Single-crystal elastic constants of Fe-15Ni-15Cr alloy

Resonant ultrasound spectroscopy (RUS) and pulse-echo (PE) superposition techniques have been used to determine the three independent elastic-stiffness constants C₁₁, C₁₂, and C₄₄ as a function of temperature for single crystals of 70Fe-15Ni-15Cr alloy. The values of the elastic moduli determined using RUS and PE are in very good agreement within the range of uncertainties. This particular ternary composition of Fe, Ni, and Cr undergoes an fcc-bcc structural phase transformation near 190 K resulting in a low-temperature ferromagnetic phase. The Debye characteristic temperature was determined to be 447 K from PE and 451 K from RUS measurements. The Zener elastic anisotropy A=2C₄₄/(C₁₁−C₁₂) is nearly constant: A=3.53±0.16 in Fe-Ni-Cr alloys with similar compositions. For these alloys, only small variations are observed in the Grüneisen parameter, γ≈2.08, and in the Poisson ratio, v _[hkl]=0.293±0.013.     

Electronic origin of elastic properties of titanium carbonitride alloys

We have carried out numerical ab initio calculations of the elastic constants for several cubic ordered structures modeling titanium carbonitride (TiC_xN_1−x) alloys. The calculations were performed using the full-potential linear augmented plane-wave method (FPLAPW) to calculate the total energy as functions of volume and strain, after which the data were fit to the traditional Murnaghan equation of state and to a polynomial function of strain to determine the formation energy; the bulk modulus; and the elastic constants C ₁₁, C ₁₂ and C ₄₄. The predicted equilibrium lattice parameters are slightly higher than those found experimentally (on average by 0.2 pct). The computed formation energy indicates that the alloys are stable in the entire range of the carbon concentration x and the maximum stability is obtained for 0.5≤x≤0.75. The computed bulk modulus, the shear modulus G, and the Young’s modulus E are within approximately 2, 1, and 2 pct of the experimentally measured characteristics, respectively. The maximum deviation is observed for TiC and TiN. The moduli G, E, and Poisson’s ratio reach a maximum value at approximately the middle of the concentration range, which is due to the fact that the shear modulus C ₄₄ shows a maximum value for a valence electron concentration (VEC) in the range of 8.25 to 8.5. The other shear modulus (C ₁₁−C ₁₂)/2 does not exhibit any maximum overall concentration range and instead has a flat dependence in the range mentioned previously. Such a concentration behavior of the elastic constants is related to specific changes in the band structure of TiC_xN_1−x alloys caused by the orthorhombic and monoclinic strains that determine the shear moduli (C ₁₁−C ₁₂)/2 and C ₄₄, respectively. This article is based on a presentation made in the symposium entitled “Fourth International Alloy Conference”, which occurred in Kos, Greece, from June 26 to July 1, 2005, and was sponsored by Engineering Conferences International (ECI) and co-sponsored by Lawrence Livermore National Laboratory and Naval Research Laboratory, United Kingdom.     

The effect of elastic anisotropy on dislocations in Ni3Fe

The single crystal elastic constants of Ni₃Fe were measured by an ultrasonic interferometric technique in the temperature range -196° to 300°C. Both C₁₁ and C₄₄ decrease with increasing temperature, while C₁₂ remains almost constant below room temperature, then increases with temperature up to 100°C and subsequently decreases as temperature increases further. The constants have been used to calculate 1) the interaction force between parallel Shockley partial dislocations and 2) the energy factor of a straight perfect dislocation as a function of dislocation orientation. While dissociation of a screw dislocation seems quite normal, the forces between partials in a dissociated edge dislocation are attractive at -196° and 100°C. In general, the maximum stacking fault energy for which dissociation is energetically favorable, γ_m, decreases as temperature increases. Inverse Wulff plots indicate that thea/2 <110> total dislocation in Ni₃Fe is stable for all orientations and temperatures.     

Elastic interaction energy of two spherical precipitates in an anisotropic matrix

Following the difference method of Eshelby, the elastic interaction energy between two spherical precipitates embedded in an infinite matrix of cubic anisotropy is studied as a function of their distance of separation and alignment direction. When the precipitates are positioned along the [100] direction of the matrix phase, the elastic interaction is found to be attractive and often to exhibit a maximum value at an intercenter distance of two to three radii. For the [110] and [111] alignments, the results depend on the sign of the anisotropic factor,H=2C₄₄+C₁₂−C₁₁, of the matrix phase. When it is positive as in Cu and Ni, the interaction is found to be repulsive. In the reverse case, the situation is substantially different; for the [111] alignment with a Mo matrix, the interaction is found to be of an attractive nature.     

