Giant Violation of Wiedemann Franz Law in Nanoscale Granular Nickel
1 Violation of WiedemannโFranz Law in Nanoscale Granular Nickel
Vikash Sharma , Gunadhor Singh Okram and Yung-Kang Kuo UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore 452001, Madhya Pradesh, India. Department of Physics, National Dong-Hwa University, Hualien 97401, Taiwan
Abstract
Violation of the WiedemannโFranz law through decoupling the charge and heat transports in a material not only leads to new fundamental physics, but also is a boon for many of the advanced materials including thermoelectric materials for achieving their novel or superior properties. Here, we demonstrate this in nickel nanoparticles with incredible enhancement in Lorentz number to several orders of magnitude as size drops. This is in stark contrast to Fermi liquid behavior of conventional metals, revealing the compelling confirmation for unconventional quasiparticle dynamics where charge and heat transport independent of each other.
Introduction : The cornerstone of Landauโs Fermi-liquid theory is the existence of quasiparticles for the modern theory of metals. Their elastic transport of both electric charge and entropy gives rise to the ratio (Lorentz number ๐ณ = ๐ฟ ๐ ๐๐ป ) between electronic thermal (ฮบ e ) and electrical (ฯ) conductivities a universal Sommerfeld value ๐ณ = ๐ ( ๐ ๐ฉ ๐ ) = 2.44x10 -8 WฮฉK -2 at zero temperature, known as WiedemannโFranz (WF) law , where k B is the Boltzmann constant and e is the electronic charge. Validity of this relation in a variety of materials has firmly establish the quasiparticle picture. However, WF law (i.e. ๐ณ โ ๐ณ ) has also been found violated theoretically and experimentally due naturally to the inelastic scattering in the various materials including Luttinger liquids , VO nanobeams , nanoscale Au and Pt , granular metal , Bi Te Se thin films , Au thin films , graphene and quasi-one-dimensional conductor Li Mo O
17 13 . Interestingly, violation of the WF law is beneficial for achieving large dimensionless figure of merit,
๐๐ = ๐ ๐๐ ๐ in thermoelectric (TE) materials and hence their efficiency, where S is Seebeck coefficient. Low dimensional and nanostructured materials are the crux for this . Nonetheless, this violation has so far been marginal 2 with L showing either simply deviated from L or 0.1L , 1.1L o 15 , 3.5L , 7L , 22L and 35L
0 13 . Therefore, comprehensive understanding of the limitations of WF law in low dimensional or nanostructured materials is of critical importance. In this context, transport properties of nickel nanoparticles (NPs) could be of special interest when the size is small and uniform since they show many fascinating properties, for example, of self nanolattice formation , structural phase transition in the smallest particle size , anomalous electrical transport , and quantum size effect in heat capacity as the crystallite size changes. We establish here another remarkable property of these NPs of the extreme evolutionary violation of WF law with a systematic small crystallite size control through the quantity of trioctylphosphine (TOP). It evolves from metallic to semiconducting and then to finally completely semiconducting behavior, combined with a systematic crossover from n-type to p-type conduction with decrease in crystallite size. The value of L skyrockets up to a tremendous 4 orders of magnitude compared to L in metallic regime. They are attributed to the coating of the metallic core NPs by the insulating TOP on the surface (
