Description Features of Metals Dynamics at Solid and Liquid States with Phase Transitions at Intensive Pulsed Flows Impact

Transcription

1 N.B. Volkov, E.A. Chingina Description Features of Metals Dynamics at Solid and Liquid States with Phase Transitions at Intensive Pulsed Flows Impact Institute of Electrophysics UB RAS Amundsen street 106, Yekaterinburg, , Russia The work is carried out under partial financial support of the RFBR (project No a, project No mol_a) and FASO within the Presidium of Russian Academy of Sciences fundamental research program (UB RAS project No.12-P-1005, state registration No ).

2 Outline 1. Motivation; 2. Model; 3. Solid metal; 4. Liquid metal; 5. Some reasons; 6. Conclusion; 7. Future work.

3 Motivation The ultra-fast intense processes simulation within mechanics and electrodynamics of continuum media at local thermodynamic equilibrium requires equations of matter states and electronic transport coefficients for its determination. This coefficients are defined by charged particles scattering on density fluctuations, which within long-wave approximation are dependent of isothermal compressibility, i.e. equations of states for matter.

4 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

5 According to J.I. Frenkel and H. Eyring any liquid has a short-range quasi-crystal order in the vicinity of melt curve. Jakov Il ich Frenkel Henri Eyring January 29, 1894 January 23, 1952 February 20, 1901 December 26, 1981

6 John Michael Ziman (May 16, 1925 January 2, 2005) According to Ziman any liquid has topologically disordered structure!

7 Examples of the topological disorder Fig. 2.1 from Models of Disorder by J.M. Ziman a lattice order; b topological disorder; c continual disorder. a b c Fig. 2.5 from Models of Disorder by J.M. Ziman A hot crystal is not topologically disordered!

8 a Fig from Models of Disorder by J.M. Ziman The topological disorder (a) in liquids always can be presented as crystal including a great number of strongly coupled dislocations (b). However the representation is ambiguous (c). b c

9 A model of the liquid disorder according to A.I. Gubanov [A Quantum-Electron Theory of Amorphous Semiconductors. M.: USSR Academy of Science Press, 1963] and A.Z. Patashinskii and B.I. Shumilo. [Theory of condensed matter based on the hypothesis of a local crystalline order. // Sov. Phys. JETP, V. 62. No. 1. P. 177.]: Fig from Models of Disorder by J.M. Ziman

10 According to Bernal any liquid has the statistically distributed densely packed structure. In other words the liquid represents an amorphous solid with the greatest possible density. John Desmond Bernal (May 10, September 15, 1971)

11 According to A.S. Bakai the amorphous solids received at fast cooling of liquids have a poly-cluster short-range order. The polycrystalline short-range order is a special case of the poly-cluster one. A. S. Bakai, academician of the NANU September 16, 1938

12 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

13 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

14 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

15 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

16 From [T. Iida and R.I.L. Guthrie // The physical properties of liquid metals. Oxford: Clarendon Press, 1988]

17 1. On the basis of the analysis of the radial distribution functions submitted above it is possible to assert, that clusters with the short-range order have radiuses about 1-2 nanometers! 2. Cluster symmetry differs from symmetry of a crystal lattice near to the melting curve. Symmetry difference affects, basically, in an oscillatory spectrum of clusters. HOWEVER, a thermal capacity of liquid and solid metal on a melting curve is equal to 3kT/MA. Therefore the cluster oscillatory spectrum can be described as a spectrum of the Debye model, or - the Einstein model, or, that is much more exact, - superposition of spectra of these models. 3. The electron density of liquid and solid metal on the melting curve is unaffected, the fact confirmed by Knight shift registration experiments. An electrical conductivity change during melting is connected first of all with variations of the structure factor S (q). 4. It is possible, according to J.I. Frenkel, to suppose, that melting occurs as a result of a lattice stability loss due to the avalanche-like growth of the point defects, i.e. vacancies and Frenkel pairs («vacancy - interstitial atom»), near to the melting curve. Thus the free volume is concentrated in the intercluster domains with the gas disorder.

18 Solid metal model Free energy: F ( VT, ) = ε ( V) + F ( VT, ) + F ( VT, ), s π sl se ε ( V ) F ( VT, ) π sl Were cold energy; F ( VT, ) se - a thermal excitation of electrons. 13 ( 1 ) a thermal excitation of the lattice; 1 η δ 13 1 aδ bδ επ ( δ ) 1 α exp exp η α ( 1 δ ) + + =Λ α 1 α 1+ a+ b 1/3 2/3 Constants a and b we find from the requirement of agreement with the Thomas - Fermi model with quantum and exchange corrections..

