Controlling the material properties under extreme conditions and in the

vicinity of phase transitions

WORK CYCLE RECOMMENDED FOR THE STATE PRIZE OF UKRAINE IN SCIENCE AND TECHNOLOGY IN 2019

NOMINATED BY THE ACADEMIC COUNCIL OF IVAN FRANKO NATIONAL UNIVERSITY OF LVIV 01.02.2019

Institutions

• Ivan Franko National University of Lviv, Ministry of Education and Science of Ukraine (2)

• Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, Lviv (2)

• National Science Center Kharkiv Institute of Physics and Technology, Akhiezer institute for theoretical physics (NSC KIPT) (3)

Publications

The work consists of 148 publications, including 6 monographs, 4 chapters in collective monographs, 2 reviews and articles in scientific journals referenced by SCOPUS, as well as in 2 popular scientific papers. According to ISI Web of Knowledge, the scientific works included in the cycle received about 1780 quotes, and their h-factor is 22, while according to Google Scholar the corresponding numbers are 2285 and 28. During this period 4 Dr.Sci. and 18 Ph.D. theses were defended.

Participants from Lviv

Plevachuk Yuriy, born in 1958, doctor of physical and mathematical sciences, senior researcher, head of Research and Development department of Ivan Franko National University of LvivSklyarchuk Vasyl, born in born in 19591959, , doctor of physical and mathematical sciences, senior researcher of Ivan Franko National University of LvivBrykBryk TarasTaras, , born in 1963, 1963, doctor of physical and mathematical sciences, Research Deputy Director of the Institute for Condensed Research Deputy Director of the Institute for Condensed Matter PhysicsMatter PhysicsKozlovskiiKozlovskii MykhailoMykhailo, , born in 19521952, , doctor of physical and mathematical sciences, professor of the Institute for Condensed of the Institute for Condensed Matter PhysicsMatter Physics

Participants from NSC KIPT

Peletminskii Olexander,, born in born in 1975, 1975, PhD (PhD (physical and mathematical sciences)), , senior researchersenior researcher

Slyusarenko Yuriy, , born in born in 19571957, , doctor of physical and mathematical sciences, professor, f, fullull member of member of NNASU, ASU, head of departmenthead of department

Sotnikov Andriy, , born in born in 1983, 1983, ((physical and mathematical sciences)), , senior researchersenior researcher

Controlling the material properties under extreme conditions and in the vicinity of phase transitions

The aim of the work is to describe and analyze the phase The aim of the work is to describe and analyze the phase states, which arise in materials under extreme conditions states, which arise in materials under extreme conditions and possess new and unusual properties, in particular in and possess new and unusual properties, in particular in the vicinity of the phase transformation points, in order to the vicinity of the phase transformation points, in order to obtain new knowledge about materials and their possible obtain new knowledge about materials and their possible application in qualitatively new technologies of the future. application in qualitatively new technologies of the future. The work cycle covers aThe work cycle covers a complex study of different types complex study of different types of phase transformations in various physical systems, in of phase transformations in various physical systems, in wide ranges of control parameters such as temperature, wide ranges of control parameters such as temperature, pressure and external fieldpressure and external field. .

Controlling the material properties under extreme conditions and in the vicinity of phase transitions

The novelty and reliability of the results are based on The novelty and reliability of the results are based on the combination of three main methods of study of the combination of three main methods of study of physical phenomena: physical phenomena:

•• microscopic theories, microscopic theories,

•• firstfirst--principle computer principle computer ssimulationsimulations, ,

•• precise experiments at extreme thermodynamic precise experiments at extreme thermodynamic conditions in conditions in nnationalational and European laboratories.and European laboratories.