16, 17 ), and their collective response as evident from the cotunnelling, Coulomb blockade and grain boundary (inelastic) scattering results. The ultralow thermal conductivity is smaller than those of the many well-known TE materials. The colossal value of S observed is larger than those of ionic and solid-state thermoelectric supercapacitors . Results and discussion : Ni NPs used here namely Ni1 to Ni7 were synthesized using solvothermal method as given elsewhere and it is briefly described in electronic supplementary information (ESI). They show face-centered cubic (fcc) crystal structure of bulk Ni, without any impurity peak for Ni1-Ni5. This has been confirmed from the (Rietveld) analysis of their laboratory X-ray diffraction (XRD) and synchrotron beamline XRD patterns (Fig. 1A & inset, Fig. S1). However, Ni6 and Ni7 were found to contain hexagonal closed packed structure along with fcc structure (table S1), in consistent with the earlier report . XRD peaks are broadened with increase in TOP, manifesting decrease in crystallite size that is in line with the earlier report . The average crystallite size of Ni1, Ni2, Ni3, Ni4, Ni5, Ni6 and Ni7 evaluated from Scherrer formula was found to be 23.1ยฑ0.3, 15.3ยฑ0.2, 10.9ยฑ0.4, 8.4ยฑ0.2, 6.8ยฑ0.3, 3.2ยฑ0.2 and 1.3ยฑ0.3, respectively; we use here the terminology โcrystallite sizeโ to mean size of the particle in general throughout the paper, distinct from particle size (of say transmission electron microscopy (TEM)) that may include non-crystalline outer region due to surfactant. The random morphology and broad size distribution of Ni1 (Fig. 1B,C, inset), and narrower size distribution in Ni4 compared to Ni1 can be seen from TEM micrographs (Fig. 1 3 D,E, inset) while Ni7 exhibits reasonably monodispersed NPs with approximately similar morphology (Fig. 1F,G, inset). The average TEM particle size is 70.5ยฑ4.2, 10.9ยฑ0.5, and 4.5ยฑ0.3 nm for Ni1, Ni4 and Ni7, respectively. As TOP increases, particle size decreases, and size distribution becomes narrower; the trend is consistent with crystallite size. Increase in broadening of XRD peaks with increase in TOP corroborates with the decrease in the degree of crystallinity with drop in particle size as obtained from selected area diffraction patterns (SAED) (Fig. 1C,E,G) and high resolution TEM of Ni1, Ni4 and Ni7 (Fig. S2A-C). The particles of Ni7 in field emission scanning electron microscopy (FESEM) (Fig. S2D,E) are relatively smaller with narrower size distribution compared to Ni1 and Ni4, which is consistent with TEM data.
24 36 48 60 72 84
Ni1 Ni2 Ni3 Ni4 Ni5 Ni6 Ni7 I n t e n s i t y ( a . u . ) ๏ฑ (degree) A
45 60 75
Ni1Ni2Ni6
Ni7
Fig. 1. (A) Laboratory source X-ray diffraction patterns of Ni1 to Ni7. Inset: synchrotron radiation x-ray diffraction patterns of Ni1, Ni2, Ni6 and Ni7. Transmission electron microscopy images (B, D, F)) and selected area electron diffraction patterns (C, E, G) of Ni1, Ni4 and Ni7, respectively, and insets in C, E, G represent their size distributions.
