Engineering Natural Layered Framework for Low and Anisotropic Thermal Conductivity

The development of nano–manufacture technology in the twenty‐first century has paved the way for artificial nanostructure constructions like man–made superlattices, providing historical breakthroughs in thermal physics and thermoelectrics by the modulation of phonons. Still, high–performance thermal insulators haven't come into operation due to the arduousness, costing and unscalability of artificiality. Herein, intentional engineering on a so–called ‘natural superlattice’ with alternating PbSe– and Bi2Se3–layer crystal structure is brought forth to recreate the mechanism of artificial superlattices and boost phonon localization. The thermal conductivity notably shows a direction–specific reduction, leading to minimum approaching and enhanced anisotropy. The modification of the natural framework and its effects have been supported by various transport and structure studies. This work sets a generalizable example for natural layered material engineering that bridges between the inflexible, changeless but self–assembled natural layered compounds, and the highly efficient, delicately tailored but unscalable artificial superlattice complexes. The methodology promises new horizons for practicable thermal management.


Introduction
In the context of global growing demands on renewable clean energy facilities, and flexible self-powered devices, the gearing-free thermoelectric (TE) generator to exploit low-quality heat energy has always kept in researchers' interest.Performance of a working TE material is determined by its power factor, PF, and thermal DOI: 10.1002/apxr.202200125conductivity, , through ZT = PF  T, where ZT is dimensionless TE figure of merit and T is temperature.A serviceable TE generator wants a large ZT value of several units or tens at working temperature.The late 1940s has seen a milestone Ioffe reached [1] when employing the mass fluctuation, [2] and since then it has been conventional TE research paradigm called 'Phonon Glass Electron Crystal' to exact and to perfect thermal transport, while still to optimize electronic transport.Generally for ZT greater than unity, the superlow thermal conductivity is necessitated and deciding rather than expected.
Besides the reliance of TE applications, the concept of intelligent device also wants systematic thermal management for ordinary subjects [3,4] and electronic circuits, [5][6][7][8] and even calls for thermal circuits. [9]Therefore, needs for sophisticated thermal-managing semiconductors are arising.The great pullulation of Large Scale Integration was accompanied by development of nano-fabrication technologies, and it rebounded on a couple of subjects of physics researches on nano-constitutions beyond integrated circuits.Epitaxy had been appreciated as effective TE and thermal-insulating material in very early years [10][11][12][13][14][15][16] when dense boundaries in it are found to effectively scatter phonons.For example the well-known Pb-SeTe/PbTe quantum dots superlattice stood out as a PbTe-family material with  = 0.62 W m −1 K −1 and ZT = 1.3 at room temperature as early as 2000. [11,12]t the same time, the turn-up of graphene opened a new era in electronics along with a decade of researches on monolayered, multilayered and many-layered van der Waals (vdW) material and other more nanostructured material.At present, layered TE material is one trending research topic for its low thermal conductivity. [17,18]Considering most of great thermal-insulating materials being layered, it's natural to think of layered structure as the simple thermal-insulating mechanism, like the functioning of storeyed stucture in artificial superlattice.This is a premature conception and there're still a lot of theories.Many layered materials are hardly called poor thermal conductors [19,20] while a big part of poor thermal conductors are PbTe-like materials with simple crystal structures, [21,22] and even layered materials with analogous layer structure can have huge disparities in thermal conductivities. [23,24]This originates from the difference between crystalline layers and epitaxial storeys, which makes the layered structure more a supersize lattice than a superlattice.Phonons and charge carriers transport coherently in layers as a whole, and atomically sharp and perfect crystal faces in natural substances don't act like boundaries according to the textbook Bloch's theorem.[27] The roughness of boundaries is found to determine the decoherence.To restore superlattice phenomena in natural layered substances, there're natural layered materials discovered with contrived layer structure restricting quasiparticles, [27][28][29][30] but they're particularities.Also there're natural intercalation superlattices similar to epitaxial ones, [25,[31][32][33] but they're drudgeries.
