EMINGTON
`
`Lupin Ex. 1071 (Page 1 of 18)
`
`

`
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`current information, including contraindications, dosages and precautions.
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`Printed in the United States of America
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`ia the Office of the Librarian of Congress, at Washington DC
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`Copyright 1889, 1894, 1905, 1907, 1917, by Joseph P Remington
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`Copyright 1926, 1936, by the Joseph P Remington Estate
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`Copyright 1948, 1951, by the Phi]adelptda College of Pharmacy and Science
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`Copyright 1956, 1960, 1965, 1970~ 1975, 1980, 1985, 1990, i995, by the Phila-
`delphia College of Phal~acy and Science
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`Notice--This text is not intended to represent, nor shall it be interpreted to be, the
`equivalent of or a substitute for the official United States Pharmacopeia (USP)
`and/or the National Formulary (NF). In the event of any difference or discrep-
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`Lupin Ex. 1071 (Page 2 of 18)
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`

`
`MOLECULAR STRUCTURE, PROPERTIES, AND STATES OF MA’~q’ER
`
`1Ta
`
`atoms. It is possible, however, to study the details of molecules
`without lenses, by means of diffraction experiments. Of the
`three types of radiation, X-rays have proved to be the most
`usefu! and fruitful for studying molecular structure.
`
`Crystalline State
`
`Figure 13-5. Bragg condition for reflection.
`
`Atoms and molecules tend to organize themselves into their
`most favorable thermodynamic state, which under certain con-
`ditions results in their appearance as crystals. This form is
`characterized by a highly ordered arrangement of the mole-
`cules, associated with which is a three-dlmensional periodiclty.
`The repeating three-dimensional patterns, ideally depicted as
`lattices, are essential for X-ray structural analysis.
`
`X-ray Diffraction
`
`In 1912 yon Lane and two of his students, Friedrich and Knip-
`ping, carried out an experiment with X-rays that opened the
`door to crystallographic structural analysis. They allowed a
`beam of nonhomogeneous X-rays to pass through a crystal of
`copper sulfate pentahydrate; they recorded, by means of pho-
`tographic plates, the diffracted X-ray beam. A diagram of the
`experiment is shown in Figure 13-4.
`The results showed that X-rays, which had been discovered
`by Roentgen less than two decades earlier, had wave charac-
`teristics (wavelength: approximately 1 .~.). As a crystal is com-
`posed of a regular array of atoms with interatomic separations
`of the angstrom (~) range, they were able to show that the
`diffraction pattern obtained on the plates was due to the crystal
`a&ing as a three-dimensional diffraction grating towards the
`X-rays.
`This discovery led Bragg to make use of X-rays for the study
`of the internal structures of c~jstals. He considered that X-rays
`are reflected from planes of atoms within the crystal lattice.
`The reflections from a particular family of planes will occur
`only at a particular angle of incidence and reflection. The
`essential condition for reflection is diagramed in Figure 13-5.
`In this figure the crests of the ~wo incident waves will stay in
`phase if the thickened portion of the path (as shown in the
`diagram) of one wave is an integral multiple (n) of the wave-
`length (2,). The condition for reflection is given by the well-
`known Bragg equation:
`
`k
`
`The equation is satisfied only when n = 1, 2, 3,... Ifn is not a
`whole number, there wi!l be. destructive interference between
`the diffracted waves.
`I~ any crystal there are an infinite number of families of
`planes that can be constructed. These planes usually are de-
`
`noted by their Miller indices (hkl), as shown in Figure 13-6.
`These indices dictate the spacing between the planes (dhk~) for
`a particular crystal. Because the highest value of 0 that is
`theoretically possible to measure is 90° (reflected beam comes
`back along the incident beam’s path), the number of planes
`(highest order) that one is capable of orienting in a diffracting
`position is limited by the wavelength of the radiation.
