S R Popuri

R Decourt

J A Mcnulty

M Pollet

$ A D Fortes

F D Morrison
email: finlay.morrison@st-andrews.ac.uk

J W G Bos

Phonon-glass and heterogeneous electrical transport in A-site deficient SrTiO3

The phonon-glass electron crystal concept is one of the key guiding principles for the development of efficient thermoelectric materials. Here, we confirm that SrTiO3 with vacancies on the perovskite A-site is a phonon-glass for 27% A-site vacancies. Furthermore, we find that these samples are electrically inhomogeneous with a core-shell grain structure that limits the electron crystal properties. Thermal conductivity, heat capacity and neutron powder diffraction, complemented by representational analysis and phonon calculations, were used to investigate the thermal transport. This reveals that the heat carrying modes are dominated by Sr motions and that these become more localised upon the introduction of the A-site vacancies. Impedance spectroscopy and DC electrical measurements were used to probe the heterogeneous electrical structure of insulating and conducting samples. This reveals the coring of grains due to oxidation on cooling from sintering temperatures. The resultant insulating shell limits the thermoelectric power factor to S 2 / = 0.45 mW m -1 K -2 and the figure of merit to ZT = 0.15 at 900 K for Sr0.20La0.530.27Ti0.95Nb0.05O3-. The thermal properties of these materials are therefore controlled by an intrinsic feature of the microstructure (i.e. the A-site vacancies), while the electrical properties are grain boundary limited, which in principle can be controlled independently to raise S 2 / and ZT.

Introduction

The design of phonon glass electron crystal (PGEC) materials has been one of the key guiding concepts of modern thermoelectrics research. [START_REF] Slack | CRC Handbook of Thermoelectrics[END_REF] The aim is to create materials with the good electrical properties of crystalline solids but with the low thermal conductivity of a structural glass.

If this can be achieved, then high thermoelectric figures of merit, ZT = (S 2 /)T and efficient waste heat recovery become possible. [START_REF] Rowe | Thermoelectrics and its Energy Harvesting[END_REF][START_REF] Snyder | Complex thermoelectric materials[END_REF] Here, S is the Seebeck coefficient,  is the electrical resistivity and the thermal conductivity  is the sum of lattice and electronic components. Classical examples of PGEC materials are host-guest materials, [START_REF] Nolas | Semiconducting Ge clathrates: Promising candidates for thermoelectric applications[END_REF][START_REF] Cohn | Glasslike heat conduction in high-mobility crystalline semiconductors[END_REF][START_REF] Sales | Filled skutterudite antimonides: A new class of thermoelectric materials[END_REF][START_REF] Nolas | Skutterudites: A phonon-glass-electron crystal approach to advanced thermoelectric energy conversion applications[END_REF] such as clathrates and skutterudites that consist of a framework for electrical conduction and loosely bound rattling atoms that reduce the thermal conductivity. The rattler ions lead to a low-energy non-dispersive mode in the phonon bandstructure, which causes an avoided crossing and lowers the group velocity of the heat carrying acoustic modes. [START_REF] Toberer | Phonon engineering through crystal chemistry[END_REF][START_REF] Christensen | Avoided crossing of rattler modes in thermoelectric materials[END_REF][START_REF] Koza | Breakdown of phonon glass paradigm in La-and Ce-filled Fe4Sb12 skutterudites[END_REF] The observation of Einstein modes in heat capacity is often a key indicator for these localised vibrations.

