Function Of Pillar Diameter Research Articles

Effect of temperature on small-scale deformation of individual face-centered-cubic and body-centered-cubic phases of an Al0.7CoCrFeNi high-entropy alloy

High-entropy alloys (HEAs) represent an important class of structural materials because of their high strength, ductility, and thermal stability. Understanding the mechanical response of isolated phases of a FCC/BCC dual-phase HEA is integral to understanding the mechanical properties of these alloys in the bulk. We investigate the compressive response of single-crystalline cylinders with diameters between 400 nm and 2 μm excised from individual grains within FCC and BCC phases of the dual-phase Al0.7CoCrFeNi HEA at 295 K, 143 K, and 40 K. We observed a “smaller is stronger” size effect in the yield strength as a function of pillar diameter, D, of both alloy phases for all temperatures, with a power-law exponent, m, decreasing with temperature for the FCC phase, and remaining constant for all temperatures in the BCC phase. We found reduced work-hardening rates and more extensive strain bursts during deformation at lower temperatures in all samples. We performed molecular dynamics simulations of similar FCC and BCC HEA compression that displayed deformation dominated by dislocation slip at all temperatures. We discussed theories of low-temperature strengthening in HEAs, compared them to our experimental data and assessed how they manifest in the observed temperature-dependent size effect and work-hardening.

The size dependent strength of Fe, Nb and V micropillars at room and low temperature

The strength of focussed ion beam (FIB) machined [001] orientation single crystal micropillars of body centred cubic structured (bcc) metals Fe, Nb and V, with diameters 200–5000 nm, have been measured at 296 K and 193 K using nanoindentation equipment. The metals have similar critical temperatures for screw dislocation mobility, Tc, close to 350 K. All three metals deform on the (110) plane at both test temperatures and show very similar behaviour of the plastic flow stress, σp, normalised by the shear modulus resolved on the slip plane, μ, as a function of pillar diameter, d, normalised by the Burgers vector, b. At room temperature all metals show a size effect on strength described by power law relation σp/μ=A(d/b)n with n ≈ −0.6 and this is shown to mirror the behaviour of face centred cubic metals. At 193 K the three metals show a higher strength and larger size exponent n ≈ −0.3 and again their normalised flow data is very similar. The behaviour is consistent with the observation that the deformation size effect in bcc materials converges to that seen with face centred cubic (fcc) structure metals as testing temperature approaches Tc. The temperature and size dependence of the experimental data shows similarity with the prediction of strength models based on the geometric confinement of dislocation sources (the single dislocation arm model) and a temperature dependent friction stress. However the model cannot consistently capture the behaviour for the three metals studied.

Effect of Temperature on Small-Scale Deformation of Individual FCC and BCC Phases of Al0.7CoCrFeNi High Entropy Alloy

High Entropy Alloys (HEAs) represent an important class of structural materials because of their high strength, ductility, and thermal stability due to the solid solution nature of the multi-component metallic system. Understanding the mechanical response of isolated phases (FCC and BCC) of a dual-phase HEA is integral to understanding mechanical properties of these special alloys in bulk. We investigate the compressive response of single crystalline cylinders with diameters between 400 nm and 2 µm excised from individual grains within FCC and BCC phases of Al0.7CoCrFeNi HEA at 295 K, 143 K and 40 K. Micro-compression experiments were conducted in an in-situ SEM equipped with a custom-constructed cryogenic setup; FCC samples had a [324] crystallographic orientation, and those extracted from the BCC phase had a [001] orientation. We observed a smaller is stronger size effect in the yield strength as a function of pillar diameter, D, of both alloy phases for all temperatures, τ_y ∝D^m with a power law exponent, m, decreasing from -0.68 at 295K to -0.47 at 143K to -0.38 at 40K for FCC phase, and remaining constant at ~-0.33 for all temperatures for the BCC phase. We also observed reduced work hardening rates and more extensive strain bursts during deformation at lower temperatures in all samples. All deformed FCC samples contained multiple parallel slip offsets for all pillar sizes and temperatures; compressed BCC pillars had wavy slip traces, which are evidence of multiple intersecting slip systems. Transmission Electron Microscopy (TEM) microstructural analysis of the compressed FCC samples reveals parallel slip lines and distorted slip planes, while compressed BCC samples contained entangled dislocation networks, as well as several twinned regions in samples deformed at 40 K. Molecular dynamics (MD) simulations of representative FCC and BCC HEA compressions reveal that deformation in FCC HEAs is dominated by nucleation and propagation of partial dislocations along parallel slip planes but by partial dislocation/twinning in the BCC HEA at all temperatures. Simulations also predict a decrease in stacking fault energy with increased alloying. For example, a reduction in the stable stacking fault energy of the FCC HEA up to 55% with respect to pure constituents is observed. This reduction in stable stacking fault energy may drive the observed deformation mechanisms. We also discuss theories of low-temperature strengthening in HEAs, compare them to our experimental data and assess how they manifest in the observed temperature-dependent size effect.

