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Joint Institute for High Temperature (Russian Academy of Science)Moscow Institute of Physics and Technology (State University)
Igor Iosilevskiy
Hypothetical Non-Congruenceof Quark-Hadron Phase Transition and Critical Point
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
UO2
0
PCP
0,5
CP1P
RE
SS
UR
E, G
Pa
T, K
Dubna_2008_2009
HIC for FAIR
EMMI_Wroclaw_2009
Neutron Stars_2008 PNP_2009_Moscow
Extreme Matter Institute – EMMI
arXiv:1005.4186v1
Critical Point and Onset of DeconfinementJINR Dubna, Russia, August 2010
Prerow_2009
1st order // 1‐D // Unbounded (no end‐point)
1st order // 2‐D // No end‐point (stripe)
Coexistence of Macroscopic Phases1st order // 1‐D // End‐point
1st order // 2‐D // End‐point
1st + 2nd +… // 1‐D // 2‐D // Several end‐points
? ? ? ?
Mark Gorenstein (Dubna‐2006)
?
R. Pisarski, Wroclaw‐2009 // L. McLerran Bad Honnef‐2009
Triple point ? Quadruple point ?
INTAS Project (1995–2002) // ISTC Project (2002–2005)Cooperation: MIPT – IHED RAS – IPCP RAS – OSEU – MPEI – ITEP – VNIIEF ⇔ ITU (JRC, Germany) GSI (JRC, Germany)Managing, science and coordination: – V. Fortov (RAS, Moscow)/B. Sharkov (ITEP, Moscow) /C. Ronchi (ITU, JRC)
Expected temperature at hypothetical severe accidentat fast-breeder nuclear reactor
T
3000 4000 5000 6000 7000 8000 9000 10000
4
2
Melting point
Boiling of Fuel
UO2
0
CP
1
3
PRES
SU
RE
, GPa
T, K
Non‐congruent phase transition in uranium‐bearing mixturesThe base
Gas-Core Nuclear Reactor Project (1957–1980)
Strong competition: Soviet Union ⇔ United StatesProject Leader in Soviet Union – academician Vitalii Ievlev (RAS)
Non-Congruent Phase Transitions in Cosmic Matter and LaboratoryEMMI Workshop and XXVIth Max Born Symposium, Wroclaw, 2009
Acta Physica Polonica B, 3 (2010)http://th‐www.if.uj.edu.pl/acta/sup3/pdf/s3p0589.pdf
‐ Construction of Equation of State (EOS)
‐ Phase coexistence parameters calculation
Two problems:
Study of non‐congruent evaporation in U‐O system
Theoretical ModelTheoretical Model ComputationsComputations Input DataInput DataSOLIDSOLIDIonic
Crystal Model
[1]
LIQUIDLIQUID VAPORVAPOR ““IVTANTERMO” DATABASE
IDEAL-GAS PARTITION FUNCTIONS
Qj(T)
THERMOCHEM.PARAMETRS
{ΔSH 0}
DEVELOPMENT OF THE EFFECTIVE NUMERICAL
ALGORITHM
“SAHA” code [3]
COMPUTING
Thermodynamic Functions
Equilibrium Composition
Phase Boundaries
INDUSTRIAL APPLICATIONin Nuclear Safety AnalysisHypothetical Severe Accident
on Fast Breeder Reactors
Properties ofCONDENSED PHASE
in Melting Point
EOS model CALIBRATION
SCOPE of EXPERIMENTAL DATAfor
condensed phase
Critical ASSESSMENTof the data
EOS model VALIDATION
SOLIDSOLID LIQUIDLIQUID
SOLIDSOLID LIQUIDLIQUID
DEVELOPMENT OF THE EFFECTIVE NUMERICAL
ALGORITHMIONIC Molecular Mixture(Neutral & Charged)
Final Two-phase EOS Model [2]
Molecular Mixture(Neutral & Charged)
INTAS Project (1995–2002)
Vladimir Youngman (JIHT RAS)Lev Gorokhov (=“=)Michael Brykin (=“=)= = = = = = = = = = = = = = = = = = = = = =
Gerard J. Hyland (Warwick, UK)
Victor Gryaznov (Russia)Eugene Yakub (Ukraine)Alexander Semenov (Russia)I.L.I. (Russia)= = = = = = = = = = = = = = = = = = = =Claudio Ronchi (JRC, Karlsruhe)Gerard J. Hyland (Warwick, UK)
Victor Gryaznov & I.I.