SrTiO3 is one of the best explored oxide thermoelectric materials with peak ZT = 0.4 at high temperatures. [START_REF] Kikuchi | A large thermoelectric figure of merit of La-doped SrTiO3 prepared by combustion synthesis with post-spark plasma sintering[END_REF][START_REF] Ohta | Large thermoelectric performance of heavily Nb-doped SrTiO3 epitaxial film at high temperature[END_REF][START_REF] Lu | High-Figure-of-Merit Thermoelectric La-Doped A-Site-Deficient SrTiO3 Ceramics[END_REF][START_REF] Kovalevsky | Enhancement of thermoelectric performance in strontium titanate by praseodymium substitution[END_REF][START_REF] Kovalevsky | Towards a high thermoelectric performance in rare-earth substituted SrTiO3: effects provided by strongly-reducing sintering conditions[END_REF][START_REF] Yaremchenko | Boosting Thermoelectric Performance by Controlled Defect Chemistry Engineering in Ta-Substituted Strontium Titanate[END_REF][START_REF] Dehkordi | Large Thermoelectric Power Factor in Pr-Doped SrTiO3-d Ceramics via Grain-Boundary-Induced Mobility Enhancement[END_REF][START_REF] Lin | Thermoelectric Power Generation from Lanthanum Strontium Titanium Oxide at Room Temperature through the Addition of Graphene[END_REF] It is characterised by large power factors S 2 /  3 mW m -1 K -2 at ~500 K in single crystals, [START_REF] Okuda | Large thermoelectric response of metallic perovskites: Sr1-xLaxTiO3 (0 < x < 0.1)[END_REF][START_REF] Ohta | High-temperature carrier transport and thermoelectric properties of heavily La-or Nb-doped SrTiO3 single crystals[END_REF] which is competitive with many of the best semiconductor thermoelectrics. The limitation is the relatively large lat ~ 10 W m -1 K -1 near room temperature, [START_REF] Muta | Thermoelectric properties of reduced and La-doped single-crystalline SrTiO3[END_REF][START_REF] Popuri | Glass-like thermal conductivity in SrTiO3 thermoelectrics induced by A-site vacancies[END_REF] which is far larger than lat ~ 1 W m -1 K -1 that is desirable to achieve high ZT values. For this reason, great effort has been expended to reduce lat via substitutions on the Sr, Ti and sites and through oxygen deficiency. [START_REF] Kato | The effect of Eu substitution on thermoelectric properties of SrTi0.8Nb0.2O3[END_REF][START_REF] Yamamoto | Thermoelectric phase diagram in a CaTiO3-SrTiO3-BaTiO3 system[END_REF][START_REF] Fukuyado | Thermoelectric properties of the electron-doped perovskites Sr1-xCaxTi1-yNbyO3[END_REF] This work has led to a substantial reduction to lat, RT ~ 3-4 W m -1 K -1 but always maintained a T -z temperature dependence, [START_REF] Wang | Interfacial Thermal Resistance and Thermal Conductivity in Nanograined SrTiO3[END_REF] typical of crystalline materials. Recently, we used Sr vacancies to manipulate the thermal transport via the perovskite A-site, while leaving the conducting Ti-O framework unaffected. [START_REF] Popuri | Glass-like thermal conductivity in SrTiO3 thermoelectrics induced by A-site vacancies[END_REF][START_REF] Popuri | A-Site Deficient SrTiO3: A Possible Phonon-Glass Electron-Crystal?[END_REF] This sublattice engineering resulted in controlled transition to a glass-like  for 27% vacancies with a nearly temperature independent value of ~2.5 W m -1 K -1 . This value is close to the predicted minimum  for SrTiO3. [START_REF] Popuri | Glass-like thermal conductivity in SrTiO3 thermoelectrics induced by A-site vacancies[END_REF] The introduction of Sr vacancies leads to a large mass disorder parameter  = 0.49 for 27% vacancies, which is far larger than attained by conventional alloying (e.g. mixing Sr and La with max = 0.08), suggesting that structural disorder is an important factor. However, at the same time, a large fraction of the Sr-O chemical bonds is broken, and this is expected to lead to an Einstein-like localisation of phonon modes involving Sr. Although the high-temperature data signalled a dramatic change in (T), [START_REF] Popuri | Glass-like thermal conductivity in SrTiO3 thermoelectrics induced by A-site vacancies[END_REF] confirmed by other groups, [START_REF] Lu | High-Figure-of-Merit Thermoelectric La-Doped A-Site-Deficient SrTiO3 Ceramics[END_REF][START_REF] Jackson | Neodymium-Strontium Titanate: A New Ceramic for an Old Problem[END_REF][START_REF] Azough | Concurrent La and A-Site Vacancy Doping Modulates the Thermoelectric Response of SrTiO3: Experimental and Computational Evidence[END_REF][START_REF] Kovalevsky | Effect of A-Site Cation Deficiency on the Thermoelectric Performance of Donor-Substituted Strontium Titanate[END_REF] low-temperature data are needed to confirm the suppression of the peak in (T), which signals the emergence of a phonon-glass. Recently, a near identical transition to phonon-glass behaviour was observed in Na0.5La0.5TiO3, [START_REF] Daniels | Phonon-glass electron-crystal behaviour by A site disorder in n-type thermoelectric oxides[END_REF] where Sr has been replaced by an equal mixture of Na + and La 3+ . This leads to a similar mass disorder parameter ( = 0.54) but phonon calculations also point towards a localisation of the lattice vibrations due to the highly divergent (weak/strong) Na-O and La-O bond strengths.

In terms of the electron crystal properties, our earlier results showed a reduction in S 2 / as the amount of A-site vacancies is increased. [START_REF] Popuri | Glass-like thermal conductivity in SrTiO3 thermoelectrics induced by A-site vacancies[END_REF][START_REF] Popuri | A-Site Deficient SrTiO3: A Possible Phonon-Glass Electron-Crystal?[END_REF] For example, samples with 7% vacancies were found to have S 2 / = 1.3 mW m -1 K -2 at 500 K, which decreased to ~0.15 mW m -1 K -2 at 800 K for 27% vacancies. The suppression of the ~500 K peak is caused by the appearance of a semiconducting tail near room temperature, which is absent for small amounts of vacancies. A nearly identical optimisation of S 2 / and ZT near 5-10% vacancies was found by Lu et al. [START_REF] Lu | High-Figure-of-Merit Thermoelectric La-Doped A-Site-Deficient SrTiO3 Ceramics[END_REF] The Na0.5La0.5TiO3 phonon-glass system without A-site vacancies has similar S 2 / and ZT ~ 0.20, compared to a SrTiO3 reference sample, demonstrating that it is possible to combine phonon-glass and electron crystal properties in SrTiO3 based perovskites. [START_REF] Daniels | Phonon-glass electron-crystal behaviour by A site disorder in n-type thermoelectric oxides[END_REF] In this manuscript, we confirm the presence of a vacancy induced phonon-glass state in SrTiO3 and provide insight into its origins. Heat capacity measurements demonstrate an increase in Einstein character at low energies, signalling a flattening and localisation of phonon modes. In addition, we reveal the presence of a heterogeneous core-shell grain structure. This suppresses the electron crystal properties due to the presence of an oxidised shell, which forms on cooling from high-temperature sintering conditions and increases the electrical resistivity.

