J . Phys. Chem. 1990, 94, 11 10-1 113
1110
excited state. It also indicates that the value is more sensitive to substrate structure in the excited state than in the ground state but that result can be derived directly from the data in Table I and does not require any estimation of (vh- V,). The change in sign of the pressure dependence of the strain energy, on the other hand, does depend on the estimates of (V, - V,). We believe that the change in sign is real, and the preceding equations permit it. If we assume, as before, that the strain energy is dominated by volume strain according to eq 3, and that I, and Ih have the same sign (k, and kh are both positive), the pressure dependences of Gstrain,*and Gstrain,h would have opposite signs if the anharmonic term, Le., the term in (AU3,were dominant. Considering the size of AV, that is distinctly possible. Strains by other mechanisms may also have opposite signs in the FranckCondon ground and excited states. For instance, the deviation of the reaction field from equilibrium, for the present substrates, is positive in the Franck-Condon ground state and negative in the excited state. Acknowledgment. This work was supported by a grant from the National Science Foundation. Appendix In this section we shall summarize a derivation based on the model of polarizable point dipoles interacting with their reaction fields. The derivation shows that, for a Franck-Condon transition taking place in a medium of high dielectric constant, (vah - vem) is independent of the solvent refractive index. In addition, it predicts that, in our experiments, the contribution to the pressure effect on umax due to the interaction of dipoles with their reaction fields is quite small. The full derivation is presented as supplementary material.l8 Let subscript 1 denote the solvent, i the electronic ground state of the solute, and k the electronic excited state of interest. Let e l denote the dielectric constant of the solvent, aiand a k denote molecular polarizabilities, and ai and ak denote radii of the cavities containing the respective solute molecules at solvation equilibrium. Thus in a Franck-Condon absorption [i k], the cavity radius is ai; in a Franck-Condon emission [k i], it is ak. Furthermore, let = 2(c1 - 1)/(2tl + l), yi = ai/ai3and yk = ak/a2. We shall treat the dipole vectors pi and C(k as parallel. (The full derivationI8 does not make this assumption.) These vectors are precisely parallel for substrates I and V, and nearly
--
so for 11, 111, and IV; sample vector diagrams and predicted excited-state resonance structures are shown in Scheme 11. Upon treating fii and pk as parallel, the solvation energy difference derived in the supplementary material (eq S.15) reduces to eq A.l. r
To reduce the number of unknown parameters, two further assumptions are often made.I4-l6 (i) ai and ak are assigned a common value a which is treated as independent of the medium. (ii) yi and Y k are assigned a common value y. As a corollary of (i) and (ii), ai= a k . On introducing these assumptions, (A.1) simplifies to (A.2). For polar molecules in liquid dielectrics, y hC(vabs - vem) = 2(1.(k- Wi)''#'l/[a3(1 - '#'IT)]; ai = ak; ai = ak; pi and pk are parallel (A.2) is always C1 and typically between 0.25 and 0.5." For the present substrates, y = 0.4. On using that value and introducing values of e l for water as a function of pressureg at 25 OC, one finds that a In (vah - ve,)/dp is +O.OOl/kbar. Values of (va& - (v,& in Table I are about 10000 cm-I for I and 5000 cm-' for 11,111, and IV. Hence a(vah - vem)/apis predicted to be +10 cm-'/kbar for I and +5 cm-'/kbar for 11, 111, and IV. Registry No. I, 4854-84-6; 11, 19840-99-4; 111, 91-44-1; IV, 4126776-9; V, 100-01-6.
Supplementary Material Available: General derivation of eq A.l and vector diagram of dipole moments (8 pages). Ordering information is given on any current masthead page. (34) Bottcher, C. J. F. Theory of EIectric Polarization; Elsevier: New York, 1952; Chapter 3. (35) Baumann, W. J. Mol. Struct. 1978, 47, 237. (36) (a) Exner, 0. Dipole Moments in Organic Chemistry;Georg Thieme: Stuttgart, 1975. (b) Ananta Krishnan, S.V.; Jacob, P. J. Indian J . Chem. 1969, 7, 234. (c) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, 1963; p 349.
Shock Wave Compression of Mixtures of Powders with Liquefied Gases G . A. Adadurov and V. I. Goldanskii* N . N . Semenov Institute of Chemical Physics, USSR Academy of Sciences, Ulitsa Kosygina, 4, 1 1 7334, Moscow, USSR (Received: June 1 1989; In Final Form: October 13, 1989) ~
A new approach in physical chemistry at high pressures has been theoretically proposed and experimentally confirmed. The approach is based on shock compression of solid particles placed in liquefied gas with preservation of the products after compression. Shock compression of such heterogeneous systems has been shown to result in very high temperature states with subsequent rapid and deep cooling of the solid phase due to heat dissipation into the evaporating gas which expands after compression during the isentropic decrease of pressure. The cooling promotes preservation of the shock-formed metastable structures. As a result of specific combinations of high pressures and temperatures, usually inaccessible and insufficiently known regions of the P,T-state diagram can be achieved.