Different EOS for coexisting phases
Ionic model (Liquid)
U6+ + U5+ + U4+ + U3+ + O2− + O−
Multi-molecular model (Vapour)
U + O + O2 +UO +UO2 + UO3
Interactions: (Pseudopotential components)– Intensive short-range repulsion– Coulomb interaction between charged particles– Short-range effective attraction between all particles
Interaction corrections: (Modified for mixtures)– Hard-sphere mixture with varying diameters– Modified Mean Spherical Approximation (MSAE+DHSE)– Modified Thermodynamic Perturbation Theory {TPT- σ(T ); ε(T )}
Quasi‐chemical representation for liquid and vapour phases
* Iosilevskiy I., Gryaznov V., Yakub E., Ronchi C., Fortov V. Contrib. Plasma Phys. 43, (2003)
* Iosilevskiy I., Yakub E., Hyland G., Ronchi C. Int. Journal of Thermophysics 22 1253 (2001)
* Iosilevskiy I., Yakub E., Hyland G., Ronchi C. Trans. Amer. Nuclear Soc. 81, 122 (1999)
* Ronchi C., Iosilevskiy I., Yakub E. Equation of State of Uranium Dioxide / Springer, Berlin, (2004)
* Iosilevskiy I., Son E., Fortov V. Thermophysics of non‐ideal plasmas. MIPT (2000); FIZMATLIT, (2010)
Combined ionic-molecular modelU + O + O2 +UO +UO2 + UO3 +U+ + UO+ +UO2
+ + O− + UO3− + e−
Unique EOS for both coexisting phases
1
2
No critical point !
Critical point exists !
Different EOS for coexisting phases
Ionic model (Liquid)
U6+ + U5+ + U4+ + U3+ + O2− + O−
Molecular model (Vapour)
U + O + O2 +UO +UO2 + UO3
Interactions: (Pseudopotential components)– Intensive short-range repulsion– Coulomb interaction between charged particles– Short-range effective attraction between all particles
Interaction corrections: (Modified for mixtures)– Hard-sphere mixture with varying diameters– Modified Mean Spherical Approximation (MSAE+DHSE)– Modified Thermodynamic Perturbation Theory {TPT- σ(T ); ε(T )}
Quasi‐chemical representation for liquid and vapour phases
* Ronchi C., Iosilevskiy I., Yakub E. Equation of State of Uranium Dioxide / Springer, Berlin, (2004)
Combined ionic-molecular modelU + O + O2 +UO +UO2 + UO3 +U+ + UO+ +UO2
+ + O− + UO3− + e−
Unique EOS for both coexisting phases
1
2
No critical point !
Critical point exists !
U
O
U+
UO
UO2
UO3
O‐
Quasi‐chemical representation(”Chemical picture” ‐ in plasma community )
Multi-molecular-ionic model(Liquid & Gas)
U + O + O2 +UO +UO2 + UO3U+ + UO+ +UO2
+ + O− + UO3− + e−
UO2 U + 2O O2 2OU U+ + e
UO3 + e UO3–
. . . . . .
Strange (hybrid) stars U – O system
μUO2 = μU + 2μUμO2 = 2μO
μU = μU+ + μeμUO3 + μe = μUO3–
. . . . . . . . . . . . .
UO3
O‐U+
Different EOS for coexisting phases
No critical point !
Unique EOS for coexisting phasesCritical point exists !
O‐U
O‐
O‐
O‐
Unique EOS for coexisting phases
Critical point exists !
Why not ?