`The planes that are accessible for a particular wavelength
`(X-ray) can be brought into a diffracting position by the proper
`orientation of the crystal relative to the colllmated beam. In
`t~rn, many sets of planes can be recorded on a photographic
`plate by the movement of the crystal, when each of the planes
`will come into its diffracting position. In diffraction photo-
`graphs, in which the crystal has been oscillated about an axis
`relative to the incident radiation, the various spots on the film
`arise from reflections from different plmTes; each spot can be
`i~dexed, according to the Miller indices of the respective plane,
`by its location on the film. The spacing between the various
`spots enables one to de,~ve the distances and angles between
`the primitive ~ransla~ons--that is, the unit-cell dimensions.
`In most cases little information can be gleaned from a
`knowledge of the unit-cell dimensions alone. To learn about the
`crystal and molecular structure, it is necessary to consider the
`intensities of the Bragg reflections.
`
`Application of X-ray Diffraction
`
`MOLECULAR WEIGI-IT--The measurement of the ua~it-
`cell paran~eters provides a mea~s of accurately determining
`molecular weights of compounds. The density of a crystal can
`be obtained by means of flotation in mixtnres of suitable liq-
`uids, the density of which may be altered by dilution until it
`matches that of the crystal.
`The density (g/cm~) is proportional to the molecular weight
`of the material in the unit cell
`The relationship is
`
`where N~ is Avogadro’s number (6.023 × 10u~) and Z is the
`number of molecules in the unit cell. The wait-ceil volume
`can be measured to a very high degree of accuracy. The number
`of molecules in the unit cell (Z) must be a whole number, with
`values of 1, 2, 4, and 8 being the most common among organic
`materials. When there is a high degree of solvatien, it is nec-
`essary to approximate the amount of liquid bound by another
`means.
`IDENTIFICATION OF MATERIALS~Every compotmd
`that is crystalline will give a characteristic X-ray diffraction
`pattern. These patterns can be very useful for identification
`
`A
`
`B
`
`C
`
`D
`
`Figure 13-4, Diagram of Laue experiment:{A) x-ray tube, (B) lead
`slits, (C) crystal, (D) photographic plate.
`
`Figure 13-6. Crystal axes intercepted by a crystal plane.
`
`b l =
`
`Lupin Ex. 1071 (Page 3 of 18)
`
`

`
`174
`
`CHAPTER 13
`
`purposes, and also for quantitative analysis of solid mixtures
`(see Chapter 34). They also have been used to a great extent by
`the pharmaceutical industry for the identification and classifi-
`cation of polymorphic and solvated forms of drugs. The powder
`method, in which the specimen is ground to a fine powder
`containing minute crystals oriented in every possible direction
`and a large number with their Bragg planes in correct orien-
`tation for reflection, is a valuable technique when quick com-
`parisons of different forms are to be made and also when
`quantitative work is done. An example of such a comparison
`between the hydrated and anhydrous form of theophylline is
`shown in Figure 13-7.
`Extraction of quantitative information from diffraction pat-
`terns permits measurements of the physical and chemical sta-
`bility of solid dosage forms. The kinetics of phase transforma-
`tions are obtained easily by following the disappearance and/or
`appearance of various diffraction maxima corresponding to cer-
`tain solid states as a function of time. One easily can visualize
`how this can be accomplished for theophylline hydrate by Iook-
`ing at the patterg, s in Figure 13-7.
`STRUCTURE DETEI1MINATION--The body of sub-
`stances of medicina! value whose structures were elucidated
`primarily by X-ray diffraction techniques is quite large. They
`range in molecular size from penicillin to vitamin Bin, and on
`up to the globular proteins. The structural determinations, in
`most instances, have played a major rote in uncovering the
`secrets associated with the biological functions of the various
`molecules. A photograph of the ribonuclease molecule as deter-
`mined by the X-ray studies of Kartha, Belle, and Harker is
`shown in Figure 13-8. This enzyme catalyzes the hydrolysis of
`phosphodiester bonds in RNA chains.
`There also are large numbers of macromolecules of biologi-
`cal importance that do not form three-dimensional crystals in
`the usual sense, but will form fibers. The bundles of molecules
`in the fiber are aligned with respect to one another in a some-
`what crystalline manner. These materials give X-ray diffrac-
`
`TH EOPHYLLIN E - ANHYOF!OUS
`
`THEOPHYLLINE
`
`Figure 13-8. Model of bovine ribonuclease derived from X-ray data.