Experimental

Polycrystalline Sr1-xLa0.67x0.33xTiO3 (x = 0, 0.4 and 0.8) samples were prepared on a 3-gram scale by heating cold pressed pellets containing ground mixtures of SrCO3 (Alfa Aesar, 99.99%), La2O3 (Sigma-Aldrich 99.99%) and TiO2 (Alfa Aesar, 99.99%) at 1200  C for two times 12 hours, and at 1400  C for 4 hours in air, with intermediate regrinding between steps. 1% excess SrCO3 was used for the x = 0.4 and x = 0.8 samples. Oxygen deficient and Nb substituted Sr0.20La0.530.27Ti1-yNbyO3- (0  y  0.15; Nb2O5 from Alfa Aesar, 99.9985%) samples were prepared in a similar manner but all heating steps were done under 5% H2 in N2 with the samples placed on graphite disks. The final heating step for these two samples was 1450  C for 4 hrs. The densities of the sintered pellets are 92-97% of the theoretical values (see Table S1).

Laboratory X-ray powder diffraction data were collected on a Bruker D8 Advance diffractometer with Cu K1 radiation. X-ray diffraction patterns (8 hr data collection) for all samples are shown in Fig. S1 in the Supplementary Information. The microstructure and homogeneity of a Sr0.2La0.530.27TiO3 sample sintered in air was examined using a Quanta 650 FEG Scanning Electron Microscope. This showed the sample to be well sintered with large grains and a uniform elemental distribution (Fig. S2).

Temperature dependent neutron powder diffraction (NPD) data were collected on an 8-gram Sr0.2La0.530.27TiO3 sample (sintered in air) using the time-of-flight High Resolution Powder Diffractometer (HRPD), equipped with a closed-cycle refrigerator (4-290 K) and furnace (300-1000 K), at the ISIS neutron and muon source, UK. Rietveld fits were performed using the GSAS/EXPGUI programmes. [START_REF] Toby | EXPGUI, a graphical user interface for GSAS[END_REF] Low-temperature thermal conductivity measurements were made using the Thermal Transport Option of a Quantum Design Physical Property Measurement System (PPMS). The heat capacities of SrTiO3 and Sr0.2La0.530.27TiO3 (both sintered in air) were measured between 2 and 300 K using the heat capacity option of the PPMS. High temperature thermal diffusivity () and heat capacity (Cp) were measured using a Netzch LFA 457 and Perkin Elmer DSC 8500. The thermal conductivity was evaluated from the heat capacity and diffusivity data using: =(T)Cp(T)d, where d is the sample density. Electrical resistivity and Seebeck measurements were made using a Linseis LSR-3 instrument under a He atmosphere. Immittance spectroscopy was carried out on ceramic pellets over the frequency range 5 Hz -13 MHz using an HP4192A Impedance Analyser under an applied ac voltage of 100 mV. Ag paint electrodes (RS components) were applied to opposing pellet faces and cured at 120 °C for 20 minutes. Samples were mounted in a sample holder of in-house design and placed in a non-inductively wound tube furnace allowing data to be collected from ambient to 923 K. All data were subsequently corrected for sample geometry (electrode area and sample thickness); as a result, resistance (R) values extracted by modelling on equivalent circuits consisting of RC elements (discussed below) correspond to resistivities. Symmetry analysis of the atomic displacement at the high-symmetry points in the Brillouin zone were done using the web based program ISODISTORT using the Pm-3m perovskite, with a setting placing the A-site at the origin of the unit cell as the parent reference structure. [START_REF] Campbell | ISODISPLACE: a web-based tool for exploring structural distortions[END_REF] Phonon Eigen vector and values of high symmetry SrTiO3 were calculated using CASTEP [START_REF] Clark | First principles methods using CASTEP[END_REF] in the density functional perturbation theory (DFPT) approximation [START_REF] Refson | Variational density-functional perturbation theory for dielectrics and lattice dynamics[END_REF] for 28 points in reciprocal space.

For the DFT calculations we used the GGA PBEsol exchange correlation functional [START_REF] Perdew | Restoring the density-gradient expansion for exchange in solids and surfaces[END_REF] with normconversing pseudo potentials with a plane wave basis set cut-off energy of 600 eV and an 8  8  8 k-grid with respect to the cubic cell. The relaxed cell volume after geometry optimisation was 3.880995 Å. The change in unit cell stress was less than 0.015 GPa in the final optimisation cycle.

A custom written script was used to plot the phonon dispersion curves with grey-scale weightings reflecting the magnitude of the projected atomic displacements according to the Eigen vectors as calculated by DFPT.