Neutron scattering studies of premartensitic indium-thallium alloys

A set of measured phonon dispersion curves for In-Tl at a temperature slightly greater thanjhe structural transformation temperature,T _m , has failed to show phonon softening of the [ζζ0] [ζζ-z0] branch to within ζ = 0.15 of the zone center. To reconcile this with the known softening of the elastic constant, 1/2 (C ₁₁ —C ₁₂) requires that the dispersion curve show a strong positive curvature at low ζ along this branch. Experiments on a second set of crystals, grown as oriented flat plates, were designed to investigate the [ζζ0] [ζζ-z0] phonons and their temperature dependence in the premartensitic temperature regime. The results from these crystals support the positive curvature at low ζ for the [ζζ0] [ζζ-z0] branch. In addition the low-ζ, [ζζ0] [ζζ-z0] phonons show the normal trend of frequency increasing (hardening) as temperature is decreased toward the transformation temperature, indicating that the phonon softening predicted by the temperature dependence of the elastic modulus, 1/2 (C ₁₁ -C ₁₂), is confined to smaller phonon wave vectors than can be resolved in the present experiments. This paper is based on a presentation made in the symposium “Pretransformation Behavior Related to Displacive Transformations in Alloys≓ presented at the 1986 annual AIME meeting in New Orleans, March 2–6, 1986, under the auspices of the ASM-MSD Structures Committee.     

The effect of Nb and W alloying additions to the thermal expansion anisotropy and elastic properties of Mo<Subscript>5</Subscript>Si<Subscript>3</Subscript>

The directional thermal expansion and elastic properties of Mo₅Si₃, (Mo_0.8Nb_0.2)₅Si₃, and (Mo_0.85W_0.15)₅Si₃ have been studied as a function of temperature through the use of single crystals. Thermal expansion anisotropy was reduced by Nb and W alloying. The decrease in thermal expansion anisotropy by Nb alloying was only found to occur at low temperatures, and thermal expansion anisotropy of (Mo_0.8Nb_0.2)₅Si₃ was similar to that for the other two compounds at 800 °C. Values for the polycrystalline Young’s, bulk, and shear moduli calculated from the measured single-crystal elastic constants are reduced by Nb alloying, and increased by W alloying at all temperatures studied. The elastic modulus E was calculated for the orientations between [100]-[001] and [100]-[010]. In contrast to the effects of Nb on thermal expansion anisotropy, Nb alloying increased the E _[001]/E _[100] elastic anisotropy. This article is based on a presentation made in the symposium entitled “Beyond Nickel-Base Superalloys,” which took place March 14–18, 2004, at the TMS Spring meeting in Charlotte, NC, under the auspices of the SMD-Corrosion and Environmental Effects Committee, the SMD-High Temperature Alloys Committee, the SMD-Mechanical Behavior of Materials Committee, and the SMD-Refractory Metals Committee.     

Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components ε* _xx and ε* _yy . For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t=ε* _yy /ε* _xx . We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t=1) and those with pure shear misfit (t=−1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (−1<t<1; t ≠ 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0<t<1. For systems which allow an invariant line (−1≤t<0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0<t≤1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.     

Structure and properties of multicomponent eutectic alloys based on chromium and titanium carbide

We have investigated alloys in the Cr-Mo-Ti-C, Cr-Re-Ti-C, and Cr-Mo-Re-Ti-C systems in the eutectic <Cr>+<TiC> crystallization region. We found a four component quasibinary eutectic <Cr, Mo>+<TiC> with 4–8 at. % molybdenum content with melting point 1630°C. Additions of 3–11 at. % Mo or 5–20 at. % Re to the base eutectic alloy Cr₇₉Ti₁₂C₉ doubles the Vickers hardness at 1000°C (to approximately 2000 MPa), and simultaneous introduction of molybdenum and rhenium (the alloy Cr₅₁Mo₈Re₂₀Ti₁₂C₉) raises the hardness to 3000–3500 MPa. Ukrainian Materials Science Institute, National Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 1–2, pp. 15–23, January–February, 1997.     

