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1 Mar 1962

Volume 33, Issue 3, pp. 771-1382

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Absorption Edge in Degenerate p‐Type GaAs

I. Kudman and T. Seidel

J. Appl. Phys. 33, 771 (1962); http://dx.doi.org/10.1063/1.1777165 (3 pages) | Cited 53 times

Online Publication Date: 11 June 2004

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Infrared absorption for p‐type degenerate GaAs is studied at room temperature for various hole concentrations. At high absorption coefficients, a Burstein‐like shift is observed for samples doped above 1019∕cm3; this shift is interpreted as a decrease in the valence band electron population. A direct transition analysis was made on 1017∕cm3 material, yielding an energy gap of 1.39±0.02 ev. The free carrier absorption was extrapolated to shorter wavelengths and subtracted from the data. The resulting absorption edges extend to energies beyond the fundamental edge and reveal the presence of an added absorption mechanism.

Contact Potential in Thin Metal Films

Stanley M. Bryla and Charles Feldman

J. Appl. Phys. 33, 774 (1962); http://dx.doi.org/10.1063/1.1777166 (3 pages) | Cited 2 times

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Attempts were made to observe a work function variation with thickness of thin gold, platinum, and silver films. The films were vacuum deposited onto fused silica substrates at pressures of about 10−8 torr. The vibrating capacitor method was used to measure the contact potential difference between the films and a platinum reference surface as a function of film resistance. The measurements were carried out at pressures of 10−8−10−10 torr. The contact potential difference was found to be independent of film resistance in the range of 5 ohms∕sq to 108 ohms∕sq.

X‐Ray Diffraction Studies in the 100 Kilobar Pressure Range

John C. Jamieson and A. W. Lawson

J. Appl. Phys. 33, 776 (1962); http://dx.doi.org/10.1063/1.1777167 (5 pages) | Cited 86 times

Online Publication Date: 11 June 2004

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A new technique using ``amorphous'' boron as a pressure vessel yields satisfactory Debye—Scherrer patterns for substances subjected to quasi‐hydrostatic pressures ranging up to at least 150 kbar. The pressure attained depends on sample size and its compressibility. In general, the pressure attained is higher for the more incompressible substances. The following substances have been used to test the apparatus: Fe, NaCl, KCl, AgCl, CaCO3, and NaNO3. Evidence for polymorphic transitions was found for all substances except NaCl. The changes in lattice spacings and the observed transformations are consistent with the transition pressures and volume decrements determined by Bridgman or by shock‐wave experiments in the case of Fe. The high‐pressure structures are tentatively identified.

An Extension of a Theory of Mechanical Damping Due to Dislocations

D. H. Rogers

J. Appl. Phys. 33, 781 (1962); http://dx.doi.org/10.1063/1.1777168 (12 pages) | Cited 45 times

Online Publication Date: 11 June 2004

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The theory of damping due to dislocations developed by Granato and Lücke concerning a model of a dislocation line pinned by major (unbreakable) and minor (breakable) pins, the latter distributed at random along its length, is extended in two ways: the hysteretic breakaway loss is calculated for higher amplitudes; and the frequency dependent or dynamic loss is shown to be, also, amplitude dependent. The presence in a crystal of two dislocation systems of different average loop lengths is considered as an explanation of the discrepancy between some of the experimental results and the G and L theory. The configuration of the combined dynamic and breakaway loss for the long loop system for various LN∕Lc ratios and LN values is described, where LN, Lc are the average loop lengths between major and minor pins, respectively. An interesting feature is the prediction of a low amplitude maximum in the decrement. The theory does not extend to the high frequency region and like the G and L theory is unreliable for LN∕Lc less than 5.

Ultrasonic Damping at Kilocycle Frequencies in Aluminum at Low Temperatures

T. S. Hutchison and D. H. Rogers

J. Appl. Phys. 33, 792 (1962); http://dx.doi.org/10.1063/1.1777169 (8 pages) | Cited 16 times

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Measurements of 40‐kc acoustic damping in well‐annealed polycrystalline, 99.996% pure aluminum at temperatures between 4.2° and 273°K are compared with theories of dislocation damping by Granato and Lücke and by Rogers. Two dislocation systems are indicated, both pinned by impurity atoms, with the average loop length of the one greater than that of the other. An amplitude‐dependent dynamic loss and an amplitude‐dependent breakaway loss for the long‐loop system, and the usual amplitude‐dependent breakaway loss for the short‐loop system are observed. The temperature dependence of various parameters important to the several types of damping is discussed and limits to the values of the types deduced for different temperatures. Electron‐lattice damping is observed at temperatures below 60°K and is found to be larger than theory predicts.