Metal to insulator transition : Fig. S3 shows the systematic evolution of the electrical resistivity ฯ from metal to insulator transition (MIT) as the crystallite size decreases. Ni1 and Ni2 show clear metallic behavior in 5 โ 300 K (Figs. S3A,B and S4A). Ni3, Ni4 and Ni5 show this behavior down to near 70 K, 100 K and 170 K, respectively, but below this, it starts to increase with decrease in T revealing their semiconducting behavior (Figs. 3C-E and S4B). They therefore exhibit a temperature-driven MIT, which shifts to higher T with decrease in crystallite size. The MIT completely disappears in Ni6 and Ni7 showing entirely semiconducting nature in the whole range of 10 to 300 K (Figs. S3F,G) with enhanced feature to nearly insulating behavior in Ni7 (Fig. S3G). Overall, ฯ increases by 17 orders of magnitude relative to bulk Ni at 10 K in Ni7. The evolution of these MITs may indicate that electrical transport via phonon-assisted tunneling or variable range hopping (VRH) rather than the long range hopping among (220) (200)(111)
Ni1 C oun t s ( a . u . ) Particle Size (nm) C oun t s ( a . u . ) Particle Size (nm)
50 75 100 C oun t s ( a . u . ) Particle Size (nm) B C DE GF
4 the NPs through the grain boundaries (GBs) and surfactant matrix, wherein single electron charging becomes significant resulting in Coulomb blockade behavior and localization of carriers on individual particles . Similar MITs having Efros-Shklovskii (ES) VRH (ES-VRH) conductivity have previously been reported . However, the magnitude of ฯ observed here is unprecedented. It shows a logarithmic rise to sixteen and to ten orders of magnitude at 10 K and 300 K, respectively, in Ni7 compared to Ni1 (Fig. 2A). This is much larger than 10 ฮฉ in 1 nm thin Ni film at 300 K . The ratio of ฯ at 300 K and 10 K i.e. ฯ /ฯ decreases with decrease in crystallite size (Fig. 2B) and indicates enhanced disorders as crystallite size reduces. Temperature coefficient of resistivity (TCR= ๐๐๐๐๐ ) at 10 K to 300 K is positive for Ni1 and Ni2 (Fig. 2C), but negative below 70 K, 100 K and 170 K in Ni3, Ni4 and Ni5, respectively, and in the whole T range in Ni6 and Ni7. The absolute value of TCR systematically increases with decrease in crystallite size and attains a negative value of around -1.1 K -1 at 10 K in Ni7 (Fig. 2D) that indicates onset of insulating phase below about 8 nm as depicted in Fig. 2E. Semiconducting regimes of the ฯ of these NPs were fitted with ES-VRH (ฯ โ exp (T ES /T) ), Mott-VRH (ฯ โ exp (T M /T) ) and Arrhenius models (ฯโexp (E a /k B T)) in different temperature regimes in order to get deeper insight into the transport mechanisms (Fig. S5) since fitting Arrhenius model alone was not satisfactory, where ๐ป ๐ด = ๐ต(๐ฌ ๐ญ )๐ ๐ฉ and ๐ป ๐ฌ๐บ = ๐บ๐ are the characteristic temperatures for Mott-VRH and ES-VRH, respectively, and E a is the activation energy with ๐ต(๐ฌ ๐ญ ) , ๐ and ๐บ are electronic density of states (DOS) at the Fermi level, localization length and dielectric constant of the material, respectively. The obtained parameters from the fitting and calculations are shown in table 1. There is a crossover from ES-VRH to Mott-VRH and finally Arrhenius behavior with increase in T and crystallite size (Fig. 2E). The crossover temperature between Mott-VRH to ES-VRH defined by ๐ป ๐ช = ๐๐ ๐ป ๐ฌ๐บ๐ ๐ป ๐ด increases with decrease in crystallite size (table S2), in excellent agreement with the insulating behavior of smaller size NPs . The calculated value of crossover temperature T C,cal is close to experimental T