Two problems in phase transition calculation
‐ Phase coexistence parameters calculation
‐ Construction of Equation of State (EOS)
Ordinary way:in pressure P(V) – Maxwell (equal squares) orin free energy F(V) – “Double tangent”
Phase coexistence parameters calculation(standard approach)
(see for example: Iosilevskiy I., Encyclopedia on low‐T plasmas. III‐1, 2000, P.327‐339); III‐1 (suppl) 2004, P.349‐428)
P(V) F(V)
“Plasma” phase transition(in xenon)
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Saturation curve(Double-tangent construction)
0
CP
0,5
1
PR
ES
SU
RE
, GP
a
T, K
1
2000
4000
6000
8000
10000
12000
CP
T =TC
432 5
T >TC
00,5
P, bar
ρ, g/cm3
Forced‐congruent evaporation in U‐O systemPressure - Density diagram Pressure - Temperature diagram
• Stoichiometry of coexisting phases are equal: x’ = x’’
• Van der Waals loops (at T < Tc) corrected via the “Double tangent construction”
• Standard phase equilibrium conditions: P’ = P” // T’ = T” // G’(P,T, x) = G”(P,T, x)
• Standard critical point:(∂P/∂V)T = 0 // (∂2P/∂V 2)T = 0 // (∂3P/∂V 3)T < 0
2-phase
x’ ≠ x’’
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
IsothermsMaxwell (Double tangent)Two-phase boundary
It should be instead
It should be (Gibbs)
T<TC
Standard
Critical point
Maxwell
Maxwell
Phase equilibrium in reacting Coulomb system
T’ = T’’ P’ = P’’
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
neutral species
Phase - In1’ + n2’ +…+ nk’
Phase -IIn1’’ + n2’’ +…+ nk’’
ϕ’ ϕ’’
Particle Exchange
Equilibrium reactionsab a + b
Uranium – Oxygen systemμU’(P,T, x’) = μU’’(P,T, x”)μO’(P,T, x’) = μO’’(P,T, x”)
Charged speciesNB! - Chemical potentials of charged species
are not equal
For example: Iosilevskiy I., Encyclopedia of Low‐T Plasmas. III‐1 (suppl)Moscow, 2004
(reduced number of basic units)
(Gibbs – Guggenheim conditions)
Bulk potential
Bulk potential
(Gibbs)
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
(Guggenheim)
Phase equilibrium in reacting Coulomb system
T’ = T’’ P’ = P’’
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
neutral species
Phase - In1’ + n2’ +…+ nk’
Phase -IIn1’’ + n2’’ +…+ nk’’
ϕ’ ϕ’’
Particle Exchange
Equilibrium reactionsab a + b
Uranium – Oxygen systemμU’(P,T, x’) = μU’’(P,T, x”)μO’(P,T, x’) = μO’’(P,T, x”)
Charged speciesNB! - Chemical potentials of charged species
are not equal
NB! Electro-chemical potentials are equal
NB! Potential drop at mean-phase interface in equilibrium Coulomb system
For example: Iosilevskiy I., Encyclopedia of Low‐T Plasmas. III‐1 (suppl)Moscow, 2004
(reduced number of basic units)
(Gibbs – Guggenheim conditions)
Bulk potential
Bulk potential
(Gibbs)
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
(Guggenheim)
11
. . . . . . . . . . . .
kk
μ
μ
μ
μ
′′
′′′
=
=
′
( , , )( , , ) kk k kk kP T x Z e P T x Z eμμ μ ϕ μϕ′ ′ ′= ′′ ′′ ′′++ == ′′
Δϕ(T) = ϕ’ – ϕ”
kμNon‐local
Well‐defined
Electrostatics of phase boundaries in Coulomb systems
Terrestrial applications
2000 4000 6000 8000 10000 120000,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
Δϕ(Τ
) =
ϕ liqui
d(Τ )
− ϕ va
por(Τ
), V URANIUM
Gas-Liquid Interface Melting point (T=1400 K) Critical point (T=13000 K)
T, K
Quark-Hadron phase transition in NS
eΔϕHQ = (μe)Hardron phaseb – (μe)Quark phase
eΔϕHQ ≈ 200 MeV !!
Electrostatic (Galvani) potential
Iosilevskiy & Gryaznov, J. Nucl. Mat. (2005)
Классическоеплавление
Квантовое плавление
(модели OCP(#) and OCP( ))Electrostatic “portrait” of Wigner crystal in OCP
Iosilevskiy & Chigvintsev, J. Physique (2000)
δHQ ≈ 103 fm → → E ~ 1018 V/cm
For comparison: Alcock et al., 1986: →→ E ~ 1017 V/cm
Quantum melting
Classicalmelting
eΔϕHQ ≈ 160 MeV
Bhattacharya A., Mishustin I., Greiner W., arXiv:0905.0352v1
eΔϕHQ ≈ 200MeV
ZieΔϕ = (μi)1 – (μi)2
Duality: Chemical Electrochemical potentials
(Gibbs – Guggenheim conditions)
Thermodynamic equilibrium in Coulomb systems – What’s a problem?
