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Kautsar et al. Energy Mater. 2025, 5, 500129 https://dx.doi.org/10.20517/energymater.2025.26 Page 3 of 14

This study aims to investigate how variations in grain size and intergranular phase (IGP) influence σ , κ,
xx
and S in the Nd-Fe-B permanent magnets. These magnets were fabricated from rapidly solidified
ANE
Nd-Fe-B ribbon powders with an initial nano-sized grain structure [36,37] . During the different processing
stages of hot-pressing, hot-deformation, and grain boundary diffusion process (GBDP), significant
microstructural changes occur [38-41] , which will be systematically analyzed. The findings are expected to shed
light on the relationship between microstructural evolution and transport properties in the Nd-Fe-B
magnets, contributing to the design and optimization of permanent magnet materials for transverse
thermoelectric applications.

EXPERIMENTAL
Nd-Fe-B magnets preparation
The starting material used in this study was a commercial Nd-Fe-B crushed melt-spun ribbon powder,
MQU-F, with the composition of Nd Fe Co Ga B (at%), supplied by Magnequench Co. Ltd. The
6.6
0.6 5.6
73.6
13.6
MQU-F powder was first hot-pressed at 650 °C under 300 MPa to produce a hot-pressed (HP) compact.
This HP compact was then hot-deformed at 750 °C with a 75% height reduction, resulting in an anisotropic
hot-deformed (HD) magnet. To produce GBDP magnets, alloy ribbon flakes of Dy Nd Cu (at%),
60
20
20
Nd Cu (at%), and Pr Cu (at%) were prepared using a single-roll melt-spinning machine, followed by
80
20
20
80
mechanical crushing. These diffusion sources were chosen based on prior reports demonstrating their
effectiveness in achieving high coercivity in the ultra-fine grained Nd-Fe-B magnets [39-41] . Due to the limited
studies on the impact of GBDP on ANE performance, this factor was not considered in the selection
process. The c-plane surfaces of the HD magnet (2 mm thick) were coated by diffusion sources in the form
of ribbon flakes (~20 wt%) using a polymer adhesive. The magnets were then heat-treated at 650-750 °C for
3 h under vacuum, followed by furnace cooling to ambient temperature, resulting in RE-Cu (RE = Dy-Nd,
Nd, Pr) GBDP HD magnets.
Characterization and measurements
Microstructural analysis was conducted using Scanning Electron Microscopy (SEM, Carl ZEISS CrossBeam
1540EsB) and Transmission Electron Microscopy (TEM, FEI Titan G2 80-200). Sample preparation for
these analyses was carried out using a focused ion beam (FIB)-SEM device (FEI Helios G4). The magnets
were sectioned into specific sample dimensions to suit each type of measurement, with the c-axis indicating
the easy magnetization direction of the magnet (if applicable): 1.5 mm (c-axis) × 1.0 mm × 1.0 mm for
magnetic property measurements, 2 mm (c-axis) × 2 mm × 15 mm for σ and thermoelectric
xx
measurements, 1.5 mm (c-axis) × 10 mm × 10 mm for thermal diffusivity (D) measurements, and 0.5 mm (c
t
-axis) × 1 mm × 5 mm for Hall measurements. Magnetic properties were evaluated by measuring the
magnetization curves of the samples using a 7 T superconducting quantum interference device vibrating
sample magnetometer (SQUID-VSM, Quantum Design MPMS3). A demagnetization correction factor for a
prism-shaped magnet, as described in ref. , was applied to the measured hysteresis loop to account for the
[42]
open-loop measurement. This resulted in a correction factor of 0.25 for the sample used in magnetic
property measurements and 0.47 for the samples used in lock-in thermography (LIT) measurements. Grain
alignment was assessed using X-ray diffraction (XRD, Rigaku MiniFlex600, Cr Kα source) by analyzing the
surface normal to the pressing direction for all bulk samples. The values of σ and the Seebeck coefficient
xx
(S ) were simultaneously determined using Seebeck Coefficient/Electric Resistance Measurement System
xx
(ZEM-3, ADVANCE RIKO, Inc.). To quantify S , we measured the anomalous Ettingshausen effect
ANE
(AEE), Onsager reciprocal of ANE, using the LIT method [27,43-48] . The LIT technique, based on infrared
thermometry, enables high-resolution observation of temporal response and spatial distribution induced by
an external periodic input, with exceptional sensitivity (< 0.1 mK) and spatial resolution (~20 µm) . In the
[23]
LIT measurements, the thermal images were captured using an infrared camera while applying a
square-wave modulated AC charge current with amplitude J = 1.0 A, frequency f = 1.0-10.0 Hz, and zero
c