`The snakelike tube marks the backbone of the protein. (Courtesy Dr
`G Kartha.)
`
`tien patterns which have proved very useful in deriving molec-
`ular information. By fitting models to the X-ray pattern, many
`valuable biological polymers have had their secrets exposed.
`The two best examples are the ~-helices of keratin and the
`double helix of deoxyribonucleic acid.
`Ln recent years X-ray studies have been coupled with com-
`puter graphic and quantitative structure-activity relationship
`(QSAR) approaches in computer-asslsted drug design (CADD)
`(see Chapter 28 for a more detailed discussion).
`INTRAMOLECULAR BONDING AND CONFIGUtlA-
`TIONN--The precise determination of a crystal skructure
`ables the bond lengths and angles between the various atoms to
`be determined accurately. This information is extremely valu-
`able in the further understanding of how various chemical
`substituents influence the valence states and configurations of
`a molecule. With such knowledge, structure~activity relation-
`ships, which are of fundamental interest to the medicinal
`chemist, have much more depth. The observed bond orders also
`serve as experimental criteria by which theoretical models can
`be judged. It also is possible to compare quantum mechanical
`calculations relating drug interaction with actual observation.
`Intramolecular steric effects, which tend to distort mole-
`cules, are unraveled easily by the scrutiny of their structures.
`It is possible to distinguish between repulsive and attractive
`effects of substituents. The torsional angles about various
`bonds can be calculated from the atomic positions and are
`extremely helpful in correlating NMR data to structure.
`In recent years the combination of X-ray and neutron-
`diffraction studies has enabled informalSon on the bonding and
`nonbonding electrons within a molecule to be delineated
`clearly. Neutron-diffractlon experiments enable atomic nuclei
`in a crystal to be positioned accurately; on the other hand,
`X-rays locate the electron clouds. Bo~h types of data can be
`combined to calculate three~dimensional electron density maps
`with the inner-core electrons around each atom subtracted;, this
`makes the unshared pairs and bonding electrons clearly visi-
`ble. The atomic positions derived from ~eutron data are ,used
`for phases in calculating electron density maps with the X-ray
`data.
`Refer to Chapter 34 for additional information on the phys-
`ical methods discussed in this chapter.
`
`= THETA
`
`STATES OF MATTER
`
`Figure 13-7. A tracing of the powder~diffraction patterns of the-
`ophylline monohydrate and an anhydrous form,
`
`The aim of this section is to discuss both generalities and
`specifics, mos~ of which are not related explicitly to dosage
`
`Lupin Ex. 1071 (Page 4 of 18)
`
`

`
`MOLECULAR STRUCTUR~=, PROPERTIES, AND STATES OF MA’I-I’ER 17~
`
`..
`
`forms, because the latter will be discussed in other chapters.
`Some of the principles should be useful to have in mind when
`dosage forms and their manufacture and processing are stud-
`ied by the product-development pharmacist. It should be noted
`that due to the range of subjects covered by the section title it
`was necessary to take an eclectic approach in developing
`mostIy quahtutive discussions. The goal has been not to pro-
`duce a difficult, in-depth section, but rather one that presents
`a mostly macroscopic overview of the significant states of
`matter.
`Normally, matter exiStS in one of three states: solid, liquid,
`or gas. Although it is not pharmaceutically important, two
`other states of matter exist: the plasma state, in which maser
`exists as a hot gaseous cloud of atoms and electrons; and a more
`specula~ive state, possibly having only a momentary existence~
`is one which has characteristics of a superdense supermetai.
`The latter transient state is produced when matei~ial i~s sub-
`jected to very high pressures such as those used to make
`diamonds when compressing graphite.
`To avoid the pitfalls of semantics, there is no need to call
`attention to other systems of classffication, because for all
`practical purposes it is convenient to ~doik only of the three
`most obvious states. These states are actually a continumn,
`with two common factors determining the position on the scale
`of states.
