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Both elastic strain energy due to the transformational shape change and frictional resistance opposing interfacial motion are shown to contribute significantly to the observed thermodynamic changes which accompany thermoelastic martensitic transformations in Cu-14 Al-2.5 Ni alloys. However, for the special case of single-interface transformations in single crystals of the parent phase, elastic strain energy is not generated because the transformational shape change takes place freely without surrounding constraints. The temperature (T0) of zero-change in chemical free energy can then be bracketed unambiguously between the interface-advance temperature on cooling and the interface-reverse temperature on heating. Also, by means of calorimetric measurements, the chemical enthalpy, entropy and free-energy changes can be determined. Concomitantly, the frictional resistance can be estimated from the hysteresis between the interface-advance and interface-reverse temperatures; the frictional energy turns out to be approximately 5% of the chemical enthalpy change. In multiple-interface transformations, the cooling and heating transformation curves are altered in form and depressed to lower temperatures due to the storage of elastic strain energy, and there is a corresponding effect on the measured thermodynamic quantities, e.g. as a function of decreasing grain size. Such differences relative to the single-interface results permit evaluation of the stored elastic strain energy; it amounts to about 15% of the chemical enthalpy change.

The discrete-lattice concept of coherency applied to interphase boundaries and the elasticcontinuum concept applied to enclosed particles are shown to be mutually consistent. In line with these concepts, a general discrete dislocation description of interphase-boundary structure is developed. It is shown that a coherent interface can contain partial dislocations which we call transformation or ‘coherency’ dislocations. These dislocations accomplish the transformation lattice deformation between the two phases and maintain continuity of the lattice. They are capable of conservative climb and/or glide during the transformation, but their motion is restricted to the plane of the dislocation loop. Strain energy associated with the coherency dislocations can be reduced by misfit or ‘anticoherency’ dislocations, generally having lattice Burgers vectors and producing a lattice-invariant deformation which disrupts the uniformity of the lattice correspondence across the interface and thereby reduces coherency. The anticoherency dislocations move as conventional dislocations.

The reversal in the temperature dependence of the elastic limit accurately determines the Mσs temperature of retained austenite in 4340 steel. Two models, one based on an exponential distribution of pre-existing nucleation sites and another based on an autocatalytic-site potency distribution, were compared in predicting the constitutive behavior of the steel in the stress-assisted transformation regime (T

Pseudoelasticity in β Fe-Be has been observed and rationalized in terms of pseudotwinning. a type of stress-assisted martensitic transformation which arises from the interaction of long-range order and twinning in this alloy. The ordered structure, which gives rise to a chemical contribution for the reversion of the pseudotwin upon release of the stress, is not homogeneous DO3 as was previously reported, but a decomposed α + B2 microstructure. A crystallographic model predicts that the pseudotwinning process is describable by the stress-assisted martensitic phase transformation Pm3m (B2) → Cmmm. The electron diffraction evidence presented here to confirm this prediction is believed to be the first experimental proof of long-standing theories regarding the interaction of order and twinning. The macroscopic mechanical behavior of β Fe-Be has been investigated in compression at room temperature. Maximum pseudoelasticity is observed for specimens water-cooled and aged at 325–425°C. which gives rise to a modulated α + B2 microstructure. Aging at higher temperatures causes a sharp drop-off in pseudoelasticity and the disappearance of the modulated microstructure. In addition, pseudotwins in specimens exhibiting little pseudoelasticity always have accommodation dislocations associated with them. It is concluded that the modulated microstructure promotes pseudoelasticity by strengthening the parent matrix, thereby enabling it to accommodate the pseudotwins in an elastic manner.

