Understanding the formation of multiply twinned structure in decahedral intermetallic nanoparticles

The formation of multiply twinned structures in decahedral intermetallic nanoparticles has been explored and a general framework proposed to understand it.

Synthesis of Au Seed nanoparticles (NPs). Au seeds were prepared with modified procedures from earlier work (Chen et al., 2010). 0.1g of HAuCl4·3H2O was dissolved in 10 mL of oleylamine and 10 mL of o-xylene at 10 ºC under Ar flow and vigorous magnetic stirring. 0.5 mmol of borane tertbutylamine complex dissolved in 1 mL of oleylamine and 1 mL of o-xylene via sonication was injected into the HAuCl4 solution. After stirring for 1 h at 10 ºC, ethanol was added to precipitate Au NPs via centrifugation. The precipitate was re-dispersed in hexane before addition of ethanol and centrifugation.
And the final product was dispersed in hexane again for AuCu intermetallic NP synthesis.
Synthesis of AuCu Chemically Ordered Decahedral NPs. AuCu ordered intermetallic NPs were synthesized with a typical synthesis procedure in a Schlenk line. 0.25 mmol of Cu(CH3COO)2·H2O was mixed with 0.5 mL of oleic acid and 2.25 mL of tri-n-octylamine in a 25 mL three-neck flask. After heated at 80 ºC for 30 min, the solution became clear and 0.25 mmol of Au NPs dispersed in 20 mL of hexane was added. Once hexane evaporated completely, the mixture was heated at 120 ºC for 20 min under Ar and then quickly heated to 300 ºC for 50 min before cooling down. The product was collected by ethanol addition, centrifugation and re-dispersed in 20 mL of hexane for use.

S2. Model
AuCu intermetallic decahedral multiply-twined particles (MTPs) were constructed with the VESTA software (Momma & Izumi, 2011). As shown in Figure S1, two different models were displayed with both cross-sectional and three-dimensional view. As mentioned in the main text, constructing a AuCu MTP with the original body centered tetragonal (BCT) lattice parameters will cause an overlap. We adjusted the lattice parameters properly based on the rules discussed in the main text to remove the overlap.

S3. Image simulation
STEM image simulations were performed using a plane wave reciprocal space interpolated scattering matrix (PRISM) method (Ophus, 2017). Above mentioned models were taken as input structural models here. The accelerating voltage was 300 kV and interpolation factor was chosen as 8. The probe convergence angle was 17 mrad and collection angle was from 70 to 200 mrad. Spherical aberration CS was set to 0, considering an aberration-free probe. For comparison, model constructions and image simulations of a AuCu single-crystal nanoparticle (NP) have also been performed in the same way. The result is shown in Figure S2. The difference in the intensity of outer three layers also demonstrates the existence of gold-enriched shell over the AuCu core as the case of AuCu MTPs.

S4. EELS
IUCrJ (2019). 6, doi:10.1107/S2052252519002562 Supporting information, sup-3 STEM-EELS line profiles were performed to demonstrate the existence of the gold enriched shells in AuCu NPs. An example is shown in Figure S3. STEM-EELS line profile was measured along the green arrows' line in Figure S3b and the result was shown in Figure S3a. The EELS counts has been normalized. Au counts were slightly higher than Cu on the edge of the NP. This may support the conclusion drawn from Figure 2 and S2 that gold-enriched shells existed.

S5. Data of Au and FePt
To investigate the effect of different disclination on the atomic structure of MTPs, an aberrationcorrected high-resolution TEM (AC-HRTEM) image of a Au MTP (Gautam, 2017) was adopted to serve as a comparison ( Figure S4). The image was taken at 600 ºC and its five-fold structure could be observed from both HRTEM image and its FFT. For the FePt, analysis has been performed using the data published before (Li et al., 2014).

S6. Strain mapping
In order to obtain a strain mapping on the atomic-scale, Gaussian fitting of the atom column positions was performed (Yu et al., 2016), and then strain maps were drawn (Gan et al., 2012;Yu et al., 2016).
The area of the triangle composed by three Au atom columns was calculated and then converted to strain. As shown in Figure S5a, for the case of Au, each vertex of a triangle corresponds to a gold atom column. While for the case of AuCu in Figure S5b, still the Au-atom-triangle was calculated, and the copper atoms were not counted in owing to the lower contrast which may bring inaccuracy when fitting its position. The area of each triangle (A(x1,y1), B(x2,y2), C(x3,y3)) was calculated with the formula: where S is the area. Strain was calculated with the following formula: where the 0 represents the standard area in single-crystal NPs. The value of the overall strain could be obtained by the following formula: where the ���� and ���� corresponds to the arithmetical mean value of dA' and dB', respectively. dA' and dB' are the expanded lattice parameters measured in each BCT cell. Table S1 lists the standard lattice parameters and the rotation angles of the disclination of several materials (Johansson & Linde, 1936;Yuasa et al., 1994;Warlimont, 1959) that were discussed in this manuscript. The experimental data for Au, FePt, and AuCu MTPs, as well as the predicted CoPt, FeNi, and FePd MTPs are also listed. The chosen of the latter three materials for prediction is because that intermetallic phase of FePd (Persson, 2016), FeNi (Clarke & Scott, 1980), CoPt (Woolley et al., 1964) have been reported before. As can be seen, the angles of circumference would become closer to 360º after lattice expansion. The less expansion in Au MTP could be related to the strain relaxation at high temperature. Derivation is as following:

S7. Derivation of the relationship between strain and rotation angle of the disclination
For the single-crystal NP, we have: For the decahedral MTP, we have: By definition, strain can be calculated as: Here, dA and dB are the original lattice distances, and dA' and dB' are the lattice distances after expansion.
Combining the above three formulas, we can derive the relationship in the following. Here, we separate it into two cases, with positive rotation angle and negative rotation angle, respectively.