Pb 5 Bi 6 Se 14 or (PbSe) 5 (Bi 2 Se 3 ) 3 , which has archetypal crystal structure consisting of alternating PbSe-and Bi 2 Se 3like layers, [34] is a member of the cannizzarite compounds (PbSe) 5m (Bi 2 Se 3 ) 3n with (m, n) = (1, 1), [35] belonging to the class of homologous series compounds.][41][42][43][44][45] Pb 5 Bi 6 Se 14 has very low thermal conductivity with homely TE performance compared to its kindreds [46] on account of its unpleasant electronic structure.In this work, in attempt to build a quantum dots superlattice akin to PbSeTe/PbTe, we AgSb-codoped only the PbSe-layer part of the 'natural superlat-tice' Pb 5 Bi 6 Se 14 , similar to how researchers have AgSb-codoped bulk PbTe to get the nanodots-loaded AgPb m SbTe m + 2 (LASTm) material. [22]We vindicated the existence of intentionally introduced scattering centers, and we found them break interlayer bonds to restore the structure of vdW layered compounds [27] that are true natural superlattices.The dopants conduce to the phonon localization and lead to further reducing of the already very low thermal conductivity down to near the Cahill's lower bound.We further unveiled the orientation-preferential nature of this engineering element and found an enhanced anisotropy.This study confirms the feasibility and merit of partial engineering, and offers a common tool for both material mechanism and application researches.

Results and Discussion
Samples with nominal composition of (Ag 0.5x Pb 1−x Sb 0.5x Se) 5 (Bi 2 Se 3 ) 3 (Pb-Bi-Se-Ag-Sb, PBS-AS) where x=0.00, 0.05, 0.10, 0.15 and 0.20 are successfully synthesized.Powder X-ray diffraction patterns (XRD) (Figure 1a) are consistent with existing literature reports, [34,40,42] and the patterns correspond well to simulated single-crystal pattern of the parent compound (PbSe) 5 (Bi 2 Se 3 ) 3 based on the crystallographic data published by Sassi et al. [34] The results should suggest successful insertion of dopants and high purity of samples in the same way of Sassi et al. [43] Energy-dispersive X-ray spectroscopy (EDXS) experiments were carried out with scanning electron microscope (SEM) to further confirm the homogeneity of samples.Figure 2a shows the SEM image of the hot-pressed PBS-AS x=0.20 sample surface and corresponding EDXS mapping of individual elements to it.(see Figure S1, Supporting Information, for other samples) The dispersion is uniform at the micrometer scale with atomic percentages close to nominal values, showing no seperated micro impurity grains or domains which we found to speckle the pre-annealing samples.The determined chemical compositions are given in Table S1 (Supporting Information).Pb signal shows gradient descent and Ab-Sb signal shows compatible ascent, indicating the doping sites.The biased proportion estimation can be attributed to the low sensitivity of SEM-EDXS and heavy overlap between different elemental signals according to literature. [47]We performed X-ray photoelectron spectroscopy  S1 (Supporting Information) lists the atomic percentages from XPS supporting EDXS results.According to database, [48] the valence states are identified as Pb(+2), Bi(+3), Se(-2), Ag(+1) and Sb(+3) as expected.The Ag 3d spectrum, Bi 4f spectrum and Pb 4f spectrum correspond well to those of Bi 2 Se 3 [49] and Ag-doped PbSe, [50,51] and to mineral cannizzarite Pb 46 Bi 54 (S, Se) 127 . [47]The trailing of Bi 4f peaks can be assigned as another small pair of Bi 4f peaks from BiO x that possibly results from inevitable in-test surface air exposure, pretty much like the case of Bi 2 Se 3 . [49]Bi atomic percentage is possibly underestimated owing to this.The Se 3d spectrum and Sb 3d spectrum show complex structures.Main Se 3d peaks coincide with those of PbSe, Bi 