Experimental Evidence of Landau Damping in Electron Beams

M. Caulton, B. Hershenov, and F. Paschke

J. Appl. Phys. 33, 800 (1962); http://dx.doi.org/10.1063/1.1777170 (4 pages) | Cited 15 times

Online Publication Date: 11 June 2004

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Investigations have been made of plasma oscillations by studying space‐charge waves in velocity‐modulated electron beams. The convection current in a velocity‐modulated slowly‐drifting electron beam was measured as a function of distance from the modulating cavity. The experiments indicate that in the presence of an appreciable velocity spread, the fast space‐charge wave is damped while the slow space‐charge wave remains unattenuated. The measurements were made under conditions where the velocity spread is dominated by lens effects in the electron‐optical system. The results confirm qualitatively the theory of Berghammer and thus demonstrate the existence of the much disputed Landau damping.

Kinetic Theory of Dislocation Climb. I. General Models for Edge and Screw Dislocations

R. M. Thomson and R. W. Balluffi

J. Appl. Phys. 33, 803 (1962); http://dx.doi.org/10.1063/1.1777171 (14 pages) | Cited 36 times

Online Publication Date: 11 June 2004

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General kinetic models are established for the climb of edge and screw dislocations. The climb of a straight unconstrained edge dislocation is considered in terms of the diffusion of nonequilibrium point defects to (or from) the line and their absorption (emission) and destruction (creation) at the line. The climb is nucleated by the formation of short rows of defects which are attached to the edge of the extra plane and are bounded by jog pairs. Climb occurs by the growth of these aggregates until they destroy each other by mutual collisions. No a priori assumptions are made about the ability of either the dislocation or the jogs to maintain local point defect equilibrium during climb, and account is taken of rapid defect diffusion along the core. Effects of nonequilibrium defects in perturbing the jog population are also included. Equations describing this edge dislocation climb are developed but are left in a general form. Complete solutions are worked out in a following paper (Part II). Complications which arise when geometrical constraints and line curvature are present are discussed, and a description of the relationships between curvature, macroscopic line tension, and jog density is given. It is concluded that the results for the unconstrained climb model can be used in many such cases over a considerable range of conditions. The treatment of screw dislocation climb focuses attention on the climb of an initially straight dislocation into a multi‐turned helix. The detailed mechanisms are found to depend strongly upon the geometry and mobility of point defects and point defect aggregates on the core, and therefore only a qualitative theory is given. It is suggested that in many crystals vacancies largely dissociate into kinks when they enter the core, and that the helical turns build up rather uniformly along the line by the aggregation of ordered arrangements of these kinks.

Kinetic Theory of Dislocation Climb. II. Steady State Edge Dislocation Climb

R. W. Balluffi and R. M. Thomson

J. Appl. Phys. 33, 817 (1962); http://dx.doi.org/10.1063/1.1777172 (10 pages) | Cited 17 times

Online Publication Date: 11 June 2004

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Quantitative expressions for the steady state climb rate of a straight unconstrained edge dislocation are obtained. The results represent specific solutions to a general kinetic model of climb developed in preceding work (Part I). Solutions are obtained for the case where interstitials in the lattice can be neglected compared to vacancies, where the dominant point defects responsible for fast diffusion along dislocation cores are vacancies, and where unlike jogs attract one another. No a priori assumptions are made about the ability of the dislocation or its jogs to maintain local point defect equilibrium. A wide range of conditions is treated including positive and negative climb where the vacancy concentrations may be either near or far from equilibrium. Positive and negative climb are shown to be inherently different processes, and it is found that dislocations tend to get joggy in crystals far from equilibrium. Several brief applications to problems of current interest are given. A need for critical experiments is emphasized.

Alumina Whisker Growth on a Single‐Crystal Alumina Substrate

P. L. Edwards and R. J. Happel

J. Appl. Phys. 33, 826 (1962); http://dx.doi.org/10.1063/1.1777173 (2 pages) | Cited 11 times

Online Publication Date: 11 June 2004

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Alumina whiskers have been grown on single‐crystal alumina substrates by heating aluminum filings, located near the crystals, to 1400°C in a stream of wet hydrogen. The whiskers grew crystallographically coherent with the substrate, and had their axes either parallel to the c axis or in one of 12 equally spaced directions in the basal plane. These 12 directions divide into two distinct sets, a 〈1120〉 set and a 〈1100〉 set, each having sixfold symmetry, and with the directions of one set midway between the directions of the other. These growth directions are the screw‐dislocation directions in alumina, hence it seems plausible that the whiskers grew coherently with the substrate at the site of emergent screw dislocations.

