Volume 09 - Metallography and Microstructures Part 15 doc

supersaturated matrix and spatially partitions the structure into transformed and untransformed regions; it is termed discontinuous precipitation. Figures 10 and 11 depict the cellular reaction propagating into the supersaturated matrix from the grain boundaries. The lamellar morphology of the transformation product is clearly revealed. The cellular reaction often moves into a matrix in which a less stable transition precipitate has already precipitated. The residual chemical-free energy drives the reaction front, and the duplex colonies consume the initial precipitate and produce a matrix of modified composition, as shown in Fig. 12 and 13. Fig. 10 Cellular or discontinuous precipitation growing out uniformly from the grain boundaries in an Fe- 24.8Zn alloy aged 6 min at 600 °C (1110 °F). 2% nital. 1000×. (W.C. Leslie) Fig. 11 Cellular colonies growing out from grain boundaries in Au- 30Ni alloy aged 50 min at 425 °C (795 °F). 50 mL 5% ammonium persulfate and 50 mL 5% potassium cyanide. 100×. (R.D. Buchheit) Fig. 12 Transmission electron micrograph showing early stages of cellular reaction in a Cu-3Ti alloy aged 10 4 min at 375 °C (710 °F). The cellular product consumes the fine, coherent precipitates, which are revealed by strain contrast in the matrix. 57,400×. (J. Cornie) Fig. 13 Cellular reaction in a Cu-4Ti alloy aged 10 3 min at 600 °C (1110 °F). The cellular reaction produces the lamellar equilibrium phase and leads to overaging and loss of ductility. Diagonal band is a n annealing twin in the matrix phase. 1245×. (A. Datta) Reference cited in this section 1. D.A. Porter and K.E. Easterling, Phase Transformation in Metals and Alloys, Van Nostrand Reinhold Co., 1981 Precipitation Sequence In many precipitation systems and in virtually all effective commercial age-hardening alloys, the supersaturated matrix transforms along a multistage reaction path, producing one or more metastable transition precipitates before the appearance of the equilibrium phase. The approach to equilibrium is controlled by the activation (nucleation) barriers separating the initial state from the states of lower free energy. The transition precipitate is generally crystallographically similar to the matrix, allowing the formation of a low energy coherent interface during the nucleation process. Classical nucleation theory shows that the nucleation barrier ∆G* is proportional to 32 /() MPvs GG σ − ∆+ , where σ M-P is the interfacial energy of the matrix-precipitate interphase interface, ∆G v is the thermodynamic driving force per unit volume of the nucleus (which is proportional to the undercooling), and G s is the strain energy per unit volume associated with the coherency strains. Because the nucleation rate is proportional to exp - ∆G*/kT (k is Boltzmann's constant, and T is the absolute temperature), the transition phase nucleates more rapidly despite the smaller driving force (∆G v ) for its formation compared to the equilibrium precipitate. Transmission electron microscopy reveals coherent transition precipitates formed during aging before the formation of the equilibrium phase (Fig. 14 and 15). Fig. 14 Coherent transition precipitates revealed by strain contrast (dark- field) in transmission electron microscopy. The specimen is a Cu- 3.1Co alloy aged 24 h at 650 °C (1200 °F). The precipitate is a metastable fcc phase of virtually pure cobalt in the fcc matrix. The particles are essentially spherical, and the "lobe" contrast is characteristic of an embedded "misfitting sphere." This strain contrast reveals the particles indirectly through their coherency strain fields. 70,000×. (V.A. Phillips) Fig. 15 Coherent (Co,Fe) 3 Ti metastable precipitates in a Co-12Fe-6Ti alloy aged 10 4 min at 700 °C (1290 °F). The ordered particles are imaged in dark-field transmission electron microscopy using an L1 2 superlattice reflection. This imaging mode reveals the actual size of the particle, because the superlattice reflection stems only from the precipitate. The precipitates are aligned along the <100> directions of the matrix. The foil normal is near [100]. 