Controlling the material properties under extreme conditions and in the vicinity of phase transitions

The methods of research proposed and implemented by The methods of research proposed and implemented by the authors allowed to combine a number of results of the authors allowed to combine a number of results of fundamental and applied importance for the following fundamental and applied importance for the following objects: magnetic systems, including highobjects: magnetic systems, including high--density ones; density ones; systems composed of alkali metal atoms in a wide range systems composed of alkali metal atoms in a wide range of temperature and pressure changes (from ultraof temperature and pressure changes (from ultra--cold cold vapor to metals) and under the influence of an external vapor to metals) and under the influence of an external electromagnetic field; complex alloys based on tellurium electromagnetic field; complex alloys based on tellurium and selenium at different temperature ranges and and selenium at different temperature ranges and concentrationsconcentrations

Controlling the material properties under extreme conditions and in the vicinity of phase transitions

The research opens the prospects for using the obtained The research opens the prospects for using the obtained results in metallurgy, instrumentation and engineering, results in metallurgy, instrumentation and engineering, space technology, for development of a number of new space technology, for development of a number of new composite materials of special purpose: anticomposite materials of special purpose: anti--friction wearfriction wear--resistant, electrical, magnetic; with the development of resistant, electrical, magnetic; with the development of atomic lasers, supersensitive optical switches, devices for atomic lasers, supersensitive optical switches, devices for focusing and energy storage in solar panels in dark focusing and energy storage in solar panels in dark weather, and also for controlling the group speed of the weather, and also for controlling the group speed of the light in a Bose condensate (up to its complete stop!) with light in a Bose condensate (up to its complete stop!) with the help of an external magnetic field.the help of an external magnetic field.

Theory of spatially-periodic states in Bose-Einstein condensate (BEC)

Periodic phases in BEC are obtained and investigated(analog of the superfluid crystal)

A.S.A.S. Peletminskii, S.V.Peletminskii, S.V. Peletminskii, and Yu.V.Peletminskii, and Yu.V. Slyusarenko,Slyusarenko, Laser Phys., 2002, Vol. 12, No.1 p. 162Laser Phys., 2002, Vol. 12, No.1 p. 162--185185..

A.S.A.S. Peletminskii, S.V.Peletminskii, S.V. Peletminskii, and Yu.V.Peletminskii, and Yu.V. SlyusarenkoSlyusarenko, , Theor. Math. Phys., 2000, Vol. 125, No.1, p. Theor. Math. Phys., 2000, Vol. 125, No.1, p. 14311431--1452; doi: 10.1007/BF02551046.1452; doi: 10.1007/BF02551046.

Ultaslow-light phenomenon

g =/

cvn nω ω+ ⋅∂ ∂

212 2( , ) 1 ( )

2n ng

k iα β

αβαβ βα βα

ω σπ ω ε γ

− −= +

− Δ +∑k kε

The optical pulses can be slowed in the regions of high transparency and strong dispersion (close to resonances) down to

Yu. Slyusarenko and A. Sotnikov. Physical Review A 78, 053622 (2008)

3-level system

3 (l=1)

2 (l=0)

1 (l=0)

( ) iαβ αβσ ≈k kd

Refractive index Transmitted light

n ≈ ε300 /gv м c∼

Slowing of microwave radiation

3 -3 16 -31 210 cm | | 10 cmn n− << − <<

2

1

133 Cs : 9 2εΔ =hf . GHz

610γ − Hz∼

Cesium atoms in the BEC state with the density 13 -3

1 1.3 10 смn = ⋅

Group velocity of the pulses:

g 0,06 cm/sv ≈

Yu.V. Slyusarenko, A.G. Sotnikov. Journal of Low Temperature Physics 2008, V.150, N.3/4

Dam

ping

fa

ctor

Ref

ract

ive

inde

xFrequency detuning (µHz)

Controlling of the light velocity by an external magnetic field

π-signal withconstant frequency

mF=-2mF=0

3P3/2

3S1/2

Res

onan

ce fr

eque

ncie

s (M

Hz)

Magnetic field (Gauss)Magnetic field (Gauss)

Gro

pup

velo

city

(m/s

)Tr

ansm

itted

ligh

t

Zeeman splitting

Yu. Slyusarenko and A. Sotnikov. PhysPhys. . LettLett. . AA, 2009, , 2009, VolVol. 373, . 373, pp. . 13921392--13951395..