C,exp obtained from ฯ data for Ni4 and Ni5 (table S2). Although it is higher in Ni6 and Ni7 corresponding to coexistence of both ES-VRH and Mott-VRH conduction, it is within the range of investigated temperature. This behavior is similar to the doped semiconductor but is in contrast to T c of โ1400 K in Au NPs . 5 T CR ( K - )
10 K 300 K
Crystallite size (nm)
Crystallite size (nm) ๏ฒ K / ๏ฒ K Crystallite size (nm) -7 DC B
10 K 300 K ๏ฒ ๏ ( ๏ ๏ญ m ) A Ni1 Ni2 Ni3 Ni4 Ni5 Ni6 Ni7 T CR ( K - ) Temperature (K) T e m p e r a t u r e ( K ) Crystallite size (nm)
Metal
ES-VRHMott-VRH Th e r m a l A c t i va t i on (E) I n s u l a t o r Fig. 2. (A) Resistivity at 300 K (ฯ ) and at 10 K (ฯ ), and (B) ฯ /ฯ as a function of crystallite size. Error bars of the data are shown in (A) and (B). (C) Temperature coefficient of resistivity (TCR) for Ni1 to Ni7, (D) TCR at 10 K and 300 K versus crystallite size. (E) Schematic illustration of metal-insulator phase transition diagram versus the crystallite size. The crossover of the mode of electrical transport from ES-VRH to Mott-VRH model in Ni4 - Ni7 manifests opening of the Coulomb gap ๐ซ ๐ช๐ฎ โ ๐ ๐ต(๐ฌ ๐ญ ) ๐บ โ ๐ ๐ฉ ( ๐ป ๐ฌ๐บ๐ ๐ป ๐ด ) at the Fermi level, and ฮ CG increases as crystallite size decreases (table 1). Since the dielectric constant ษ= ยต โ 2.2, ๐ = ๐ ๐ป ๐ฌ๐บ and hopping distance ๐น ๐๐๐ = โ ๐ ๐๐๐ ๐ฉ ๐ป๐ ๐บ๐บ at 10 K were calculated using refractive index ยต=1.468 for TOP. The value of ๐ โ 2.7 nm with its average TEM particle size 4.5 nm implies localization of electrons, and R hop at 10 K around is 37 times larger than ๐ and exceeds 22 NPs for Ni7 (table 1). This is in excellent agreement with that of Au NPs ( ), and indicates that carriers are transported through cotunneling at low temperature. Similar transport is indicative from R hop > ๐ in Ni4 - Ni7 (table 1); ษ =2.2 was used for other samples also to calculate their ๐ and R hop at 10 K since OA has ยต ~ 1.460, comparable to that of TOP. However, hopping conduction in higher T is expected for Ni3 as ๐ > R hop . This is consistent with small change in ฯ in semiconducting regime (at 10 K) relative to metallic regime (300 K). Overall, while there are decrease in both ๐ and R hop , there exist increase in the parameters T ES , T M and ๐ซ ๐ช๐ฎ with decrease in crystallite size (table 1). Further evidences for cotunneling transport of electrons are ๐น ๐ฌ๐บ ๐ >1 in Ni6 and Ni7 and ~ 1 in Ni5 and ๐น ๐ด ๐ >1 in Ni5 - Ni6 (table S1) when we use the ratio of hopping distance to ๐ for Mott-VRH (R M ) and ES-VRH (R ES ) of ๐น ๐ด ๐ = ( ๐ป ๐ด ๐ป ) and ๐น ๐ฌ๐บ ๐ = ( ๐ป ๐ฌ๐บ ๐ป ) , respectively . Table 1
ES-VRH temperature (T ES ), Mott-VRH temperature (T M ), calculated Coulomb gap energy ( ๐ซ ๐๐ ), localization length ( ๐ ), hopping length (R hop ), activation energy (E a ) and charging energy (E c ). Sample (TEM size, nm) T ES (K) T M (K) ๐ซ ๐ช๐ฎ (meV) ๐ (nm) R hop (nm) E a (meV) E c (meV) Ni3 1.5 2.3 - 5400 4510 0.34 - Ni4 (10.9) 2.8 6.0 0.16 2700 3190 0.62 118 Ni5 14.4 110.2 0.44 527 1410 1.4 - Ni6 671.0 9.17ร10 ๐ ๐ = ๐ ๐ for single NP with radius r for Ni4 and Ni7 was calculated since we have TEM particle size of these samples (table 1). Large ๐ ๐ โ 297 meV for Ni7 that is almost 12 times that of thermal energy at 300 K suggests strong Coulomb blockage behavior. This E C may be overestimated but cannot be lower than E a โ 26 meV which also manifests the Coulomb blockade behavior in Ni7. Now, we use prediction of ES-VRH on the DOS at Fermi level that varies as ๐ต(๐ฌ) = ๐ต |๐ฌ โ ๐ฌ ๐ญ | ๐ธ to calculate the value of ๐ธ from ฯ to see energy dependence on DOS as 2 to 2.5 (Fig. S6, for more detail see ESI). It decreases with decrease in crystallite size (table S1) that is in excellent agreement with earlier reports . This