Giant Optical Pulsations from Ruby

F. J. McClung and R. W. Hellwarth

J. Appl. Phys. 33, 828 (1962); http://dx.doi.org/10.1063/1.1777174 (2 pages) | Cited 61 times

Online Publication Date: 11 June 2004

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Giant pulses of optical maser radiation have been produced which are several orders of magnitude larger than the commonly observed spontaneous pulses. The pulses were produced by varying the effective reflectivity of the reflecting surfaces at the ends of the ruby rod through a Kerr‐cell switching technique. The measured pulse characteristics are found to be in agreement with theoretical predictions.

Piezoelectric and Dielectric Properties of Lead Titanate Zirconate Ceramics at Low Temperatures

Robert Gerson

J. Appl. Phys. 33, 830 (1962); http://dx.doi.org/10.1063/1.1777175 (3 pages) | Cited 4 times

Online Publication Date: 11 June 2004

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The piezoelectric and dielectric properties of polarized lead titanate zirconate ceramics were measured between 4° and 77°K. The materials were found to retain strong piezoelectric activity at the lower temperature. For one type of ceramic the planar piezoelectric coupling in liquid helium was about 80% of its room temperature value. Its free relative dielectric constant, measured at 1 kc, rose almost linearly from 380 at 4°K to 1300 at room temperature. The mechanical losses decreased sharply at low temperatures, suggesting a reduction in domain wall mobility.

Temperature Dependence of Ferromagnetic Uniaxial Anisotropy Coefficients

Earl R. Callen

J. Appl. Phys. 33, 832 (1962); http://dx.doi.org/10.1063/1.1777176 (4 pages) | Cited 5 times

Online Publication Date: 11 June 2004

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The problem of a spin one Weiss molecular field Hamiltonian with uniaxial anisotropy is solved exactly. The free energy contains magnetocrystalline anisotropy terms of all even order Legendre polynomials. The P2 coefficient varies as the third power of the magnetization rather well even for fairly large anisotropy, and over the entire temperature range. The higher order terms can be of both signs, and all change sign as the temperature is increased.

Low‐Noise Beams from Tunnel Cathodes

G. Wade, R. J. Briggs, and L. Lesensky

J. Appl. Phys. 33, 836 (1962); http://dx.doi.org/10.1063/1.1777177 (6 pages) | Cited 9 times

Online Publication Date: 11 June 2004

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The tunnel cathode consists of a metal‐insulator‐metal sandwich in which the electrons tunnel through the insulator material. This paper presents an analysis of the noise associated with the space‐charge waves of a beam emitted from such a cathode. The beam noise temperature for a refrigerated tunnel cathode is shown to be 2730 δ, where δ is the value in volts of a built‐in energy window for the emitted electrons. The value of δ is adjustable by means of a dc potential. Assuming a beam noise temperature of 30°K, the current density is calculated for a variety of cathode parameters. A discussion is presented of the significance of the parameters and of the difficulties which would be encountered in constructing such cathodes for low noise.