The influence of thermal activation on the nature of the interactions between an array of particles and a migrating grain boundary is considered, adapting concepts from the theory of thermally activated deformation. Thermally activated unpinning of boundaries is found to become significant at small particle sizes and high temperatures. For a given particle array, this leads to a time dependent average grain size which is coarser than the predictions of the traditional “Zener-Gladman” static equilibrium model. For grain sizes and temperatures of interest in ferrous alloys, substantial reductions in particle size and volume fraction of grain refining dispersions can be achieved before thermal activation interferes with the effectiveness of boundary pinning.

Based on the vacancy mechanism of diffusion, a method is given for correlating the frequency factors and activation energies of self-diffusion in cubic metals. The activation energy is shown to be proportional to an appropriate elastic constant and the cube of the lattice parameter, both referred to 0°K. Reasonable agreement is found among the more recent self-diffusion determinations, with the proportionality constant being 0.0514 for face-centered cubic metals and 0.0695 for body-centered cubic metals. The theory also yields values for the fraction (λ) of the activation energy that goes into lattice straining during the elementary diffusion act. For face-centered cubic metals, λ is 0.64. For body-center cubic metals, λ cannot be calculated with any assurance because of inadequate data, but a tentative value is 0.84. These quantities, together with the above proportionality constants, permit the calculation of the self-diffusion coefficients as a function of temperature in cubic metals.

Interdiffusion coefficients of iron, nickel and cobalt in aluminum have been determined over a temperature range of 350 to 630°C, using radioactive tracers and the residual-activity technique. The results are summarized as follows (in units of cm2/sec): D Fe A1 = 4.1 × 10 −9 exp ( −13,900 RT ) D Ni A1 = 2.9 × 10 −8 exp ( −15,700 RT ) D co A1 = 1.1 × 10 t-6 exp ( −19,900 RT ) These frequency factors and activation energies are quite small compared to those for zinc diffusion in aluminum and for self-diffusion in aluminum. This contrast in behavior is explained on the basis of the extremely low solid solubilities of iron, nickel and cobalt in aluminum, which reduce the flux through the lattice to the point where diffusion along short-circuiting paths becomes controlling. The appropriate solution of the diffusion equation and the quantitative results obtained suggest that normal concentrations of dislocations can provide the necessary short-circuiting paths.

The initiation of cleavage microcracks in two coarse-grained vacuum-melted ferrites containing 0.035 and 0.007 per cent carbon was studied by means of tensile tests carried out between room temperature and −195°c in conjunction with special metallographic procedures. The latter involved surface replication of prepolished tensile specimens at various stages along the stress-strain curve as well as progressive sectioning of such specimens to reveal the internal details. In this way, the roles of carbides, mechanical twinning and slip in the initiation of cleavage were determined. Cleavage microcracks develop in ferrite throughout the strain-hardening portion of the stress-strain curve at subzero temperatures, and are mainly initiated by the cracking of carbides. Twinning does not play an important part in crack initiation in these materials at temperatures down to − 195°c. Although carbides may crack copiously during plastic deformation, they lead to microcracking of the ferrite only when the applied stress is high enough to permit the carbide cracks to act as griffith cracks. A model for microcrack initiation by such carbide cracking is proposed.

Self-diffusion in high-purity iron (99.97 per cent Fe) has been determined over the temperature range from 700 to 1436°C. The temperature dependence of the self-diffusion coefficient in face-centered cubic and in body-centered cubic iron can be expressed as follows (in cm2/sec): Gamma-iron: D = 0.18 exp (−64,500/RT) Alpha-iron (paramagnetic): D = 1.9 exp (−57.200/RT) (above 790° C) Alpha-iron (ferromagnetic): D = 2.0 exp (−60,000/RT) (below 750° C). The diffusivity below the magnetic transformation is lower than expected from an extrapolation of the diffusion data for paramagnetic alpha-iron.