clearly reveals that there is Coulomb gap in ES-VRH where DOS varies nearly in quadratic form in the smallest particle size sample. Therefore, cotunneling transport at low temperature gives rise to ES-VRH conductivity, and increase in T gives way from the Mott-VRH to activation type of conduction (Fig. 2E). Ultralow thermal conductivity : To correlate the electrical transport, their thermal conductivity ฮบ was investigated. It varies monotonically with T associated with a broad hump-like feature around 200 K in Ni1 (Fig. 3A), which is attributed to enhanced scattering of electrons with defects. It drops quite significantly with decrease in crystallite size, consistent with single Ni nanowire . However, such trend has been changed in Ni3 with a peak near 32 K with a broad hump-like feature around 200 K still persevering. This peak near 32 K evolves gradually more distinct, and it is the sharpest in Ni7 while hump-like feature slowly disappearing turning to a straight line as the size decreases (Fig. 3A, inset for clarity). The peak near 32 K is tentatively attributed to monodispersity and nanolattice formation of the particles which is in line with its small value unlike that in metals where its values are relatively very large. The value of ฮบ at 300 K falls fast nearly linearly but that at 10 K increases slowly and then drops again with 7 decrease in crystallite size (Fig. 3B). Their trends are distinct from that of ฯ (Fig. 2), but consistent with earlier theoretical report on Ni NPs . This distinct trend is a clear signal for violation of the WF law. ๏ซ ( W m - K - ) L / L o L / L o ๏ด Ni1 Ni3 Ni4 Ni5 Ni7 ๏ซ ( W m - K - ) T (K) A T (K)Crystallite size (nm)
Ni3 C T (K)
120 240 L ( V K - ) Ni4 -9 -4
300 K B
10 K 300 K
Ni5
Size (nm)T (K) D L / L o ๏ด Fig. 3. (A) Thermal conductivity for Ni1, Ni3, Ni4, Ni5 and Ni7. (B) Thermal conductivity at 10 K and 300 K as a function of crystallite size. Error bars of the data are shown in (B). Ratio of effective Lorentz number for the nanoparticles (L) in metallic regime to Sommerfeld value (L o ) i.e. L/L o of (C) Ni3, and (d) Ni5. Inset: (C) shows the L/L o of Ni1, (D) Ni4 (left), and (D) L versus crystallite size (right). There are thus tendencies of evolution of decreasing ฮบ values, changing shape and slope with decrease in crystallite size. While the lowest value of ฮบ is โ 0.13ยฑ0.01 W/m-K at 10 K, it is โ 0.52ยฑ0.05 W/m-K at 300 K in Ni7 around 1/175 of Ni bulk of โ 91.0 W/m-K, showing its ultralow value . This is significantly smaller than the well-known TE materials (Fig. S7) such as nanocrystalline Si Ge and Bi Te , PbTe, TiS and CuFeS ref. and references therein. Further, it is realized that the values of x range from 0.7 to 1.3 in ฮบ โ T x depending on crystallite size at low temperature (Fig. S8). This is consistent with anatase TiO , but in contrast to the phonon-like T dependence for granular metals . The sharp drop in ฮบ at low temperature is likely to be due to the strong grain boundary scattering of charge carriers and localization effects associated with a decrease in ๐ with decrease in size and scattering of carriers with defects including point defects, dislocations and GBs (Figs. 1B-G & S2A-C). They may play important roles in Ni3 to Ni7 in their electrical transport with the crystallite size smaller than the mean free path of the electrons (โ 14 nm) in bulk Ni . In order to understand the deviation of the WF law, we calculated Lorentz number L using ๐ณ = ๐ฟ ๐ ๐๐ป taking ฮบ e = ฮบ. Figs. 2C,D, insets depict 8 the normalized Lorenz ratio L/L as a function of T for Ni1, Ni3, Ni4 and Ni5. Remarkably, while the ratio L/L ranges around 