2 Se 3 and Pb 46 Bi 54 (S, Se) 127 , but they are broadened. [47,49,50]Airproof storage was considered so the samples weren't long-term exposed to air and SeO x doesn't take place, whose peak should be on the site just apart from the envelope in the spectrum.Also simply adding a single peak of precipitated pure selenium which should be in middle of the single pair of 3d peaks can't fit well for our broadened spectrums.We see this broadening as results of asymmetric bonding structures in the distorted PbSe-frame (Figure 1b displays the crystal structure) and multiple pairs of Se 3d peaks may exist.The Sb spectrum is analyzed thoroughly with O1s peaks of BiO x isolated and two pairs of Sb 3d peaks left.One pair dubbed letter-B has lower binding energy.Considering the relatively weak electronegativity of Se, the small difference between coordination numbers of Pb and Bi in the substance, and the charge-compensating electron transfer between PbSeand Bi 2 Se 3 -layer, we don't think the lowering of energy as possible results of being in different chemical environment.Credible atomic percentages of Sb-A and Sb-B are respectively obtained and also presented in Table S1 (Supporting Information).One can see the contrast between them varies among samples.One tentative explanation could be that when Ag and Sb have different charging states, pair together, and create local distortions like they do in the supposed prospect of LAST-m, [22] they are co-doping the substance as acceptor-donor.When Sb as a donor is far from Ag, it's independently excited.But Sb can also be near Ag forming a 'Donor + Acceptor − ' associated center with constant or discontinuous distance.The ionic interaction from acceptor may lower binding energy of donor, and cause one more single kind of excitation.From another perspective, the locally-strained atomic clusters created by Ag-Sb pairs may also have different binding energy comparing to that of a relaxed bulk atomic frame, committing the low-energy excitation.It needs further research to figure out the underlying mechanism, but existence of Ag-Sb local structures is suggested from the XPS result.Chemical shifts of Ag are normally imperceptible so we didn't observe counterpart phenomenon in acceptors.
TE properties of sintered PBS-AS samples were measured.(Figure S3, Supporting Information) Electrical conductivity decreases and absolute value of Seebeck coefficient increases when doping amount increases, resulting in a counterbalanced Power Factor PF = S 2 , which improves a little compared to that of undoped sample.It is demonstrated that PBS-AS samples show degenerate or metallic electrical transports resembling behaviors of doped Bi 2 Se 3 .Early researches on the band structure near Fermi surface [37,52] can explain this Bi 2 Se 3 -dominated behavior.With non-deteriorated electrical properties, the thermal conductivity decreases very much after doping.An improved TE performance ZT = PF  T manifests because a tiny disparity in an already small denominator causes a large improvement.The thermal transport should be interesting in this system and we further conducted acoustic-recording, Raman-spectroscopic and electronmicroscopic measurements to study the phonon transport step by step.
Room-temperature acoustic velocities of sintered PBS-AS plates were recorded.(Figure 3a) Longitudinal velocity decreases accompany the doping, demonstrating dopants mire phonon transport, while it doesn't seem so for transverse velocity.Using Leont'ev model, [53,54] acoustic kinematic properties can relate to elastic kinetic properties through Equation (S2) and (S3).Bulk modulus shows decreases while shear modulus doesn't vary a lot.It suggests that vertical-to-layer bonds are impaired.