Introduction The physical chemistry of shock compression is based on proin which mechanisms and kinetics are determined by specific conditions appearing during the shock wave (sw)passage through the sample. In the experiments with preservation of substance in ampules, isentropic unloading waves rapidly lower the pressure 0022-3654/90/2094-11 l0$02.50/0
and temperature. The rate of cooling at this stage is estimated to be 10' K/s.' However, due to the irreversible nature of shock compression, samples remain heated even after the pressure relief. This often results in the annealing O f structural changes which (1) Adadurov, G. A. Russ. Chem. Rev. 1986, 55, 282.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1111
Shock Wave Compression of Powders
X u
K,
Moo
c.
v
20
B
!E
P4
xx)O
10 1000
.V
I
-
GAS MASS PERCENT
,
2000
4000 6000 8000 TEMPERATURE ( K )
100
Figure 1. Pressure-temperature dependencies under shock compression for various substances, based on the available experimental and calculated data.
occurred during compression because a preserved compact sample in the ampule cools by the ordinary heat conduction laws. At present there are several approaches to tempering of shock compression products. One can use heterogeneous mixtures of solids, e.g., graphite-copper. Under shock compression the components are loaded, compressed, and heated, each by its own laws: graphite (or shock-formed diamond) is heated more and copper less. Under the unloading and after the pressure relief in a compact mixture, diamond transfers some of the heat to copper, thus increasing the yield of diamond.2 Another approach is in the prior cooling of the ampule with the sample. But in this latter case the effect is observed only for thin samples; for instance, films of organic substances quickly transfer heat to the walls of metallic
In the present work we consider the possibility of strong heating of solid particles by shock compression of their mixture with liquefied gases and subsequent rapid cooling of the solid phases due to heat dissipation into the evaporating gas which expands with the velocity of several kilometers per second during isentropic unloading. Shock Compression of the System Solid-Liquefied Gas The liquefied gases in the SW experiments have become an object of interest in connection with the derivation of the equation of state of detonation product^,^ with the metallization of dielectrics, and with the development of models of giant planet^.^ Shock wave Hugoniots for liquid N2 and CO2? Ar, N2,and 02,5 H2 and D2,6Xe7 have been reported. Transparency of the liquefied gases also makes it possible to register experimentally the temperature of shock wave compression of Ar and N2.8-1* The method of formation of high-velocity gas streams due to the impact of strong S W on free surfaces of liquid N2 and H2 was suggested in ref 12. It should be pointed out that the cited paper and other papers do not contain any calculated or experimental data on the cooling of gases under unloading. The formation of cold gas ~
(2) Cowan, G. R.; Dunnington, B. N.; Holtzmann, A. H. US Patent No. 3401019, IO Sept. 1968. (3) Adadurov, G.A.; Gustov, V. V.; Yampol'skii, P. A. Combust. Explos. Shock Waves (Engl. Transl.) 1971,7, 243. (4) Zubarev, V. N.; Telegin, G.S. Sou. Phys. Dokl. 1962, 7, 34. (5) Nellis, W. J.; Mitchell, A. C. J. Chem. Phys. 1980,73,6137. (6)Dick, R. D.; Kerley, G. J. J . Chem. Phys. 1980,73, 5264. (7) Nellis, W. J.; Van Thiel, M.; Mitchell, A. C. Phys. Rev. Lett. 1982, 48, 816. (8) Voskoboinikov, I. M.; Gogulia, M. F.; Dolgoborodov, A. Yu. Sou. Phys. Dokl. 1979,246, 579. (9) Grigorev, F. G.; Kormer, S.B.; Mikhailova, 0. L.; Tulochko, A. P.; Urlin, V. D. Sou. Phys., JETP Lett. 1972,16, 201. (10) Radouskv. H. B.: Nellis, W. J.; Ross, M.; Hamilton, D. C. Phys. Rev. Letj. i986.57,i419. ( 1 1) Radousky, H. B., Ross, M. High Pressure Res. 1988,1, 39. (12) Titov, V. M.; Silvestrov, V. V. Recent Developments in Shock 'I 'ube Research. Proc. Ninth Inr. Shock Tube Symp. 1973,526.