Crystallization kinetics of amorphous magnesium-rich magnesium-copper and magnesium-nickel alloys

Amorphous magnesium-rich alloys Mg _y X_1-y (X=Ni or Cu and 0.82<y<0.89) have been produced by melt spinning. The crystallization kinetics of these alloys have been determined by in situ X-ray diffraction (XRD) and isothermal and isochronal differential scanning calorimetry (DSC) combined with ex situ XRD. Microstructure analysis has been performed by means of transmission electron microscopy (TEM) and electron energy loss spectroscopy (EELS). Crystallization of the Mg-Cu alloys at high temperature takes place in two steps: primary crystallization of Mg, followed by simultaneous crystallization of the remaining amorphous phase to Mg and Mg₂Cu. Crystallization of the Mg-Cu alloys at low temperatures takes place in one step: eutectic crystallization of Mg and Mg₂Cu. Crystallization of the Mg-Ni alloys for a Mg content, y>0.85, takes place in two steps: primary crystallization of Mg and of a metastable phase (Mg_∼5.5Ni, with Mg content y=0.85), followed by the decomposition of Mg_∼5.5Ni. Crystallization of the Mg-Ni alloys for a Mg content y<0.85 predominantly takes place in one step: eutectic crystallization of Mg and Mg₂Ni. Within the experimental window applied (i.e., 356 K<T<520 K and 0.82<y<0.89), composition dependence of the crystallization sequence in the Mg-Cu alloys and temperature dependence of the crystallization sequence in the Mg-Ni alloys has not been observed.     

Ductile and High Strength White Cast Iron of Ultrafine Interconnected Network Morphology

Fe_100–x C _x melts (x = 18 to 24) can be cast under B₂O₃ flux into solids of interconnected network morphology, with a wavelength in the submicron range. There are two major constituent subnetworks, which are a brittle Fe₃C subnetwork and a ductile αFe subnetwork. The Fe_100–x C _x network alloys, therefore, are white cast iron of novel microstructure. Fe_100–x C _x specimens of x = 18 to 21 are ductile and the yield strength can be as large as ~3200 MPa. Fe_100–x C _x specimens of x = 22 to 24 are in the regime of a ductile-to-brittle transition. The compressive strength is high, at ~2700 MPa. Microstructural analysis indicates that the ultrafine network morphology and the ductile αFe subnetwork are responsible for the ductility exhibited in Fe_100–x C _x network alloys of x = 17 to 21. They are also responsible for the high compressive strength in Fe_100–x C _x network alloys of x = 22 to 24.     

Alloy structure and phase-equilibrium diagram FCR the Sc-Ru-Rh system. Part 3, 1400°C isothermal section of the partial system Ru-ScRu-ScRh-Rh

An isothermal section at 1400°C is considered for the partial system Ru-ScRu-ScRh-Rh. As no ternary compound is formed in this system, one finds that the equilibria in the solid state at this temperature involve phases based on the binary compounds ScRu₂ and ScRh₃ and the δ phase (a continuous series of solid solutions between isostructural phases of CsCl type based on ScRu and ScRh) and solid solutions based on ruthenium and rhodium, which form five single-phase regions in the isothermal section, seven two-phase ones, and three three-phase ones: <Ru>+<ScRu₂>+δ, <Ru>+δ+<ScRh₃>, and <Ru>+<Rh>+<ScRh₃>. Materials Science Institute, Ukrainian National Academy of Sciences, Kiev. Translated from Poroshkovaya Metalurgiya, Nos. 7–8, pp. 38–43, July –August, 1997.     

Dislocation production in alpha Fe-C alloys by rapid heating

It is demonstrated that metastable carbide particles in α-Fe act as sources of dislocations when heated rapidly to a temperature where the particles are unstable. The type and arrangement of such dislocations are dependent on the rate of heating. At moderate heating rates, the particles produce well-defined groups of equally spaced interstitial dislocation loops lying on {100} planes, with Burgers vectors ofa<100>. Cementite (Fe₃C) particles of comparable size dissolve without producing dislocations. The original metastable particle sites retain carbon in the form of small globular particles which may be graphite. At faster heating rates, the dislocation arrangement becomes more disorderly with both b =a<100> and b =a/2<111> dislocations emanating from the same particle.     

