Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Line of density maxima

Molecular dynamics simulations can easily be performed in the metastable region, because the duration of the simulation is short enough to make nucleation highly improbable, except very close to the spinodal limit. The simulated EoS is therefore accessible. On the other hand, only a few attempts have been made to gain exper imental knowledge on the EoS of water at negative pressure, which could put to a test the interaction potential used in the simulations. As explained in Section IV.C, the first work is due to Meyer [69] who used a Berthelot-Bourdon tube to measure the relation between pressure and density down to —3.4 MPa at 24°C. Henderson and Speedy later measured the line of density maxima down to —20.3 MPa where it reaches 8.3°C [27,70], and the metastable melting curve down to -24 MPa [98]. [Pg.72]

The thermodynamic behavior of both WAC and BKS silica have been examined in the region of the compressibility miiximum, and in both cases, the pattern of thermodynamic anomalies that occur have been found to be the same, and analogous to those found in simulation studies of water. An example is shown in Figure 2, that compares the equation of state features of ST2 water [7] with WAG silica [9] in the P-T plane. In both cases, a retracing line of density maxima occurs above a monotonic spinodal boundary. The qualitative similarity of these features, despite the widely different T and P scales, is striking, and certainly suggests that a search for an LLPT in these silica models, of the kind found in water simulations, is justified. This is discussed in the next section. [Pg.376]

Figure 4. Phase diagram of the Yoshida-Kamakura interaction model for a = 2.1. Pressure P and temperature T are in rmits of e/a and e/ks, respectively, ks being Boltzmann s constant. Full symbols are two-phase coexistence points. The data points lying on the T = 0 axis are exact solid-solid boundaries. The dashed line connecting crosses is the locus of density maxima in the fluid phase. Curves A and B connect points of maximum and minimum values of —52, respectively. The open region between A and B is the structurally anomalous region. Data are from Ref. [77]. Figure 4. Phase diagram of the Yoshida-Kamakura interaction model for a = 2.1. Pressure P and temperature T are in rmits of e/a and e/ks, respectively, ks being Boltzmann s constant. Full symbols are two-phase coexistence points. The data points lying on the T = 0 axis are exact solid-solid boundaries. The dashed line connecting crosses is the locus of density maxima in the fluid phase. Curves A and B connect points of maximum and minimum values of —52, respectively. The open region between A and B is the structurally anomalous region. Data are from Ref. [77].
Figure 2. Phase diagram proposed by Angell and coworkers 18 based on simu lations of the SW potential, with a liquid-amorphous transition line that is negatively sloped. The locus of density maxima and the tensile limit line are also shown. (From Angell et al. 18 with permission.)... Figure 2. Phase diagram proposed by Angell and coworkers 18 based on simu lations of the SW potential, with a liquid-amorphous transition line that is negatively sloped. The locus of density maxima and the tensile limit line are also shown. (From Angell et al. 18 with permission.)...
Figure 2.27 STM image of incommensurate charge density wave (CDW) state in Nbo.04Tao.96S2. Black lines highlight the insertion of extra rows of CDW maxima in the lattice (From Dai Lieber, 1993). Figure 2.27 STM image of incommensurate charge density wave (CDW) state in Nbo.04Tao.96S2. Black lines highlight the insertion of extra rows of CDW maxima in the lattice (From Dai Lieber, 1993).
The electron density is a continuous function that is experimentally observable, hence uniquely defined, at all points in space. Its topology can be described in terms of the distribution of its critical points, i.e. the points at which the electron density has a zero gradient in all directions. There are four kinds of critical point which include maxima (A) usually found near the centres of atoms, and minima (D) found in the cavities or cages that lie between the atoms. In addition there are two types of saddle point. The first (B) represents a saddle point that is a maximum in two directions and a minimum in the third, the second (C) represents a saddle point that is a minimum in two direction and a maximum in the third. One can draw lines of steepest descent connecting the maxima (A) to the minima (D), lines whose direction indicates the direction in which the electron density falls off most rapidly. Of the infinite number of lines of steepest descent that can be drawn there exists a unique set that has the property that, in passing from the maximum to the minimum, each line passes successively through a B and a C critical point. This set forms a network whose nodes are the critical points and whose links are the lines of steepest descent connecting them. [Pg.216]

Distributions Ap(r) have been determined for various derivatives of 1 by both ab initio and X-ray diffraction studies66. In Figure 10, a contour line diagram of Ap(r) in the ring plane of cis, cw-1,2,3-tricyanocyclopropane is shown66a. Positive difference densities are found between the three C atoms, but the Ap(r) maxima are displayed up to 0.3 A from the intemuclear axis66. The displacement of the maxima is considered to indicate the bent bond character of the CC bonds of 1. [Pg.64]