From the equations we find E = 33.4GPa and  = 2.139 for the undoped sample, suggesting weak and highly-anharmonic bonding in this material.We can conclude that dopants further soften the elastic bonding, drag the vibrational wave and cause a drop of already low thermal conductivity.The modulation displays in an anisotropic style.Raman tests were taken on hot-pressed samples to study detailed effects of dopants on vibrations.(Figure 3b) The signals around 245.3 cm −1 and 471.0 cm −1 associate to vibrations of Bi 2 Se 3 (237 cm −1 )-and PbSe (480 cm −1 )-structure respectively according to database of bulk Bi 2 Se 3 and PbSe. [55]The shortwave peak at 802.5 cm −1 has to do with the 790 cm −1 polaronic peak of PbSe. [56]The broad longwave peak around 100−−200 cm −1 is accredited to combination of signals from both PbSe-and Bi 2 Se 3 -parts since they both have multifold adjacent peaks in this range, like the E g (132.9 cm −1 ), E u (125 cm −1 ), A 1g (175.4 cm −1 ) and A 2u (129 cm −1 , 160 cm −1 ) modes of Bi 2 Se 3 , [57] and the LO(Γ)(140 cm −1 ) and 2LO(X)(168 cm −1 ) modes of PbSe, [58] to name a few.The sharpest 245.3 cm −1 peak of our spectrum serves for analysis.Peak of undoped sample blueshifts from that of bulk Bi 2 Se 3 , probably due to mutual compression from the distorted PbSe-structure strengthening the Bi-Se bonds.Peak position and intensity both change with respect to dopants addition.It's seen that redshifting peaks are sharper and higher revealing that compression suppresses Bi 2 Se 3 -vibration, and the shifts exactly match   the varyings of Sb-B/Sb-A atomic percentage ratio in XPS results.(Table S1) Continuing from our previous theory, we believe single Sb +3 atom causes more compression for its smaller radius and stronger electro-force, while Ag +1 Sb +3 pair results in many-atomic distorted regions which soften average bondings and break compressing bonds between PbSe and Bi 2 Se 3 .The microscale bond-breakings are exhibited as vertical-to-layer mechanical impairment at macroscale.We turned from spectroscopy to microscopy experiments for clear analysis of dopants.Figure 4a is a well-captured high-resolution transmission electron microscopy (HRTEM) picture of a real crystal grain showing typical layered structure as in Figure 1b.To check structural transfiguration, zoomed-in pictures of several layers of doped (x=0.15) and undoped samples were taken.(Figure 4b,c) The two pictures contrast strongly.Nanodots are directly visualized with eyeable intertwined lattice in image, and nanodots are in reality map-like irregular mesoscale existences as we expected.
Implementing Fast Fourier Transformation (FFT) on the shipshape crystal lattice of undoped sample restores electron diffractive patterns, two crystal face spacings can be read out.(see Fig- ure 4d) The spacings are 10.62 Å and 2.99 Å respectively, conforming to simulated values [34] 10.68 Å and 2.93 Å of [002] and [502] planes diagrammed in the inset.This is a typical [010] side cleavage and we also performed same processing for doped sample, but the ordered crystal domain is much smaller so resolution is low with only [006] and [502] points recognizable.(see Figure S4, Supporting Information) FFT was executed on both doped and undoped samples with the same low spatial resolution to get the ratio of doped sample's spacing to undoped sample's spacing, and crystallographic data of the doped one is acquired by scaling from the high-resolution result of undoped sample.(listed in Table S2, Supporting Information) Notice the [002] face is perpenticular to horizontal line, while the [502] face is almost parallel to PbSe-and Bi 2 Se 3 -layers.Therefore it's deduced that doping laterally stretches out the layers keeping interlayer spacing constant, and relative horizontal atomic shifts break some diagonal bonds between PbSe-and Bi 2 Se 3 -layers (see Figure 1b) freeing the suppressed mismatch between PbSe and Bi 2 Se 3 .The conclusion from Raman tests is confirmed by these results.The results also confirm that the dopants are not existing at the interstitial sites, supporting our basic hypothesis of partial engineering in PbSe-layers.