At atmospheric pressure, iron-ruthenium alloys containing less than 12 atom percent ruthenium exhibit a diffusionless α(b.c.c.) ⇄ γ(f.c.c.) transformation on heating and cooling, while alloys containing 12–36 atom percent ruthenium exhibit a diffusionless ϵ(h.c.p.) ⇄ γ(f.c.c.) transformation. High pressure displaces the α → γ reaction to lower temperatures, but shifts the ϵ ⇄ γ reaction to higher temperatures. These effects appear to be governed by the pressure dependence of the thermodynamic properties. The application of pressure also produces a new transformation, α ⇄ ϵ, at room temperature in alloys which contain the α-phase at atmospheric pressure. Pressure-temperature diagrams at constant composition thus contain triple points involving α(b.c.c.), γ(f.c.c.) and ϵ(h.c.p.). As the ruthenium content is increased, the triple-point pressure decreases significantly. Comparison of the alloy pressure-temperature diagrams with the high-pressure behavior of iron demonstrates that the pure metal also exhibits a triple point, at which the high-pressure, low-temperature phase is ϵ. A thermodynamic analysis has yielded values of ΔFα → ϵ[T] for pure iron, thus establishing the relative stability of the ϵ-phase in iron.

The ratio of grain-boundary to surface energy has been determined as a function of composition in the gold-copper system. From interferometric measurements of the boundary groove angles in specimens thermally etched at 850°C, the following average grain-boundary to surface-energy ratios were obtained: 0.25, 0.28, 0.34, 0.42, 0.37, and 0.36 at 0, 20, 40, 60, 80, and 100 at. % copper, respectively. Existing data for the surface energies yield 370, 320, 310, 390, 430 and 590 erg cm −2 , respectively, for the absolute grain-boundary energies. A calculation is included of the boundary adsorption corresponding to this energy variation, and an estimate is made of the minimum number of atoms required at the grain boundary to accommodate the calculated absorption.

The internal-friction peak due to the stress-induced migration of carbon in b.c.c. iron has been studied in a series of high-purity iron-carbon alloys with variations in grain size and intercarbide distance. It is found that when these microstructural parameters are small the height of the carbon damping peak does not correspond to the equilibrium solubility at the solutionizing temperature. An explanation is suggested in terms of the rapid precipitation of carbon during the quench from the solution temperature, the sites being provided by grain boundaries or ferrite-carbide interfaces. Only when the grain size and mean distance between carbides are sufficiently large can the equilibrated carbon content be retained in solution on quenching to room temperature. The same phenomena are involved when martensite is tempered to ferrite-carbide aggregates.

The diffusivities of iron, cobalt and nickel into otherwise pure gold were determined by the residual-activity technique, after checking this procedure against the better-known sectioning method for self-diffusion in gold. The results may be summarized as follows (in units of cm 2 sec): D Au = 0.117 exp (−42,100/ RT ) D Fe Au = 0.082 exp (−41,600/RT) D Co Au = 0.068 exp (−41,600/RT) D Ni Au = 0.034 exp (−42,000/RT) The frequency factors and activation energies for the diffusion of the transition elements into gold are quite normal relative to the values for self-diffusion in gold, and suggest that lattice diffusion is operative, in contrast to the corresponding situation for the diffusion of these elements into aluminum where shortcircuiting paths appear to be operative. This difference in behavior is explained in terms of the marked difference in solid solubilities in the two series. The above results, involving variations in the frequency factor with no significant change in activation energy, are not accounted for by available theories.

The kinetics of isothermal martensitic transformations in an Fe-24Ni-3Mn alloy can be satisfactorily analyzed in terms of autocatalytic nucleation, wherein the nucleation rate first increases and then decreases as a function of reaction time. When the volume per martensitic plate is measured by quantitative metallography, instead of relying on calculation by geometric partitioning, the autocatalytic factor is found to be relatively insensitive to the transformation temperature, and amounts to about 10 10 new embryos per cm 3 of martensite formed. The activation energy characteristic of the overall isothermal reaction (and hence, of the autocatalytic nucleation) decreases with decreasing temperature, and is of the order of 10 kcal/mole, as previously reported for the activation energy corresponding to the initial transformation.