Filtering of optical pulses by atomic BEC

Yu.V. Slyusarenko, A.G. Sotnikov, Low Temperature Physics, 2010, V.36 р.671

First pass Second pass

Bose-Einstein condensation of photons in ideal atomic gases

The realization of a BEC of photons in thermodynamic equilibriumwith the ideal Fermi- and Bose-gases is proposed. Atoms can be in two (ground and excited) states. Photons are confined by mirrors.

Yu.Yu. Slyusarenko, A.Slyusarenko, A. Kruchkov,Kruchkov, PhysPhys.. RevRev.. AA,, 20201313, Vol.8, Vol.888, No.5, , No.5, 013615 (1013615 (1--12) 12)

Photon fraction in the condensate

nph0

nph

( )3 2

0* *

1 11 expph phс с

Tn T nT T T

⎧ ⎫⎪ ⎪⎡ ⎤⎛ ⎞ ⎛ ⎞⎪ ⎪⎟ ⎟⎪ ⎪⎜ ⎜⎢ ⎥⎟ ⎟≈ − −Δ −⎜ ⎜⎨ ⎬⎟ ⎟⎢ ⎥⎜ ⎜⎟ ⎟⎜ ⎜⎪ ⎪⎝ ⎠ ⎝ ⎠⎢ ⎥⎪ ⎪⎣ ⎦⎪ ⎪⎩ ⎭

“Avalanche”-condensation

regime

( )1

3 20 1 ,

c

Tn T nTα

⎧ ⎫⎪ ⎪⎛ ⎞⎪ ⎪⎟⎪ ⎪⎜ ⎟≈ −⎜⎨ ⎬⎟⎜ ⎟⎜⎪ ⎪⎝ ⎠⎪ ⎪⎪ ⎪⎩ ⎭

Density of the atomic BEC

*c cT T≈

N.P.N.P. Boychenko, Yu.V.Boychenko, Yu.V. Slyusarenko,Slyusarenko, Cond. Matter Phys., 2015, Vol. 18, No 4, 43002 (1Cond. Matter Phys., 2015, Vol. 18, No 4, 43002 (1––18); doi: 18); doi: 10.5488/CMP.18.4300210.5488/CMP.18.43002..

“Stopped light”

Due to “avalanche” condensation of almost all photons below critical temperature, and because the group velocity is zero for

condensed photons, this regime can be viewed as“the stopped light”.

In addition, the regimes of inverse occupation of atomic levels by the temperature lowering (without employing artificial

electromagnetically-induced transparency) are suggested.

( )0

0gk

d kv

dkω

=

⎛ ⎞≡ =⎜ ⎟⎝ ⎠

Atomic and photonic BEC for the everyday human needs

Nonlinear optics: creation of extremely sensitive optical switches (due to low laser power)Data storage (?)Sensitive detectors of magnetic fields (group velocity strongly depends on the atomic spectrum)Quantum information devices (?)Filters for electromagnetic pulses

Stopping of electromagnetic pulsesCreation of new laser sourcesFocusing and accumulating of the solar energy in cloudy weather

BECt=0t=0 tt 10 10 µµss

Pulse is not distortedPulse is not distorted

((the intensity is reduced onlythe intensity is reduced only))

Slowing of electromagnetic pulses

Quantum magnetism of three-component fermionic mixtures in optical lattices

The finite-temperature phase diagram is obtained for the first time;Thermodynamic properties of phases and transitions are comprehensively investigated;Crucial advantages of these mixtures for approaching magnetic ordering are pointed out(higher entropy).