Figure 2. Dependence of shock compression temperature (lines 1-5) and residual temperatures (lines 3'-5') on mass percentage of gaseous phase in the mixtures of H e ( l ) , H2(2), and Nz(3,3'-53') with carbon.
streams was reported and an estimation of several tens of kelvin for H2 is given in ref 12. Liquefied gases are among the objects most heated under shock compression due to their large compressibility. Figure 1 shows the pressuretemperature ( P - 0 dependencies for some solids and liquefied gases. As is seen at equal pressures, the highest temperatures are reached for liquefied gases, particularly monatomic ones. The temperature needed for the evaporation of liquefied gases at the stage of unloading can be easily reached due to lower intermolecular bond energies and critical temperatures than those of the solids. According to estimations,12the shock wave pressures required for full evaporation during the unloading of liquid N2 and H2 are 4.8 and 1.3 GPa, respectively. Analysis of the data available on temperature decrease during the unloading for the SW-subjected solid shows that the more compressible the heated solid, the sharper and deeper it C O O ~ S . ' ~ In view of all the above-mentioned concepts it seemed to be of interest to study the mixtures of fine, dispersed powders of solids with liquefied gases. The state of such mixtures under the shock compression should differ from that of the mixtures of solids. During the passage of the shock wave the solid particles placed in liquid should experience compression close to hydrostatic conditions. When the sizes of solid particles are less than 1 pm, they are heated from the high-temperature, shock-compressed gas. Equilibrium temperatures of the mixture will naturally be lower than that of the gas but higher than the temperature of particles during the shock passage. During the stage of unloading, the gas cools upon expansion and takes heat from the solid phase, thereby tempering it. When calculating the thermodynamic parameters of shock compression and unloading of the mixture, it was assumed that the compression is hydrodynamic. Parameters in front of the shock wave and behind it are linked by the mass, momentum, and energy conservation laws for one-dimensional flow of multiphase system. To calculate the parameters of the system during the unloading, the thermodynamic conditions assumed fixed values of entropy at either volume or pressure. The equation of the state of Becker-Ki~tiakowsky-Wilson~~ was used as a thermodynamic equation of the gaseous phase. The equation of state of Cowan'' was chosen for calculating the parameters of solids in the mixture. The coefficients in the equations were selected from the experimental shock Hugoniots of the initial substances. Calorific equations of state of the products under standard pressure were described as polynomial dependencies of enthalpy, entropy, and heat capacity of individual substances under temperature on the basis of standard thermodynamic data.l6~l7 (1 3) High-Velocity Impact Phenomena; Kinslow, Ray, Ed.;Academic Press: New York, 1970. (14) Mader, C. L. Numerical Modeling of Detonation; California Press: Berkeley, CA, 1979. (15) Cowan, R. D.; Fickett, W. J. Chem. Phys. 1956,24, 932.
1112 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
Adadurov and Goldanskii
3
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a
b
Figure 4. Scanning electron micrograph of shock-synthesized Z-BN under shock compression of a mixture of H-BN + N2.
Figure 3. Experimental schemes for generating the plane (a) and converging (b) shock waves in the mixtures under study: (1) detonator, (2) generator of the plane detonation wave, (3) explosive, (4) impactor ( 5 ) Styrofoam container, (6) mixture under study.
Figure 2 shows the equilibrium temperature dependencies of shock-compressed mixtures of graphite with liquid He (line l), H2 (line 2), and N2 (lines 3-5) on the mass percentage of the liquefied gases in shock-compressed mixtures with the increasing mass percentage of liquefied gas in the mixture. At a given mass and molar ratio, the higher temperature is reached in the mixtures with light gases such as He and H2 (in comparison to N2). In the process of isentropic expansion the pressure in the system drops to the normal one. On account of increased entropy due to the irreversibility of the shock compression process, the temperature of the expanded system remains higher than the initial one. Accordingly, the information about the residual temperatures is quite important in experiments with the preservation of products. Figure 2 gives the values of Tres(res = residual) after the shock compression of mixtures of graphite with liquid nitrogen (line 3’, 25 GPa; 4’,20 GPa; and 5’, 15 GPa). As is seen from that figure the T,, rises with increasing pressure and drops as the mass percentage of nitrogen in the mixture grows. These aspects are studied in more detail in ref 12 where a possibility of a phase transition of graphite to diamond is considered under corresponding pressures and temperatures. Experimental Details Figure 3 presents two kinds of explosive devices for generation of either plane or converging shock loading in the systems under study. The experiments were conducted in a stationary rigid hermetically sealed reusable container. In scheme a the shock waves in the studied mixture were produced by the impact of metallic plates accelerated to velocities from 1 to 4.5 km/s. In this case the pressure ranged from 5.0 to 30.0 GPa for various mixtures. When the shock wave reached the bottom surface of a Styrofoam container, the latter broke and solid particles were dispersed within the expanded gas flow. In scheme b the detonation wave propagating along the cylindrical container produced converging conical shock compression in the mixture. The latter forms a Mach wave configuration spreading through the stationary area with the detonation velocity of the expl~sive.’~ For example, at the detonation velocity of 8.0 km/s in argon the following values of parameters can be achieved: shock velocity U = 8.0 km/s, mass velocity u, = 4.5 km/s, P = 50 GPa, and T = 14000 K. In liquid nitrogen u, = 4.75 km/s, P = 30 GPa, and T = 6000 K. In the mixture of crystalline quartz (16) JANAF Thermochemical Tables, 2nd ed.; U.S. Department of Commerce, National Bureau of Standards: Washington, DC, 1970. ( 17) Thermodynamic Properties of Simple Substances. Handbook; Gurvich, L. V., et al., Eds.; Nauka: Moscow 1978-1982; in Russian. (18) Adadurov, G. A., Gubin, S. A., Odintsov, V. V., Sergeev, S. S. IVth All-Union Meet. Detonation, Rep. 1988, I , 6 .