Electrochemical potential – well‐defined, observablebut non‐local !
Chemical potential – assumed to be local, intuitively understandable, but
have no correct definition in non‐uniform Coulomb system
( ) { ( ), ( ), ( )}k k P T xμ μ ′≠r r r r
Furtunately: In macroscopic, uniform Coulomb system
{ , , }k k kP T x Z eμ μ ϕ= +
ϕ – average electrostatic (Galvani) potential
T’ = T’’ P’ = P’’
μ1’(P,T, x’) = μ1’’(P,T, x”)μ2’(P,T, x’) = μ2’’(P,T, x”)
. . . . . . . . . . . .μk’(P,T, x’) = μk’’(P,T, x”)
Neutral species
ϕ’ ϕ’’
Equilibrium reactions
μa’(P,T, x’) = μa’’(P,T, x”)μb’(P,T, x’) = μb’’(P,T, x”)
Uranium – Oxygen system
Charged species
μ1’(P,T, x’) = μ1’’(P,T, x”) + Δϕ Z1eμ2’(P,T, x’) = μ2’’(P,T, x”) + Δϕ Z2e
. . . . . . . . . . . .μe’(P,T, x’) = μe’’(P,T, x”) – Δϕ e
μU + μO= μUOμUO + μO= μUO2μUO2 + μO= μUO3
. . . . . . . . . . .
2μO = μO2. . . . . . . . . . .
Electroneutrality
nU+ + nU++ + nUO2+ + nUO3+ = ne + nO‐ + nO2– + nUO3–
μU+ + μe = μU μUO3 + μe= μUO3–μUO+ + μe = μUO μO + μe = μO–
μUO2+ + μe = μUO2 . . . . . . . . . . .
Phase equilibrium in reacting Coulomb system(Gibbs – Guggenheim conditions)Phase - I
n1’ + n2’ +…+ nk’Phase -II
n1’’ + n2’’ +…+ nk’’
11
. . . . . . . . . . . .
kk
μ
μ
μ
μ
′′
′′′
=
=
′
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Double-tangent construction (standard procedure )
UO2
0 SC BC
PCP
0,5
1
PR
ES
SU
RE
, GP
a T, K
Non‐congruent evaporation in U‐O system
1
2000
4000
6000
8000
10000
12000
UO2
PCP
T =TC*
432 5
T >TC
SC BC
00,5
P, bar
ρ, g/cm33000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Non-congruent phase boundaries
UO2
0
SC
BC
PCP
0,5
Critical Point1
PR
ES
SU
RE
, GP
a T, K
Pressure - Temperature Diagram
1
2000
4000
6000
8000
10000
12000
2
432 5
T =TC
SCBC
00,5
CP
1
Pressure - Density Diagram
1 – Non‐congruent (total) equilibrium2 – Forced‐congruent (partial) equilibrium
BC – Boiling liquid conditionsSC – Saturated vapor conditions
• Stoichiometry of coexisting phases are different: x’ ≠ x’’
• Total phase equilibrium conditions for mixture are valid instead of the “double tangent construction for Van der Waals loops ” :
P’ = P” // T’ = T” // μi’(P,T, x’) = μi”(P,T, x”) (i = all neutral species)
NB! 2‐dimensional two‐phase region instead of standard P‐T saturation curve
NB! High pressure level of non‐congruent phase decomposition
NB! Critical point should be of non‐standard type: (∂P/∂V )T ≠ 0 (∂2P/∂V 2 )T ≠ 0It should be instead: (O/U)liquid = (O/U)vapor and {||∂μi /∂nk||T }CP = 0
No anomalous fluctuations of standard critical point !