2 - 2.5 in the metallic Ni1, it increases to about 3 orders of magnitude at 300 K for Ni3 and Ni4, respectively in their metallic regimes. Fig. 3D, right inset, shows its colossal dependence on crystallite size. They clearly show a large violation of WF law in metallic samples but an extreme violation of this law in these MIT-induced and semiconducting NPs. They are attributed to the systematic decrease in quasiparticles as crystallite size drops . Colossal Seebeck coefficient : The systematic evolution of the enhancement in the ฯ as the crystallite size drops has been corroborated with the evolution of their S (Fig. S9). The phonon drag minimum (PDM) is systematically suppressed with the broad hump-like feature shifting at โ 140 K in Ni1 and Ni2 compared to Ni bulk and then, S crosses over from negative to positive sign near 207 K and 275 K for Ni1 and Ni2 as T increases, but when crystallite size decreases (Fig. S9A). These features are considerably transformed with further decrease in crystallite size with just a feeble phonon drag effect in each of Ni3 and Ni4 (Fig. S9B), and PDM is completely suppressed in Ni5 to Ni7 (Fig. S9C). Consequently, a large positive value in the whole T range for Ni3 and Ni4, and colossal positive values in Ni5 to Ni7 at 10 K. This shows evolution of electrical conduction from n-type to p-type as crystallite size drops. Fig. 4A illustrates the trend in S of the samples at 10 K and 300 K that shows approximately 400 times increase of S in Ni7 compared to that in Ni1; this value could be much larger when it is extrapolated to 10 K but considered just at 30 K for Ni7 (see ESI). This enhancement also is not that gigantic as that in ฯ where it is 17 orders of magnitude enhancement (Fig. 2A), indicating that S and ฯ have also been decoupled in these nanostructures. The maximum values of S are 68.6ยฑ2.8 and 1.87ยฑ0.07 mVK -1 at 30 K and 300 K, respectively for Ni7. These values are very large compared to other materials (Fig. S9D) including CoSbS , Cu Se and ionic and solid-state thermoelectric supercapacitors . The linear fits of S versus 1000/T (Fig. S10) give the slopes and hence the transport energy level differences from the Fermi level (E F -E T ) i. e. 3.0ยฑ0.1 meV, 3.5ยฑ0.2 meV, 15ยฑ1 meV, 153ยฑ5 meV and 396ยฑ14 meV for Ni3, Ni4, Ni5, Ni6 and Ni7 (Fig. 4D; see ESI for more details). This trend indicates that transport energy drops fast with decrease in particle size, enhancing inelastic transport and hence deviation from WF law. 9 E F E T Decrease in particle size and enhance monodispersity E F -E T E F -E T E F -E T E n e r g y DOS B Crystallite size (nm) S ( m V K - ) Crystallite size (nm)
10 K 300 K A C S / L
10 K 300 K
Fig. 4. (A) Seebeck coefficient at 10 K and 300 K as a function of crystallite size; inset: expanded view at smaller scale, (B) schematic illustration of difference in Fermi level and transport level (E F -E T ) as a function of simultaneously particle size and monodispersity. (C) Electronic figure of merit at 10 K and 300 K as a function of crystallite size. Error bars of the data are shown in (A) and (C) in which the values were taken at 30 K for 1.3 nm Ni7, instead of 10 K. Thermoelectric figure of merit : The value of dimensionless electronic figure of merit, S /L, is found to be of about 2.4 ร 10 -4 and 1.6 ร 10 -4 at 300 K and 10 K, respectively in Ni1 that is similar to โ 10 -4 for a bulk Ni (Fig. 4C). Moreover, S /L deviates at least one order of magnitude in the investigated temperature range with decrease in crystallite size (Fig. 4C) which support the non-quasiparticle dynamics that is in line with earlier report . The power