William C. Lenthe

Three-dimensional sampling of material structure for property modeling and design

Newly developed 3-D tomographic techniques permit acquisition of quantitative materials data for input to structure-property models. At the mesoscale, techniques that enable sampling of larger material volumes provide information such as grain size and morphology, 3-D interfacial character, and chemical gradients. However, systematic approaches for determining the characteristic material volume for 3-D analysis have yet to be established. In this work, the variability in properties due to microstructure is discussed in the context of a methodology for defining volume elements that link microstructure, properties, and design. As such, we propose a 3-D sampling methodology based on convergence of microstructural parameters and associated properties and design considerations.

Quantitative voxel-to-voxel comparison of TriBeam and DCT strontium titanate three-dimensional data sets

Recently, techniques for the acquisition of three-dimensional tomographic and four-dimensional time-resolved data sets have emerged, allowing for the analysis of mm3 volumes of material with nm-scale resolution. The ability to merge multi-modal data sets acquired via multiple techniques for the quantitative analysis of structure, chemistry and phase information is still a significant challenge. Large three-dimensional data sets have been acquired by time-resolved diffraction contrast tomography (DCT) and a new TriBeam tomography technique with high spatial resolution to address grain growth in strontium titanate. A methodology for combining three-dimensional tomographic data has been developed. Algorithms for the alignment of orientation reference frames, unification of sampling grids and automated grain matching have been integrated, and the resulting merged data set permits the simultaneous analysis of all tomographic data on a voxel-by-voxel and grain-by-grain basis. Quantitative analysis of merged data sets collected using DCT and TriBeam tomography shows that the spatial resolution of the DCT technique is limited near grain boundaries and the sample edge, resolving grains down to 10 µm diameter for the reconstruction method used. While the TriBeam technique allows for higher-resolution analysis of boundary plane location, it is a destructive tomography approach and can only be employed at the conclusion of a four-dimensional experiment.

Microstructural statistics for fatigue crack initiation in polycrystalline nickel-base superalloys

In advanced engineering alloys where inclusions and pores are minimized during processing, the initiation of cracks due to cyclic loading shifts to intrinsic microstructural features. Criteria for the identification of crack initiation sites, defined using elastic-plastic loading parameters and twin boundary length, have been developed and applied to experimental datasets following cyclic loading. The criteria successfully quantify the incidence of experimentally observed cracks. Statistical microstructural volume elements are defined using a convergence approach for two nickel-base superalloys, IN100 and René 88DT. The material element that captures the fatigue crack-initiating features in René 88DT is smaller than IN100 due to a combination of smaller grain size and higher twin density.

Three-dimensional multimodal imaging and analysis of biphasic microstructure in a Ti–Ni–Sn thermoelectric material

The three-dimensional microstructure of levitation melted TiNi1.20Sn has been characterized using the TriBeam system, a scanning electron microscope equipped with a femtosecond laser for rapid serial sectioning, to map the character of interfaces. By incorporating both chemical data (energy dispersive x-ray spectroscopy) and crystallographic data (electron backscatter diffraction), the grain structure and phase morphology were analyzed in a 155 μm × 178 μm × 210 μm volume and were seen to be decoupled. The predominant phases present in the material, half-Heusler TiNiSn, and full-Heusler TiNi2Sn have a percolated structure. The distribution of coherent interfaces and high-angle interfaces has been measured quantitatively.

Bayesian inference of elastic properties with resonant ultrasound spectroscopy

Bayesian modeling and Hamiltonian Monte Carlo (HMC) are utilized to formulate a robust algorithm capable of simultaneously estimating anisotropic elastic properties and crystallographic orientation of a specimen from a list of measured resonance frequencies collected via Resonance Ultrasound Spectroscopy (RUS). Unlike typical optimization procedures which yield point estimates of the unknown parameters, computing a Bayesian posterior yields probability distributions for the unknown parameters, and HMC is an efficient way to compute this posterior. The algorithms described are demonstrated on RUS data collected from two parallelepiped specimens of structural metal alloys. First, the elastic constants for a specimen of fine-grain polycrystalline Ti-6Al-4 V with random crystallographic texture and isotropic elastic symmetry are estimated. Second, the elastic constants and crystallographic orientation for a single crystal Ni-based superalloy CMSX-4 specimen are accurately determined, using only measurements of the specimen geometry, mass, and resonance frequencies. The unique contributions of this paper are as follows: the application of HMC for sampling the Bayesian posterior of a probabilistic RUS model, and the procedure for simultaneous estimation of elastic constants and lattice-specimen misorientation. Compared to previous approaches these algorithms demonstrate superior convergence behavior, particularly when the initial parameterization is unknown, and enable substantially simplified experimental procedures.