60,000×. (J.W. Shilling) The decomposition of a supersaturated solid solution typically occurs by a sequence of reactions: α o → α'' + Guinier-Preston zones (Metastable) → α' + β' → α eq + β eq (Metastable) (Stable equilibrium) (Eq 1) where α o is the supersaturated parent phase. Each step in the precipitation sequence leads to a decrease in the free energy and represents a state of metastable or stable equilibrium. The (n + 1) transition phase tends to (but not exclusively) nucleate heterogeneously at the interphase boundaries of the n th transition phase. This is due to the role of the interfaces in catalyzing the nucleation process and to the reduction of the available driving force resulting from the prior precipitation of the n th transition phase. The precipitation scheme can be depicted in a free-energy composition diagram, as shown in Fig. 16. The metastable phases have corresponding solvus curves determined by the common tangent construction at each temperature. The metastable solvi are included in the hypothetical phase diagram of Fig. 17, which shows that the solubility is less the more thermodynamically stable the phase. Fig. 16 Free- energy composition diagram showing the metastable and stable equilibria in the precipitation sequence. The points of common tangency at compositions C'', C', and C eq are points on the metastable and stable solvi at this temperature. Fig. 17 Hypothetical simple phase diagram showing the locus of metastable and stable solvus curves. L, liquid Guinier-Preston (GP) zones are coherent, solute-rich clusters resulting from phase separation or precipitation within a metastable miscibility gap in the alloy system. They may form by homogeneous nucleation and grow at small undercoolings or by spinodal decomposition at large undercoolings or supersaturations (see the article "Spinodal Structures" in this Volume). After GP zone formation, the appearance of a more stable phase (for example, β' in Eq 1) leads to the dissolution of the zones, as revealed in Fig. 18. Each successive step replaces the less stable phase by a more stable one, lowering the free energy. In Fig. 19, the equilibrium phase is shown growing by a cellular reaction into a metastable Widmanstätten structure. Fig. 18 GP zones (dark spots) in matrix of an Al-15Ag alloy dissolving near plates of the more stable γ ' precipitates (dark lines). Transmission electron micrograph of a specimen aged 1200 h at 160 °C (320 °F). 22,500×. (J.B. Clark) Fig. 19 Colonies of cellular precipitation reaction growing out and consuming a m etastable Widmanstätten precipitate in an Al-18Ag alloy aged 4 h at 300 °C (570 °F). 0.5% HF. 1000×. (J.B. Clark) Microstructural Features The microstructures that evolve during the aging of a supersaturated solid solution are governed by the complex interplay of thermodynamic, kinetic, and structural factors controlling the basic processes of nucleation, growth, and coarsening. The precipitation system maximizes the rate of free energy release and not the overall free energy change as it decomposes toward the state of stable equilibrium. Thus, coherent transition precipitates often appear in preference to the equilibrium phase, because of more favorable nucleation kinetics. Precipitation of these metastable phases generally produces uniform, fine-scale microstructures that can enhance the physical and mechanical properties of commercial alloys. The location of metastable solvus curves is essential to understanding and controlling the precipitation sequences of age-hardening systems. The distribution and morphology of the precipitate phase depend on the nature of the active nucleation sites, the compromise between surface and strain energies, and the type of interphase interface that develops between the precipitate and matrix. A two-phase mixture can also evolve during precipitation through a cooperative growth mechanism similar to the cellular phase separation in eutectic and eutectoid transformations. This cellular precipitation reaction often leads to the formation of the equilibrium