Magnetism is Magnetism is beyond beyond the reach the reach at Sat S>0.7Nk>0.7NkB B ((experimental situationexperimental situation) )

A. A. SotnikovSotnikov, , Physical Review APhysical Review A 9292,, 023633 (2015).023633 (2015).

Magnetism isMagnetism is within the within the reachreach atat S>0.7NkS>0.7NkB B ((experimental situationexperimental situation) )

Experimentalrealization of samples

Application as universal quantum simulators

High-Tcsuper-conductivity

TwoTwo--component mixturecomponent mixture ThreeThree--component mixturecomponent mixture

Self-lubricated bearings in car engines (Cu-Sn-Pb, Al-Pb, Al-Bi, Al-Si-Pb, Al-Si-Bi) Composite superconductors (Cu-V)Granular GMR (Cu-Co)Smelting of Ag (Ag-Pb-Zn)Electrical contacts and switches (Ni-Ag)

Production problems:

Rapid phase separation prevents the production of finely dispersed mixtures with the prospect of practical applicationHigh temperatures

Causes of rapid phase separation:

gravity-dependent sedimentationMarangoni convection etc.

The The monothecticmonothectic systems studied are promising materials for systems studied are promising materials for finely dispersed mixturesfinely dispersed mixtures

Important information about the effect of Important information about the effect of thermocapillarythermocapillaryconvection on the process of phase separation in metal convection on the process of phase separation in metal melts under microgravity conditions, was obtained. The melts under microgravity conditions, was obtained. The formation of the dispersed melt structure was studied and formation of the dispersed melt structure was studied and the density of the droplet flow of one of the phases was the density of the droplet flow of one of the phases was calculated along the other matrix, and also the calculated along the other matrix, and also the temperature and temperature dependences of this temperature and temperature dependences of this process were investigated.process were investigated.

Investigation of critical phenomena in Investigation of critical phenomena in monotecticmonotectic systemssystemsin laboratory conditions and in spacein laboratory conditions and in space

Marangoni convectionCritical parametersNucleation

Determination of binodal lines, based on the electrical conductivity and viscosity data

Determination of separation surfacesDetermination of separation surfacesin liquidin liquid--liquid phasesliquid phases

The Association Agreement between Ukraine and the EU allows the transition to economic integration, which involves transition to European standards.

This means that according to the EU and EU This means that according to the EU and EU Directives (WEEE "Waste Electrical and Electronic Directives (WEEE "Waste Electrical and Electronic Equipment" and 2002/95 / EC "Restriction of the Equipment" and 2002/95 / EC "Restriction of the Use of Some Hazardous Substances (Use of Some Hazardous Substances (RoHSRoHS) in ) in Electrical and Electronic Equipment"), the use of Electrical and Electronic Equipment"), the use of leadlead--free solders instead of traditional free solders instead of traditional SnSn--PbPb will be will be mandatory.mandatory.

In this regard, the deployment of domestic production of lead-free solders can be more cost-effective than importing foreign analogues.

New materials for leadNew materials for lead--free soldersfree solders

The purpose: The methods and technological processes for the implementation of nanoparticles in materials for new lead-free solders based on Sn are proposed. Experimental samples of nano-dispersed materials for the solders Sn-Co, Sn-Cu-Ag (SAC) with metallic and nonmetallic nanoparticle impurities for use in stepwise soldering mode in different temperature ranges were obtained. The nanoparticles stabilize the structure of the solder, which undergoes during the crystallization significant modifications under external influences (electric and magnetic fields, temperature gradients, cooling velocities, vibrations), prevent the formation of frictional fissures and the spread of contacts, reduce graininess, and improve wetting of the surface.

Innovative aspect. The technology of obtaining materials for solders in the form of thin foil or ribbon of thickness 20-30 μm by the method of fast quenching is used. The shape of these tapes is convenient for soldering wide sections with precisely defined sizes, which is important for the connection of composites with metal matrices.

