Modigliani–Miller theorem

Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid or a gas below its freezing point without it becoming a solid.

A liquid below its standard freezing point will crystallize in the presence of a seed crystal or nucleus around which a crystal structure can form creating a solid. However, lacking any such nuclei, the liquid phase can be maintained all the way down to the temperature at which crystal homogeneous nucleation occurs. Homogeneous nucleation can occur above the glass transition temperature, but if homogenous nucleation has not occurred above that temperature an amorphous (non-crystalline) solid will form.

Water normally freezes at 273.15 K (0 °C or 32 °F) however it can also be "supercooled" at standard pressure down to its crystal homogeneous nucleation at almost 224.8 K (−48.3 °C/−55 °F). The process of supercooling requires that water be pure and free of nucleation sites, which can be achieved by processes like reverse osmosis, but the cooling itself does not require any specialised technique. If water is cooled at a rate on the order of 10⁶ K/s, the crystal nucleation can be avoided and water becomes a glass. Its glass transition temperature is much colder and harder to determine, but studies estimate it at about 165 K (−108 °C/−162.4 °F). Glassy water can be heated up to approximately 150 K (−123 °C/−189.4 °F). In the range of temperatures between 231 K (−42 °C/−43.6 °F) and 150 K (−123 °C/−189.4 °F) experiments find only crystal ice.

Droplets of supercooled water often exist in stratiform and cumulus clouds. Aircraft flying through these clouds seed an abrupt crystallization of these droplets, which can result in the formation of ice on the aircraft's wings or blockage of its instruments and probes, unless the aircraft are equipped with an appropriate de-icing system. Freezing rain is also caused by supercooled droplets.

The process opposite to supercooling, the melting of a solid above the freezing point, is much more difficult, and a solid will almost always melt at the same temperature for a given pressure. For this reason, it is the melting point which is usually identified, using melting point apparatus; even when the subject of a paper is "freezing-point determination", the actual methodology is "the principle of observing the disappearance rather than the formation of ice". It is, however, possible, at a given pressure to superheat a liquid above its boiling point without it becoming gaseous.

Supercooling is often confused with freezing-point depression. Supercooling is the cooling of a liquid below its freezing point without it becoming solid. Freezing point depression is when a solution can be cooled below the freezing point of the corresponding pure liquid due to the presence of the solute; an example of this is the freezing point depression that occurs when sodium chloride is added to pure water.

Constitutional supercooling

Constitutional supercooling – phase diagram, concentration, and temperature

Constitutional supercooling, which occurs during solidification, is due to compositional changes, and results in cooling a liquid below the freezing point ahead of the solid–liquid interface. When solidifying a liquid, the interface is often unstable, and the velocity of the solid–liquid interface must be small in order to avoid constitutional supercooling.

Supercooled zones are observed when the liquidus temperature gradient at the interface is larger than the temperature gradient.

$\left.{\frac {\partial T_{L}}{\partial x}}\right|_{x=0}>{\frac {\partial T}{\partial x}}$

or

$m\left.{\frac {\partial C_{L}}{\partial x}}\right|_{x=0}>{\frac {\partial T}{\partial x}}$

The slope of the liquidus phase boundary on the phase diagram is $m=\partial T_{L}/\partial C_{L}$

The concentration gradient is related to points, $C^{LS}$ and $C^{SL}$, on the phase diagram:

$\left.{\frac {\partial C_{L}}{\partial x}}\right|_{x=0}=-{\frac {C^{LS}-C^{SL}}{D/v}}$

For steady-state growth $C^{SL}=C_{0}$ and the partition function $k={\frac {C^{SL}}{C^{LS}}}$ can be assumed to be constant. Therefore the minimum thermal gradient necessary to create a stable solid front is as expressed below.

${\frac {\partial T}{\partial x}}<{\frac {mC_{0}(1-k)v}{kD}}$

For more information, see the equation (3) of

In plants

Some plants are able to supercool the fluid in their cells cytosol and vacuole and thereby survive temperatures down to −40 °C. This is partly achieved through the synthesis of antifreeze proteins that prevent ice nucleation.

In animals

The osmotic concentration of the body fluids of fish is lower than the osmotic concentration of sea water. Therefore the freezing point of fish can be above the temperature of sea water. The freezing point can be lowered by anti-freeze agents, but there are some fish (within the teleostei infraclass) whose freezing point is higher than the temperature of the surrounding sea water, and therefore the body fluids of these fish are supercooled. These fish must live well below the water surface, because they must not come into contact with ice nuclei (otherwise they would freeze immediately).

Applications

One commercial application of supercooling is in refrigeration. For example, there are freezers that cool drinks to a supercooled level so that when they are opened, they form a slush. Another example is a product that can supercool the beverage in a conventional freezer. The Coca-Cola Company also briefly marketed special vending machines containing Sprite in the UK, and Coke in Singapore, which stored the bottles in a supercooled state so that their content would turn to slush upon opening.

See also

• Amorphous solid
• Pumpable ice technology
• Subcooling
• Ultracold atom
• Viscous liquid
• Freezing rain

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Further reading

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• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
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  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

External links

• Video example
• Video example #2
• Video example #3
• Supercooled liquids on arxiv.org