precipitate and subsequent degradation of such properties as strength and ductility. Therefore, control of this reaction can be critical to optimizing properties in age-hardenable alloys. Trace element additions have been used effectively to suppress the nucleation and growth of this microconstituent. Spinodal Structures David E. Laughlin, Professor of Metallurgical Engineering and Materials Science, Carnegie-Mellon University; William A. Soffa, Professor of Metallurgical and Materials Engineering, University of Pittsburgh Introduction SPINODAL STRUCTURES are finescale, homogenous two-phase mixtures resulting from a phase separation that takes place under certain conditions of temperature and composition. The conjugate phases produced by the spinodal decomposition of a supersaturated solid solution differ in composition from the parent phase, but have essentially the same crystal structure. Precipitation by spinodal decomposition may occur in conjunction with an ordering reaction, as discussed below. The simplest phase transformation that can produce a spinodal reaction product is decomposition within a stable or metastable miscibility gap, as shown in Fig. 1. If a solid solution of composition C 0 is solution treated in the single-phase field at a temperature T 0 , then aged at an intermediate temperature T A (or T A' ), the single-phase alloy tends to separate into a two-phase mixture. At the temperature T A , the compositions of the conjugate phases α 1 , and α 2 under equilibrium conditions are C 1 and C 2 , respectively. However, the supersaturated solid solution may decompose into two phases along two different reaction paths. Fig. 1 Schematic showing miscibility gap in the solid state and spinodal lines (chemical and coherent) At small undercoolings or low supersaturations (T A' ), the solution is metastable; appearance of a second phase requires relatively large localized composition fluctuations. This is the classical nucleation process, giving rise to "critical nuclei," which can grow spontaneously. As the particles of the new phase grow by diffusion, the matrix composition adjusts toward equilibrium. At large supersaturations (T A ), the solution is unstable, and the two-phase mixture gradually emerges by the continuous growth of initially small amplitude fluctuations (see Fig. 2). The rate of reaction is controlled by the rate of atomic migration and the diffusion distances involved, which depend on the scale of decomposition (undercooling). Therefore, spinodal structures refer to phase mixtures that derive from a particular kinetic process governing the initial stages of phase separation. The "spinodal line" shown in Fig. 1 is not a phase boundary but a demarcation indicating a difference in thermodynamic stability. Fig. 2 Schematic illustrating two sequences for the formation of a two- phase mixture by diffusion processes: nucleation and growth and spinodal decomposition. (Ref 1) Reference 1. J.W. Cahn, Trans. Met. Soc. AIME, Vol 242, 1968, p 166 Theory of Spinodal Reactions The spinodal reaction is a spontaneous unmixing or diffusional clustering distinct from classical nucleation and growth in metastable solutions. This different kinetic behavior, which does not require a nucleation step, was first described by Gibbs in his treatment of the thermodynamic stability of undercooled or supersaturated phases. The spinodal line in Fig. 1 indicates a limit of metastability with respect to the response of the system to compositional fluctuations. The locus, called the "chemical spinodal," is defined by the inflexion points of the isothermal free energy (G) composition curves ( ∂ 2 G/ ∂ C 2 = 0). Within the spinodes where ∂ 2 G/ ∂ C 2 < 0, the supersaturated solution is unstable and spinodal decomposition can occur. Spinodal decomposition or continuous phase separation involves the selective amplification of long wavelength concentration waves within the supersaturated state resulting from random fluctuations. The transformation occurs homogenously throughout the alloy via the gradual buildup of regions enriched in solute, resulting