Results

Thermal properties

Thermal conductivity: Combined low-and high-temperature (T) data for a selection of Sr1-xLa0.67x0.33xTi1-yNbyO3- samples with 0% (x = 0), 13% (x = 0.4) and 27% (x = 0.8) vacancies are shown in Figure 1. The (T) measurements confirm the suppression of the 25 K peak in (T) and the emergence of phonon-glass state for the samples with 27% vacancies. Only marginal differences are evident between the 27% A-site vacancy samples sintered in air (labelled with O3) and under 5% H2 in N2 (labelled with O3-), suggesting that any oxygen vacancies have a minimal impact on (T), and that the A-site vacancies are the key driver for the phonon-glass state. In all cases, the electronic contribution to  is negligibly small due to the relatively high (T) of these samples (see below).

Phonon Eigen Vector Analysis: Symmetry analysis was used to obtain information on which atomic displacements contribute to the various phonon Eigen vectors at the high symmetry points in the Brillouin zone (BZ). These modes are visualised in Figure 2 and an overview of the atoms that are allowed by symmetry to enter in to the various characters of the Eigen vectors at the high-symmetry points are given in Table 1. This analysis reveals that the modes that corresponds to Eigen vectors of character R4 -, M3 -M5 -, X3 -and X5 -points contain Sr displacements and can therefore be expected to be strongly affected by the vacancy engineering. Furthermore, as the characters of the phonon Eigen vectors are expected to vary continuously, lines of dispersion connecting these points, (e.g. X5 -to R4 -and Γ to X3 -) will also have Eigenvectors that are dominated by A-site displacements even though by symmetry, the character of the different atoms are now allowed to mix (see Table 2). To validate this assertion, the symmetry analysis results are compared to our atom resolved calculations of the phonon dispersion, which are shown in Figure 2. This reveals that most of the phonon density of states below 130 cm -1 can be attributed to a single band of low-energy modes that are essentially of Sr nature with only minor Ti and O admixture. While at the zone boundaries the group velocity of the phonon modes will clearly be zero, the fact that they have significant dispersion across the BZ, means that they are expected to have a substantial effect on the low temperature thermal transport properties of the system that we study here. Indeed, the calculated 300 K cumulative lat from Ref. 37, replotted in Figure 2, alongside our atom resolved phonon dispersion curves, reveals that up to 50% of the lattice conductivity is attributable to phonon modes of energy <130 cm -1 , and that this is dominated by phonons with predominantly Sr character. As noted before, 37 some of the optic modes have considerable dispersion and therefore contribute to the thermal transport. Many of these heat conducting modes are dominated by Ti motions, and are mainly at higher energies.

Oxygen contributes to most of the modes throughout the BZ (in keeping with the symmetry analysis in Tables 1,2). It should be noted that the imaginary frequencies at the R-point are due to an instability related to an octahedral rotation present as a structural distortion (Pm-3m to I4/mcm) below 110 K. The main result is hence a very striking low-energy mode that is dominated by Sr motions, which can be expected to be strongly affected and localised by the disruption of the Sr-O bonding network.

Heat capacity: Cp data (2-873 K) for SrTiO3 and Sr0.8La0.530.27TiO3 (sintered in air) are shown in Figure 3. These data were fitted using a small electronic contribution (T) and a combination of two Debye (Di) and two Einstein (Ei) modes with the total number of oscillators equal to the number of atoms per formula unit (i.e. ni = 5 for x = 0 and ni = 4.73 for x = 0.8): 38

𝐶 𝑝 = 𝛾𝑇 + ∑ [9𝑛 𝐷𝑖 𝑅 ( 𝑇 𝜃 𝐷 𝑖 ) 3 ∫ 𝑥 4 𝑒 𝑥 (𝑒 𝑥 -1) 2 𝑑𝑥 𝜃 𝐷 𝑖 𝑇 ⁄ 0 ] 2 𝑖=1 + ∑ [3𝑛 𝐸𝑖 𝑅 ( 𝜃 𝐸 𝑖 𝑇 ) 2 𝑒 𝜃 𝐸𝑖 𝑇 ⁄ (𝑒 𝜃 𝐸𝑖 𝑇 ⁄ -1) 2 ]
2 𝑖=1

(1)

The energies and weighting of these modes are summarized in Table 3 and the quality of the fits is evident from the Cp(T), Cp/T 3 (T) and Cp/T(T 2 ) plots in Figure 3 shown in Figure 4a. The sample undergoes a structural phase transition from the simple cubic Pm-3m perovskite to a tetragonal I4/mcm superstructure between 473-573 K (Fig. S3). The I4/mcm structure is characterised by a 0 a 0 c -octahedral tilting [START_REF] Howard | Group-theoretical analysis of octahedral tilting in perovskites[END_REF] with no evidence for the ordering of the Asite vacancies in vacancy-rich and poor layers. [START_REF] Battle | A-site cation-vacancy ordering in Sr1-3x/2LaxTiO3: A study by HRTEM[END_REF][START_REF] Howard | Crystal structures and phase transition in the system SrTiO3-La2/3TiO3[END_REF] The temperature dependence of the isotropic thermal displacement parameters (Uiso) for the Sr/La, Ti and O sites is given in Figure 4b. This plot shows that all atomic sites have significant residual disorder at 4 K, indicating that the Sr vacancies affect the Ti and O sublattices. To facilitate fits to the Uiso(T), a weighted average of the O Uiso's on the 4c and 8d sites of the I4/mcm structure was calculated. Fits were undertaken using both the Debye and Einstein models: [START_REF] Willis | Thermal Vibrations in Crystallography[END_REF][START_REF] Popuri | Evidence for hard and soft substructures in thermoelectric SnSe[END_REF]