1
u.5pm,
Figure 5. Electron micrograph of shock-synthesized H-BN under shock compression of a mixture of B N2. Moire fringes are clearly seen.
+
with liquid nitrogen at the initial density of 1.78g/cm3 the pressure will be even higher: U = 8.0 km/s, u, = 4.45 km/s, and P = 53 GPa. After the shock wave reaches the bottom of the container and the latter breaks, a high-speed flow of the gas with solid particles is formed. After the experiment the container was unsealed and the solid products of compression were extracted for physicochemical analysis. Results and Discussion The experiments were conducted with mixtures of hexagonal boron nitride H-BN (particle size below 100 pm) with liquid nitrogen and argon, of elemental amorphous boron (particle size below 20 pm) with liquid nitrogen, and of graphite with liquid nitrogen at different ratios of components and pressures of shock compression. It is shown in the present work that, during the shock compression of the H-BN mixtures with liquid nitrogen or argon, the wurtzite-type (W-BN) or zinc blende-type (2-BN) of boron nitride can be formed depending on the conditions of shock loading. Z-BN crystals with a specific surface 45 m2/g and density 3.45 g/cm3 (Figure 4) were obtained after shock wave compression of H-BN and N mixture. Oxidation starting temperature was found to be 1000 “Cand phase transition in H-BN began above 1000 OC. The total duration of the thermal treatment was 10-15 min. The calculations analogous to those for the graphite-liquid nitrogen system (Figure 2) demonstrated that at a pressure of 15.5 GPa in the mixture of H-BN with liquid nitrogen (density 1.1 1 g/cm3) the following initial temperatures are reached: ca. 3000 K in nitrogen and ca. 500 K in H-BN. After the loading the
J. Phys. Chem. 1990, 94, 11 13-1 117 equilibrium temperature of the mixture is ca. 2000 K and after the isentropic unloading only 260 K. Shock compression of the mixture of amorphous boron with liquid nitrogen leads to the chemical synthesis of H-BN (Figure 5 ) . In the case of shock compression of the mixture of fine, dispersed graphite with liquid nitrogen under the described conditions, cubic diamond is formed. It is important to note that, unlike the products of usual shock compression of solids, the products obtained during the compression of the solid-liquefied gas system possess a high degree of crystallinity of their structure (see Figures 4 and 5 ) and increased resistance to acids and to oxidation in air. It should be stressed here that at the present stage of our study we had no intention of optimizing the conditions for maximum output of the compression products. Yield of Z-BN in experiments with mixtures H-BN + N2 was up to 20%. Among the possible mechanisms of formation of dense highpressure phases, the most interesting and probable is the supposition of partial or full melting of graphite and H-BN, with subsequent crystallization of dense phases from the melt. Thus, it is shown herein that under the shock compression of the mixtures of solid particles with liquefied gases conditions of strong heating in shock compression and deep cooling of the particles during unloading can be achieved. The highest temperatures in shock compression and the lowest residual temperatures are observed in the case of light and monatomic gases.