Thermoelectric Properties of Bismuth‐Antimony Alloys

G. E. Smith and R. Wolfe

J. Appl. Phys. 33, 841 (1962); http://dx.doi.org/10.1063/1.1777178 (6 pages) | Cited 64 times

Online Publication Date: 11 June 2004

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The thermoelectric figure of merit (z), resistivity, and Seebeck coefficient have been measured between 20° and 300°K on single crystals of several alloys in the range from 1% to 40% antimony in bismuth. These materials are semimetals (0 to 5% antimony) or small energy gap intrinsic semiconductors (5 to 40% antimony) and all are n type. The Seebeck coefficients and figures of merit are anisotropic, the larger values being those measured parallel to the threefold symmetry axis. In the 12% antimony alloy the larger z rises from 1.0×10−3∕°K at 300°K to a maximum of 5.2×10−3∕°K at 80°K and falls rapidly at lower temperatures. All of the alloys between 3% and 16% antimony have a maximum z near 5×10−3∕°K at a temperature between 70°K and 100°K. The 5% antimony alloy has the highest z at room temperature (z=1.8×10−3∕°K). In this material, the Seebeck coefficient is practically constant (S=−110±10 μv∕°K) between 77° and 300°K and the ratio of the thermal to electrical conductivities is close to the theoretical Wiedemann‐Franz ratio above 100°K. As a result, z is inversely proportional to the absolute temperature (zT=0.52±0.05) between 100° and 300°K. In the 12% antimony alloy, S rises from −110 μv∕°K at 300°K to −220 μv∕°K at 20°K. A specimen of this material, doped with 0.01% lead, is p type below 42°K. A qualitative explanation of these results is given in terms of mixed conduction by electrons and holes having properties similar to those in pure bismuth. The use of these alloys (and semimetals in general) in thermoelectric refrigeration at low temperatures is discussed.

A Photometric Procedure for Weight Determination of Submicroscopic Particles Quantitative Electron Microscopy

Elmar Zeitler and Gunter F. Bahr

J. Appl. Phys. 33, 847 (1962); http://dx.doi.org/10.1063/1.1777179 (7 pages) | Cited 56 times

Online Publication Date: 11 June 2004

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A photometric procedure for rapid determination of weight of isolated particles down to a size of 200 A is described. Under normal conditions of electron microscopy, weights of down to 10−18 g can be determined with an inaccuracy of less than 10%. By lowering the accuracy or using more elaborate measures (such as very low accelerating voltage) one to two orders of magnitude for the lower weight limit can be gained. The method can now be applied to population studies of biologic particles, especially those of inhomogeneous and odd‐shaped entities. Individual losses of matter through the action of enzymes and the uptake of specific stains can be measured quantitatively. The method extends the possibilities of individual mass‐weight determination to the biologically important region of submicroscopic particles.

A Quantitative Theory for the Dislocation Multiplication during the Early Stages of the Formation of Glide Bands

H. Wiedersich

J. Appl. Phys. 33, 854 (1962); http://dx.doi.org/10.1063/1.1777180 (5 pages) | Cited 24 times

Online Publication Date: 11 June 2004

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A quantitative theory of dislocation multiplication in the early stages of glide band formation is proposed. It is based on the model of double cross slip suggested by W. G. Johnston and J. J. Gilman [J. Appl. Phys, 31, 632 (1960)]. Moving screw dislocations are believed to undergo cross slip but return in a random fashion into slip planes parallel to the original slip planes. The edge dislocation parts created between the two cross slip events cannot follow the screw dislocations, thus creating dipole dislocation trails. If the distance between the dipole dislocations is large enough that they pass each other under the applied stress, a new dislocation loop is formed in the parallel plane and the original dislocation is restored completely in its glide plane. On this basis, expressions for the number of trails and for the number of new loops created directly and indirectly by a moving dislocation are derived. The results of the theory are found to be in good agreement with the limited available data, namely the measurements on dislocation multiplication in LiF by W. G. Johnston and J. J. Gilman [J. Appl. Phys. 30, 129 (1959)].

Flow and Recovery Properties of Nearly Stoichiometric Polycrystalline Uranium Carbide and the Mechanism of Work Hardening of Crystalline Solids

Roger Chang

J. Appl. Phys. 33, 858 (1962); http://dx.doi.org/10.1063/1.1777181 (6 pages) | Cited 18 times

Online Publication Date: 11 June 2004

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The flow and recovery properties of nearly stoichiometric polycrystalline uranium carbide were studied in the temperature range 1500° to 1900°C at strain rates varying between 2×10−5∕sec to 2×10−3∕sec. The flow data seem to follow a relationshipmath ≅ Kσ5exp(−37 500/RT), wheremath is the strain rate, K a proportionality constant, R the gas constant, T the absolute temperature, and σ the flow stress at strain =0.001. A mathematical evaluation from recovery data of the activation volume associated with dislocation motion is presented and its potential to yield basic information on the mechanism of work hardening is discussed.