Modification of structurally sensitive properties of materials for production of new lead-free solders by nanoparticles

Microstructure (SEM) of soldered joints of SAC305 alloy with admixtures of Al2O3 nanoparticles

Solder in the form of a ribbon obtained by fast quenching, used for soldered joints of large surfaces

Positive influence of ceramic Positive influence of ceramic nanoparticlesnanoparticles on on mechanical properties of leadmechanical properties of lead--free soldersfree solders

Morphology and growth of the Morphology and growth of the interphaseinterphase layer of IMCS on solder / Cu borderlayer of IMCS on solder / Cu border

b)

SEM images (a) SAC387(b) (SAC387)99.9(nanoCo)0.1

Samples of the cross-section of solders were obtained using a standard metallographic technique

a)

Reduction of intermetallic layers

Influence of carbon nanotubes on the physical properties of lead-free solders

carbon carbon nanotubesnanotubes

carbon carbon nanotubesnanotubes

coated with Aucoated with Au

Nanoparticles TiO2, coated by Au

Addition of carbon nanotubes in certain proportions:Improves mechanical properties (strength,

shear resistance, plasticity)Improves solder solubility of the surfaceDoes not affect the electrical characteristicsPrevents the formation of intermetallics

LeadLead--free soldered free soldered nanoparticlesnanoparticles are the key to are the key to miniaturizing the contacts in electronic devicesminiaturizing the contacts in electronic devices

27

Model of micro-separation process

The metastable non-equilibrium quasieutectic

structure in the melt

Areas with different thermodynamic stability, which, like in monotectics, are separated by spinodaland binodal lines, and are abnormal concentration fluctuations.

At.% Bi50 55 60 65

Tem

pera

ture

, K

400

500

600

700

800

900

The similarity of systems with monotechics and eutectics with respect to the mechanism of phase decay and crystallization is proved: the systems are not solutions, but the two-phase systems of high dispersion

In In monotecticmonotectic systems, temperaturesystems, temperature--time regimes time regimes regulate the size of particles of one phase in another, regulate the size of particles of one phase in another, which leads to macroscopic separation.which leads to macroscopic separation.

In eutectic systems, as a special case of systems with In eutectic systems, as a special case of systems with limited solubility of components, the size of parts of limited solubility of components, the size of parts of one of the phases, varying in temperature changes, one of the phases, varying in temperature changes, do not reach such sizes as in do not reach such sizes as in monotecticsmonotectics, and , and sedimentation stability persists to the temperature of sedimentation stability persists to the temperature of the beginning of solidification.the beginning of solidification.

Free energy of the Free energy of the IsingIsing model in the outer fieldmodel in the outer field

( )

( )

( ) ( )

2 202 0 1 2

2 2 2

12 2 2 22( 2) 2

0 2

lna s h

a

dd

s s a c

dd d

h a a c a c

F F F F

F kTN chh F h

F kTN h h

F kTN e h h h e h h

γ γ τ γ τ

γ +

+ +

= + +

= − − + + +

= − +

⎡ ⎤= − + − +⎢ ⎥

⎣ ⎦

00 1 2; ln lnp

c ah p E Eτ δβ= = =

The marginal value of the The marginal value of the fieldfieldKozlovskiiKozlovskii M.P. Phase Transition M.P. Phase Transition ((2007).2007).

( )1

0

; /ka c c

c T T Tf

τ τ τ= = −

Temperature and field behavior of the order parameter11 ( )( )T a c

dFM h hN d

δσ00= − = +H

-- crossover form of state equationcrossover form of state equation

2 5dδ = + =

βτ )(0 0 −=⇒= tMMh δτ /100 hMM h=⇒=

302.0

In extreme casesIn extreme cases

=β

The order parameter of the system as a function of temperature (The order parameter of the system as a function of temperature (left) at different values of the field, left) at different values of the field, and as a function of the field (right) for some temperature valuand as a function of the field (right) for some temperature valueses

M.KozlovskiiM.Kozlovskii, , R.RomanikR.Romanik, JML, 2012, JML, 2012

Ab initio simulations of condensed systems at extreme conditions

•• Classical equations of motion for NClassical equations of motion for N ionsions

real mass of ions real mass of ions

•• Each time step one calculatesEach time step one calculates Nz/2 Nz/2 eigenfunctionseigenfunctions of Kohnof Kohn--Sham HamiltonianSham Hamiltonian