`The first factor is the intensity ofintermolecular forces of all
`kinds: solids have the strongest"forceg, and gases have the
`weakest. The other common factor is temperature. Obviously,
`as the temperature of a substance is raised, it tends to pass
`from a solid to a ]iquid to a gas. When the phrase "as temper-
`ature is iucreased" is used, it should be remembered that this
`is a relative phrase. Even at what is called room temperature,
`some of the effects of a temperature increase are present be-
`cause room temperature is far above absolute zero.
`SOLVATES AND HYDRATES---During the process of
`crystallization, some compounds have a tendency to trap a
`fixed molar ratio of solvent molecules in the crysta~ine (solid)
`state. These are called solvates. When water is used as the
`solvent, hydrates may be formed. Some recent pharmaceutical
`examples include gallium nitrate (Ga(NOs)s" 9H20) and na-
`farehn acetate, where each decapeptide contains 1-2 molecules
`of acetic acid and 2-8 molecules of water.
`As a point of historical interest, note that Lavoisier, the
`great "father of modern chemistry," thought of heat as a type of
`matter; the v~ew even as late as the 18th century was that the
`three states of aggregation differ only with respect to how much
`heat they contain. Thus, although not all are satisfied with tide
`phraseology, the term enthalpy (or heat content) is still used in
`thermodynamics.
`Thinking further back to the ancient Greek philosophers
`and their origLual four elements (earth, air, fire, and water),
`note again the great significance attached to heat. Although the
`ancient philosophers’ concepts of the nature of matter were not
`correct, they did recognize heat as an integral part of the
`scheme of things, and nothing coutd b~ truer. Heat, a vital form
`of energy, the mirror of molecular motion, is the form of energy
`of greatest importance to mankind.
`As aIluded to above, there is no clear line of demarcation
`between the states of matter, but the following arbitrary divi-
`sion may make the approach this sec~on takes more coherent.
`
`Changes of State
`
`As a solid becomes a liquid and then a gas, heat is absorbed and
`the enthalpy (heat Content) increases as the material passes
`through these phase changes. Thus, the enthalpy of a liquid is
`greater than that of its solid form, and the enthalpy of a gas is
`greater than that of its liquid form, because heat is absorbed
`when melting and vaporization occur. The eniwopy (a measure
`of the degree of total molecular randomness) also ~ucreases as
`materials go from sohd to liquid to gas.
`
`It is the baiance of enthalpy, entropy, and temperature that
`determines if changes proceed spontaneously. Obviously, if sys-
`tems tend to settle to states of lowest energy, it means that
`enthalpy and entropy considerations may com~teract each
`other. Much of thermodynamics is concerned with explaining
`and quantitating the changes which systems undergo.
`Latent heat is heat absorbed whe~.a change of state takes
`place without a temperature change, as when ice turns to water
`at 0% This example is erie in which the heat required to produce
`the change of state is designated the heat of fusion. The coun-
`terpart, the heat of vaporization, is used when a change of state
`from liquid to gas is involved.
`As molecules of a liquid in a closed, evacuated container
`continually leave the surface and go into the free space above it,
`some molecules return to the surface, depending on their con-
`centration in the vapor. Ultimately, a condition of equilibrium
`is established, and the rate of escape equals the rate of return.
`The vapor then is saturated and the pressure is known as the
`vapor pressure.
`Vapor pressure depends on the temperature, but not on the
`amounts of liquid and vapor, so ]ong as equilibrium is estab-
`lished and both liquid and vapor are present. Heat is absorbed
`in the vaporlzat~on process, and therefore the vapor pressure
`i~ucreases with temperature. As the temperature is raised fur-
`ther, the density of the vapor increases, ~nd that of the liquid
`decreases. Ulth-natety~ the densities equal each other and liquid
`and vapor cannot be distinguished. The temperature at wldch
`this happens is called the critical temperature, and above it
`there can be no liquid phase.
`A very important process that involves a change of state
`from liquid to vapor and back to liquid is that of distillation.