factor (S ฯ) and ZT as function of temperature and crystallite size show similar trends (Fig. S11). The maximum values of S ฯ and ZT are found to be โ 450ยฑ49 ยตW/m-K and โ 0.020ยฑ0.004, respectively in Ni5 at 10 K which is significantly larger than that of bulk Ni. Conclusion : We have experimentally demonstrated a gross violation of Wiedemann-Franz law in colloidal Ni nanoparticles which is evolutionary as the size drops. They show novel transport phenomena such as metal to insulator transition, colossal Seebeck coefficient along with change in conduction from n-type to p-type and ultralow thermal conductivity. These results not only deliver a window into the unconventional electronic dynamics of these nanoparticles, but also can be useful in thermoelectrics and heat dissipation in nanocrystal array-based electronics. 10
Experimental Section/Methods
Synthesis of Ni Nanoparticles (NPs)
Nickel acetylacetonate, Ni(acac) (95%), trioctylphosphine (TOP, 90%) and oleylamine (OA, 70%), purchased from Sigma Aldrich, were used as received. Typically, 3 g Ni(acac) and 10 ml OA were mixed in three-neck round bottom flask and heated at 210 o C for 2 hours under nitrogen atmosphere. The reaction product was cooled down to room temperature and centrifuged after the addition of n-hexane and ethanol to extract the NPs. This was done three times to remove excess OA, TOP or acetate and then the particles were dried at 60 o C for characterizations. This sample was coded as Ni1. 0.25 ml of preheated TOP at 200 o C is added in a solution of 3 g Ni(acac) in 10 ml OA, already degassed at 120 o C for 30 mins with remaining reaction conditions the same. This sample was coded as Ni2. Similarly, samples coded as Ni3, Ni4, Ni5, Ni6 and Ni7 were prepared in 1 ml, 3 ml, 5 ml, 7 ml and 10 ml TOP, respectively. More details are given in table S1.
Characterizations
X-ray diffraction (XRD) measurements of Ni NPs were performed on powder samples using Bruker D8 Advance X-ray diffractometer with Cu Kฮฑ radiation (0.154 nm) for laboratory source and beamline BL-18, KEK, Japan for synchrotron source. Transmission electron microscopy (TEM) measurements were performed using TECHNAI-20-G on NPs dispersed over carbon-coated TEM grids by drop-casting the well-sonicated NPs. Field emission scanning electron microscopy (FESEM) measurements were carried out on compacted pellets using FEI Nova nanosem450. Resistance measurements were performed using four-point probes of Ni1 to Ni5 and two-point probes of Ni6 and Ni7 (Fig. S4) . Seebeck coefficient measurements using differential direct current setup in the temperature range of 5โ300 K in a specially designed commercially available Dewar . Thermal conductivity was measured using a dc pulse laser technique in the temperature range of 10 - 300 K . Typical uncertainty in the measurements of these physical parameters were less than 3, 4 and 10%, respectively. These transport measurements were done on pellets made from cold-pressed powder at 1.9 GPa. Acknowledgments
Authors gratefully acknowledge Dr. Mukul Gupta, UGC-DAE Consortium for Scientific Research, Indore, India for providing laboratory XRD data and Dr. Jaiveer Singh, IPS Academy, Indore, India for collecting synchrotron radiation XRD at KEK, Photon factory, Tsukuba, Japan. The FESEM and TEM data were obtained from CIL, Harisingh Gour University, Sagar and MRC, MNIT, Jaipur, India, respectively. 11
Author contributions
VS; Conceptualization, Methodology, Investigation and Writingโoriginal draft, GSO; Visualization, review & editing, and YKK; provided thermal conductivity data.
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