An algorithm is presented to fit precipitates in atom probe tomographic data sets as equivalent ellipsoids. Unlike previous techniques, which measure only the radius of gyration, these ellipsoids retain the moments of inertia and principle axes of the original precipitate, preserving crystallographic orientational information. The algorithm is applied to study interconnected γ ′ -precipitates (L1 2 ) in the γ-matrix (FCC) of a Ni-Al-Cr alloy. The precipitates are found to coagulate along 110 -type directions.One of the principle challenges that analyzing three-dimensional atom-probe 1 tomographic (APT) results poses is the amount of raw data that the instru-2 ments are now able to collect [1,2]; we have collected continuous data sets as 3 large as 2.1 × 10 8 properly ranged atoms from a single specimen. It is neces-4 sary to extract information about spatial and compositional measures, such 5 as precipitate size from these data sets. A common method to measure the 6 size of precipitates is to calculate a single radius of gyration (or, from this, the 7 Guinier radius) [3,4]. While this technique works well for equiaxed, spheroidal 8 precipitates [5,6], many alloy systems investigated by APT have non-spherical 9 features [7,8,9,10,11,12,13,14,15]. Improperly reconstructed data sets, which 10 have preferential evaporation or local-magnification effects, may also exhibit 11 non-spherical features [16]. Techniques that measure the angular eccentricity 12 of features can be used to quantify the accuracy of a reconstruction. The radius 13 of gyration technique does not, however, retain three-dimensional information 14 concerning precipitate orientation.
15In this article, a more general alternative to the radius of gyration is presented 16 and applied. Best-fit ellipsoids have equivalent centroids, moments of inertia, 17 and principle axes for arbitrarily shaped precipitates. The crystallographic 18 orientations of the resulting ellipsoids are then used to study the coagulation-19 coalescence coarsening mechanism in a Ni-Al-Cr alloy, which occurs when 20 the γ ′ -precipitate number density is large (> 10 24 m −3 ) and the edge-to-edge 21 distance between adjacent γ ′ -precipitates is small (< 2 nm) [17,18].
22In lattice kinetic Monte Carlo simulations, a coagulation-coalescence coarsen-23 ing mechanism is reported [18]. This mechanism is caused by non-equilibrium 24 overlapping diffusion fields, which originate from the long-range vacancy-solute 25 binding energies and a small mean edge-to-edge interprecipitate distance. The 26 non-equilibrium concentration profiles observed at the γ ′ -precipitate/γ-matrix 27 interfaces lead to a higher interfacial free energy than for fully equilibrated 28 γ ′ -precipitates. The excess free energy of the region of overlapping concen-29 tration profiles ("diffuse neck") can decrease by changing the concentration 30 thereof into a well-formed neck [18]. Phase-field simulations find that the rate 31 of γ ′ -precipitate coalescence is increased when the γ/γ ′ -interfacial width is 32 incr...