Clustering and nearest neighbour distances in atom-probe tomography

The measurement of chemical composition of tiny clusters is a tricky problem in both atom-probe tomography experiments and atomic simulations. A new approach relying on the distribution of the first nearest neighbour (1NN) distances between solute atoms in the 3D space composed of A and B atoms was developed. This new approach, the 1NN method, is shown to be an elegant way to get the composition of tiny B-enriched clusters embedded in a random AB solid solution. The theoretical statistical distributions of first neighbour distances P(r) for both random solid solution and solute-enriched clusters finely dispersed in a depleted matrix are established. It is shown that the most probable distance of P(r) gives directly the phase composition. Applications of this model to both one-phase SiGe alloy and boron-doped silicon containing small clusters indicate that this new approach is quite reliable.     

Positive effect of natural pre-ageing on precipitation hardening in Al–0.44 at% Mg–0.38 at% Si alloy

Age hardening in a purely ternary Al-Mg0.4–Si0.4 (0.44 at% Mg, 0.38at%Si) alloy that is similar to AA6060 was investigated by hardness measurement, TEM and three-dimensional atom probe (3D-AP). In particular, the effect of natural pre-ageing before artificial ageing, which is known to have a positive effect in this alloy, was studied by comparing three different conditions: natural ageing only, artificial ageing for 1.5 h at 180 °C only and combined natural pre-ageing and subsequent artificial ageing for 1.5 h at 180 °C. Natural ageing influences the mechanical properties significantly. Naturally aged alloys exhibit a hardening response that is governed by the presence of small clusters. Subsequent artificial ageing of naturally aged specimens increases the value of peak hardness, which is attributed to the increase of the number density of needle-shaped precipitates as compared to the samples without natural ageing. It is assumed that besides these precipitates, the small Si clusters formed at room-temperature storage remain stable during artificial ageing.     

Clustering and pair correlation function in atom probe tomography

The measurement of the composition of small clusters from 3D maps as provided by atom probe tomography or Monte-Carlo simulations is a very tricky issue. A method based on pair correlation functions was developed. The analytical expression of the pair correlation function as a function of the phase composition, the number density and the size of spherical particles for a two-phase mono-dispersed system has been established. A best-fit procedure applied to experimental pair correlation function is shown to be a simple, fast and elegant way to determine the concentration of clusters and that of the parent phase as well as the radius and the number density of clusters. Application to carbon-doped silicon demonstrates the validity of this approach. Results were found very close to those derived by other means. This method was also applied to boron clustering in implanted silicon where clusters are not visible in 3D images. The advantage of this approach over other methods such as erosion or cluster identification is discussed.     

Estimating the physical cluster‐size distribution within materials using atom‐probe

A limiting characteristic of the atom‐probe technique is the nondetection of ions and this embodies a significant “missing information” problem in investigations of atomic clustering phenomena causing difficulty in the interpretation of any atom‐probe experiment. It is shown that the measurable cluster‐size distribution can be modeled by a mixed binomial distribution. A deconvolution method based upon expectation‐maximization (EM) algorithm is presented to obtain the original physical distribution from an efficiency‐degraded distribution, thereby providing means to calculate accurate cluster number densities from atom probe results. The accuracy of this restoration was predominantly dependent upon the detector efficiency and was proved to be highly accurate in the case of conventional atom‐probe detector efficiencies (? = 57%). Such considerations and measures are absolutely necessary when the number density of clusters and small precipitates is in any way regarded as important. We conclude that limitations in detector efficiency are more limiting for cluster‐finding analyses via atom‐probe techniques than spatial resolution issues, and therefore the current endeavors for improving detector technologies are well found. Microsc. Res. Tech., 2011. © 2010 Wiley‐Liss, Inc.     

A sensitivity analysis of the maximum separation method for the characterisation of solute clusters

Variants of the maximum separation method have become the de-facto methodologies for the characterisation of nanometre scale clusters in atom probe tomography (APT) data obtained from dilute solid solutions. All variants rely on a number of parameters and it is well known that the precise values for these parameters strongly influence estimates of cluster size and number density. Quantitative analyses require an improved understanding of the inter-relationship between user-defined parameters, experimental parameters such as detection efficiency and the resultant parameterisation of the microstructure.A series of simulations has been performed to generate clusters with a range of compositions (50-100%) and diameters (1.5-2.5 nm) in a dilute solid solution. The data were degraded to simulate the effects of the finite detection efficiencies and positioning uncertainties associated with the ECOPoSAP and LEAP-3000X HR.An extensive analysis of each resultant dataset, using a range of values for the maximum separation parameters was then performed. Optimum values for each material condition were identified and it is shown that it is possible to characterise cluster size, number density and matrix chemistry. However, accurate estimates of cluster compositions are more difficult and absolute measurements must be treated with caution. Furthermore, it is shown that D_MAX must increase with decreasing detection efficiency and consequently clusters of a specific size will appear slightly larger in atom probes with a lower detection efficiency.     

