Phase separation

Miscible and immiscible liquids

• Alcohol and water mixture: single homogeneous liquid exists over a broad compositional range of relative alcohol and water concentrations.
• Oil and water mixture: spontaneous separation into two liquids, with the less dense floating on the surface of the more dense one.
• Vigorous shaking: small, dispersed droplets of one of the liquids in a matrix of the other liquid.

• Viscous liquids: more dense liquid will rapidly sink to the bottom of the flask, while the less dense liquid rises to the surface.
• Highly viscous immiscible liquid mixtures: Reduction in the rate of separation.
• Rapid freezing: frozen solid consists of dispersed droplets of one material in a continuous matrix of the other.
• The identity of the matrix and droplet materials would be controlled by their relative concentrations: Oil in water vs. water in oil

Thermodynamics of liquid/liquid phase separation

• Liquid-liquid immiscibility, or phase separation, is a common phenomenon in liquid systems and it is also a common in melts.
• Far more binary glass forming melts exhibit liquid-liquid immiscibility than exhibit homogeneous liquid behavior.
• Why do some liquids or melts separate into two liquid phases while others remain homogeneous??
• If mixing of two components yields a lower free energy, the mixture will remain homogeneous.
• If, however, separation of the mixture into two components yields a lower free energy, separation will occur if allowed by kinetic considerations.

​

​

​

​

• The entropy of mixing, ΔS_m will always be positive since X₁ and X₂ are less than unity (the logarithm of a number less than unity is negative).
• The value of ΔG_m, will be either positive or negative, depending on the value of ΔH_m.

​

​

​

​

• If ΔH_m is negative, ΔG_m will always be negative, with a minimum at X₁ = X₂, and the system will not exhibit phase separation: Characteristics of two miscible liquid.
• If ΔH_m is positive, there will be a competition between the contributions from ΔH_m and TΔS_m , and the sign on ΔG_m will be a function of temperature T.
• At T = 0K, the entropy term TΔS_m, will be zero, and the free energy will be positive: The mixture will separate into the end member components if allowed by kinetics.

• At a sufficiently high temperature (upper consolute, or critical temperature, T_c), TΔS_m term will always dominate and the free energy of mixing will always be negative: Characteristics of single miscible liquid.

​

​

• System will be homogeneous for any temperature above T_c.
• At intermediate temperatures (between 0 and T_c), competition between the enthalpy and entropy terms will result in a saddle in the free energy versus composition curve.

​

​

• This curve has two minima, which approach each other with increasing temperature, until they merge at T_c.
• If a tangent is drawn between the minima, the free energy will be less if the liquid separates into two phases, than if it remains homogeneous so that the free energy is given by the solid curve.

​

• The actual compositions of phases A and B are obtained from the abscissa of the phase diagram.
• This compositions will be a function of temperature, with a decreasing difference in composition as the temperature approaches T_c.
• The line connecting phases A and B is known as a tie-line.
• The tie-line will connect the compositions of the phases in equilibrium at a specified temperature.
• A different tie-line exists for each temperature, with different compositions for the two phases.

​

• The relative concentrations of phases A and B can be determined by the familiar lever rule used in all phase diagrams.
• The fractional concentration, or relative proportion, of phase A is given by the distance between the bulk composition Y and the composition of B, divided by the distance from A to B.

Immiscibility dome and spinoidal decomposition

• Plot of limiting phase compositions as function of temperature: Phase diagram.
• Phase diagram resulting from phase separation exhibits a symmetric dome, within which the liquid will spontaneously separate (if allowed by kinetics), into two components, or phases.
• Compositions of these two phases are given by their location on the dome.
• The region inside the curve describing this dome is called the binodal, immiscibility limit or boundary, or the phase boundary.
• It is also often called the miscibility gap (region with a lack of miscibility) or immiscibility region (region where immiscibility occurs).

• Area within the immiscibility dome known as the spinodal: Result of the points of inflection of the free energy curve.
• A melt within this dome will spontaneously separate if the mobility of the ions is great enough.
• If the initial composition of the melt is outside the spinodal dome, phase separation will not take place spontaneously, but will require the formation of nuclei.

​

Mechanisms of phase separation

• Thermodynamic model only predicts when phase separation will occur. Additional factors decide how the phase separation will occur.
• Two mechanisms by which phase separation can actually occur.
• The first mechanism is similar to the precipitation of crystals from a melt, where a nucleus is formed and then grows with time: Nucleation and growth mechanism
• Many of the same factors which control crystal formation also affect phase separation by this mechanism.
• Second mechanism is termed spinodal decomposition: This mechanism involves a gradual change in composition of the two phases until they reach the immiscibility boundary.
• Which of these mechanism will be preferred is determined by the local curvature of the free energy of mixing at the bulk composition of the melt.