The local atomic arrangements in gold-nickel alloys are determined as a function of composition by observations of diffuse X-ray scattering. Measurements are made at − 190°C on alloys quenched from above the solubility gap, there being experimental evidence to show that the high temperature atomic configurations can be retained on quenching. The X-ray data reveal that these alloys exhibit a preference for unlike neighbors above the solubility temperature and have short range order analogous to that in copper-gold alloys. The sizes of the atoms in the solid solutions are also measured from the diffuse scattering. The gold atom in solution is smaller than in the pure metal, but larger than the average atomic dimension calculated from the lattice parameter of the solution. Correspondingly, the nickel atom in solution is larger than in the pure metal, but smaller than the average atomic dimension of the solution. Moreover, the size of each atom varies with the composition of the solution.

The relative thermodynamic properties of solid iron-aluminum alloys were obtained in the vicinity of 900°C by e.m.f. measurements, using a molten chloride electrolyte. The heats of mixing are large and negative, with H M = −8200 cal/g atom at 50 at.%. Large negative entropies of mixing were also observed, with S M = −1.8 e . u . at the equiatomic composition. The negative entropy changes are discussed in terms of magnetic, vibrational and electronic effects.

The self-diffusion rate of gold in gold-nickel alloys was measured as a function of composition and temperature in the region of complete solid solubility, using an autoradiographic method to trace the diffusion of Au198. The diffusion data reveal no anomalies that correlate with the miscibility gap. However, the D Au ∗ , D o,Au ∗ and Q Au ∗ values show maximum deviations from the linear averages of the pure metal values in the composition range corresponding to the minimum in the solidus curve.

The self-diffusion rates of radioactive Zn65 and the interdiffusion rates have been determined in f.c.c. aluminum-zinc alloys. The self-diffusivity of zinc D Zn ∗ increases as the zinc content is increased, while the thermodynamic driving force decreases with increasing zinc content until a minimum is reached at about 38 at. % Zn, just above the miscibility gap. As a result of these two opposing trends, the inter-diffusion coefficient D changes only slightly with variation in composition. The values of D follow the relationship: D = X Al D Zn ∗ (1 + d ln ƒ Zn dl ln X Zn ) , where XAl and XZn are the respective atomic fractions, and ƒ Zn is the thermodynamic activity coefficient of zinc. The lack of an observable contribution of D Al ∗ to the interdiffusion coefficient indicates that the self-diffusivity of aluminum is considerably smaller than that of zinc over the ranges of temperature and composition studied.

Diffusion coefficients of iron, cobalt and nickel in silver have been determined over the temperature range 600–850°C using radioactive tracers and the residual-activity technique. The results are as follows (in units of cm2/sec): D Fe Ag = 9.4 × 10 −7 exp (−29,600/RT) D Co Ag = 3.0 × 10 −7 exp (−29,700/RT) D Ni Ag = 8.5 × 10 −7 exp (−28,700/RT) The frequency factors and activation energies are quite small relative to those for self-diffusion in silver. It appears that the extremely low solid solubilities of iron, cobalt and nickel in silver reduce the flux through the lattice to the point where diffusion along dislocation short-circuiting paths becomes the controlling mechanism. This is in line with the diffusion results previously obtained for these tracer elements in aluminum.

The growth path of a preexisting martensitic embryo is analyzed in terms of its radial-growth and thickening kinetics. For embryo sizes near the free-energy saddle point, radial growth is favored over thickening in the start-up process, but the thickening rate soon accelerates to establish a steadystate thickness-to-radius ratio. The kinetics of these processes have been calculated, based on the transformational stresses and dislocation dynamics involved at typical transformation temperatures. Some continued thickening and a decreasing rate occurs after the radial growth is stopped by an obstacle; the resulting aspect ratio of a fully-grown martensitic plate can be computed from these considerations.