Atom probe characterization of precipitation in an aged Cu-Ni-P alloy

A temporal evolution of clusters associated with age hardening behavior in a Cu-Ni-P alloy during ageing at 250 °C for up to 100 ks after solution treatment has been carried out. A three-dimensional atom probe (3DAP) analysis has showed that Ni-P clusters are present in the as-quenched condition, and that the cluster density increases as the ageing time increases. The clusters have a wide range of Ni/P ratios when they are relatively small, whereas larger clusters exhibit a narrow distribution of the Ni/P ratio, approaching a ratio of approximately two. These results would indicate that the clusters with various Ni/P ratios form at the early stage of precipitation and the ratio approaches a value identical to that of the equilibrium phase at 250 °C as the clusters enlarge during ageing.     

Effect of decomposition of the Cr-Fe-Co rich phase of AlCoCrCuFeNi high entropy alloy on magnetic properties

Splat-quenched, as-cast and aged (2 h at 600 °C after casting) AlCoCrCuFeNi high entropy alloys were investigated by means of transmission electron microscopy and three-dimensional atom probe (3D-AP). 3D-AP revealed anti-correlated fluctuations of the Cr and Fe-Co compositions in Cr-Fe-Co-rich regions of the as-cast alloy. The ferromagnetic behavior of AlCoCrCuFeNi high entropy alloy was correlated with the decomposition of the Cr-Fe-Co-rich regions into ferromagnetic Fe-Co-rich and antiferromagnetic Cr-rich domains, the size of which was determined by statistical analysis of 3D-AP data. The splat-quenched alloy showed a softer magnetic behavior as compared to the as-cast and aged alloys. The aged alloy possessed a higher saturation magnetization and coercivity as compared to the as-cast alloy.     

Some aspects of the field evaporation behaviour of GaSb

In-depth analysis of pulsed laser atom probe tomography (APT) data on the field evaporation of the III-V semiconductor material GaSb reveals strong variations in charge states, relative abundances of different cluster ions, multiplicity of detector events and spatial correlation of evaporation events, as a function of the effective electric field at the specimen surface. These variations are discussed in comparison with the behaviour of two different metallic specimen materials, an Al-6XXX series alloy and pure W, studied under closely related experimental conditions in the same atom probe instrument. It is proposed that the complex behaviour of GaSb originates from a combination of spatially correlated evaporation events and the subsequent field induced dissociation of cluster ions, the latter contributing to inaccuracies in the overall atom probe composition determination for this material.     

Statistical analysis of atom probe data: Detecting the early stages of solute clustering and/or co-segregation

Statistical analysis of atom probe data has improved dramatically in the last decade and it is now possible to determine the size, the number density and the composition of individual clusters or precipitates such as those formed in reactor pressure vessel (RPV) steels during irradiation. However, the characterisation of the onset of clustering or co-segregation is more difficult and has traditionally focused on the use of composition frequency distributions (for detecting clustering) and contingency tables (for detecting co-segregation).     

Detecting density variations and nanovoids

A combination of simulated and experimental data has been used to investigate the size range of nanovoids that can be detected in atom probe tomography data. Simulated atom probe tomography data have revealed that nanovoids as small as 1 nm in diameter can be detected in atom probe tomography data with the use of iso-density surfaces. Iso-density surfaces may be used to quantify the size, morphology and number density of nanovoids and other variations in density in atom probe tomography data. Experimental data from an aluminum-yttrium-iron metallic glass ribbon have revealed the effectiveness of this approach. Combining iso-density surfaces with atom maps also permits the segregation of solute to the nanovoids to be investigated. Field ion microscopy and thin section atom maps have also been used to detect pores and larger voids.     