The original (PbSe) 5 (Bi 2 Se 3 ) 3 compound is different from the misfit layered compounds like (SnS) 1.17 (NbS 2 ) n [27] with interlayer bonds and forced commensurability. [37,47,52]It's the special vdW bonding in the latter makes a layers amount of scatterings possible, [59] and causes incoherent phonon transport in an atomically sharp superlattice [27] .The vdW misfit compounds are however particular.We expect the breakings of interlayer bonds can realize a similar form in the general layered compound, and make this substance more a true superlattice of stacking PbSe and Bi 2 Se 3 films with quantum dots every layer like PbSeTe/PbTe.Also, the dopant atoms are originally isotropic but they cause anisotropic local structural transmutations when put together interactively in this substance environment.The dopants in this condensed matter can equivalently be considered to have anisotropic micro-structure.The anisotropic functioning of anisotropic dopants becomes an interest.We further conducted anisotropic transport experiments for undoped and doped (x=0.15)samples.Figure 5a-c set out TE characters of anisotropic experiment samples.[38][39][40][41][42][43] Our samples following same synthetic routes are consistent, but anisotropic samples slightly deviate.Reasons could be that different molding size results in different inherent Bi Pb defect concentration which plays a major role in determining carrier density. [39,52]Large moldings can also result in insufficient doping which should influence transport.Previous thin PBS-AS discs perform better than anisotropic samples but we can't machine z-direction bars from those discs.It turns out, after the anisotropic doping, more significant degradation of transport occurs in z direction and brings in enhanced anisotropy.(Figure 5d) Pb 5 Bi 6 Se 14 itself has ordinary anisotropy at the rate of about 1.5 because of its bonds-connected structure, unlike vdW materials.Improved thermal anisotropy in an excellent thermal insulator (which results in an 'anisotropic glass') and nearly doubled electrical anisotropy are both unusual.Electrical transport properties were further illustrated by Hall measurements.(Figure 5e,f) Carrier density remains steady with respect to temperature at the level of 10 20 cm −3 .In the in-plane direction, post-doping loss of carrier mobility is low, and the two sample mobilities fit well to power law with alike exponent of about −0.9 representing T −1 electron-phonon scattering.However, in the out-of-plane direction, the post-doping loss is significant and there's also loss of mobility gradient from −0.71 to −0.42.In original sample, the complicacy of interlayer bonds may hinders carrier transport and produces a portion of hopping carriers making the exponent slightly deviate from −1, especially in z-direction.Doping obviously magnifies the uncommon part of scatterings.It's possible that simple dopants in one kind of layers form lasagnestructured alternate scattering atmospheres just like intercalation layers, which screen z-direction movement but let go carriers moving in Bi 2 Se 3 2D layer in xy-direction.Likewise, breaks of interlayer bonds by anisotropic doping may scatter or gap vertical transport.Lastly, anisotropically localized phonons could have transcendent electron-phonon interaction with different exponent as well.All possibilities may contribute to spontaneous build-up of alternate blocking layers acting like spontaneous intercalation, and it's done by simple doping.The phenomenon can endow the simple and isotropic dopant element effectively an emergent anisotropic scattering structure.We also analyzed anisotropic thermal transport.Electronic thermal conductivity  e was calculated from electrical conductivity  by Widemann-Franz Law  e = LT, where the Lorenz number L was calculated by Single-Parabolic-Band model to avoid overestimated value of 2.45 × 10 −8 W Ω K −2 .We took lattice thermal conductivity as  l =  −  e .(Figure 5g) Thermal conductivity shows some upturns near 500 K.There is also turnaround in the same temperature region in reported electronic conductivity curve by Sassi et al. [42,43] We believe that temperature works together with doping.Bulk PbSe is reported to go through structure transmutation from simple cubic structure to distorted orthorhombic structure under applied pressure, and the certain pressure is higher when temperature is higher. [60]PbSe in the stressed low-symmetry phase has loosened elastic bondings.It can be inferred that the PbSelattice distorted by Bi 2 Se 3 in Pb 5 Bi 6 Se 14 also slightly relaxes with heated vibration, and the bonds-breaking doping which creates local relaxations assists the process.The redshifts in Raman peaks (480 cm −1 ) of our samples with respect to PbSe-structure demonstrate the loosened bonding in the distorted structure, and it's possible that shifted structure also has stronger elastic structure.The shifted PbSe-lattice at high temperature should be more like in the high-symmetry phase and make contributions to the thermal conductivity.Counterpart distortions in Bi 2 Se 3 -layers which are only compressed but not distorted are not expected since bulk Bi 2 Se 3 is not considered as structurally pliant.We can further identify trails for phonon localization behavior in this natural material with no vdW structure, which was only studied in vdW materials before when talking about natural materials. [27,30,61]Cahill has proposed that when scattering is strong enough to destroy authenticity of phonons and localized atomic vibrations are independent with interlocking coherence vanishing, which means coherent length l ≃  where  is phonon wavelength, a crystal lattice reaches its minimum thermal conductivity. [62,63] l,min = (  6 Θ and N are Debye temperature and number of atoms per volume, and V l and V t are longitudinal and transverse sound velocities.For our sample, it reads that Debye temperature is 138.90K with the equation k B Θ = ℏV a (6 2 N) 1/3 .