​

• Compositions between points a and c, and those between points d and b, where c and d are inflection points on the free energy of mixing curve, lie in regions where the second derivatives of the free energy of mixing with composition are positive.
• Since thermodynamics require that the compositions change to the lowest energy states, the actual compositions will change to those represented by points a and b.
• If the bulk composition lies in the region a-c, the composition of one phase must change to that of liquids near point b in order to reduce the free energy of mixing.

​

• Any attempt to alter the composition of a bulk liquid lying in either region by a slight amount, the free energy of mixing will increase and the system will tend to return to the homogeneous state.

• Bulk compositions in the region between points c and d: second derivative of the free energy of mixing is negative.
• A small change in composition by separation into two phases will decrease the free energy.
• Any fluctuation in local composition will tend to grow and the compositions of the two phases will gradually change until they reach the compositions represented by points a and b.
• Since these changes occur spontaneously, this region is unstable with regard to immiscibility. Phase separation in this region occurs by spinodal decomposition.
• The curve representing the positions of the inflection points as a function of temperature is called the spinodal boundary.

Phase separation in glasses

• The liquid formed during melting of a glass batch in some cases, spontaneously separate into two very viscous liquids, or phases.
• These liquids are initially intimately mixed, complete separation into two layers would be a slow process.
• Cooling the melt to a temperature below the glass transformation region would be equivalent to freezing the immiscible liquid mixture.
• The resulting glass is now said to be phase separated as a result of liquid-liquid immiscibility.
• Since the material is now a solid, no further separation would occur unless the glass were reheated to a temperature where flow processes would allow separation to continue.

• In some cases, the glass forming liquids are so fluid that complete separation into two layers readily occurs before T_g is reached.
• If such a melt is cooled without disturbing the layers, the resulting sample is separated into two pieces of glass (core-shell glasses), each of which has a different composition and properties: Optical fiber glass

• If the melt is so viscous that the degree of separation is very small, the droplets cannot be detected without use of very high magnification and the sample appears to be a homogeneous glass.
• A large number of commercial sodium borosilicate glasses exhibit this type of phase separation.

Phase separation and crystallization of Phosphate–Silicate glass cores of preforms of fiber optics: Micro-photographs in Z-contrast mode and distribution of elements in preforms after (a) 3 and (b) 15 melting cycles of sample. 

• In many Silicate and Borate melts, liquid/liquid phase separation can be observed above or below the liquidus.
• The latter is called sub-liquidus or metastable immiscibility.
• Common binary Silicate systems which exhibit stable immiscibility above the liquidus usually contain divalent metal oxides like SrO, CaO, FeO, ZnO and MgO.
• Sub-liquidus immiscibility is often found in Silicate melts that have an S-shaped liquidus, such as Na₂O, Li₂O and BaO.
• By using phase separation process, Silica glass articles can be made by conventional glass making methods, which are much easier than those starting from a pure Silica melt.

Microstructure formation by nucleation and growth

• The mechanisms of nucleation and growth and spinodal decomposition result in quite different microstructures in the glass so formed.
• Since nucleation and growth closely resembles crystallization, the microstructure formed by this process has some similarities to that found in crystallizing samples.
• Growth occurs on individual, isolated nuclei, so that the regions of second phase formation are clearly separated.
• Since the second phase is a liquid, the surface energy will be minimized for spheres, so the second phase will occur as isolated spheres of one equilibrium composition randomly dispersed through a matrix of the other equilibrium composition.

Microstructure formation by nucleation and growth

• The spheres will have the composition of the phase with the lesser volume fraction. i.e., that which differs the most from the bulk composition.
• Since nucleation occurs randomly throughout the melt, the second phase will also occur randomly.
• Local connectivity of spheres may exist when two neighbouring spheres intersect, but the connectivity of the minor phase will generally be quite low.

(a) TEM image of pristine glass showing phase separated microstructure, (b) 3D view of spheroid phase (micro-tomography), 

Microstructure from spinoidal decomposition

• The morphology developed by spinodal decomposition will be quite different from that due to nucleation and growth.
• Both phases will gradually and continually change in composition until they reach the compositions of the equilibrium liquids.
• The interface between the phases will initially be very diffuse, but will sharpen with time.
• The second phase will be regularly distributed in space and characterized by a regular size.
• The distance between centers of either phase is termed the wavelength of the microstructure.
• Both phases will have a high degree of connectivity, so that continuous pathways through the material exist for each phase.