𝑈 𝑖𝑠𝑜 = 3ℏ 2 𝑚𝑘 𝐵 𝜃 𝐷 [ 1 4 + ( 𝑇 𝜃 𝐷 ) 2 ∫ 𝑥 𝑒 𝑥 -1 𝑑𝑥 𝜃 𝐷 𝑇 ⁄ 0 ] + 𝑑 2
(2)

𝑈 𝑖𝑠𝑜 = ℏ 2 2𝑚𝑘 𝐵 𝜃 𝐸 𝑐𝑜𝑡ℎ 𝜃 𝐸 2𝑇 + 𝑑 2 (3)
The best fit to the A-site Uiso's was obtained using the Einstein model, which had a ~10% lower 21 M cm at 300 K. The magnitude of C is typical of a bulk response for a non-ferroelectric material, [START_REF] Irvine | Electroceramics: Characterization by Impedance Spectroscopy[END_REF] i.e. it represents a significant volume fraction of the sample. The size of the semi-circular arc and the M" peak height remained invariant upon heating, indicating that the capacitance is relatively temperature independent. However, the M" peak was displaced to higher frequency, indicating a decrease in time constant due to a decrease in , Fig 5a . As the semi-circular arc was increasing hard to fully resolve, C and  were estimated from the M" peak at each temperature according to:

𝐶 = 𝜀 0 2𝑀 𝑚𝑎𝑥 " (4) 𝜌 = 1 2𝜋𝑓 𝑚𝑎𝑥 𝐶 (5)
where 0 is the vacuum permittivity, M"max is the imaginary modulus peak height and fmax is the frequency (in Hz) at which the peak maximum occurs. [START_REF] Morrison | Characterization of Lanthanum-Doped Barium Titanate Ceramics Using Impedance Spectroscopy[END_REF] Using this methodology conductivity values for the bulk response, b1 (b1 = 1/b1) were determined at each temperature at which a peak "coring", is well known to occur in titanate dielectrics, [START_REF] Reaney | Microwave Dielectric Ceramics for Resonators and Filters in Mobile Phone Networks[END_REF] whereby oxygen is lost during high temperature sintering releasing (conduction) electrons:

On cooling, and post densification, slow diffusion kinetics mean that these oxygen vacancies are not filled homogeneously and can result in either a semiconducting pellet interior with an insulating "skin", or semiconducting grain interiors with an oxidised (insulating) grain shell. [START_REF] Morrison | Characterization of Lanthanum-Doped Barium Titanate Ceramics Using Impedance Spectroscopy[END_REF] In the case of the former, polishing can remove this layer. In our case, polishing of the sample had no effect on the IS data indicating the latter microstructure, see Fig 6 inset. Such coring effects are not detectable by conventional DC conductivity measurements but are often visually evident by a dark grey-blue colouring below a lighter yellow-beige surface; the effect can also exacerbated by pressing defects. [START_REF] Reaney | Microwave Dielectric Ceramics for Resonators and Filters in Mobile Phone Networks[END_REF] By contrast IS data for Sr0.2La0.53•0.27TiO3 sintered in O2 at 1400 °C indicates an electrically homogenous microstructure with no evidence of a conductive core. The impedance and modulus data obtained above 700 K are dominated by a single response, with associated capacitance of ca. 8-9 pF, characteristic of a bulk response (Figure S4). [START_REF] Irvine | Electroceramics: Characterization by Impedance Spectroscopy[END_REF] As with the air-sintered sample, grain boundary and electrode effects make a small contribution to the total sample resistance but over the temperature range studied T  b. The bulk conductivity (b) exhibits (from 600-1000 K) was observed for the y = 0.05 sample. This is 2-3 times smaller than the best reported values for polycrystalline SrTiO3 based thermoelectrics, thus limiting ZT to ~ 0.15 at 873 K, despite the reduction of (T) and emergence of a phonon-glass state by the introduction of A-site vacancies. We note that S 2 / increases monotonously and does not show a peak at ~500 K, which is caused by the semiconducting (T) near room temperature.

Another important observation is the non-monotonous relation between electrical conductivity,  = 1/, and S. Within a single band approximation, increases in S are linked to a reduction in carrier concentration, n, thus leading to a reduction in  = ne, where e is the electron charge and  is the carrier mobility. For the current materials, there is no systematic S()

dependence and an almost random variation is observed (Table 4). This non-systematic variation, can be explained using a core-shell model, analogous to the samples sintered in air. Here, the shell occurs due to an increase in partial oxygen pressure upon cooling from sintering conditions under 5% H2 in N2, leading to oxidation of the outer layer of the grains. [START_REF] Sinclair | CaCu3Ti4O12: One-step internal barrier layer capacitor[END_REF] In a two-component model electrically connected in series, S and  are given by: 48