Thermoelectric Properties of Some Cerium Sulfide Semiconductors from 4° to 1300°K

F. M. Ryan, I. N. Greenberg, F. L. Carter, and R. C. Miller

J. Appl. Phys. 33, 864 (1962); http://dx.doi.org/10.1063/1.1777182 (5 pages) | Cited 17 times

Online Publication Date: 11 June 2004

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The thermal conductivity, Seebeck coefficient, and resistivity were measured for a series of sintered cerium sulfide compounds of the thorium phosphide structure. The compounds were in the composition range CeSx (1.33 ≤ x ≤ 1.5) and were prepared with and without strontium sulfide doping. The electrical resistivity and Seebeck coefficient increased with temperature for all samples, similar in appearance to the temperature dependency of a metal. The addition of strontium sulfide to compositions for (x > 1.33) usually led to a decrease in the resistivity and Seebeck coefficient while maintaining the same temperature dependence. The thermoelectric ``figure of merit'' is given for one of the samples and some remarks are made on the conduction mechanism in the system.

Superconducting Film Geometry With Strong Critical Current Asymmetry

H. H. Edwards and V. L. Newhouse

J. Appl. Phys. 33, 868 (1962); http://dx.doi.org/10.1063/1.1777183 (7 pages) | Cited 6 times

Online Publication Date: 11 June 2004

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It is shown that film critical current, defined as the maximum current for which a film shows no resistance, can be strongly increased in one direction and strongly decreased in the other by the field from two current carrying conductors placed parallel to the film edges.
The effect is shown to be due to mutual cancellation of the magnetic fields normal to the film created by the wire currents and the film current. It appears to make a flat film superconductive rectifier possible.
It is proved that the symmetrical increase of critical current due to the proximity of a superconducting ``shield'' plane is due to a similar mechanism, and that fields normal to the film surface are largely responsible for the broad current induced transition of flat ``unshielded'' films.
It is also shown that with mutually opposed wire currents the variation of critical current with wire current exhibits a significant hysteresis. This effect may have applications to digital storage.

Approach to the Ideal Magnetic Circuit Concept through Superconductivity

P. P. Cioffi

J. Appl. Phys. 33, 875 (1962); http://dx.doi.org/10.1063/1.1777184 (5 pages) | Cited 5 times

Online Publication Date: 11 June 2004

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The ideal magnetic circuit concept in which leakage and fringing flux are absent has not heretofore been realized because of the absence of magnetic insulators under normal conditions. Below the transition temperature, however, a superconductor is a perfect magnetic insulator and a superconducting enclosure of PbBi around the source of mmf and the air gap of an experimental electromagnet operating in liquid helium has been found to reduce leakage flux from 5.1 to 0.39 maxwells per maxwell of air gap flux. The small residual leakage flux observed is accounted for by leakage in the space occupied by the winding. No detectable fringing flux was observed outside the superconducting magnetic insulator surrounding the air gap. The flux within the air gap follows the contour of the superconducting enclosure and the degree of field uniformity within is determined by the precision of alignment of the enclosure surfaces. The large reduction in size and weight possible under ideal magnetic circuit conditions makes operation in liquid helium feasible. In a magnetic circuit for maser application, a reduction in weight of nearly 2 orders of magnitude was possible partly because of the reduction in air gap length resulting from the inclusion of the magnetic circuit in the cryostat and partly because of ideal magnetic circuit operation.

Ions Sputtered from Copper

R. C. Bradley and E. Ruedl

J. Appl. Phys. 33, 880 (1962); http://dx.doi.org/10.1063/1.1777185 (9 pages) | Cited 17 times

Online Publication Date: 11 June 2004

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Positive ions sputtered from copper under a variety of different bombardment and surface conditions have been mass analyzed and found to include species characteristic of the incident ions (``reflected'' ions), of copper and some of its compounds, and of alkali metal impurities. A model is described which accounts for most of the properties of the ``reflected'' ions, not in terms of reflection but in terms of the amount of gas trapped and released by the surface. The ionizing agent is unknown but is thought to be the bombarding ions (or their secondary electrons) rather than the surface. The Cu+ ions, on the other hand, seem to be surface ionized sputtered particles originating from patches of high local work function. Yield data seem to correlate qualitatively with probable changes in work function caused by adsorption of impurities, sputtering, or vacuum annealing. The CuO+ peak is believed to be caused by dissociation and ionization of cuprous oxide molecules under the action of the ion bombardment. The rates of formation and disappearance of this peak were studied under various circumstances. An unusually high sputtering rate was found to occur at an argon bombarding energy of 75 ev. Na and K impurities sputtered from and ionized by the copper surface showed some interesting transient effects which can be interpreted in terms of a low sputtering probability compared to the base metal. The relevance of these experiments to sputtering theories, ion pumping, oxidation, cleanup, and surface ionization theory is discussed.

