Reduction into a rational fraction of a thermodynamic property of the liquid state: Experimental determinations in the case of CO2andn‐butane. Extension to the other properties

1985 ◽  
Vol 82 (1) ◽  
pp. 384-393 ◽  
Author(s):  
Christiane Alba ◽  
Léon Ter Minassian ◽  
Armelle Denis ◽  
Alain Soulard
Keyword(s):  
Thermodynamic Property ◽  
Liquid State ◽  
The Other ◽  
Rational Fraction

scholarly journals II. On evaporation and dissociation. —Part I

1886 ◽  
Vol 177 ◽  
pp. 71-122 ◽  
Keyword(s):  
Free Path ◽  
Liquid State ◽  
Chemical Compounds ◽  
The Other ◽  
Complex Molecules ◽  
Gaseous State ◽  
Form Complex ◽  
Mutual Attraction ◽  
Rapid Motion ◽  
The Difference

1. The phenomena exhibited by gases when exposed to varying temperatures and pressures have been shown by many eminent observers to be explicable by an extension to molecules of the laws of motion of matter which are known to be true in the case of large bodies. Such molecules of gas are supposed to be in a state of very rapid motion, the free path of each molecule bearing a very large ratio to the diameter of the molecule. As a liquid is formed by the condensation of a gas, it is clear that its molecules are in closer proximity to each other, and that the average free path of each molecule in the liquid state cannot be nearly so great as in the gaseous state. It was pointed out by Naumann (Ann. d. Chem. u. Pharm., 1870, 155, 325; see also Ramsay, Proc. Roy. Soc., 1880, April 22 and December 16) that it is conceivable that an explanation of the closer proximity of molecules in a liquid than in a gas may be that two or more gaseous molecules have united to form complex molecular groups, analogous to those complex molecules which are known as chemical compounds, in which two or more elements exist in combination. On the other hand, it is held by some that the difference between gas and liquid is due solely to the greater proximity of the molecules in the liquid state, by reason of which they come within the sphere of mutual attraction, but do not necessarily coalesce to form groups of molecules analogous to the group of atoms in the molecule of a compound.

scholarly journals On the algebraic expression of the number of partitions of which a given number is susceptible

1851 ◽  
Vol 5 ◽  
pp. 950-950
Keyword(s):  
Rational Function ◽  
Royal Society ◽  
The Other ◽  
Rational Fraction ◽  
Algebraic Expression ◽  
Integer Number ◽  
Exponential Functions ◽  
Exact Integer ◽  
Independent Variable ◽  
Uniform Treatment

The object of this paper is to exemplify and extend the mode of analysis explained by the author in two former communications to the Royal Society “ On the Development of Exponential Functions,” and “ On Circulating Functions,” to a case in the theory of numbers in which they afford remarkable facilities, viz. that of the partitions of which a given number is susceptible. The separation of the symbols of operation from those of quantity, in the mode explained in the former of those communications, allows of the expression of the sums of certain series entering into this theory, under a form susceptible of resolution (by a theorem here given) into two portions, one of which, a rational function of the independent variable or number to be subdivided, expresses approximately, as a rational fraction, the number of partitions; the other, a periodic or circulating function, expresses the fraction, less than unity, by which the other portion differs from an exact integer number, and which, applied with its proper sign to that former portion, reduces it to an integer. In the mode of procedure here followed all subdivision into cases according to the numerical constitution of the number to be subdivided is avoided, and a uniform treatment is carried throughout.

Morphology and Intermetallics Study of (Sn-8Zn-3Bi)-1Ag Solder under Liquid-State Aging

2012 ◽  
Vol 620 ◽  
pp. 273-277 ◽  
Author(s):  
Nor Aishah Jasli ◽  
Hamidi Abd Hamid ◽  
Ramani Mayappan
Keyword(s):  
Growth Rate ◽  
Electron Microscope ◽  
Liquid State ◽  
Intermetallic Layer ◽  
Intermetallic Phase ◽  
The Other ◽  
Ag Addition ◽  
Cu Substrate ◽  
X Ray ◽  
Scanning Electron

This study investigated the effect of Ag addition on the morphology and growth rate of Cu5Zn8, Cu6Sn5 and Cu3Sn intermetallics in the Sn-8Zn-3Bi solder. The solder was prepared by mixing 1wt% of Ag into 99wt% of Sn-8Zn-3Bi solder. The intermetallics were formed by liquid-state aging, whereby the solders were reacted on Cu substrate above the melting temperature of the solder. The reflow was done at 250°C and 270°C at various soldering times. A scanning electron microscope (SEM) was used to observe the morphology of the intermetallic phase and energy dispersive X-ray (EDX) was used to identify the elemental composition. The Sn-8Zn-3Bi solder reacting with Cu substrate formed a single Cu5Zn8 intermetallic layer with a flat structure. On the other hand, the reaction between (Sn-8Zn-3Bi)-1Ag solder and Cu substrate produces Cu6Sn5 intermetallic. This Cu6Sn5 intermetallic has a scallop structure. As the soldering time increases, a second layer, identified as Cu3Sn starts to grow. The thickness of the intermetallics increases with aging temperatures and time. The addition of Ag into the Sn-8Zn-3Bi solder has significantly suppressed the formation of Cu5Zn8 intermetallic and promoted the growth of Cu6Sn5 intermetallic.