Non‐congruent phase boundaries
(Gibbs ‐ Guggenheim conditions)
Non‐congruent melting “stripe”
Chemical Composition of Coexisting Phases
2 4 6 8 101
2
3
4
5
6
7
8
Solid
UO2
Vapor
Liquid (boiling conditions)
Sublim
ated vap
our
Mel
ting
Tmelt
(O/U)max
(boiling conditions)
CP
TEMPERATURE, 103 K
O/U
2 4 6 8 101,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
(O/U)min
Liquid (saturation conditions)
UO2
Mel
ting
Tmelt
Vapor (saturation conditions)
Tmax
CP
TEMPERATURE, 103 K
O/U
Liquid (O/U = 2.0) Vapor (O/U > 2.0)
First vapor bubbles in boiling UO2.0(oxygen enriched)
Last liquid drops in vapor UO2.0(oxygen depleted)
Vapor (O/U = 2.0) Liquid (O/U < 2.0)
Boiling Conditions Saturation Conditions
3000 4000 5000 6000 7000 8000 9000 10000 11000
UO2.0
0
PCP
0,5
1
PR
ESS
UR
E, G
Pa
T, K
BCSC
CP
Liquid
Vapor
P = const
1 2 3 4 5 6 7 8
0,2
0,4
0,6
0,8
1,0
BCSC
T= 10'500 K
10'000
9500
Tmax
8000
70006000
8500
CP
P, G
Pa
Density, g/cm3
CP - Critical pointBC - Boiling curveSC - Saturation curveTmax - Crycondentherm
Standard pressure-density diagram
Fischer E.A. J. Nucl. Sci. Eng. (1989)
Isotherms in two‐phase regionNon-congruent pressure-density diagram
Non-congruent evaporation in U – O system
• Isothermal phase transition starts and finishes at different pressures
• Isobaric phase transition starts and finishes at different temperatures
End‐Points of Non‐Congruent Phase Transition
NB !‐ Point of temperature maximum ‐ Point of pressure maximum ‐ Point of chemical potential extremum‐ Critical point (thermodynamic singularity)
are four different points !
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Non-congruent phase boundaries
UO2
0
SC
BC
PCP
0,5
Critical Point1
PR
ESS
UR
E, G
Pa
T, K
Maximumpressure
Maximumtemperature
Critical point
Non-Congruent Phase Transitions in Cosmic Matter and Laboratory
Two‐phase region of non‐congruent phase transition must betwo‐dimensional region (instead of one‐dimensional curve)
N‐C Phase Transition Thermodynamics
Two‐phase region in intensive variables (P‐T, μ‐T,μ‐P)
It should be instead: (O/U)liquid = (O/U)vapor and {||∂μi /∂nk||T }CP = 0
Critical pointCritical point of non‐congruent phase transition must be of non‐standard type, i.e. (∂P/∂V )T ≠ 0 (∂2P/∂V 2 )T ≠ 0
Two‐phase region in intensive variables (P‐T, μ‐T,μ‐P)
N‐C Phase Transition DynamicsParameters of non‐congruent phase transformationstrongly depend on the rapidity of transition
Hypothetical non‐congruence ofQuark‐hadron PT in high‐density matter
|← R ~ 10 km →|
Compact stars
White Dwarf
Neutron and “Strange” Stars
Hybrid StarsQuark core + Hadron Crust
|← R ~ 10 km →|
White dwarfs, Neutron stars, “Strange” (quark) stars, Hybrid stars
Supernova Collapse in the Phase Diagram
(after D.Blaschke, “Extreme Matter”, Elbrus-2010 )
|← R ~ 10 km →|
Compact stars
White Dwarf
Neutron and “Strange” Stars
Hybrid StarsQuark core + Hadron Crust
|← R ~ 10 km →|
White dwarfs, Neutron stars, “Strange” (quark) stars, Hybrid stars
Hybrid WD Mathews, Weber et al.
2006
Supernova Collapse in the Phase Diagram
(after D.Blaschke, “Extreme Matter”, Elbrus-2010 )
Non‐congruent phase transformation in two‐phase region
3000 4000 5000 6000 7000 8000 9000 10000 11000
UO2.0
0
PCP
0,5
Phase Diagram P-T of Non-congruent Evaporationi U i Di id
1
PR
ES
SU
RE
, GP
a
T, K
Liquid Vapor
CP T = const
First liquid droplets in saturated vapor Last vapor bubbles in boiling liquid
Oxygen depleted liquid! Different stoichiometry !
Oxygen enriched vapor! Different stoichiometry !