Precision Orientation of Germanium Crystals in the [111] Direction Using Alloy Pits

R. Dreiner and R. Garnache

J. Appl. Phys. 33, 888 (1962); http://dx.doi.org/10.1063/1.1777186 (4 pages) | Cited 1 time

Online Publication Date: 11 June 2004

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A method is described for orienting germanium crystals in the [111] direction with an accuracy within six minutes of arc. N‐type germaniun is alloyed by liquid indium. The indium is then etched off and the resulting alloy pits are inspected by means of interference fringes. The information obtained from these pictures is used to determine the orientation with the accuracy noted above. An alternate method is described using information obtained from delineated P‐N junctions on two angle lapped bevels.

Effects of Thermal‐Mechanical Treatments on Faulting in Some fcc Alloys

D. E. Mikkola and J. B. Cohen

J. Appl. Phys. 33, 892 (1962); http://dx.doi.org/10.1063/1.1777187 (7 pages) | Cited 25 times

Online Publication Date: 11 June 2004

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An increase in stacking fault probability associated with a solute with the same atomic size but a higher valence than the solvent was found by comparing filed Ag and Ag‐6 at. % Al. The stacking fault and twin fault probabilities in ordered Cu3Au, where the atoms differ in size only, were higher than for either pure Cu or Au after deformation at and below room temperature. The stacking fault probability was lower in filings of quenched Cu3Au and Cu‐14.3 at. % Al alloys, than in slowly cooled specimens. There is a close correlation between measured fault probabilities and available data on fault energies and Fermi surface configurations.
Twin faults were found in Cu‐base alloys deformed at room temperature as well as at low temperatures.
Stacking faults in filings of Cu‐14.3 at. % Al annealed out in two stages. The second stage was associated with recrystallization, with an activation energy similar to that for interdiffusion in this system. Twin faults were more stable than stacking faults.

Effects of Electron Random Motion on Microwave Propagation through a Plasma Parallel to a Magnetic Field

Joseph E. Willett

J. Appl. Phys. 33, 898 (1962); http://dx.doi.org/10.1063/1.1777188 (9 pages) | Cited 2 times

Online Publication Date: 11 June 2004

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Expressions for the propagation of a circularly polarized microwave through a plasma parallel to a uniform and static magnetic field are derived from the Boltzmann equation and, alternately, from the equation of motion of an individual electron. Both methods yield identically the same formulation in which effects of the random motion of the electrons are predicted to result from (i) the Doppler shift due to electron motion parallel to the direction of propagation, (ii) electron free paths extending over distances significant compared to the attenuation length, and (iii) variation of collision frequency with electron velocity. The results of a numerical study of the propagation of a right‐handed wave indicate that the first two of these effects are important in the region of cyclotron resonance even at moderate temperatures (e.g., in re‐entry plasmas) provided that the collision frequency is small compared to the signal radian frequency. Substantial reduction of the attenuation of a right‐handed wave in a plasma may be achieved by means of a magnetic field aligned parallel to the direction of propagation. The cyclotron frequency must be of the order of the signal radian frequency or larger and such that the enhanced attenuation arising from the electron random motion is avoided. The effectiveness of a given magnetic field in reducing the attenuation increases with decreasing ratio of collision frequency to signal radian frequency.

Effect of Noncrystallizable Components on the Crystallization Kinetics of Polymers

F. Gornick and L. Mandelkern

J. Appl. Phys. 33, 907 (1962); http://dx.doi.org/10.1063/1.1777189 (7 pages) | Cited 24 times

Online Publication Date: 11 June 2004

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The effects of chain irregularities, treated as randomly introduced copolymeric units and of added monomeric diluents, on the nucleation rate of crystallizing polymeric systems have been calculated. A marked attenuation in the nucleation rate is expected under certain conditions as a consequence of the varying composition of the melt. The decrease in the nucleation rate becomes more pronounced at the lower undercoolings and as the concentration of the noncrystallizing component increases.
The Avrami mathematical formulation for the kinetics of phase changes can be generalized to allow for nucleation and growth rates which vary with the amount of material transformed. The resulting isotherms for copolymers are no longer superposable, superposability being characteristic of crystallization under conditions of constant nucleation and growth. Possible error in the interpretation of crystallization kinetics utilizing the simplified version of Avrami's equation is pointed out, as is the extreme sensitivity of the crystallization process to the presence of small amounts of chain irregularities.
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