The general set of the seven 4f orbitals. The gray and white regions in each orbital bear positive and negative signs, respectively. Placed to die left of the i orbital is a cross section of i 2(z3), in which dots indicate the electron-density maxima, and contour lines are drawn for t2/tmax =ai-... [Pg.296]

Figure 8. Location of Na+ and CP ions on the ice basal surface over the simulation time of 1.5 ns (symbols). Each symbol + corresponds to the position of a maxima in a single-ion density profile accumulated over each time window of 60 ps. The solid line in the left frame corresponds to the mass-density profile accumulated over the first 60 ps. Figure 8. Location of Na+ and CP ions on the ice basal surface over the simulation time of 1.5 ns (symbols). Each symbol + corresponds to the position of a maxima in a single-ion density profile accumulated over each time window of 60 ps. The solid line in the left frame corresponds to the mass-density profile accumulated over the first 60 ps.
Fig. 5.26 Projection along the crystallographic c-axis (origin and unit cell axes are labelled) of the thirty highest residual density maxima. Two of the benzoate molecules are close to the crystallographic twofold axes (drawn as dashed vertical lines) and appear to be disordered. Fig. 5.26 Projection along the crystallographic c-axis (origin and unit cell axes are labelled) of the thirty highest residual density maxima. Two of the benzoate molecules are close to the crystallographic twofold axes (drawn as dashed vertical lines) and appear to be disordered.
Figure 3. Top panel spherically averaged momentum distribution (4 r n(p)) of deuterons at T = 292.15K (solid line) and T = 276.15 K (dashed line). Bottom panel spherically averaged momentum distribution 4jr n p)) of deuterons at T = 276.15K (dashed line) compared to that of protons at T = 269.15K (black line), according to the shift of 7K due to the temperature difference between the density maxima of the two liquids. Figure 3. Top panel spherically averaged momentum distribution (4 r n(p)) of deuterons at T = 292.15K (solid line) and T = 276.15 K (dashed line). Bottom panel spherically averaged momentum distribution 4jr n p)) of deuterons at T = 276.15K (dashed line) compared to that of protons at T = 269.15K (black line), according to the shift of 7K due to the temperature difference between the density maxima of the two liquids.
Figure 2. Equation of state features of (a) ST2 water and (b) WAC silica, projected into the P T plane. Density maxima (dashed lines) and liquid spinodal boundaries (dot-dashed lines) are shown. Isochores of P as a function of T are shown as symbols joined by thin solid lines. Equally spaced isochores are shown from bottom to top in (a) from p = 0.8 to 1.1 g/cm, and in (b) from p = 1.8 to 2.4 g/cm. ... Figure 2. Equation of state features of (a) ST2 water and (b) WAC silica, projected into the P T plane. Density maxima (dashed lines) and liquid spinodal boundaries (dot-dashed lines) are shown. Isochores of P as a function of T are shown as symbols joined by thin solid lines. Equally spaced isochores are shown from bottom to top in (a) from p = 0.8 to 1.1 g/cm, and in (b) from p = 1.8 to 2.4 g/cm. ...
Figure 14. Density against temperature for different isobars from NPT MD simulations using the SW potential. The temperature of the maxima along the isobars as a function of the pressure de fines the TMD line. Figure 14. Density against temperature for different isobars from NPT MD simulations using the SW potential. The temperature of the maxima along the isobars as a function of the pressure de fines the TMD line.
Temperature of Maximum Density The TMD line is defined as the locus of isobaric maxima of density p vs. T dp/dT) p = 0) or the locus of isochoric minima of pressure P vs. T dP/dT)v = 0). For pressure values above P = —3.80 GPa, the TMD line was obtained from NPT MD simulations. Below P = —3.80 GPa, cavitation in NPT MD simulations was observed and hence NVT MD simulations were performed to locate isochoric minima of pressure. The TMD obtained from density maxima along isobars and pressure minima along isochors are shown in Figs. 14 and 15, respectively. [Pg.483]


See other pages where Line of density maxima is mentioned: [Pg.54]    [Pg.74]    [Pg.470]    [Pg.54]    [Pg.74]    [Pg.470]    [Pg.471]    [Pg.490]    [Pg.49]    [Pg.166]    [Pg.175]    [Pg.133]    [Pg.205]    [Pg.220]    [Pg.202]    [Pg.262]    [Pg.202]    [Pg.13]    [Pg.16]    [Pg.478]    [Pg.145]    [Pg.231]    [Pg.205]    [Pg.286]    [Pg.166]    [Pg.175]    [Pg.175]    [Pg.34]    [Pg.477]    [Pg.13]    [Pg.506]    [Pg.445]    [Pg.162]    [Pg.119]    [Pg.133]    [Pg.381]    [Pg.483]    [Pg.395]   
See also in sourсe #XX -- [ Pg.54 , Pg.56 , Pg.58 , Pg.64 , Pg.72 ]




SEARCH



Density maximum

© 2024 chempedia.info