1113
Decrease in the mass fraction of the solid component leads to the rise in shock temperature and also to more rapid and deep cooling of solid products. These conditions promote both phase transformations and chemical reactions and preservation of a new phase after unloading. Quite specific conditions seem to be realized during the shock compression of the mixtures that were studied; solid is compressed almost hydrostatically and heated in lod s due to heat transfer from the strongly heated liquefied gas. The conditions open the possibility of achieving almost inaccessible regions of pressuretemperature phase diagrams when strong heating can be obtained at relatively low pressures. The gases, inert to the studied substance as well as interacting with it, can be used for such purpose. Substantial heating can result in melting or even evaporation of the solid component thereby promoting the Occurrence of unusual chemical reactions. Sharp and deep cooling of products during the unloading the expansion of the system ensure a high degree of crystallinity. It is desirable to undertake further more detailed investigations for obtaining the high-pressure phases, e.g., directly during the pulsed compression of the mixtures of boron with liquid nitrogen. There is hope of obtaining superstoichiometric compostions of nitrides and oxides on synthesis of superconducting high-temperature oxide ceramics. It is also of value to study the behavior of organic substances under the conditions considered.
Phase Transitions of the System Ag2Hg14-Cu2Hg14at Normal and High Pressure Studied by Differential Scanning Calorimetry Milan Friesel, Bogdan Baranowski: and Arnold LundBn* Department of Physics, Chalmers University of Technology, Goteborg, Sweden (Received: June 6, 1989; In Final Form: October 23, 1989)
Differential scanning calorimetry has been applied for studying the system Ag2Hg14-Cu2Hg14at both normal and high pressure. It is confirmed that there is a miscibility gap in the ordered phase and that the order-disorder phase transition has a eutectoid point at 307 K and 42.7 mol % Cu2Hg14at normal pressure, which is about 30 K higher than expected from a calculation for ideal eutectic behavior. The order-disorder transition is of first-order character over the whole composition range, confirming the interpretation by Suchow and ruling out the suggestion by Jaffray that it should be of second-order character in the middle part of the range. The transition enthalpy is equal to 7.3 i 0.2 kJ/mol for the eutectoid composition. The phase diagram of the eutectoid composition was determined for pressures up to 0.72 GPa, and the temperature of the orderdisorder transition increased from 307 to about 325 K. The correlation was not linear over the whole pressure range, but an average dT/dp slope of 25 K/GPa is in good agreement with the 24 K/GPa calculated by means of van Laar’s formula. The transition enthalpy (kJ/mol) decreased linearly with increasing pressure with dAH/dp = -4.0 kJ/(mol GPa). A calculation from a simple additive rule gives instead dAH/dp = -1.5 kJ/(mol GPa).
Introduction Both Ag2Hg14and Cu2Hg14are characterized by an orderdisorder transition at a temperature slightly above ambient, 325 and 343 K, respectively, at which there is a distinct change in color (thermochromism) as well as a pronounced increase in the electrical conductivity. For these reasons they have been studied by means of a large number of experimental techniques. We have performed a series of studies of the silver salt’-’ and one of the copper salt,s and we have found that (i) differential scanning calorimetric (DSC) analysis of the order-disorder transition is a very efficient way to determine the status of the sample (impurities, metastable states, etc.),2~3~8 (ii) coprecipitation of some impurity easily occurs during the synthesis,2*6(iii) a mechanical treatment such as one-dimensional pressing or grinding can create ‘Permanent address: Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52 P1-01-224 Warszawa, Poland.
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a metastable impurity of some high-pressure phase,3 and (iv) the phase diagram of the silver salt has several unusual features at high pressure^.^^^^^ (1) Baranowski, B.; Friesel, M.; LundCn, A. Solid State Ionics 1983, 9, 10, 1179. (2)LundCn, A.; Friesel, M.; Baranowski, B. Transport-Structure Relations in Fast Ion and Mixed Conductors. Proceedings of the Sixth R i m International Symposium on Materials Science; Poulsen, F. W., Hessel Andersen, N.,Clausen, K.,Skaarup, S., Toft Ssrensen, O., Eds.; Rim National Laboratory: 1985; p 407. (3) Friesel, M.; Baranowski, B.; LundCn, A. Phys. Reu. B 1985,32,2506. (4)Baranowski, B.; Friesel, M.; Lundh, A. Physica 1986, 239,240,263. ( 5 ) Baranowski. B.: Friesel. M.: LundCn. A. Phvs. Rev. B 1986.33.7753. (6) Friesel, M.; Baranowski; B.;.LundCn,.A. Thlrmochim. Acta .1988,131, 191. (7) Baranowski, B.; Friesel, M.; LundCn, A. Solid State Ionics 1988, 28-30, 194. ( 8 ) Friesel, M.; Baranowski, B.; LundCn, A. Phys. Scr. 1987, 35, 34.
0 1990 American Chemical Society