Application of Fourier transform and autocorrelation to cluster identification in the three-dimensional atom probe

Because of the increasing number of collected atoms (up to millions) in the three‐dimensional atom probe, derivation of chemical or structural information from the direct observation of three‐dimensional images is becoming more and more difficult. New data analysis tools are thus required. Application of a discrete Fourier transform algorithm to three‐dimensional atom probe datasets provides information that is not easily accessible in real space. Derivation of mean particle size from Fourier intensities or from three‐dimensional autocorrelation is an example. These powerful methods can be used to detect and image nano‐segregations. Using three‐dimensional ‘bright‐field’ imaging, single nano‐segregations were isolated from the surrounding matrix of an iron–copper alloy. Measurement of the inner concentration within clusters is, therefore, straightforward. Theoretical aspects related to filtering in reciprocal space are developed.     

Quantitative analysis of intramembranous particles in rapidly frozen 10T1/2 cell monolayers

A simple method for ultrarapid freezing of cell cultures in monolayers was developed. Unfixed and unglycerinated cells were grown on glass substrates. No special treatments of the glass or cells were necessary to facilitate freeze-fracture along the upper plasma membranes. A reliable nonbiased method was developed to detect intramembranous particles (IMP) from the background by totally automatic means using the Cambridge Instruments Quantimet 920 Image Analysis system. Size and density data of IMP from a large number of electron micrographs can be rapidly and objectively quantitated. The automatic determination of locational coordinates for each IMP enables subtle determination of spatial distributional differences by the nearest neighbour function and the differential density distribution function, which are measurements of randomness. Quantitative analysis of the IMP distribution on the fracture face of C3H/10T1/2 mouse embryo fibroblasts upon various drug treatments was demonstrated.     

Ordering and site occupancy of D03 ordered Fe3Al-5 at%Cr evaluated by means of atom probe tomography

Addition of ternary elements to the D0₃ ordered Fe₃Al intermetallic phase is a general approach to optimise its mechanical properties. To understand the physical influences of such additions the determination of the probability of site occupancies of these additions on the lattice site and ordering parameters is of high interest. Some common experimental techniques such as X-ray diffraction or Atom Location by Channelling Enhanced Microanalysis (ALCHEMI) are usually applied to explore this interplay.Unfortunately, certain published results are partly inconsistent, imprecise or even contradictory. In this study, these aspects are evaluated systematically by atom probe tomography (APT) and a special data analysis method. Additionally, to account for possible field evaporation effects that can falsify the estimation of site occupancy and induce misinterpretations, APT evaporation sequences were also simulated. As a result, chromium occupies most frequently the next nearest neighbour sites of Al atoms and local ordering parameters could be achieved.     

Exploring the next neighbourhood relationship in amorphous alloys utilizing atom probe tomography

A new algorithm is developed to explore the next neighbourhood atomic vicinity from the analysed data obtained using the tomographic atom probe (TAP) technique. The presented algorithm allows to calculate the atomic distances among different next neighbours of different elements as applied to bulk amorphous alloys. The results obtained for Pd55 Cu23 P22 bulk amorphous alloys show reasonable consistency to already available data from different diffraction techniques. The Pd-Pd atoms have highest probability to be a next neighbour than others. The established view that P is not a direct next neighbour to each other is also manifested from these results. Normalizing the distances of the next neighbours to the first neighbour distance in this particular amorphous system possesses a definite order for all elemental correlations. Furthermore, the algorithm was processed for different critical reconstruction parameters to explore the corresponding effect on the distance distribution of next neighbouring atoms. The minor changes in the product of the geometric factor and the evaporation field of the sample does not make any egregious difference on the next neighbourhood evaluation (NNE).     

Field evaporation behaviour in the gamma phase in Ti-Al during analysis in the tomographic atom probe

A Ti-48 at% Al alloy has been successfully investigated, using atom probe field ion microscopy and transmission electron microscopy. After a specific heat treatment, this alloy has a (alpha2 + gamma) lamellar microstructure. Using the tomographic atom probe (TAP), it has been possible to image the stacking of superlattice planes of gamma and to identify titanium as the highest evaporation field element. In addition, the influence of analysis site on atom probe measurements has been estimated for this phase. A TAP analysis has also made it possible to observe an extremely thin step along a gamma/gamma interface at a near atomic scale.     