𝑆 = (1-𝑥 𝑠 ) 𝑆 𝑐  𝑐 +𝑥 𝑠 𝑆 𝑠  𝑠 (1-𝑥 𝑠 )  𝑐 + 𝑥 𝑠  𝑠 (7)
𝜌 = (1 -𝑥 𝑠 )𝜌 𝑐 + 𝑥 𝑠 𝜌 𝑠 (8) Here, xs is the volume fraction of the "insulating" shell and Ss (Sc) and s (c) are the S and  of the shell (core).  does not change much upon reduction in 5% H2 (see Fig. 1) and  ~ 2.5 W m -1 K -1 was assumed for both the core and shell regions. The measured S and  are therefore volume weighted averages of the core and shell regions. In order to evaluate the thermoelectric properties of the Sr0.20La0.530.27Ti1-yNbyO3- samples reported here, we use the near universal S() relationship that exists for conducting La and Nb substituted SrTiO3 crystals. [START_REF] Bouzerar | Unified modelling of the thermoelectric properties in SrTiO3[END_REF][START_REF] Kang | Thermopower-conductivity relation for distinguishing transport mechanisms: Polaron hopping in CeO2 and band conduction in SrTiO3[END_REF] The variation in S spans 1-2 orders of magnitude (10s-1000s V K -1 ), while  varies by 4-5 orders of magnitude. The impact of the shell is therefore much more pronounced on  than it is on S. Previous work making an explicit comparison between single and polycrystalline Sr1-xLaxTiO3 (x < 0.05) suggested a ~ 70 nm thick insulating acceptor layer. [START_REF] Moos | Electronic transport properties of Sr1-xLaxTiO3 ceramics[END_REF] Assuming a similar 50 nm insulating shell and cube shaped grains with 10  10  10 m 3 dimensions, this leads to a 0.3 volume % fraction of shell material. Using the measured S, and the S() relation this enables an estimate of c and of s, as summarized in Table 4.

For the Sr0.20La0.530.27Ti1-yNbyO3- samples, the values of s fall within a factor of five, between 8-40  cm. This shows that the shell region remains reasonably conducting but is resistive enough to lead to a 1-2 order of magnitude increase in  at 300 K, thereby severely reducing the maximum attainable S 2 /. At higher temperatures, the impact of the insulating shell is reduced and (T) takes its usual metal-like form and S 2 / is 50-60% reduced compared to samples without vacancies.

The near room temperature semiconducting (T) can be used to obtain an estimate of the EA for carrier transport through the shell. Inspection of a log(1/T) plot for the Sr0.20La0.530.27Ti1-yNbyO3- samples reveals linear, thermally activated, behaviour between 300-580 K for the most insulating (y = 0, y = 0.15) samples, and 300-380 K for the more conducting y = 0.05 and y = 0.1 samples (Fig. S5). The y = 0 sample was found to have EA = 0.147(3) eV, while the Nb substituted samples have similar EA = 0.098(3) eV (Table S1). We note that these values are much lower than observed from immittance spectroscopy on samples sintered in air (EA ~ 1.4 eV),

where the shell is truly insulating. This analysis also suggests that the presence of Nb to some degree prevents the formation of the insulating shell upon cooling the samples.

Discussion

Thermal transport: Low-temperature (T) data confirms the presence of a vacancy induced phononglass state, while Cp fitting demonstrates a transfer of spectral weight into a E ~ 120 cm -1 Einstein mode (), which is centred on a line of dispersion observed in the first principles phonon calculations and whose character is dominated by Sr displacements. Symmetry analysis was used to visualise the low-energy modes at the high-symmetry points and these are indeed dominated by Sr motions (Figure 2). The change in Cp signals a significant localisation of the heat carrying phonon modes upon the introduction of A-site vacancies, consistent with the removal of a large fraction (27%) of the Sr-O chemical bonds, leading to a flattening of the Sr dominated phonon modes. The experimental data therefore indicates that the breaking of chemical bonds underpins the observed phonon-glass state, and that it is not only attributable to mass disorder in an otherwise "rigid" phonon band structure. The residual disorder that is apparent from the thermal displacement parameters affects all atomic sites, with the largest d 2 for the nearest neighbour to the vacancy (O), followed by Ti and then Sr/La. This is in keeping with recent high-resolution STEM imaging that reveals that all sites are affected by the introduction of A-site vacancies. [START_REF] Azough | Concurrent La and A-Site Vacancy Doping Modulates the Thermoelectric Response of SrTiO3: Experimental and Computational Evidence[END_REF] The interpretation of this residual disorder is in terms of static displacements from the equilibrium position that are enabled by the removal of many of the Sr atoms. This disorder will impact on (T) but the magnitude of the displacements (d < 0.11 Å for O at 2 K) remains small, in particular compared to thermal motion at elevated temperatures, where the glass state survives, so cannot be the dominant contribution to reduction of (T).