in a two-phase modulated structure. The continuous amplification of a quasi-sinusoidal fluctuation depicted in Fig. 2 is rather general, because this sinusoidal composition wave may be viewed as a Fourier component of an arbitrary composition variation that grows preferentially. The essential features of the spinodal process can be understood by considering this diffusional clustering as the inverse of the homogenization of a nonuniform solid solution exhibiting a sinusoidal variation of composition with distance. In metastable solutions, the small deviations from the average concentration, C 0 , will decay with time according to the equation ∆C = ∆C 0 exp (-t/τ), where the relaxation time τ ≈ λ 2 / ∆; λ is the wavelength of the fluctuation and D is the appropriate diffusion coefficient. In a binary system D ∝ ∂ 2 G/ ∂ C 2 , and within the spinodes ∂ 2 G/ ∂ C 2 < 0; that is, the curvature of the free energy-composition curve is negative. Therefore, in an unstable solid solution D ¨is negative, and "uphill" diffusion occurs. The amplitude of the concentration wave grows with time, that is, ∆C = ∆C 0 exp (+ R(β)t), where the amplification factor R(β) is a function of the wave number β= 2π/λ. The factor R(β) is a maximum for intermediate wavelengths. Long wavelength fluctuations grow sluggishly because of the large diffusion distances; short wavelength fluctuations are suppressed by the so-called gradient or surface energy of the diffuse or incipient interfaces that evolve during phase separation. Therefore, the microstructure that develops during spinodal decomposition has a characteristic periodicity that is typically 2.5 to 10 nm (25 to 100 A o ) in metallic systems. The factors controlling the spinodal reaction and resultant structures are clarified by examining the energetics of small- amplitude fluctuations in solid solutions. The free energy of an inhomogenous solution expressed as an integral over the volume, V, of the crystal can be written as: G = ∫{ f (C) + K ∇ C 2 + E s }dV where f (C) is the free energy per unit volume of a uniform solution of composition C, K is the gradient energy parameter, and E s is a strain energy term that depends on the elastic constants and misfit (difference in lattice parameter) between the solute-enriched and solute-depleted regions. For a sinusoidal composition fluctuation C - C 0 = A sin βx (where A is the amplitude of the sine wave), the gradient or surface energy term varies as Kβ 2 and prohibits decomposition on a fine scale. The wavelength of the dominant concentration wave that essentially determines the scale of decomposition varies as K 1/2 (∆T) -1/2 , where ∆T = T S - T A , in which T S is the spinodal temperature. The coherency strain energy term is independent of wavelength, but can vary markedly with crystallographic direction in elastically anisotropic crystals. Therefore, the dominant concentration waves will develop along elastically "soft" directions in anisotropic systems. For most cubic materials, the <100> directions are preferred, although <111> waves are predicted in certain alloys, depending on the so-called anisotropy factor. The strain energy can also stabilize the system against decomposition and effectively displace the spinodal curve (and the solvus), thus defining a "coherent spinodal" (Fig. 1). Periodic composition fluctuations in the decomposing solid solution cause diffraction effects known as "satellites" or "sidebands." The fundamental reflections in reciprocal space are flanked by satellites or secondary maxima, and the distance of the satellites from the fundamental varies inversely with the wavelength of the growing concentration wave. This diffuse scattering arises from the periodic variation of the lattice parameter and/or scattering factor. The strain effects are negligible around the origin of reciprocal space. Small-angle x-ray and neutron scattering can be used to study quantitatively the kinetics of the reaction by monitoring the changes in the intensity distribution around the direct beam due to changes in the structure factor modulations. The electron diffraction