Atom probe tomography analysis of nanostructure evolution in Ni-Cr-Mo low alloy steel under neutron irradiation

Ni-Cr-Mo low alloy steels are being considered as alternative materials to replace the Mn-Mo-Ni low alloy steels used in reactor pressure vessels in nuclear power plants, because of their higher strength and toughness. However, the neutron irradiation occurring during reactor operation causes degradation of Ni-Cr-Mo low alloy steel. In this study, irradiation-induced clusters in a Ni-Cr-Mo model alloy irradiated in the High-flux advanced neutron application reactor (HANARO) research reactor were investigated via Atom probe tomography (APT). The irradiated specimens showed irradiation-induced hardening and embrittlement. The neutron irradiation caused Si clustering, and these spherical clusters were homogeneously distributed within the matrix. Ni was also clustered at the Si clusters. However, the other elements did not clearly exhibit clustering behavior. Si and Ni atoms were also located at the dislocations. To quantify the nano-sized clusters, a method based on the Density-based spatial clustering of applications with noise (DBSCAN) algorithm was implemented. The total number of clusters was calculated to be ~7 × 10^-4 n/nm³ and the average cluster radius was less than 2 nm. The APT approach was demonstrated to be well suited for discovering the irradiation defect structures.     

The influence of voxel size on atom probe tomography data

A methodology for determining the optimal voxel size for phase thresholding in nanostructured materials was developed using an atom simulator and a model system of a fixed two-phase composition and volume fraction. The voxel size range was banded by the atom count within each voxel. Some voxel edge lengths were found to be too large, resulting in an averaging of compositional fluctuations; others were too small with concomitant decreases in the signal-to-noise ratio for phase identification. The simulated methodology was then applied to the more complex experimentally determined data set collected from a (Co_0.95Fe_0.05)₈₈Zr₆Hf₁B₄Cu₁ two-phase nanocomposite alloy to validate the approach. In this alloy, Zr and Hf segregated to an intergranular amorphous phase while Fe preferentially segregated to a crystalline phase during the isothermal annealing step that promoted primary crystallization. The atom probe data analysis of the volume fraction was compared to transmission electron microscopy (TEM) dark-field imaging analysis and a lever rule analysis of the volume fraction within the amorphous and crystalline phases of the ribbon.     

Comparison of radiation-induced segregation in ultrafine-grained and conventional 316 austenitic stainless steels

Due to a high number density of grain boundaries acting as point defect sinks, ultrafine-grained materials are expected to be more resistant to irradiation damage. In this context, ultrafine-grained 316 austenitic stainless steel samples have been fabricated by high pressure torsion. Their behavior under ion irradiation has been studied using atom probe tomography. Results are compared with those obtained in an ion irradiated conventional coarse-grained steel. The comparison shows that the effects of irradiation are limited and that intragranular and intergranular features are smaller in the ultrafine-grained alloy. Using cluster dynamic modeling, results are interpreted by a higher annihilation of point defects at grain boundaries in the ultrafine-grained steel.     

Determination of matrix composition based on solute‐solute nearest‐neighbor distances in atom probe tomography

In this study, we propose a fast automatic method providing the matrix concentration in an atom probe tomography (APT) data set containing two phases or more. The principle of this method relies on the calculation of the relative amount of isolated solute atoms (i.e., not surrounded by a similar solute atom) as a function of a distance d in the APT reconstruction. Simulated data sets have been generated to test the robustness of this new tool and demonstrate that rapid and reproducible results can be obtained without the need of any user input parameter. The method has then been successfully applied to a ternary Al‐Zn‐Mg alloy containing a fine dispersion of hardening precipitates. The relevance of this method for direct estimation of matrix concentration is discussed and compared with the existing methodologies. Microsc. Res. Tech., 2010. © 2010 Wiley‐Liss, Inc.     

A procedure for quantification of precipitate microstructures from three-dimensional atom probe data

New analysis software for selecting and quantifying particles in three-dimensional atom maps has been designed. The selection of solute-rich regions is performed by connecting solute atoms which lie within a fixed distance (d), and taking clusters above a certain minimum number of solute atoms (N(min)). Other atoms within some distance L greater than d are taken to belong to the cluster. However, this results in the inclusion of a shell of matrix atoms, which must be removed through an erosion step, to define the final cluster. Data filtered in this way can be used for subsequent quantification of parameters such as size, shape, composition, number density and volume fraction with better accuracy than by manual selection. The choice of d, N(min) and L values is discussed and some methods of evaluation of these parameters are proposed. Examples are presented on the application of this new software to the analysis of early stage clustering in an Al-Mg-Si-Cu alloy and a copper-containing steel.