Thermal design optimization of evaporator micropillar wicks

Heat pipes and vapor chambers act as efficient heat spreaders since they rely on phase change of the coolant. The evaporator design is critical and typically high performance is characterized by the high heat dissipation capability with low thermal resistance. In the past, there have been numerous experimental and modeling studies focused on the design of evaporator wicks of different geometries, but systematic studies to simultaneously optimize both the heat flux and thermal resistance have been limited. In this work, we developed a comprehensive model that considers both aspects to provide design guidelines for evaporator micropillar wicks. We show that capillary limited heat dissipation is best captured with a recently developed numerical model as compared to previous analytical models. We also developed a numerical model to obtain the effective wick thermal conductivity, which is a function of pillar diameter, pitch, and height. Smaller diameters with smaller pitches of the pillars had more thin film area and had larger effective wick thermal conductivities. Our parametric investigations show that trade-offs between lowest thermal resistance and maximum heat carrying load exists, and the actual wick geometry will be dictated by application specific requirements. Finally, we highlight the importance of accurately obtaining the accommodation coefficients to predict the effective wick thermal conductivity. The present work would enable in optimal design of micropillar wicks (with low thermal resistance and high dry-out heat flux) and the same methodology can be extended to other types of wick structures as well.

Silicon micropillars: high stress plasticity

AbstractSilicon micropillars obtained by FIB from Floating Zone silicon single crystal have been deformed in situ in a SEM between room temperature and 400 °C. Pillars with <123> axis were studied in order to promote single slip deformation. Mechanical data as a function of pillar diameter and surface deformation microstructures observed by SEM are reported. Yield stresses as a function of temperature are compared with those resulting from high‐pressure tests (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Size effects in the superelastic response of Ni54Fe19Ga27 shape memory alloy pillars with a two stage martensitic transformation

The superelastic behavior of Ni54Fe19Ga27 shape memory alloy (SMA) single crystalline pillars was studied under compression as a function of pillar diameter. Multiple pillars with diameters between 10μm and 200nm were cut on a single crystalline bulk sample oriented along the [110] direction as the compression axis and that had undergone fully reversible two stage martensitic transformation, i.e. L21 austenite to 10M/14M modulated martensite and then to L1o martensite. The results revealed an increase in the critical stress for stress-induced martensitic transformation and the yield strength of martensite with decreasing pillar size. The stress hysteresis also increased with the reduction in pillar size and the superelastic response started to diminish below 500nm pillar diameter. Two-stage martensitic transformation was suppressed for pillar sizes of 1μm and below, which were shown to exhibit a direct austenite to L1o transformation. Such a change in the transformation pathway, i.e. from a two stage to one stage transformation, was also observed in bulk single crystals with increasing temperature. We demonstrated the absence of two stage transformation in bulk at high temperatures. This finding suggests that decreasing the sample size and increasing the temperature have similar effects on the superelastic response of NiFeGa SMAs that had undergone two-stage transformation and indicates that a reduction in pillar diameter decreases the transformation temperature due to the difficulty of martensite nucleation on small scales. The damping coefficients of the pillars were also calculated and the results highlighted that damping capacities higher than those of bulk metallic alloys can be achieved using submicron sized pillars.

The scaling exponent in the size effect of small scale plastic deformation

Compression testing of micropillars (yield stress as a function of pillar diameter) has been interpreted in terms of very different scaling exponents for the size effect (smaller is stronger) in fcc and bcc metals and for ceramics, strongly correlated with the yield strengths of the materials. We show that the data is compatible with a single scaling exponent x=1, and that the reported exponents in the range 0–1 express no more than the micropillar diameters and bulk strengths. The single scaling exponent implies a minimum strength which scales with size in the same way for all materials. This size effect is not fundamentally different in the presence of and in the absence of a strain gradient. It is interpreted in terms of the space available for dislocation source operation. The absence of any experimental data below this minimum strength is strong confirmation of this interpretation.

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 μm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at ∼560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow (≤2 μm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 μm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2–16 μm range. For the smallest pillar (d = 2 μm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm “global” blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs.