(V a is average acoustic velocity) In the high temperature limit is slow-varying with respect to temperature.Lattice thermal conductivities are approaching this minimum possible value substantiating localized phonons.Notice that in the thermal transport, the fitting exponent of z-curves also changes from −0.44 to near-zero −0.34, while two xy-curves look parallel.The z-curve is leaning close to the plain-and-low Cahill curve while xy-curves don't show qualitative change.Phonon mean free path l can be computed through  l = 1 3 C V V a l where C V is volumetic specific heat taking Dulong-Petit value and V a is average acoustic velocity taking the room-temperature value, which should normally be higher at high temperature in favour of our conclusion.Wavelength of Debye-frequency phonons  D = hV a k B Θ is 4.93 Å being a reference of interatomic distance and wavelength lowerlimit.(Figure 5h) Unlike vdW material having random stackings, [30,59] layers are actually bonded in undoped sample, although inherent defects [39] greatly scatter phonons.Phonon mean free path l is still larger than short wavelengths, with only part of phonons localized.The l of doped samples further shortens in only one direction to near  D making great part of phonons localized.(We estimated l of previous PBS-AS x=0.00 and PBS-AS x=0.15 thin disc samples using z-electrical conductivity data of anisotropic samples.The estimated mean free path can actually cross the criterion line and is attached in the figure.)It's conceivable that our structuralized dopants break interlayer bonds and create local transformed lattice regions in PbSe-layer, which make interlayer boundaries coarse.The almost every-interstice scatterings, gaps and slowerings drastically influence vertically moving phonons, while phonons transport in layers are only weakly scattered as normal.Phonons are less influenced when looking horizontally because of the directional structure of the substance which is like densely packed sparse sieves.The doping causes more localization in z-direction with relatively small costing of xy-direction conductivity, and it ends up with an increased anisotropy in this glass-like substance.The simple doping strategy utilizes the layered structure to create augmented impact in only one direction.It's a rather easy and generalizable strategy that can be used for recent arresting thermal transport dimensionality research [64] for common layered materials.

Conclusion
In conclusion, the emergent phenomenon of anisotropic dopant was set up and confirmed from all aspects by XPS, acoustic detection, Raman spectroscopy and HRTEM experiments.The splitting of XPS peaks declares existence of special dopants.Consistent anisotropic change of acoustic properties, transformation of Raman peaks and deformation in HRTEM patterns demonstrate the structure of anisotropic dopants.The chemistry ideology of interaction both between the two doping atoms, and between dopant and background substance, is introduced to transport researches.In turn, the collective phenomenon in a condensed matter is also emphasized when thinking of dopants.The anisotropic dopant leverages on the layered structure to intensify influence anisotropically, and causes a jump of electronic anisotropy and a directional boost of phonon localization in a thermal glass.The concept of constitutive-part engineering and interlayer bonds breaking elucidate new and convenient strategies for general layered material engineering, bridges between artificial architectures and natural materials, and can be transfered to other anisotropic-or-isotropic and insulating-or-conducting materials in research of sophisticated functional materials and deep mechanisms.
The homemade Ag x Pb 1−2x Sb x Se was then grounded up and evenly mixed with Bi 2 Se 3 (99.99%from Macklin) in stoichiometric amounts.The mixtures were reacted at 1023 K for 96h in box furnace.After cooling, the ingots were annealed at 873 K for 72h twice with intermittent handgroundings and mixtures to ensure purities.
Obtained fine powders were hot-pressed into pellets of ϕ 12.7 mm × 1.0 mm for PBS-AS and pillars of ϕ 12.7 mm × 11.0 mm for anisotropic samples under axial compressive pressure of 80 MPa in a vaccum at 763 K for 30min.The bulks have geometric densities larger than 97% of theoretical value.
XRD: XRD spectras of before-pressing powder samples were acquired on a Rigaku XtaLAB mini diffractometer using a Cu K  source (=1.5418Å).