scholarly journals Polaron Dissociation at the Insulator-to-Metal Transition

1997 ◽  
Vol 11 (30) ◽  
pp. 1303-1312 ◽  
Author(s):  
P. Quémerais ◽  
S. Fratini
Keyword(s):  
Phase Diagram ◽  
Strong Coupling ◽  
Long Range ◽  
Liquid State ◽  
Large Mass ◽  
Critical Value ◽  
The Other ◽  
Phonon Coupling ◽  
Coulomb Interactions ◽  
Electron Phonon Coupling

Considering the long range Coulomb interactions between large polarons in dielectrics, we propose a model for their crystallization when no bipolarons are formed. As the density increases, the melting is examined at T=0 K. One possibility is the delocalization towards a liquid state of polarons. However, we show that this cannot happen if the electron-phonon coupling is larger than some critical value. The other competing mechanism is the dissociation of the polarons themselves, favored owing to their large mass at strong coupling. Finally, we propose a phase diagram for the insulator-to-metal transition as a function of the density and electron–phonon coupling.

Notizen: Volume Changes on Melting for Several Rare Earth Chlorides

1987 ◽  
Vol 42 (7) ◽  
pp. 777-778 ◽  
Author(s):  
K. Igarashi ◽  
J. Mochinaga
Keyword(s):  
Crystal Structure ◽  
Rare Earth ◽  
Structure Data ◽  
Liquid State ◽  
Crystal Structure Data ◽  
The Other ◽  
Melting Points ◽  
Volume Changes ◽  
Volume Increase ◽  
Molar Volumes

Molar volumes in the liquid state and melting points of several rare earth chlorides RCl3 (R = La, Pr, Nd, Gd, Dy, and Y) have been measured by dilatometry and DTA. respectively. The volume changes on melting of these chlorides were evaluated on the basis of these result and available crystal structure data. The volume increase on melting of the hexagonal chlorides from LaCl3 to GdCl3 was found to be more than 20%. On the other hand, the volume changes of the monoclinic DyCl3 and YCl3 were less than 1%.

scholarly journals XVII. On the condensation of several gases into liquids

1823 ◽  
Vol 113 ◽  
pp. 189-198 ◽  
Keyword(s):  
Sulphuric Acid ◽  
Liquid State ◽  
Royal Society ◽  
The Other ◽  
General Direction ◽  
General Application ◽  
Acid Gas ◽  
Muriatic Acid ◽  
Humphry Davy ◽  
Important Note

I had the honour, a few weeks since, of submitting to the Royal Society a paper on the reduction of chlorine to the liquid state. An important note was added to the paper by the President, on the general application of the means used in this case to the reduction of other gaseous bodies to the liquid state; and in illustration of the process, the production of liquid muriatic acid was described. Sir Humphry Davy did me the honour to request I would continue the experiments, which I have done under his general direction, and the following are some of the results already obtained: Sulphurous Acid . Mercury and concentrated sulphuric acid were sealed up in a bent tube, and, being brought to one end, heat was carefully applied, whilst the other end was preserved cool by wet bibulous paper. Sulphurous acid gas was produced where the heat acted, and was condensed by the sulphuric acid above; but, when the latter had become saturated, the sulphurous acid passed to the cold end of the tube, and was condensed into a liquid. When the whole tube was cold, if the sulphurous acid were returned on to the mixture of sulphuric acid and sulphate of mercury, a portion was reabsorbed, but the rest remained on it without mixing.

Synergetic NH3 Absorption Properties of NaBH4-LiBH4 Mixed System

2021 ◽  
Author(s):  
Machi Kanna ◽  
Hikaru Oyama ◽  
Tomoyuki Ichikawa ◽  
Keita Yamamoto ◽  
Hiroki Miyaoka ◽  
...  
Keyword(s):  
Liquid State ◽  
Lower Pressure ◽  
The Other ◽  
Mixed System ◽  
Absorption Properties ◽  
Other Hand ◽  
System P

NaBH4 does not absorb NH3 below 100 kPa, but becomes liquid state after NH3 absorption. On the other hand, LiBH4 absorbs NH3 at lower pressure than 100 kPa. Interestingly, the...