pattern of a spinodally decomposed copper- titanium alloy shown in Fig. 3 reveals the dominant <100> concentration waves that develop during the early stages of phase separation. Fig. 3 [001] electron diffraction pattern from spinodally decomposed Cu- 4Ti (wt%) alloy aged 100 min at 400 °C (750 °F) showing satellites flanking the matrix reflections. (A. Datta) Microstructure If the strain energy term in the free energy expression is negligible (small misfit) or if the elastic modulus is isotropic, the resultant microstructure will be isotropic, similar to the morphologies evolving in phase-separated glasses. In Fig. 4, an isotropic spinodal structure developed in a phase-separated iron-chromium-cobalt permanent magnet alloy is clearly revealed by transmission electron microscopy. The two-phase mixture is interconnected in three dimensions and exhibits no directionality. The microstructure is comparable to the computer simulation of an isotropically decomposed alloy shown in Fig. 5 (Ref 1). In Fig. 6, the dominant composition waves have developed preferentially along the <100> matrix directions to produce an aligned modulated structure in a copper-nickel-iron alloy. Because the homogenous phase separation process is relatively structure-insensitive, the spinodal product is generally uniform within the grains up to the grain boundaries, as revealed in the copper-nickel-chromium spinodal alloy shown in Fig. 7. Fig. 4 Transmission electron micrograph of isotropic spinodal structure developed in Fe-28.5Cr- 10.6Co (wt%) alloy aged 4 h at 600 °C (1110 °F). Contrast derives mainly from structure- factor differences. 225,000×. (A. Zeltser) Fig. 5 Computer simulation of an isotropically decomposed microstructure. (J.W. Cahn and M.K. Miller) Fig. 6 Spinodal microstructure in a 51.5Cu-33.5Ni-15Fe (at.%) alloy aged 15 min at 775 °C (1 425 °F) revealed by transmission electron microscopy. Foil normal is approximately [001], and the alignment along the <100> matrix directions is apparent. The wavelength of the modulated structure is approximately 25 nm (250 A o ). 70,000×. (G. Thomas) Fig. 7 Transmission electron micrograph of spinodal microstructure developed in a 66.3Cu-30Ni-2.8Cr (wt%) alloy during slow cooling from 950 °C (1740 °F). The microstructure is homogenous up to the grain boundary indicated by the arrow. 35,000×. (F.A. Badia) Atomic ordering and spinodal clustering can occur concomitantly in a precipitation system (see Ref 2 for a review of ordering and spinodal decomposition). In these systems, a supersaturated phase spinodally decomposes into two phases, one or both of which are ordered. A transmission electron micrograph of a spinodally decomposed iron-beryllium alloy is shown in Fig. 8, and a corresponding field-ion micrograph is shown in Fig. 9. The brightly imaged phase in the electron micrograph (Fig. 8) is the ordered phase (B2 superstructure), whereas the brightly imaged phase in the field-ion micrograph (Fig. 9) is the iron-rich disordered phase. The microstructure is periodic and aligned along the "soft" <100> directions. Fig. 8 Spinodal structure aligned along <100> directions of decomposed Fe-25Be (at.%) alloy aged 2 h at 400 °C (750 °F). The bright phase is the Be-enriched ordered B2 structure revealed by clark- field imaging using a superlattice reflection; the dark phase is the Fe- rich disordered (or weakly ordered) transformation product. The TEM foil normal is approximately [001]. 200,000×. (M.G. Burke) [...]... Copper-aluminum 19 550 1020 bcc → fcc Copper-zinc 3 7-3 8 40 0-5 00 75 0-9 30 bcc → fcc Copper-gallium 2 1-2 7 580 1075 bcc € hcp 20 600 1110 bcc → fcc Iron 700 1290 fcc → bcc Iron-cobalt 0-2 5 65 0-8 00 120 0-1 470 fcc → bcc Iron-chromium 0-1 0 60 0-8 00 111 0-1 470 fcc → bcc Iron-nickel 0-6 50 0-7 00 93 0-1 290 fcc → bcc Plutonium-zirconium 5-4 5 450 840 bcc → fcc (a) Values listed are approximate (b) bcc, body-centered... brass) Lamellar pearlite; granular pearlite °F 565 High-temperature phase and crystal structure CuBe 6 Be 605 1121 β-bcc α-fcc β'-bcc (CsCl) Lamellar pearlite Cu-In 31.4 In 574 1065 β-bcc α-fcc