Topas 4

Carbonate samples were powdered and homogenized. Mineralogical analyses were performed by X-ray diffraction on un-oriented samples scanned by a Bruker D8 Advance diffractometer (Cu K_α radiation in 3–75° 2θ range). Quantitative data were obtained with the Rietveld algorithm-based code, Topas-4, provided by Bruker. Following a displacement correction of the spectrum made on the main quartz peak, the d₁₀₄ displacement of calcite was used to estimate the MgCO₃ in mol% (ref. 38 ).
An aliquot of the powder prepared for X-ray diffraction was used for stable carbon and oxygen isotopic measurements using a GasBench II preparation line connected to a Thermo Scientific Delta V Advantage IRMS (Thermo Fisher Scientific). Carbon dioxide was produced by the reaction of the powdered sample with 103–105% concentrated phosphoric acid at 70 °C over 2 h. Reproducibility is better than ±0.15‰ for δ¹³C values. Stable isotopic compositions are reported in conventional delta (δ) units relative to Vienna Pee Dee Belemnite reference. Values are reported in Supplementary Table 1.

Morphological observation of the nanorods was carried out using field emission scanning electron microscopy (FESEM, H-800, Hitachi Co.) with energy dispersive X-ray spectrometry (EDS), and using high resolution transmission electron microscopy (HRTEM, H-9500, Hitachi-Hitech Co.). The phases after sPFE were identified by X-ray diffraction (XRD, D2 PHASER, Bruker Co.) and Rietveld analysis using TOPAS 4 software (Bruker Co.).

PXRD patterns were collected with a Bruker D8 Advance diffractometer with Cu Kα radiation (λ: 1.5418 Å, 40 kV, 40 mA) using a Si single crystal as sample holder to minimize scattering. The powder samples were re‐dispersed in EtOH on the Si surface and investigated in a 2θ range from 10 to 90° with a step size of 0.01° 2θ (counting time 0.6 s). Rietveld refinement was done with the program package TOPAS 4.2 (Bruker) to determine lattice parameters and average crystallite sizes by using the Scherrer equation.^[68] The background was modelled using Chebyshev polynomials. The structure model of Bi₂Te₃ (PDF 15–863) from the ICSD database was used. For each Rietveld refinement, the instrumental correction determined using a standard powder sample LaB₆ from NIST (National Institute of Standards and Technology) as reference material (SRM 660b; a(LaB₆)=4.15689 Å) was considered.

For the microstructural characterization, longitudinal cross-sections of the used tensile specimens were prepared by wire cutting. Prior to SEM (Vega II XLH, TESCAN, Brno, Czech), the specimen w etched with 3% alc. HNO₃ and sputtered with gold. Hardness curves along the longitudinal axis were determined with the HV1 measurement method.
The EBSD samples were mechanically polished, using a 1-µm diamond lubricant for 10 min and finely polished with OP-S suspension and distilled water for 30 min. Measurements were conducted on a Helios G4 FEG-SEM (Thermo Fisher Scientific, Waltham, MA, USA) equipped with an EBSD Hikari Plus camera (Ametek EDAX, Berwyn, PA, USA). An acceleration voltage of 20 kV, a beam current of 6.4 nA and a step size of 0.03 µm were used to separate austenite and ferrite (martensite) of the fine grain structure in a small area of 20 × 20 µm².
For X-Ray diffraction measurements, the samples were etched at about 100 µm with 80% phosphoric and 20% sulfuric acid. Measurements were carried out on an ETA 3003 diffractometer (XRD Eigenmann GmbH, Schnaittach-Hormersdorf, Germany) using Cr-k(alpha) radiation and a 0.5 mm primary X-ray beam. The phase analysis was performed over a range from 60–164° with a step size of 0.05° and a collecting time of 800 s and evaluated using the Rietveld method implemented in TOPAS 4.2 (Bruker-AXS, Billerica, MA, USA).