Microstructure formation by phase separation

Borosilicate glass

• Borosilicate glass is a type of glass with SiO₂ and B₂O₃ as the main glass-forming constituents.
• Borosilicate glasses are known for having very low coefficients of thermal expansion (~3×10⁻⁶ K⁻¹ at 20°C), about one-third that of ordinary soda-lime-Silica glasses making them resistant to thermal shock, more so than any other common glass.
• Such glass is less subject to thermal stress and is commonly used for the making reagent bottles.
• Borosilicate glass is sold under various trade names like Simax, Borcam, Borosil, Suprax, Kimax, Heatex, Endural, Schott, or Refmex, Kimble, and some (but not all) items sold under the trade name Pyrex.

​

• The composition of low-expansion borosilicate glass, such as those laboratory glasses, is approximately 80% Silica, 13% Boric Oxide, 4% Sodium Oxide and 2–3% Aluminium Oxide.
• Though more difficult to make than traditional glass due to the high melting temperature required, it is economical to produce.

Borosilicate vs. soda-lime glasses

Importance of phase separation in glasses

• An industrial application of liquid-liquid phase separation is the production of Vycor glass.
• This is made from a glass of approximate composition 8 % Na₂O, 20% B₂O₃ and 72 % SiO₂ which is heat-treated between 500°C and 800°C (liquidus is ~1100^oC).
• Liquid separation is induced and two interconnected phases form, one rich in Silica and the other rich in Boric oxide.
• When treated with dilute HCl, Silica-poor (Borate-reach) phase readily dissolves, leaving the silica-rich phase almost untouched.
• This results in a highly porous almost pure Silica glass.
• The material has been used for biological sieves.
• Further heating of the high-Silica material at ~1200°C, the pores disappear and the material becomes more compact, eventually a dense type of silica glass (Vycor) is produced.

Advantages of Borosilicate glass

• Borosilicate glass is less dense (~2.23 g/cm³) than soda-lime-Silica glass due to low atomic mass of boron.
• Softening point (temperature at which viscosity is ~10^7.6 poise) of type 7740 Pyrex is 820°C.
• Temperature differential that borosilicate glass can withstand before fracture is about 165°C, much higher than soda-lime-Silica glass, which can withstand only 37°C change in temperature
• Usages: Health ands science, Electronics (semiconductor industry in microelectromechanical systems (MEMS)), Coockware, Lighting, Optics (Most astronomical reflecting telescope use glass mirror components made of borosilicate glass because of its low coefficient of thermal expansion.)

Microstructure of manganese borosilicate glasses

• 80% Silica, 13% Boric Oxide, 4% Sodium Oxide and 2–3% Aluminium Oxide

Latest application of phase separated glass

Kinetic restrictions towards phase separation

• Since viscosity plays a major role in determining the rate of mass transport in melts, viscosity has a major effect on the kinetics of phase separation.
• Thermodynamic factors indicate that a system which exhibits liquid/liquid immiscibility should be phase separated at any temperature between absolute zero and T_c.
• Phase separation however, will not occur if the viscosity of the melt is too high.
• For most purposes, this means that no changes in morphology occur below the glass transformation region.
• Phase separation will never occur in a melt held at a temperature greater than T_c: Thermodynamic factor
• A temperature window exists between T_c and T_g where a microstructure can change by phase separation.

Kinetic restrictions towards phase separation

• If a batch is heated to a temperature above T_c, a homogeneous liquid will form.
• If this liquid could be instantaneously quenched to a temperature below T_g, a homogeneous glass would form.
• Since an instantaneous quench would prevent any mass transport, no phase separation would occur.
• We cannot actually cool a melt instantaneously: As the temperature decreases, we will encounter the upper immiscibility boundary and the melt will begin to phase separate.
• If the melt is very fluid at this temperature, a large degree of separation will occur rapidly, even if the time allowed within this temperature region is small.
• If the time allowed is large enough, a state of complete separation into two layers will be reached.
• Separation into two layers would be especially likely if the melting temperature were below T_c.

​

Core/shell structures of Fe₆₂Sn₃₄Ge₄ alloy: Growth kinetics parameters of Sn-rich phase vs. phase separation time