δ(deformed gamma brass) Lamellar pearlite; granular pearlite Cu-Si 5.2 Si 555 1031 κ-hcp α-fcc γ-cubic (β-Mn) Granular pearlite CuSn 27.0 Sn 520 968 γ-bcc α-fcc δ(gamma brass) Lamellar pearlite; needles of αabout... δ(gamma brass) α-fcc ε-orthorhombic Lamellar pearlite Fe-C 0.80 C 723 1333 γ-fcc(interstitial C) α-bcc Fe3C-orthorhombic Lamellar pearlite Fe-N 2.35 N 590 1094 γ-fcc (interstitial N) α-bcc γ'-fcc (interstitial N) Lamellar pearlite; granular pearlite Fe-O 23.3 O 560 1040 Wüstite cubic (NaCl) α-bcc Fe3O4cubic (spinel) Lamellar pearlite; granular pearlite NiZn 56 Zn 675 1247 β-cubic (CsCl) β1-tetragonal (CuAu)... (see arrows) spaced 10 to 15 nm (100 to 150 A ) in the bainite/ferrite interface of a high-silicon steel (Fe-0.4C-4.15Ni-2.01Si), austenitized at 1100 °C (2010 °F) for 30 min and isothermally transformed at 370 °C (700 °F) for 8 h 580,000× (Ref 19) Fig 11 Thin-foil transmission electron micrograph of a tempered upper bainite microstructure in a high-silicon steel (Fe-0.43C-3.0Mn-2.12Si) that was austenitized... a high-silicon steel (Fe-0.43C-3.0Mn-2.12Si) austenitized at 1200 °C (2190 °F) for 5 min and isothermally transformed at 350 °C (660 °F) for 205 min 20,000× (Ref 17) Fig 9 Thin-foil transmission electron micrograph illustrating deformation twinning in retained austenite of upper bainite microstructure in a high-silicon steel (Fe-0.4C-4.1.5N-2.01Si), austenitized at 950 °C (2120 °F) for 15 min and isothermally... metals and binary systems are given in Table 1 Table 1 Typical massive transformations Alloy system or metal Amount of solute at which transformation occurs(a), at.% Temperature during quenching at which transformation occurs(a) °C Change in crystal structure(b) °F Silver-aluminum 2 3-2 8 600 1110 bcc → hcp Silver-cadmium 4 1-4 2 30 0-4 50 57 0-8 40 bcc → fcc 50 300 570 bcc → hcp Silver-zinc 3 7-4 0 25 0-3 50 48 0-6 60... pearlite Ti-Cr 15 Cr 680 1256 β-bcc α-hcp TiCr2-fcc (MgCu2) Lamellar pearlite; granular pearlite Source: Ref 1 Fig 1 Typical pearlite structure of alternate layers of ferrite and cementite in an Fe-0.8C alloy Picral 500× Fig 2 Eutectoid region of the Fe-Fe3C phase diagram Fig 3 Nonlamellar eutectoid structure in a Cu-27Sn alloy Electrolytic etchant: 1% CrO3 150 × References 1 C.W Spencer and D.J Mack,... 2 315 4 T.B Massalski, The Mode and Morphology of Massive Transformations in Cu-Ga, Cu-Zn, Cu-Zn-Ga and Cu-Ga-Ge Alloys, Acta Metall., Vol 6, 1958, p 243 5 G.A Sargent, L Delaey, and T.B Massalski, Formation of "Feathery" Structures During Massive Transformation in Cu-Ga Alloys, Acta Metall., Vol 16, 1968, p 723 6 H Gleiter and T.B Massalski, Atomistic Model for the Growth of Feathery Structures in Duplex... congruent point (such as the bcc and hcp phases in aluminum-silver at 24.5 at.% Ag) In these instances, the critical composition line does not cross a two-phase field, and thus a possible massive transformation is not interfered with by another transformation that might require long-range diffusion and solute partitioning Therefore, in such alloys, or in others for which the two-phase field is suitably narrow,... is characteristic of a process of random and rapid growth (Fig 2) Microstructures of this type have been observed in iron, low-carbon steels, and low-nickel steels Fig 2 Fe-0.002C alloy quenched in iced brine from 1000 °C (1830 °F) Microstructure, which resulted from a massive transformation, shows ferrite grains with irregular boundaries Etchant: 2% nital 350× Two-Phase Fields Massive transformations . structure (b) Silver-aluminum 2 3-2 8 600 1110 bcc → hcp 4 1-4 2 30 0-4 50 57 0-8 40 bcc → fcc Silver-cadmium 50 300 570 bcc → hcp Silver-zinc 3 7-4 0 25 0-3 50 48 0-6 60 bcc → fcc Copper-aluminum 19. → fcc Copper-zinc 3 7-3 8 40 0-5 00 75 0-9 30 bcc → fcc Copper-gallium 2 1-2 7 580 1075 bcc € hcp 20 600 1110 bcc → fcc Iron . . . 700 1290 fcc → bcc Iron-cobalt 0-2 5 65 0-8 00 120 0-1 470 fcc. 0-2 5 65 0-8 00 120 0-1 470 fcc → bcc Iron-chromium 0-1 0 60 0-8 00 111 0-1 470 fcc → bcc Iron-nickel 0-6 50 0-7 00 93 0-1 290 fcc → bcc Plutonium-zirconium 5-4 5 450 840 bcc → fcc (a) Values