`Solids also have vapor pressures that depend on tempera-
`ture. when a solid is converted directly into gas, it is said to
`sublime. Sublimation pressures of solids are much lower than
`those of liquids at any given temperature, when a solid is
`transformed directly into a liquid, two types of melting may be
`distinguished. In the first type, crystalline melting, a rigid solid
`becomes a liquid, durlng which procedure two phases are
`present--the bulk of the solid or its inner parts are not really
`changing. The second type is amorphous melting. This ~nvolves
`an intermediate plastic-like condition that envelops the whole
`mass; the viscosity decreases and a state of liquidity follows.
`Crystalline melting involves more definite melting points and
`latent heats than does amorphous melting.
`
`Sublimation
`
`All solids have some tendency to pass directly into the vapor
`state. At a given temperature each solid has a definite, though
`generally small, vapor pressure; the latter increases with a r~se
`in temperature. Sublimation is the term applied to the process
`of trausforming a solid to vapor without intermediate passage
`through the liquid state. In pharmaceutical manufacturing the
`process commonly includes also the condensation of the vapor
`back to the solid state.
`~ A solid sublimes only when the pressure of its vapor is below
`that of the triple point for that substance. The triple point is the
`point, having a definite pressure and temperature, at which the
`solid, liquid, and vapor phases of a chemical entity are ~bl& to
`coexist indefinitely. If the pressure of vapo2 over the solid is
`above that of the t~ple point, the liquid phase will be produced
`before transformation to vapor can proceed.
`Figure13-9 depicts a phase diagram illustrating the prin-
`ciple involved. The Iine OA indicates the melting point of the
`solid form of a substance at various pressures; only along
`this line can both solid and liquid forms exist together in
`equilibrium. To the left only the solid form is stable; to the
`right only the liquid form remains permanently. The line OB
`shows the vapor pressure of the liquid form of the substance
`at various temperatures. It is called the vapor-pressure curve
`
`Lupin Ex. 1071 (Page 5 of 18)
`
`

`
`CHAPTER 13
`
`SOLID
`
`VAPOR
`
`Figure 13-9. Phase diagram to illustrate the principle of sublimation.
`
`of the liquid and represents the conditions of temperatuTe
`and vapor pressure for coexistence of liquid and vapor
`phases. Above this line only the liquid phase exists perma-
`nently; below it only vapor occurs. The line OC represents
`the vapor pressure of the solid at various temperatures. It is
`designated as the sublimation curve of the solid and repre-
`sents the conditions of temperature and vapor pressure for
`the coexistence of solid and vapor phases. To the left of this
`line only solid can exist; to the right only the vapor form is
`stable. The intersection of the three lines, point O, is the
`triple point. It is apparent from the diagram that at pres-
`sures of vapor below that of the triple point it is possible to
`pass directly from the vapor to the solid state, and vice versa,
`simply by changing the temperature.
`At pressures above the triple point the liquid phase must
`intervene in transformations between solid and vapor phases,
`in a closed system. Because the melting point of a solid com-
`. monly is taken at 1 arm (atmosphere) of pressure, it is evident
`that if the triple-point pressure is less tha~ 1 atm, fusion of the
`solid form will occur on heating in a closed vessel. If, on the
`other hand, the triple-point pressure is greater than 1 arm,
`the solid form cannot be melted by heating at atmospheric
`pressure.
`In a current of air, however, the conditions are somewhat
`different; some solids that melt when heated in a closed system
`now sublime appreciably even at ordinary temperatures,
`cause the vapor pressure of the solid does not attain the triple-
`point pressure. Thus, camphor, naphthalene, p-dicblorobenze~e,
`and iodine, all of which have a triple-point pressure below
`arm, will vaporize in a current of air but melt when heated in
`a closed system.
`
`Critical Point
`
`The critical point is expressed as a certain value of temper-
`ature or p~:essure (or nmlar volume) above which or below
`which certain physical changes will not take place or certain
`states of being will not exist. At these points, some proper-
`ties are constant hnd are referred to as the critical temper-
`a~ure, pressure, or volume. At the usual critical point, the
`properties of liquid and gas are identical and the phase
`diagram curve of P versus T ends. (Phase diagrams will be
`discussed later.) When a liquid changes to a vapor, increased
`disorder or randomness--and therefore increased entropy--
`results. At the critical temperature, the entropy of vaporiza-
`tion is zero, as is the enthalpy of vaporization, as the gas and
`liquid are indistinguishable.