Forced congruentNon-congruent
3000 4000 5000 6000 7000 8000 9000 10000 11000
UO2.0
0
PCP
0,5
1
PR
ES
SU
RE
, GP
a
T, K
Liquid Vapor
CP T = const
First quark droplets in hadron matter
Last hadron bubblesin quark matter
Non-congruent phase transitions in compact starsHypothetical phase transitions in interior of compact stars: are they CONGRUENT or NON-CONGRUENT ?
“Dew” point“Dew” point “Bubble” point
Mixed phase
Pasta
1 2 3 4 5 6 7 8
0,2
0,4
0,6
0,8
1,0
BCSC
T= 10'500 K
10'000
9500
Tmax
8000
70006000
8500
CP
P, G
Pa
Density, g/cm3
CP - Critical pointBC - Boiling curveSC - Saturation curveTmax - Crycondentherm
• Isothermal phase transition starts and finishes at different pressures
Quark‐hadron phase transition via “mixed‐phase” and “pasta” scenarios
have the same features as non‐congruent PT !
After Fridolin Weber, WEHS Seminar, Bad Honnef, 2006After David Blaschke, WEHS Seminar, Bad Honnef, 2007
Hypothetical phase transitions in ultra-dense matter:are they CONGRUENT or NON-CONGRUENT ?
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Non-congruent phase boundaries
Double-tangent construction (standard procedure )
UO2
0
SC
BC
PCP
0,5
Critical Point1
PR
ESS
UR
E, G
Pa
T, K
CP ?
? ‐ Forced‐congruent phase transition
‐ Non‐congruent phase transition
Phase diagram of quark-hadron matter
Iosilevskiy I. / Int. Conference “Physics of Neutron Stars”, St.‐Pb. Russia, 2008 T. Endo, T. Maruyama, S. Chiba, T. Tatsumi / arXiv:0601017v1
Hypothetical phase transitions in ultra-dense matter:are they CONGRUENT or NON-CONGRUENT ?
R.Pisarski & L.McLerran, EMMI‐Wroclaw /2009/, QCD‐Bad Honnef /2010/
Hypothetical phase diagram with Triple or Quadruple Point
Quadruple Point
Hypothetical phase transitions in ultra-dense matter:are they CONGRUENT or NON-CONGRUENT ?
R.Pisarski & L.McLerran, EMMI‐Wroclaw /2009/, QCD‐Bad Honnef /2010/
Hypothetical phase diagram with Triple or Quadruple Point
Quadruple Point
NON-CONGRUENT ?
What is this – Triple and Quadruple points in Non-Congruent phase transition ?
QHPT: Two macroscopic phases
(Gibbs‐Guggenheim conditions)1‐dimensional system { μb } Forced‐congruent PT
Separate EOS‐s for quark and hadron phasesNo critical point !
Unique EOS for quark and hadron phases (like in U‐O)Critical point could exist !
L.Satarov, M.Dmitriev, I.MishustinPhys. At. Nucl. (2009)
CP
A
B
(bulk Gibbs conditions for all species)2‐dimensional system { μb, μe} Non‐congruent PT
Separate EOS‐s for quark and hadron phases –● 2‐dimensional zone No critical point !
Unique EOS for quark and hadron phases (like in U-O)Non‐congruent critical point could exist !
NCP
A
B
?
QHPT: Mixed phase scenario
Envelope
Outer crust
Inner crust
“Pasta structure”Neutron star
QHPT: Structured mixed phase concept ”pasta”
Wigner-Seitz “average cell” approximation
Maruyama T., Tatsumi T., Voskresenskiy D., Tanigava T., Chiba S., Phys.Rev. C 72 (2005)
Nuclear pasta structures and charge screening effect
Structured Mixed Phase Scenario ”Pasta”
Hadrons
Quarks Maxwell
The sequence of seven (or more ?) phases !Uniform (nucleons) → Drops→ Rods→ Slabs→ Bubbles→ Uniform (quarks)
Basic question:
What is the nature of Q‐H mixture:is it “solution” or charged “suspension”
?
Weak solution of quarksin hadronic “see” ?
Weak solution of hadronsin quark “see” ?
1st order phase transitionNo critical point !
Standard Scenario
Pure hadronic phaseEOS1
Unique Equation of Statefor both phases
Pure quark phaseEOS2
Non‐Standard Scenario (*)
1st order phase transitionCritical point exists !