Interfacial Reactions between Sn-Ag-Cu-Fe Composite Solder and Cu Substrate

2013 ◽  
Vol 706-708 ◽  
pp. 138-141
Author(s):  
Xiao Ying Liu ◽  
Ming Liang Huang ◽  
Ning Zhao
Keyword(s):  
Intermetallic Compound ◽  
Solder Joint ◽  
Growth Kinetics ◽  
Liquid State ◽  
Composite Solder ◽  
Interfacial Reactions ◽  
The Other ◽  
Cu Substrate ◽  
Soldering Process ◽  
Small Cracks

The growth kinetics and morphology of intermetallic compound (IMC) between Sn-3Ag-0.5Cu -xFe (x= 0, 0.5wt.%, 1wt.%) composite solders and Cu substrate were investigated in the present work. The Sn-Ag-Cu-Fe/Cu solder joint were prepared by reflowing for various durations at 250°C. During soldering process, Fe particles quickly deposited in the vicinity of IMC, resulting in the formation of Fe-rich area. It was shown that Fe could effectively retard the growth of interfacial Cu6Sn5 and Cu3Sn layers during liquid-state reaction and reduce the size of Cu6Sn5 grains. Small cracks were observed in the Cu6Sn5 grains of Sn-Ag-Cu/Cu interface after reflowing for 30 min while they were not found in the other composite solders.

scholarly journals I. Considerations on the abrupt change at boiling or conden­ sing in reference to the continuity of the fluid state of matter

1872 ◽  
Vol 20 (130-138) ◽  
pp. 1-8 ◽  
Keyword(s):  
Liquid State ◽  
Abrupt Change ◽  
Plane Surface ◽  
Ordinary Language ◽  
The Other ◽  
Gaseous State ◽  
Temperature And Pressure ◽  
The One ◽  
Infinite Variety ◽  
Liquid States

When we find a substance capable of existing in two fluid states different in density and other properties while the temperature and pressure are the same in both, and when we find also that an introduction or abstraction of heat without change of temperature or of pressure will effect the change from the one state to the other, and also find that the change either way is perfectly reversible , we speak of the one state as being an ordinary gaseous, and the other as being an ordinary, liquid state of the same matter; and the ordinary transition from the one to the other we would designate by the terms boiling or condensing, or occasionally by other terms nearly equivalent, such as evaporation, gasification, liquefaction from the gaseous state, &c. Cases of gasification from liquids or of condensation from gases, when any chemical alteration accompanies the abrupt change of density, are not among the subjects proposed to be brought under consi­deration in the present paper. In such cases I presume there would be no perfect reversibility in the process; and if so, this would of itself be a criterion sufficing to separate them from the proper cases of boiling or condensing at present intended to be considered. If, now, the fluid sub­stance in the rarer of the two states (that is, in what is commonly called the gaseous state) be still further rarefied, by increase of temperature or diminution of pressure, or be changed considerably in other ways by alterations of temperature and pressure jointly, without its receiving any abrupt collapse in volume, it will still, in ordinary language and ordinary mode of thought, be regarded as being in a gaseous state. Remarks of quite a corresponding kind may be made in describing various conditions of the fluid (as to temperature, pressure, and volume), which would in ordinary language be regarded as belonging to the liquid state. Dr. Andrews (Phil. Trans. 1869, p. 575) has shown that the ordinary gaseous and ordinary liquid states are only widely separated forms of the same condition of matter, and may be made to pass into one another by a course of continuous physical changes presenting nowhere any interruption or breach of continuity. If we denote geometrically all possible points of pressure and temperature jointly, by points spread continuously in a plane Surface, each point in the plane being referred to two axes of rectangular coordinates, so that one of its ordinates shall represent the temperature and the other the pressure denoted by that point, and if we mark all the successive boiling- or condensing-points of temperature and pressure as a continuous line on this plane, this line, which may be called the boiling­ line , will be a separating boundary between the regions of the plane cor­responding to the ordinary liquid state and those corresponding to the ordinary gaseous state. But, by consideration of Dr. Andrews’s experimental results, we may see that this separating boundary comes to an end at a point of pressure and temperature which, in conformity with his lan­guage, may be called the critical point of pressure and temperature jointly; and we may see that, from any ordinary liquid state to any ordinary gaseous state, the transition may be effected gradually by an infinite variety of courses passing round outside the extreme end of the boiling-line.

Crystallization of undercooled liquid spinodals: Part II

1999 ◽  
Vol 14 (9) ◽  
pp. 3663-3667 ◽  
Author(s):  
K. L. Lee ◽  
H. W. Kui
Keyword(s):  
Phase Separation ◽  
Latent Heat ◽  
Spinodal Decomposition ◽  
Liquid State ◽  
Morphological Changes ◽  
Microstructural Analysis ◽  
The Other ◽  
Undercooled Liquid ◽  
Metastable Liquid ◽  
Undercooled Melt

We demonstrated in “Phase separation in undercooled molten Pd80Si20: Part I” that when a molten Pd80Si20 ingot is undercooled into its undercooling regimen with ΔT ≥ 220 K (ΔT = T1 – T, where T1 is the liquidus and T is the temperature of the undercooled melt), liquid-state phase separation by spinodal decomposition occurs. On crystallization, one of the metastable liquid spinodals becomes Pd3Si, whereas the other one turns into Pd9Si2. In both cases, Pd particles precipitate out. Microstructural analysis indicates the Pd3Si subnetwork forms first. It then acts as a seed for the subsequent crystallization of the remaining undercooled melt, which finally forms the Pd9Si2 dendrites. As crystallization proceeds, latent heat and volume contraction bring about morphological changes.

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