Variability of large-crack fatigue-crack-growth thresholds in structural alloys

The fatigue threshold of large cracks is known to show substantial variations due to microstructural variability in structural alloys. The ΔK _th variations are dependent on the stress ratio (R); they are extremely large at low R ratios, e.g., R<0.5, but are drastically reduced at high R ratios (R>0.8). The origins of these large variations due to intrinsic and extrinsic mechanisms are examined by theoretical analyses. First, an intrinsic fatigue crack growth (FCG) threshold model is developed for structural alloys by considering the cyclic slip process at the crack tip. Second, the effects of extrinsic mechanisms such as residual plastic stretch, crack deflection, fracture-surface roughness, and oxide wedging are considered both individually and concurrently in order to delineate their relative contributions to threshold variability. The theoretical results indicate that the intrinsic threshold depends on the elastic properties, magnitude of the Burgers vector, yield stress, and Taylor factor (i.e., texture), but is independent of the R ratio or the maximum applied stress intensity factor, K _max. The large variability of ΔK _th at low R ratios and their corresponding dependence on K _max appear to arise from various crack closure mechanisms. Applications of the threshold models to structural alloys show good agreement between theory and experimental data from the literature for steels, Ti, Al, Ni, Cu, Nb, and Mo alloys.     

Sulfide capacities of Na2O−SiO2 melts

Sulfide capacities of Na₂O−SiO₂ melts at 1473, 1523, 1573, 1623, and 1673 K were calculateda priori using the revised Reddy Blander model. An expression forC _S in the composition range of 0≤X _{SiO 2}<1.0 was derived. Our predictions ofC _S values are in very good agreement with the experimental data available in the range of 0<X _{SiO 2}<0.8. The sulfide capacities of slags are found to be directly related to two independent quantities: the equilibrium constant K and the activity of the base oxide.     

Mechanisms of Hf dopant incorporation during the early stage of chemical vapor deposition aluminide coating growth under continuous doping conditions

A laboratory-scale chemical vapor deposition (CVD) reactor was used to perform “continuous” Hf doping experiments while the surface of a single-crystal Ni alloy was being aluminized to form an aluminide (β-NiAl) coating matrix for 45 minutes at 1150 °C. The continuous doping procedure, in which HfCl₄ and AlCl₃ were simultaneously introduced with H₂, required a high HfCl₄/AlCl₃ ratio (>∼0.6) to cause the precipitation of Hf-rich particles (∼0.1 μm) at grain boundaries of the coating layer, with the overall Hf concentration of ∼0.05 to 0.25 wt pct measured in the coating layer by glow-discharge mass spectroscopy (GDMS). Below this ratio, Hf did not incorporate as a dopant into the growing coating layer from the gas phase, as the coating matrix appeared to be “saturated” with other refractory elements partitioned from the alloy substrate. In comparison, the Hf concentration in the aluminide coating layer formed on pure Ni was in the range of ∼0.1 wt pct, which was close to the solubility of Hf estimated for bulk NiAl. Interestingly, the segregation of Hf and the formation of a thin γ′-Ni₃Al layer (∼0.5 μm) at the coating surface were consistently observed for both the alloy and pure-Ni substrates. The formation of the thin γ′-Ni₃Al layer was attributed to an increase in the elastic strain of the β-NiAl phase, associated with the segregation of Hf as well as other refractory alloying elements at the coating surface. This phenomenon also implied that the coating layer was actually growing at the interface between the γ′-Ni₃Al layer and the β-NiAl coating matrix, not at the gas/coating interface, during the early stage of the coating growth.     

Characterization of Ti4AlN3

Bulk samples of Ti₄AIN₃ were fabricated by reactive hot isostatic pressing (hipping) of TiH₂, AlN, and TiN powders at 1275 °C for 24 hours under 70 MPa. Further annealing at 1325 °C for 168 hours under Ar resulted in dense, predominantly single-phase samples, with <1 vol pct of TiN as a secondary phase. This ternary nitride, with a grain size of ≈20 μm on average, is relatively soft (Vickers hardness 2.5 GPa), lightweight (4.6 g/cm³), and machinable. Its Young’s and shear moduli are 310 and 127 GPa, respectively. The compressive and flexural strengths at room temperature are 475 and 350 MPa, respectively. At 1000 °C, the deformation is plastic, with a maximum compressive stress of ≈450 MPa. Ti₄AlN₃ thermal shocks gradually, whereby the largest strength loss (50 pct) is seen at a ΔT of 1000 °C. Further increases in quench temperature, however, increase the retained strength before it ultimately decreases once again. This material is also damage tolerant; a 100 N-load diamond indentation, which produced an ≈0.4 mm defect, reduces the flexural strength by only ≈12 pct. The thermal-expansion coefficient in the 25 °C to 1100 °C temperature range is 9.7±0.2 × 10⁻⁶ °C⁻¹. The room-temperature electrical conductivity is 0.5 × 10⁶ (Θ · m)⁻¹. The resistivity increases linearly with increasing temperature. Ti₄AlN₃ is stable up to 1500 °C in Ar, but decomposes in air to form TiN at ≈1400 °C. graduated from the Department in June of 1999 with an MS thesis.     