Different Equation of Statefor two phases
Why not ? (*) – just like U‐O system
(suspension)
Unique EOS for quark and hadron phases
Veronica Dexheimer & Stefan SchrammA novel approach to model hybrid stars
arXiv:0901.1748v4
After Fridolin Weber, WEHS Seminar, Bad Honnef, 2006After David Blaschke, WEHS Seminar, Bad Honnef, 2007
Hypothetical phase transitions in ultra-dense matter:are they CONGRUENT or NON-CONGRUENT ?
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
Non-congruent phase boundaries
Double-tangent construction (standard procedure )
UO2
0
SC
BC
PCP
0,5
Critical Point1
PR
ESS
UR
E, G
Pa
T, K
CP ?
? ‐ Forced‐congruent phase transition
‐ Non‐congruent phase transition
Phase diagram of quark-hadron matter
Iosilevskiy I. / Int. Conference “Physics of Neutron Stars”, St.‐Pb. Russia, 2008
Conclusions and Perspectives NICA_Dubna 2009
- Non-congruent phase transition is general phenomenon.
- Non-congruent phase transition is universal phenomenon.
- If one takes into account hypothetical non-congruence of phase transitionsin cosmic matter objects (planets, compact stars, supernova etc.) he shouldrevise totally the scenario of all phase transformations in these objects.
Neutron Stars_2008
EMMI Wroclaw_2009
PNP_2009
- We have good enough reason to expect anomalous features for hydrodynamicsof isentropic expansion for QGP fireball when thermodynamic trajectory crosses the Q-H phase boundary (congruent or non-congruent)
Critical Point and Onset of DeconfinementJINR Dubna, Russia, August 2010
Conclusions and Perspectives NICA_Dubna 2009
- Presence, location and properties of Critical Point in congruent or non-congruent variants of QHPT strongly depends on basic assumption: - What is the nature of Quark-Hadron mixture – Solution (“vodka” phase) or Suspension (“milk” phase)
- QHPT as equilibrium of macroscopic phases is equivalent to force-congruentphase transition
Neutron Stars_2008
EMMI Wroclaw_2009
PNP_2009Critical Point and Onset of DeconfinementJINR Dubna, Russia, August 2010
- We have enough reason to expect partial or total equivalence of quark-hadron phase transition (QHPT) and non-congruent phase transition (NCPT)
- QHPT under simple mixed phase scenario is equivalent to the non-congruent phase transition (in both variants: - with and without critical point)
- Equivalence of NCPT and QHPT under optimized structured mixed phasescenario (pasta) is open question
3000 4000 5000 6000 7000 8000 9000 10000 11000
Melting point
UO2
0
PCP
0,5
CP1
PRE
SSU
RE
, GP
a
T, K
FAIR SIS 300
LHC
Thank youThank you!!
Support: INTAS 93-66 // ISTC 3755 // CRDF № MO-011-0 // RFBR 06-08-01166, RAS Scientific Program “Physics and Chemistry of Extreme States of Matter”
Extreme Matter Institute – EMMI
RHIC
Non‐congruent phase transitions in cosmic matter and in the laboratory
NICA
Acknowledgements
There will be enough challenges to keep us all happily occupied for years to come.
Hugh Van Horn (1990)( Phase Transitions in Dense Astrophysical Plasmas )
SupportVladimir Fortov (Russia)Claudio Ronchi (Germany)Boris Sharkov (Russia)Dieter Hoffmann (Germany)
INTAS 93-66 // ISTC 2107, 3755 // CRDF MO-011
RAS Scientific Program:“Physics and Chemistry
of Extreme States ofMatter”
Collaboration:Victor Gryaznov (Russia)Eugene Yakub (Ukraine)Alexander Semenov (Russia)Vladimir Youngman (=“=)Lev Gorokhov (=“=)Michael Brykin (=“=)Andrew Basharin (=“=)Michael Zhernokletov (=“=)Michael Mochalov (=“=)Temur Salikhov (Uzbekistan)= = = = = = = = = = = = = = =
Claudio Ronchi (JRC, Karlsruhe)Gerard J. Hyland (Warwick, UK)
MIPT Research & Educational Center“High Energy Density Physics”
Extreme Matter Institute ‐ EMMI