Electrical: Both impedance and DC electrical measurements reveal the presence of core-shell grain structures, which increase  and limit S 2 /. Removal of these oxidised shell regions will significantly enhance the thermoelectric performance, particularly at medium temperatures (450-500 K), where S 2 / usually peaks. At high-temperatures (> 600-700 K), (T) returns to the metallike dependence that is expected for degenerately doped SrTiO3, and the impact of the insulating shell is much reduced with a 50-60% reduction compared to good polycrystalline samples. A-site vacancies open-up the perovskite structure and increase oxide ion conductivity. [START_REF] Neagu | Structure and Properties of La0.4Sr0.4TiO3 Ceramics for Use as Anode Materials in Solid Oxide Fuel Cells[END_REF] It is therefore perhaps unsurprising that the formation of an insulating shell is exacerbated in samples with higher concentrations of A-site vacancies. Indeed, as discussed in the introduction, 5% H2 reduced samples with no and 7% vacancies do not show the near room temperature semiconducting tail, while samples with 13% and 27% vacancies do. Removal of the oxidised shells will enable strongly improved S 2 / near 500 K, while the gain at high-temperatures is expected to be smaller. It will thus help with creating a larger temperature-averaged power factor and broader high-ZT plateau, both of which are key features in improving power output and efficiency of a thermoelectric device. This work demonstrates that during cooling from sintering conditions in a 5% H2 in N2 atmosphere, the oxygen partial pressure increases sufficiently for an oxidized shell to form at intermediate temperatures, after which the sample is kinetically trapped in a non-equilibrium core-shell state.

Formation of this layer could be prevented by buffering the pO2 upon cooling or rapid quenching of the samples.

To conclude, the phonon-glass state is not only a result of the large mass disorder created on the perovskite A-site, but can be linked directly to the removal of the Sr-O bonds, leading to localisation of specific low-energy heat carrying Sr-O phonon modes. Electrical properties are dominated by a heterogeneous core-shell grain microstructure, which limits the electrical conductivity and thus the power factor. If the grain boundary structure can be controlled, whilst maintaining the A-site defect chemistry, significant improvements in power factor and device figure of merit are possible. SrTiO3. [START_REF] Buscaglia | Effect of nanostructure on the thermal conductivity of La-doped SrTiO3 ceramics[END_REF] The solid lines >300 K illustrate the transition from 1/T (0% vacancies) to T-linear (27% vacancies) behaviour. The two samples with oxygen deficiency ( > 0) were sintered in 5% H2 in N2.

3 )

 3 . The lowest energy Einstein mode (E2 = 17-19 K) accounts for the peak at ~ 4 K (Figure3c, d). This mode has a low weighting (nE2 < 0.001) and won't be discussed any further. The weighting of the high-energy Debye mode (nD1 ~ 3.1) does not change significantly between the two samples, while it softens from 676(3) K to 617(5) K, in agreement with the presence of vacancies and increased flexibility of the structure. For SrTiO3: D2 = 249(1) K (nD2 = 1.8) and E1 = 166(1) K with a low nE1 = 0.1. These values change to D2 = 223(1) K with a reduced nD2 = 1.1 and E1 = 175(1) K with a five-fold increased nE1 = 0.5, signalling a transfer of spectral weight from Debye into more localised Einstein modes, for the phonon-glass sample. The weighted average of the Debye and Einstein temperatures (using  𝐸 / 𝐷 ≈ √𝜋/6 decreases from 514(2) to 488(2) K, consistent with a softening of the lattice. The low-temperature Cp/T(T 2 ) data are shown in Figure3e, f and evidence significant non-linearity due to the low-energy E2 modes. The fitted values for the Sommerfeld coefficient are  = 0.2 mJ mol -1 K -2 for SrTiO3 and  = 0.5 mJ mol -1 K -2 for Sr0.8La0.530.27TiO3. This suggests a non-zero density of states at the Fermi Level, N(EF)  0, despite these samples being electrically insulating when probed by DC methods. However, as discussed below, impedance measurements indicate the presence of a conducting core -insulating shell microstructure, consistent with   0.Atomic displacement parameters: Variable temperature NPD data (4-1000 K) were collected from a Sr0.20La0.530.27TiO3 sample sintered in air. A representative Rietveld fit to the 300 K dataset is

  residual, whereas the Debye model yielded slightly better fit statistics for the Ti and O sites but with little visual difference in fit quality. The presence of a significant Einstein contribution to at least one of the Uiso's is consistent with the heat capacity fits. The final fitted values are: E = 150(5) K (Sr/La) [D = 260(10) K (Sr/La)], D = 488(11) K (Ti) and D = 664(11) K (O). The E = 150(5) K for Sr/La is in good agreement with E1 = 175(1) K from Cp fitting, suggesting that the A-site vibrations do indeed start to become more localised. A fit to a the average Uiso for the compound, yielded D = 454(9) K, in good agreement with the weighted average from the Cp(T) fits (D, av = 488(2) K). The residual disorder (d 2 ) values did not vary between the Debye and Einstein fits and are d 2 = 0.0060(2) Å 2 (Sr/La), d 2 = 0.0095(2) Å 2 (Ti) and d 2 = 0.0124(2) Å 2 (O). As can be seen from the inset to Fig. 4c, the d 2 values have a linear dependence on the distance to the A-site, confirming that the atoms nearest to the A-site vacancies (O) are affected most strongly by structural disorder. Electrical properties This section is split into two parts: the first deals with impedance spectroscopy measurements on electrically insulating Sr0.2La0.53•0.27TiO3 samples sintered in air and under flowing oxygen. The second part is focussed on the electrical properties of highly conducting Sr0.20La0.530.27Ti1-yNbyO3- samples sintered under 5% H2. Both sets of results point towards an inhomogeneous core-shell microstructure. Insulating samples: Immittance spectroscopy (IS) data for Sr0.2La0.53•0.27TiO3 sintered in air indicated it to be highly insulating with  >> 10 7  cm at 300 K. Despite the noise due to the high sample impedance, a single semi-circular arc was observed in the complex modulus (M*) plane plot, with a corresponding Debye-like peak in the imaginary modulus (M") spectroscopic plot, Fig 5a. Analysis using a parallel RC element shows that this response has a capacitance, C ~ 10 pF and  ~ 0.