`Although the gas-Iiquld critical point is the one most dis-
`cussed, others do occur. Each c~tical point marks the disap-
`pearance of a state. Note that most Hquids behave similarly not
`
`only at their critica! temperatures, but also at equal fractions of
`their critical temperatures. For .example, the normal boiling
`points of many liquids are approximately equal fractions (about
`60%) of their critical temperatures (ka absolute temperature
`degrees).
`
`Supercritical Fluid
`
`When the temperature and pressure of a liquid go beyond the
`critical points, a supercritical fluid may fo~. Under these
`stressed conditions, polar and nonpolar compounds are com-
`pletely miscible. For example, dense fluid solvents, like-
`supercritlcal CO~ (To = 31.1°, P~ = 73.8 bar) and ethane
`(% = 32.3°, Pc = 48.8 bar) have been shown to offer advantages
`for the solubilization of amino acids. Other applications of
`supercritical fluids include chromatography of polar drugs and
`elimination of toxic wastes.~a,2¢
`
`Visualization of Changes of State
`
`This section is to serve as an introduction to the following one
`on eutectics. When a pure substance cools and is transformed
`from a liquid to a solid, a graph (Fig 13-t0 ) of decreasing
`temperature versus Gme is continuous. At the temperature at
`which solid crystallizes (ie, the melting point), the cooling curve
`becomes horizontal. The same is true at the boilingpoint--the
`temperature of a liquid at which the continuing application of
`heat no longer raises the temperature, but rather converts the
`liquid into vapor. It is the point where the vapor pressure of the
`liquid (or the sum of its components) equals that of the atmo-
`sphere above ~he liquid.
`Increasing the pressure above the liquid or adding solutes
`raises the boiling point and vice versa. These plateaus observed
`at certain specific temperatures are due to ~he release of the
`heats of fusion or vaporization. Similarly, when solutions are
`cooled, the slope of the cooling curve (Fig 13-tl) changes when
`one of the components starts to crystallize. Although a truly
`horizontal plateau may not be formed, as in the case of pure
`materials, the change in slope indicates predpitation of one of
`the components. If the same plateaus are formed when binary
`solutions of varied composition are cooled, it indicates that both
`components of the binary solution are coming out together. The
`t~mpera~ure at which this occurs is the eutec$ic temperature,
`and the composition is generally called a eutectic.
`Normally, cooling curves per se are converted to phase dia-
`grams to facilitate visualization of the interrelationships as
`
`TIME
`Figure 13-t0. A single change of state as shown by s slowing of the
`cooling rate.
`
`II
`
`Lupin Ex. 1071 (Page 6 of 18)
`
`

`
`MOLECULAR STRUCTURE, PROPERTIES, AND STATES OF MA-I-FER
`
`171
`
`phase changes take place. If, instead of a minimum point or
`eutectic, a maximum point is observed, it may indicate that the
`components are reacting to form a solid compound that can
`exist in equilibrium with the melt over a range of composiLions.
`It is undoubtedly true that many unknown phase equilibria
`exist. Thus, when conditions are changed (eg, when a process is
`scaled up in a manufacturing process), different phase changes
`may take place and produce different final products. The phar-
`maceutical use of heterogeneous materials such as waxes and
`fats certainly provides ample opportunity for these chang6s to
`occur,
`
`Eutectics
`
`Although many very complex and complicated diagrams, h~-
`cludLng some three-dimensional models, are needed to charac-
`terize certain systems, most interesting to pharmacy are the
`diagrams (Fig 13-12) indicating eutectic fo~*mation. This sec-
`tion will only briefly describe this area of technology.