SEM-EDXS: SEM and EDXS experiments were performed on the hotpressed sample surfaces using a SU8220 cold field emission scanning electron microscope operating at 15 keV with an Oxford AZtec X-Flash detector for EDXS analysis.
HRTEM: The high resolution TEM imagings of the transferred ultrosonic-dispersed cannizzarite powders grounded from consolidated bulks on copper TEM grids were performed on a JEOL JEM-2100Plus TEM microscope with accelerating voltage of 200 kV.
XPS: The XPS spectras were acquired on before-pressing powder samples using Thermo ESCALAB 250Xi equipped with a monochromatic Al K source (h=1486.6eV).
Raman Spectroscopy: The room temperature Raman spectras on smooth surfaces of hot-pressed samples were acquired by LabRamHR laser Raman spectrometer system using a 325 nm laser beam.
Ultrasonic Pulse Echo Measurement: Room-temperature sound velocities were acquired by ultrasonic pulse echos on pressed discs using TECLAB UMS Advanced Ultrasonic Material Characterization System with 20 MHz longitudinal probe and 5 MHz transverse probe.
Transport Properties: Samples were well-cut and polished with shiny surfaces from pressed bulks.Bars with typical sizes of 10 mm × 2 mm × 1 mm for PBX-AS samples and xy anistropic samples, and of 1 mm × 2 mm × 10 mm for z anisotropic samples, respectively, were employed to simultaneously measure electrical conductivity  and Seebeck coefficient S by standard four-probe methods in a He atmosphere Cryoall CTA-3 system.Thermal conductivity  was calculated through  = DC p from the thermal diffusivity D obtained by flash diffusivity method (LFA 467, Netzsch) tests on round disks of ϕ 12.7 mm × 1 mm for PBS-AS samples, and square slices of 6 mm × 6 mm × 1 mm for z anisotropic samples and of 1 mm × 6 mm × 6 mm for xy anisotropic samples.Specific heats C p were taken as Dulong-Petit values.Carrier densities n were determined from Hall experiments on squre slices of 5 mm × 5 mm × 0.5 mm for xysamples in Lakeshore HMS 8400 system by standard van der Pauw methods, and carrier mobilities  were obtained through  = ne from the electrical conductivities  obtained by CTA tests.

Figure 1 .
Figure 1.a) The powder XRD patterns of simulation and PBS-AS samples with x=0.00, 0.05, 0.10, 0.15, and 0.20.b) The crystal structure of Pb 5 Bi 6 Se 14 .Layered structure is presented in which the big heavy balls are respectively Pb atoms in grey blue and Bi atoms in black with small orange balls being Se atoms.The unit cell is represented by the red parallelepiped with the Se-Bi-Se-Bi-Se quintuple layers and the Pb-Se staggered layers alternately appearing with a few bonds between them.Pb lattice is curled with disarrayed coordinations.Note that a-axis is the verticle z-direction following Sassi's notation in this paper.
(XPS) study to get elemental compositions ulteriorly.(see Figure 2b for PBS-AS x=0.20 and Figure S2, Supporting Information, for complete sample set) Table

Figure 2 .
Figure 2. a) The SEM image of sample PBS-AS (x=0.20) and the corresponding EDXS mapping and spectrum.b) XPS survey spectrum of PBS-AS (x=0.20) and the high-resolution spectra around binding energy regions of Pb 4f, Bi 4f, Se 3d, Ag 3d, and Sb 3d, respectively.

Figure 3 .
Figure 3. a) Room-temperature acoustic velocity and elastic modulus of PBS-AS.b) Scaled Raman spectrum of PBS-AS samples with insets being enlarged images at the peak.

Figure 4 .
Figure 4. a) An undoped crystal grain's HRTEM picture showing the actural layered structure.b) Zoomed-in HRTEM image of several layers of doped PBS-AS sample with roped-off shallow regions being clusters and stripes of tangled lattice.c) Zoomed-in HRTEM image of several layers of undoped PBS-AS sample showing layered crystal structure and d) FFT image of the framed region of it showing diffraction points of determined crystal planes presented in the inset schematically.