19 Free energy of the lattice: 3 9 k T k T T T 3 k Ts * T 0 1 F ( V, T D B ) B 3 ln 1 exp D D D B D = + 1. sl 8 MA MA T T 4 MA T 2 D th 2 T D 2T 1 1 β z 3 2 (, ) 0 V Free energy of the electron thermal excitations: F VT = c T 2. se e 2 z V e c0 0 1 I.S. Grigoriev, E.Z. Meylikhov. Physical Data. Handbook. Moscow: Energoatomizdat, V.E. Zinoviev. Standard Handbook of Properties: Metals at High Temperatures. New York: CRC Press, L.A. Novitskii, I.G. Kozhevnikov. Thermophysical Properties of Metals at Low Temperatures. Moscow: Mashinostroyenie, 1975.

20 1. A.A. Bakanova, I.P. Dudoladov, R.F. Trunin. // Sov. Phys. Solid state, 7, 1307 (1965). 2. S.P. March (Ed.) LASL Shock Hugoniot Data. Berkeley: California University Press, L.V. Al tshuler. // Sov. Phys. Uspekhi, 8, 52 (1965). 4. M.H. Rice. // J. Phys. Chem. Solids, 26, 483 (1965). 5. Cross-cup points of shock adiabats with calculated melting curves. Comparison of calculated and experimental Hugoniot adiabatic curves for Pb, Na and Cs

21 Free energy: were Liquid metal ( ) F = c F( VT, ) + 1 c F( VT, ) + F ( VT, ), L cl cl cl g Te V 9 kt cl cl kt T T ccl =, F ( V, T) = ε ( V) + + 3ln 1 exp cl D cl V cl π 8 MA MA T T 3k T T 3 B cl * cl0 1 kt 1 c ϕ cl ( cs ) MA 1 ln 1 ξ exp, 4MA T 2 2 T + MA c cl cl kt cl th 2T kt Fg = 1+ ln VMA, c = or ζλ MA 3 2 MAkT ζ cclλ ϕ 2 ( cl) 2π 1 ccl H. Eyring is the energy spent on formation of free volume at melting.

22 1. Constants ξζ,, Tcl* we find from a condition of equality of volume and entropy jumps on melting curve at normal pressure to experimental values. 2. The melting curve at pressure exceeding normal we find according to the following algorithm: By Lindeman criterion we estimate a melting temperature T m at given P. Afterwards we find phase densities Vsm, VLm. We check correctness of performance of equality of the Gibbs potentials for solid and liquid phases μs ( Tm, Vsm) = μ( Tm, VLm). If the equality is not fulfilled, we change T m and then repeat the procedure until this equality can be satisfied with given accuracy. We calculate the jump of entropy and then shift to new pressure value. 3. Equilibrium values of ccl, V and T outside the melting curve we find from the minimum of the Gibbs potential.

23 The melting curves for Na: 1 experimental points from [E. Gregoryanz et al. Phys. Rev. Lett., V. 94. A. no ]; 2 experimental points from [C.S. Zha, R. Boehler. Phys. Rev. B, V. 31. P ]; 3 our calculation on the two-phase equation of state (EOS); 4 our calculation on the one-phase EOS with using the Lindeman criterion; 5 the shock adiabatic curve calculated by us on the one-phase EOS.

24 a b The jumps of volume (a) and entropy (b) at the sodium melting: 1 our calculation on the two-phase EOS; 2 the experimental estimates from Stishov review [S.M. Stishov. Soviet Phys. Usp., V. 17. No. 5. P. 625.]

25 aα ()( t α = 1,2,3) β β a = N ( β = 1,2,3) N g β (,) r t = β a dr is the lattice translation vector; is a vector of the reciprocal lattice; is an integer coordinate measured in units of translation vectors; αβ α β = aa, g = aa are the invariant metric tensors of lattice; αβ α β ( αβ ) ε = ε g + ε f + ε f is the internal energy of solid metal; s l p p e e Some reasons An equilibrium relation for the diamond anvil: ( ) αβ αβ αβ ( Σ) i k ( l) ( p) ( e) α β i k Π ik = σ + λ p + λ e i k εl = nn 2 f f a a nn P.

26 The future work is aimed at: search of the most adequate description of the cluster oscillatory spectrum and the energy spent on formation of free volume at melting; calculation of shock adiabatic curves and thermo physical characteristics for liquid metals; calculation of the structural factor and electronic transport coefficients within the framework of plasma model for metal.

27 Many Thanks for Your Attention!!!