`Phase diagrams are const~ucted’ by determining the melting
`points and cooling rates of a series of binary liquid solutions of
`compositions varying from pure A to pure B. This will be
`illustrated shortly--first, consider the Fig 13-12 phase dia-
`gram. The points where the V-shaped bmmdary of the melt
`intersect the right and left vertical axes are the melting points
`of the pure materials. To the left of the base of the V (ie, when
`solutions rich in A are cooled) solid A separates as the temper-
`a~ure falls; to the right, solid B separates as shown. Thus, the
`left arm of the V is the curve that represents the temperature
`conditions under which various liquid mixtures are in equilib-
`rium with solid A, amd the right arm of the V is that curve that
`shows wbAch mixtures are in equilibrium with solid B.
`At the point of the V, both solid A and solid B are in
`equilibrium with the liquid; this point, the lowest temperature
`at which any of the infinite possible combinations of liquid
`solutions of A and B will freeze (or the lowest melting point of
`any possible mixture of solids A and B) is called the eutectic
`point. Only at this point is the cornposiiion of the solid the same
`as that of the solution.from which it is separating; tt~s does not
`mean necessarily that the composition of the eutectic is a
`chemical compound of~and B. Thus, at the eut~ctfc poiht, both
`A and B come out together in a constant proportion.
`The eutectic composition is a simple two-phase mixture, but
`when made in site it has a very fine-grained structure that
`could irapart to it different properties (eg, solubility or gastro-
`intestinal abso~ption rate), compared to a gross mixture of the
`same composition. The stxucture is very fme-grained because
`
`TIME
`Figure 13-11, Two changes of state with resulting temporary de-
`creases in cooling rate.
`
`MELT
`
`SOLID B
`+ MELT
`
`+ MELT
`
`SOLIO A
`
`SOLID B
`
`~=OID% A MOLE ~ WtW FRACTIO~
`
`1011% B
`
`Figure ]~-~2. Simple phase diagram of system showing eutect]c
`point.
`
`the crystallization was very intimate, because crystals of both
`phases were formed slmu]taneously. This is quite a different
`situation than one in which only one component is separating.
`It is importan~ to remember that one can be only at one place
`on a phase diagram at any one time; that is, the diagram
`describes what a particular system is like at a certain temper-
`ature, which components are in the liquid and/or solid state,
`and the proportions of each.
`The diagrams are constructed from informatdon obtained on
`the cooling rates of binary solutions. Consider again a cooling
`curve analysis in which temperahare versus time are plotted.
`The curves change slope to form plateaus when any solid phase
`separates; the plateaus tend to become mere horizontal as
`absolute temperatures are lower because the intensity of radi-
`ation and conduction is lessened. A final plateau results when
`the whole liquid mass (or the last of it) solidifies. Thus, if a
`molten liquid having a composition lying between, for example,
`pure A and the eutec~ic were ~ooled, the following would be
`observed in a plot of temperature versus ~ime (see Fig 13-11):
`
`First, T drops with Lime; tb, e~ solid A will come out of solution,
`release its heat of fusion, and thus slow the cooling rate to produce the
`first (upper) plateau. The temperature then s~ar~s to drop more sharply
`again as enough A comes out of solu~on, and the system changes
`composition unLi[ it contains only.the eutectic composition.
`VC~hen the eutecLic compos~Lion is reached, the second sol~d (B) also
`cepreclpitates, and the temperature remains constant (lower plateau)
`until all of A and B have solidified, after which, of course, the temper-
`a~ure will be able to drop f~rther.
`If the system being cooled started as the eutecLic composition, only
`the lower break and plateau wou!d be observed; that is, a pure mate~dal
`and a eutecLic would have similarly shaped cooling diagrams.
`Note then that a phase diagram can be constructed by studying a
`number of cooling cm’ves made on a series of raix~ures of known com-
`position. To do t~is, the temperatures at wtdch cooling-rate changes are
`plot:Led against each particular compesit;ion studied.
`Note that Figure 13-12 is idealized in that no seIid-solid solution of
`A and B is formed. If the two components are somewhat soluble in each
`other, the diagram would differ by having two thin solution areas along
`~he left and right axes; such are partly in evidence in Figure !3-13.
`
`Two pharmaceutical examples of eutectic formation,~are
`
`1. A mixture of two common antipyretic-analgesie compounds:
`aspi