Utilizing the splat-cooling technique, Nb-Ni alloys with 33–78 at.% Ni and Ta-Ni alloys with 55–67 at.% Ni were rapidly quenched from the melt. The thin foils or flakes obtained were investigated by X-ray and electron diffraction. The diffraction patterns exhibited only broad maxima instead of relatively sharp crystalline peaks. Computer calculations based on several microcrystalline models were able to account for the features of the diffraction pattern in the region of the first maximum; best agreement was attained by assuming microcrystals of about 150 atoms in a body-centered-cubic W-A2 type configuration (equivalent to spherical microcrystals 15–16 A dia.). The microcrystalline structure persists for 1 hr at 600°C; at higher temperatures it decomposes into the equilibrium phases. In the Nb-Ni decomposition, a crystalline transition phase is first formed. The transformation of the microcrystalline Ta-Ni phase to TaNi2 is regarded as an ordering reaction, combined with particle growth. A crystal-chemical relationship of the new microcrystalline phases to α-Fe may exist.

The martensitic reaction is treated as a strain transformation with shear and dilatational displacements, respectively parallel and normal to the habit plane. When external forces are acting, the resulting effect on the Ms temperature is calculated from the mechanical work done on or by the transforming region as the resolved shear and normal components of the applied stress are carried through the corresponding transformation strains. This energy term is added algebraically to the chemical free energy change of the reaction, to compute the alteration in temperature at which the critical value of the thermodynamic driving force is attained to initiate the transformation. The transformation is aided by shear stresses, but may be aided or opposed by the normal stress component depending on whether the latter is tensile or compressive. The above criterion for the action of applied stress has successfully predicted the quantitative change in the Ms temperature of iron-nickel and iron-nickel-carbon alloys under uniaxial tension, uniaxial compression and hydrostatic pressure. Ms is raised by tension, less so by compression and is lowered by hydrostatic pressure.

The local atomic configurations measured from diffuse X-ray scattering in the gold-nickel system cannot be reconciled with the observed heats and entropies of mixing on the basis of a statistical treatment of chemical bonding energies. The heats of mixing are positive (heat absorbed), and yet there is a preference for unlike neighbours in solutions above the solubility gap. It is shown that these positive heats of mixing may be explained in terms of the elastic strain energy required to form solutions from atoms of different size. The sizes of the ions in gold-nickel solutions, also measured from the diffuse X-ray measurements, are used to calculate the strain energies and reasonable agreement with the observed heats of mixing is obtained. The strain energy contribution to the heat of mixing in Cu3Au is also evaluated approximately from an X-ray determination of the atomic size effect; in this system it appears that a significant negative contribution to the heat of mixing may arise from a change in the electronic configuration on alloy formation.

A dislocation-attraction model governing the flow of carbon atoms is proposed to account for the kinetics of the first stage of tempering in steel. It is predicted that the time exponent of the isothermal reaction should be 1 3 , and the activation energy for the reaction should equal that for diffusion of carbon in martensite. On the basis of previous kinetic data, a good check of the theoretical time exponent is obtained; however, it appears that the activation energy for diffusion of carbon is about 50% higher in martensite than in α-ferrite. The slower rate of carbon diffusion in martensite is explained by the availability of paths of lower barrier energy in the b.c.c. ferrite than in the b.c.t. martensite.