Emergence of strain-rate sensitivity in Cu nanopillars: Transition from dislocation multiplication to dislocation nucleation

We demonstrate strain-rate sensitivity emerging in single-crystalline Cu nanopillars with diameters ranging from 75 up to 500 nm through uniaxial deformation experiments performed at different constant strain rates. In the range of pillar diameters and strain rates tested, we find that the size dependence of the pillar strength deviates from the ubiquitously observed power law to a relatively size-independent flow strength, markedly below the predicted theoretical strength for strain rates slower than 10 −1 s −1. We find this transition diameter, D t , to be a function of strain rate, where faster strain rates shift the transition diameter to smaller pillar diameters: D t ∼ 150 nm at 10 −3 s −1 and D t ∼ ⩽75 nm at 10 −1 s −1. We compute the activation volumes, Ω, as a function of pillar diameter at each strain rate and find that for pillar diameters below D t , the activation volumes are relatively small, Ω < 10 b 3. This range agrees favorably with atomistic simulations for dislocation nucleation from a free surface. We postulate a plasticity mechanism transition from dislocation multiplication via the operation of truncated dislocation sources, also referred to as single-arm sources, in pillars with diameters greater than D t to dislocation nucleation from the surface in the smaller samples.

In situ compression study of taper-free metallic glass nanopillars

Because tapering leads to inevitable artifacts in the analyses of compression experiments on micrometer sized pillars, in this study taper-free nanosized pillars of Zr-based metallic glass of Zr61.8Cu18Ni10.2Al10 composition with diameter ranging from 600 to 90 nm were fabricated. These pillars were compressed in situ in a transmission electron microscope as a function of pillar diameter. Under compression each pillar of large diameter exhibits predominant inhomogeneous and intermittent plastic flow characterized by shear banding (SB) events. However, pillars around 150 nm in diameter and below show homogeneous deformation during compression without SB.

Atomistic processes controlling flow stress scaling during compression of nanoscale face-centered-cubic crystals

The size dependence of strength observed in submicrometer face-centered-cubic (fcc) metallic crystals under uniform deformation depends on the interaction of pre-existing dislocations with surfaces. To date, however, the dislocation processes controlling flow stress scaling in fcc crystals less than 100 nm in size have remained an open question due to limited knowledge on microstructural evolution during deformation in such small volumes. Here, molecular dynamics computer simulations employing a technique of high-temperature annealing and quenching on porous crystals were used to generate complex dislocation microstructures in sub-75 nm Cu pillars with high initial dislocation densities of 10 16 m −2, which made it possible to quantitatively examine their evolution during compression as a function of pillar diameter. These simulations reveal a transition from a state of dislocation exhaustion, where mobile dislocations are lost at the free surface and the dislocation density steadily decreases, to a regime of intermittent plastic flow between elastic loading and source-limited activation inside the pillars. It is shown that plastic flow stresses predicted during dislocation exhaustion regime exhibit little to no size dependence, while pronounced size effects are found during source-limited activation. Remarkably, the relationship between flow stress predicted at 5% strain and diameter is found to follow closely the power-law dependence reported in past experiments with larger Cu crystals and smaller densities. A deformation mechanism map, expressed in terms of diameter, is developed and used to elucidate the origin of size-dependent plasticity in nanoscale fcc crystals.

Effects of focused ion beam induced damage on the plasticity of micropillars

The hardening effects of focused ion beam (FIB) induced damage produced during the fabrication of micropillars are examined by introducing a surface layer of nanosized obstacles into a dislocation dynamics simulation. The influence of the depth and strength of the obstacles as a function of pillar diameter is assessed parametrically. We show that for a selected set of sample sizes between 0.5 and $1.0\text{ }\ensuremath{\mu}\text{m}$, the flow strength can increase by $10--20\text{ }%$, for an obstacle strength of 750 MPa, and damage depth of 100 nm. On the other hand, for sizes larger and smaller than this range, the effect of damage is negligible. Results show that the obstacles formed during the FIB milling may be expected to alter the microstructure of micropillars, however, they have a negligible effect on the observed size-strength scaling laws.

InAs/InP quantum-dot pillar microcavities using SiO2/Ta2O5 Bragg reflectors with emission around 1.55 μm

We present optical characterization measurements from three-dimensional pillar microcavities comprising an InP spacer layer sandwiched between two SiO2/Ta2O5 Bragg reflectors. InAs quantum dots placed at the center of the InP spacer are used as broadband emitters. Emission into the lowest-order mode is observed at an energy of 820 meV in the wide-pillar limit, with shifts of approximately 30 meV in the ground state and more than 80 meV in higher-order modes for pillars of 2 μm diameter. Excellent agreement is found between the experimentally observed cavity mode energies as a function of pillar diameter and the predictions of guided-mode theory. Cavity quality factors in excess of 2200 are obtained for large diameter pillars, with a decrease to approximately 500 for pillars of 2 μm diameter.