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