HellmannHellmann--Feynman Feynman forces acting on ionsforces acting on ions

ExchangeExchange--correlation effects at high pressures correlation effects at high pressures have to account for gradient corrections have to account for gradient corrections ((GGAGGA)): BLYP, PBE, PW91, : BLYP, PBE, PW91, …………

)()( tFtRm iii =

),()(),(2

2

rrrrrrdrrWH xc ′+′−′

′+′+∇

−= ∫ μρ

Liquid Rubidium: new structural transformationat P~12 GPa was found

Existence of a structural transition in moltenExistence of a structural transition in molten RbRb at pressuresat pressures ~ ~ 12 12 GPaGPa was established was established from nonfrom non--monotonic behavior of structural functions monotonic behavior of structural functions ((pair distribution functions and pair distribution functions and structure factorsstructure factors) ) and dynamic quantitiesand dynamic quantities: : diffusivity and speed of sound propagationdiffusivity and speed of sound propagation. . Emergence of electron localization was found Emergence of electron localization was found ((electron localization functions electron localization functions -- ELFELF)) at at high pressures in moltenhigh pressures in molten RbRb ((blue areas between ionic cores in the right figureblue areas between ionic cores in the right figure).).

T.BrykT.Bryk, S. , S. DePanfilisDePanfilis, , F.A.GorelliF.A.Gorelli, , E.GregoryanzE.Gregoryanz, , M.KrischM.Krisch, , G.RuoccoG.Ruocco, , M.SantoroM.Santoro, , T.ScopignoT.Scopigno, , A.P.SeitsonenA.P.Seitsonen. Phys. Rev. . Phys. Rev. LettLett. V. 111, 077801 (2013). V. 111, 077801 (2013)

ELF, 1.2 ELF, 1.2 GPaGPa ELF, 27.4 ELF, 27.4 GPaGPa

Emergence of exotic transverse modes in molten Lithium at high pressures

Upon pressurizing one Upon pressurizing one observes another highobserves another high--frequency branch of frequency branch of collective excitationscollective excitations, , which exists only in the which exists only in the second pseudosecond pseudo--BrillouinBrillouinzonezone. .

Existence of those unusual transverse modes at high pressures waExistence of those unusual transverse modes at high pressures was s confirmed by several groups for molten Na, Zn, confirmed by several groups for molten Na, Zn, TlTl, Fe, Fe

T.BrykT.Bryk, , G.RuoccoG.Ruocco, , T.ScopignoT.Scopigno, , A.P.SeitsonenA.P.Seitsonen. J. Chem. Phys. V. 143, 104502 (2015). J. Chem. Phys. V. 143, 104502 (2015)

Positive dispersion of sound excitations as a criterion of discrimination between liquid- and

gas-like supercritical fluids

Experiments on inelastic XExperiments on inelastic X--ray scattering and molecular dynamics simulations for supercritiray scattering and molecular dynamics simulations for supercritical Argoncal Argonestablished a vanishing positive sound dispersion in the vicinitestablished a vanishing positive sound dispersion in the vicinity of y of WidomWidom lineline..G.G.SimeoniG.G.Simeoni, , T.BrykT.Bryk, , F.A.GorelliF.A.Gorelli, , M.KrischM.Krisch, , G.RuoccoG.Ruocco, , M.SantoroM.Santoro, , T.ScopignoT.Scopigno. Nature Phys.V.6. Nature Phys.V.6503 (2010) 503 (2010) The developed theory of dispersion of acoustic modes in supercriThe developed theory of dispersion of acoustic modes in supercritical fluids was able to explain the tical fluids was able to explain the observed its dependence on pressureobserved its dependence on pressureT.BrykT.Bryk, , I.MryglodI.Mryglod, , T.ScopignoT.Scopigno, , G.RuoccoG.Ruocco, , F.GorelliF.Gorelli, , M.SantoroM.Santoro. . J.Chem.PhysJ.Chem.Phys. V.133, 024502 (2010). V.133, 024502 (2010)

Closed circles Closed circles -- IXS experimentsIXS experimentsOpen circles Open circles –– MD simulationsMD simulations