), and to 8 in fluorite. 

Transition pressures were determined by equating enthalpies of different polymorphs via the common tangent construction. We found that ratile transforms to columbite structure at 11.8 GPa with a small volume change of 3%. These results agree well with experimental... 

Finally, the use of the constant pressure minimization algorithm allows searching for phenomena that can be considered as precursors of pressure-induced transitions. For example, the predicted behaviour of the anatase cell constants as a function of pressure shows that the a(P) and c(P) plots are only linear for P<4 GPa, the value that is close to both the theoretical and experimental transition pressures. At higher pressures the a constant starts to grow under compression, indicating inherent structural instability. In the case of ratile there is a different precursor effect, nami y at 11 GPa the distances between the titanium atom and the two different oxygens, axial and equatorial, become equal. Once again, the pressure corresponds closely to the phase transition point. 

Fig. 11—Demonstration of phase transition in thin fiims (a) viscosity and density versus system pressure for a five-iayer argon fiim (b) critical transition pressure as a function of the number of argon atoms.

The next development on water-oil isotherms was presented by Mohwald s group at the Max-Planck Institute in Berlin [21,22]. They investigated monolayers of dipalmitoyl phosphatidylethanolamine (DPPE) at interfaces of water and hydrocarbons -dodecane (C]2, -hexadecane (Cig), and bicyclohexyl (BCH). The transition pressure was increased and the molecular area at transition decreased in the order Cig—C12 BCH. Also the heat of transition was decreased in the same order, and was more strongly decreasing with... 

Generally, the following rules apply for pressure-induced phase transitions Pressure-coordination rule by A. Neuhaus with increasing pressure an increase of the coordination number takes place. 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

Fig. 11 Defay-Crisp diagram for a binary monolayer A, ideal mixing B, non-ideal mixing C, complete immiscibility. and n2 are the phase transition pressures of components 1 and 2.

If components 1 and 2 are miscible, then the number of surface phases in equilibrium at the transition pressure is two, and / = 2. In this case, the surface pressure varies continuously with film composition. If the components are immiscible, the number of surface phases in equilibrium at the transition pressure will be 3, and/= 1. Variation of film composition will not alter the transition pressure. 

Linewidth The spread in wavelengths or frequencies associated with a transition in an atom or molecule. There are three contributions natural linewidth associated with the lifetime of the transition pressure broadening associated with the presence with the other molecules nearby Doppler broadening associated with relative motion of the molecule and light source. 

Figure 11.7 shows schematically the resulting calculated variation of H with p for the NaCl-type and the CsCl-type phases of CaO. The NaCl-type structure, which is stable at low pressures, is the rock salt structure in which the Ca and O atoms are 6-coordinate. In the CsCl structure, stable at high pressures, both cation and anion are 8-coordinate. In the static limit where the entropy is set to zero, the thermodynamically most stable phase at any pressure is that with the lowest value of H at the thermodynamic transition pressure, ptrs, the enthalpies of the two phases are equal. For CaO the particular set of potentials used in Figure 11.7 indicates a transition pressure of 75 GPa between the NaCl-type and CsCl-type structures, which compares with experimental values in the range 60-70 GPa. 

The transition pressure of 75 GPa is much higher than the 30 GPa predicted earlier.65 This difference is likely caused by the use of a much smaller basis set (70 Ry) by Cavazzoni et al. Our results are also in disagreement with simple extrapolations of the proton diffusion constant to high temperatures.77... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The c-BN phase was first obtained in 1957 [525] by exposing hexagonal boron nitride phase (h-BN) to high pressures and low temperatures. A pressure of more than 11 GPa is necessary to induce the hexagonal to cubic transformation, and these experimental conditions prevent any practical application for industrial purposes. Subsequently, it has been found that the transition pressure can be reduced to approximately 5 GPa at very high temperature (1300-1800°C) by using catalysts such as alkali metals, alkali metal nitrides, and Fe-Al or Ag-Cd alloys [526-528]. In addition, water, urea, and boric acid have been successfully used for synthesis of cubic boron nitride from hexagonal phase at 5-6 GPa and temperature above 800-1000°C [529]. It has been... 