Creep expansion of porous Ti-6Al-4V sandwich structures

Low-density titanium alloy sandwich structures consisting of a porous core and fully dense face sheets can be produced by consolidating argon gas charged powder compacts followed by not rolling and annealing to expand the gas-filled pores. Little is known about the rate of pore expansion, its dependence upon temperature, and the morphological evolution of the pore shape during expansion. In situ eddy current and laser ultrasonic sensors have been combined with metallographic and texture measurements to measure the relative density, the elastic moduli, and the microstructural evolution of Ti-6Al-4V sandwich panels during the annealing stage of low-density core (LDC) processing. The eddy current data indicated that expansion began during, the heating phase, reached a maximum expansion rate (Δ) of 2 × 10⁻⁵ s⁻¹ at approximately 685 °C, and had almost ceased (Δ < 1 × 10⁻⁶ s⁻¹) after annealing for 4 hours at 920 °C. The elastic moduli were found to decrease with increasing temperature and volume fraction of porosity. The initial (as-rolled) microstructure consisted of a lamellar α + β microstructure with an α-phase lath thickness of 2.0 μm and contained a distribution of oblate-shaped pores with aspect ratios of up to 10. During the expansion process, it recrystallized into an equiaxed α + β structure with an α-phase grain diameter of 7.5 μm with spheroidal pores with aspect ratios of up to 3. The combination of the two sensors was found to enable the in situ determination of both the porous cores relative density and its elastic properties. These are the two material indices that govern the elastic response of a sandwich structure.     

Intermetallic-reinforced light-metal matrix in-situ composites

Transition-metal trialuminide intermetallics such as Al₃Zr and Al₃Ti, having low densities and high elastic moduli, are good candidates for the in-situ reinforcement of light-metal matrices based on Al and Mg alloys. In this work, in-situ composites based on Al and Al-Mg matrices reinforced with an Al₃Zr intermetallic were successfully processed by conventional ingot metallurgy. The microstructural studies showed that “needle” or “feathery”-like particles of Al₃Zr phase, whose volume fraction increased with increasing concentration of Zr, were formed in the Al matrix in the investigated range of Zr contents from 0.9 to 11.6 at. pct. Properties of Al-Zr alloys were investigated as a function of volume fraction of Al₃Zr. It is shown that the density, hardness, and yield strength of the in-situ Al/Al₃Zr composites can be quite adequately described by the composite rule-of-mixtures (ROM) behavior. Alloying of a binary Al-2.4 at. pct Zr alloy with Mg up to ∼25 at. pct reduces profoundly its density and, additionally, strengthens the matrix by a Mg solid-solution strengthening mechanism.     

Isothermal transformations in an Fe-9 pct Ni alloy

Isothermal transformation from austenite in an Fe-9.14 pct Ni alloy has been studied by optical metallography and examination by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). In the temperature range 565 °C and 545 °C, massive ferrite (α _q ) forms first at prior austenite grain boundaries, followed by Widmanst?tten ferrite (α _W ) growing from this grain boundary ferrite. Between 495 °C and 535 °C, Widmanst?tten ferrite is thought to grow directly from the austenite grain boundaries. Both these transformations do not go to completion and reasons for this are discussed. These composition invariant transformations occur below T ₀ in the two-phase field (α+γ). Previous work on the same alloy showed that transformation occurred to α _q > and α _W on furnace cooling, while analytical TEM showed an increase of Ni at the massive ferrite grain boundaries, indicating local partitioning of Ni at the transformation interface. An Fe-3.47 pct Ni alloy transformed to equiaxed ferrite at 707 °C ±5 °C inside the single-phase field on air cooling. This is in agreement with data from other sources, although equiaxed ferrite in Fe-C alloys forms in the two-phase region. The application of theories of growth of two types of massive transformation by Hillert and his colleagues are discussed. This article is based on a presentation made at the symposium entitled “The Mechanisms of the Massive Transformation,” a part of the Fall 2000 TMS Meeting held October 16–19, 2000, in St. Louis, Missouri, under the auspices of the ASM Phase Transformations Committee.