By means of quantitative metallography and electrical-resistivity measurements, the initial nucleation rates of the isothermal martensitic transformation were determined in a series of three iron, 23–25 wt.% nickel, 2–3 wt. % manganese alloys as a function of austenitic grain size and reaction temperature, taking autocatalytic effects into account. Typical C-curve kinetics are observed, with the temperature of maximum nucleation rate occurring at—125°C. The conventional initial nucleation rate (averaged up to 0.2% transformation, which is the first reliably detectable amount of marteusite), decreases with decreasing austenitic grain size; this trend arises because the smaller the martensitic plate size, the larger is the number of nucleation events required to generate a given amount of martensite. Thus, for a fine-grained austenite, a much larger fraction of the pre-existing embryos has to be activated to produce 0.2% martensite than in the case of a coarse-grained austenite. When this difference is taken into account, the true initial rate of nucleation is found to be independent of the grain size and austenitizing temperature within the limits studied, thereby indicating that grain boundaries are not dominant nucleation sites for the martensitic transformation in these alloys. The resulting activation energies for nucleation vary with reaction temperature in a manner predicted by the Kaufman—Cohen model, and the agreement becomes quantitative if an effective embryo radius of 180–200 A is assumed. The conditions leading to athermal nucleation are also rationalized. Self-consistent results are obtained when the number of pre-existing embryos is taken to be 10 7 /cm 3 . The probability of encountering such embryos in transmission electron microscopy is extremely small, even though they may be large enough to be resolved.

It appears that the predominant mechanism by which interstitial solute atoms influence the electrical resistivity of alloys, unlike substitutional solutes, is through the associated static displacements of the host atoms. A quantitative test of this hypothesis is possible in the case of tetragonal iron-carbon martensites, where the magnitude of the static displacements is experimentally known. The resistivity component arising from the static displacements is estimated by analogy to the mean-square thermal displacements and corresponding electrical resistivity of pure iron. The result agrees fairly well with various measurements on the effect of dissolved carbon on the resistivity of martensitic alloys. The displacement hypothesis also provides a logical explanation for the anomalous resistivity increase observed during the aging of iron-carbon and iron-nickel-carbon martensites. Spontaneous rearrangements of the interstitial atoms during aging tend to occur in such a manner as to increase the static displacements, as illustrated by theoretical treatment of the formation of carbon-atom pairs. The normal aging behavior can be altered, however, by the prior introduction of a dense dislocation substructure through thermomechanical treatment, as in ausformed martensites.

By means of X-ray diffraction, the formation of modulated structures with periodic variations in composition due to a simple interchange of atoms has been studied in copper-nickel-iron alloys as a function of composition, temperature and time. The results are compared with two models suggested for this type of “exchange transformation”. The reaction characteristics seem to favor a kinetic model rather than the Guinier model. The activation energies for the transformation, evaluated at the first detectable stage and for a later stage, show that both these stages are diffusion-controlled inside as well as outside the spinodal. This indicates that the spinodal is of no real significance with regard to the nucleation process. The variation with temperature and composition of the first wavelength to form in the modulated structure is in agreement with the kinetic model.

A model of operational nucleation for martensitic transformations is developed, foeussing attention on conditions for the growth start-up of preexisting embryos. Derivations are given for the transformational stresses in the thickness and radial directions of the embryo, which tend to cause thickening and radial growth, respectively. In the iron-nickel-manganese alloys examined here, radial growth occurs first and is controlled by the formation of new dislocation loops which become part of the interface. The activation energy for such loop formation decreases rapidly with radial growth, allowing the latter to become athermal. During this process, the transformational thickening stress rises and exceeds the yield stress of the surrounding austentie. Thus, the thickening is thought to be a function of the plastic resistance of the matrix.

The relative thermodynamic properties of solid aluminum-zinc alloys have been determined over the complete composition range by means of a galvanic cell using a molten salt electrolyte. The results evaluated at 300°C and 380°C indicate that there is a substantial positive deviation from ideal behavior. The molar heat of mixing has a maximum value of 850 cal/gm atom (heat absorbed) at about 60 atomic per cent zinc, and the entropies of mixing are slightly greater than the ideal configurational values. For the aluminum-rich solutions, the partial quantities relative to aluminum are apparently consistent with the quasi-chemical theory, but there are large deviations from the theory in the solutions containing more than 40 atomic per cent zinc. Extrapolation of the data for solid alloys indicates that the maximum heat of mixing for the liquid alloys is 440 cal/gm atom.