In the case of the graphite-to-diamond transformation, thermodynamic results predict that graphite is the stable allotrope at a fixed temperature at all pressures below the transition pressure and that diamond is the stable aUotrope at all pressures above the transition pressure. But diamond is not converted to graphite at low pressures for kinetic reasons. Similarly, at conditions at which diamond is the thermodynamically stable phase, diamond can be obtained from graphite only in a narrow temperature range just below the transition temperature, and then only with a catalyst or at a pressure sufficiently high that the transition temperature is about 2000 K. 

Also spin-lattice relaxation times T and spin-spin relaxation times T2 were measured as a function of pressure on different selectively deuterated DPPC (at C2, Cg and Ci3, respectively) by Jonas and co-workers (Fig. 14). The spin-latticed relaxation time T is sensitive to motions with correlation times tc near Uo i e., motions with correlation times in the range from 10 to 10 " s. In comparison with Ti, the spin-spin relaxation time T 2 is more sensitive to motions with correlation times near (e qQlh), i.e., in the intermediate to slow range (10 " to 10 s). The Ti and T2 values obtained showed characteristic changes at various phase transition pressures, thus indicating abrupt changes... 

Figure 19 shows the pressure effeets on the lateral self diffusion eoeffieient of sonicated DPPC and POPC vesicles. The lateral diffusion coefficient of DPPC in the LC phase decreases with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient 1 x 10 cm /s) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the... 

When a jet fire has decayed to a pressure of 10 psig the fire is assumed to have effectively ceased. This pressure is close to the transition pressure from sonic to subsonic flow. When a jet fire event has decayed to this level, its magnitude and exposure potential are considered to have reached a threshold level below which no significant further damage can occur (i.e., no escalation potential) and active fire fighting measures can effectively bring the fire under control. 

In this reaction, the crystal stmcture of each compound has been noted in the square brackets. An interesting feature of the compounds on the right-hand side is that neither of them is in the crystal structure that is the stable structure at ambient conditions. MgO, for example, prefers the NaCl structure at ambient conditions (i.e., the same crystal structure as everyday table salt). The behavior of Si02 is similar but more complicated this compound goes through several intermediate structures between ambient conditions and the conditions relevant for MgSi03 dissociation. These transformations in the structures of MgO and Si02 allow an important connection to be made between DFT calculations and experiments since these transformations occur at conditions that can be directly probed in laboratory experiments. The transition pressures... 

Suppose the required transition pressure is If the actual pressure is much greater than the reaction is of the first order, i.e.. 

The next two elements, berkelium and cahfornium, were recently found to have identical structural sequences under pressure (Fig. 2 b, c). The first high pressure transition for both Bk and Cf is dhcp ccp as in the lanthanides. Thus the lanthanide character of heavy actinides again seems confirmed. But a second transition to the low symmetry a-uranium type structure follows in both metals. This transition reflects the start of 5 f participation in bonding. The transition pressures increase monotonically on going from Am to Bk and Cf 5, 7 and 17 GPa for the dhcp ccp transition, 10, 25, 30 GPa for the ccp An III (low symmetry phase) transition. The second transition in Cm occurs at 18 GPa this transition pressure fits well into the sequence of delocalization pressures. But the dhcp hep transition in Cm occurs at 12 GPa and thus does not fit into the increasing Z sequence with respect to both structure type formed and transition pressure. ... 

In Figure 2 the ir-A and AV-A plots for SODS on O.OIM NaCl sub-solutions having different pH values are shown. In all cases, phase transitions from liquid-expanded to liquid-condensed state are evident ( ). Acidification of the subsolution Increases the transition pressure but the transition is less pronounced at the lowest pH studied. This is also accompanied by an expansion of the condensed part of the curve. Small negative surface potentials are observed over most areas. The highest potential is obtained for film spread on the pH 2.2 subsolution. For small areas, the surface potential attains a positive value. This may be related to reorientation of the dipole moments of the molecules which occur once a threshold surface concentration is exceeded (O. Mlnglns and Pethlca (7) studied the monolayer properties of SODS on various sodium chloride solutions (0.1, 0.01 and O.OOIM) at 9.5 C, and they showed that the monolayer is only stable on the more concentrated salt solutions (0.1 and O.OIM). In this work, no noticeable... 

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