Prediction of Fatigue-Initiating Twin Boundaries in Polycrystalline Nickel Superalloys Informed by TriBeam Tomography

Fatigue is the life limiting property of polycrystalline nickel-base superalloys used for turbine disks. Alloys processed through advanced powder metallurgical routes have minimal concentrations of pores, inclusions, or other extrinsic defects that commonly serve as crack initiation sites. Instead, fatigue cracks initiate at intrinsic defects resulting in microstructurally sensitive and difficult to predict fatigue response [1]. Crack formation and short crack growth accounts for 80% of lifetime in the high cycle fatigue regime resulting in highly variable lifetimes spanning up to three orders of magnitude [1, 2]. Identifying and characterizing regions amenable to initiation and initial propagation of cracks is crucial for improving fatigue life predictions.

Microstructure and Property-Based Statistically Equivalent Representative Volume Elements for Polycrystalline Ni-Based Superalloys Containing Annealing Twins

This paper has three major objectives related to the development of computational micromechanics models of Ni-based superalloys, containing a large number of annealing twins. The first is the development of a robust methodology for generating 3D statistically equivalent virtual polycrystalline microstructures (3D-SEVPM) of Ni-based superalloys. Starting from electron backscattered diffraction (EBSD) images of sections, the method develops distributions and correlation functions of various morphological and crystallographic parameters. To incorporate twins in the parent grain microstructure, the joint probability of the number of twins and parent grain size, and the conditional probability distributions of twin thickness and twin distance are determined. Subsequently, a method is devised for inserting twins following the distribution functions. The overall methodology is validated by successfully comparing various statistics of the virtual microstructures with 3D EBSD data. The second objective is to establish the microstructure-based statistically equivalent representative volume element or M-SERVE that corresponds to the minimum SERVE size at which the statistics of any morphological or crystallographic feature converge to that of the experimental data. The Kolmogorov–Smirnov (KS) test is conducted to assess the convergence of the M-SERVE size. The final objective is to estimate the property-based statistically equivalent RVE or P-SERVE, defined as the smallest SERVE, which should be analyzed to predict effective material properties. The crystal plasticity finite-element model is used to simulate SERVEs, from which the overall material response is computed. Convergence plots of material properties including the yield strength and hardening rate are used to assess the P-SERVE. A smaller P-SERVE compared to the M-SERVE indicates that the characteristic features of twins implemented in determining the M-SERVE are more stringent than those for determining material properties.

Femtosecond Laser Damage in Metals and Semiconductors During TriBeam Tomography

The incorporation of ultrashort pulsed lasers into a dualbeam electron microscope, otherwise known as the TriBeam, has enabled applications such as the fast removal of material for tomography [1], micromachining, plasma based chemical diagnostics [2], and beam chemistry [3]. The unique low damage properties of commercial femtosecond lasers arise from the large impulse of energy imparted into the electronic structure of a material over time periods typically between 20-500 femtoseconds yielding complicated thermo-mechanical loading.

Quantitative Analysis of Correlated 3D Strontium Titanate Datasets Collected by TriBeam and Diffraction Contrast Tomography

Much attention has been paid to the idea of the correlation of analytical techniques such as tomography. Recently, techniques for the acquisition of 3D tomographic and 4D time resolved datasets have emerged allowing for the analysis of mm volumes of material with nm-scale resolution. The TriBeam technique permits the acquisition of 3D EBSD datasets using a femtosecond laser to section material at unprecedented speed [1-2] with low damage [3-4] and high resolution [5]. Diffraction contrast tomography (DCT) [6], a synchrotron based X-ray technique acquires datasets non-destructively, permitting the repeated imaging of samples to collect 4D microstructural evolution [7] in crystalline materials. However, the vast majority of materials tomography datasets have been combined in a purely qualitative sense to date. In this work, a methodology for the precise alignment of tomographic datasets, including the alignment of the sample and orientation reference frames, and simultaneous identification and linking of grain structure between tomography datasets has been developed. The application of these algorithms to a pair of datasets collected from a single strontium titanate (STO) sample using both TriBeam tomography and synchrotron X-ray diffraction contrast tomography (DCT) will be presented. The resulting merged datasets have been quantitatively analyzed on the voxel scale and at the grain scale for the direct comparison of these two tomography techniques.

In situ Femtosecond Laser and Argon Ion Beams for 3D Microanalysis using the TriBeam

Advanced engineering materials require microstructural characterization in 3D across lengthscales, motivating the development of new tomography techniques and coupling with existing capabilities. The acquisition of 3D datasets with structural and chemical information at lengthscales between those accessible using Ga and Xeon FIB SEMs and those of X-ray tomography techniques is still challenging, particularly for dense multiphase materials. Femtosecond lasers have been employed for low damage [1,2] material removal, in tomography applications, over mm regions in situ in a FIB SEM as shown in Figure 1. FIB cross sections investigated by TEM have shown that dislocations can be injected to microns in depth in some materials [3], but are primarily confined to less than 100s of nanometers of the surface in the low fluence ablation regime. Parametric studies of laser fluence and beam scanning conditions in silicon in the TriBeam show that, when the propagating laser beam is scanned parallel with the sample surface, the damage is exclusively limited to that of the low fluence ablation regime. Laser ablation studies have also shown the ability to resolve surface sensitive EBSD maps from the ablated surface of many metals and/or alloys primarily containing magnesium, titanium, nickel, steel, copper, tungsten, tin and niobium.