  maximum was observed. The values exhibit the expected Arrhenius behaviour with an activation energy, EA ~ 0.33 eV, see Fig 6. On further heating to above 700 K a further semi-circular arc appears in both the complex impedance (Z*, Fig. 5c) and modulus (M*) plane plots with corresponding Debye-like peaks in the Z" and M" spectroscopic plots, Fig. 5b. The peaks are spectroscopically coincident, Fig 5b, and have an associated C ~ 3 pF at all temperatures analysed, indicating that this is associated with a bulk-like (high volume fraction) region of the sampleassigned as b2 hereafter. With increasing temperature two lower frequency responses are increasingly evident in the impedance data, Fig 5c, d; these responses have associated C of the order 10 -10 and 10 -8 F and are assigned to grain boundary and electrode responses, respectively. These responses contribute very little to the total sample resistivity, T, and to a first approximation T  b2 (and hence T  b2). b2 and Cb2 values were extracted from Z* plane plots based on a simple parallel RC model and b2 plotted as function of temperature in Arrhenius format, Fig 6. The data indicate a thermally-activated conductivity with EA ~ 1.40 eV. Overall the data indicate an electrical microstructure with coexistence of two high volume fraction regions within the sample and which have significantly different conductivity. Such a microstructure, often referred to as

Arrhenius behaviour with EA ~ 1 .

 1 41 eVvery similar in both magnitude and temperature dependence to the resistive (shell) response in the air-sintered sample, Fig 6. Sr0.2La0.53•0.27TiO3 and Sr0.2La0.53•0.27Ti1-yNbyO3- sintered in 5% H2 in N2 were too conductive to allow deconvolution of their electrical microstructure using immittance spectroscopy.Conducting samples: S(T), (T), the power factor S 2 / and ZT for several Sr0.20La0.530.27Ti1-yNbyO3- samples (0  y  0.15) sintered under 5% H2 are shown in Figure7.Small amounts of Nb substitution are known to improve S 2 /. The largest S 2 / = 0.55 mW m -1 K -2

Figure 1 .

 1 Figure 1. Temperature dependence of the thermal conductivity () for SrTiO3 with increasing

Figure 2 .

 2 Figure 2. Phonon dispersion and atom resolved phonon dispersions for SrTiO3, illustrating the low energy acoustic mode dominated by Sr at ~100 cm -1 . The characters (atomic displacements) of the

Figure 3 .

 3 Figure 3. Heat capacity (Cp) fitting for SrTiO3 and Sr0.2La0.530.27TiO3 sintered in air. Panels (a, d)

Figure 4 .

 4 Figure 4. (a) Fitted neutron powder diffraction profile for Sr0.2La0.530.27TiO3 sintered in air. Black

Figure 5 .

 5 Figure 5. Immittance spectroscopy data as a function of temperature for Sr0.2La0.53•0.27TiO3

Figure 6 .

 6 Figure 6. Arrhenius plot of conductivity of the semiconducting 'core' (b1filled circles) and

Figure 7 .

 7 Figure 7. Temperature dependence of (a) the electrical resistivity (), (b) Seebeck coefficient (S),

Table 1 .

 1 Symmetry-allowed atomic displacements (phonon character) at high-symmetry points of the Brillouin Zone (BZ) for a Pm-3m ABO3 perovskite structure. The "X" indicates that displacements of that atom type are allowed by symmetry for that irreducible representation (IR).

	Note that the segregation between A and B site displacements is almost complete at the high-
	symmetry BZ points, indicating that A and B site motions are not coupled. Labels for the IRs are as
	tabulated in the web-based program ISODISTORT based on the Pm-3m perovskite structure with A
	1a (0,0,0), B 1b (½, ½, ½), O 3c (0, ½, ½).
	Irreducible

Table 3 .

 3 Summary of heat capacity fitting parameters for SrTiO3 and Sr0.2La0.530.27TiO3 sintered in air, where θDi and θEi are the energies in degrees Kelvin of the Debye and Einstein oscillators used in the fits and the n-values give their weightings.  is the Sommerfeld coefficient in mJ mol -1 K -2 .

			θD1	nD1	θD2	nD2	θE1	nE1	θE2	nE2	ntot
	SrTiO 3	0.24(1)	676(3)	3.12(1)	249(1)	1.78(1)	166(1)	0.10(1)	19.2(1)	0.0009(1)	5.00
	Sr0.2La0.530.27TiO3	0.50(1)	617(5)	3.18(1)	223(1)	1.07(1)	175(1)	0.48(1)	17.2(1)	0.0009(1)	4.73

Table 4 .

 4 The conducting core -insulating shell composite model applied to the Sr0.20La0.530.27Ti1-yNbyO3- series sintered in 5% H2 in N2. Here, core is estimated from the measured S using the near universal S() relationship for La and Nb doped SrTiO3.[START_REF] Bouzerar | Unified modelling of the thermoelectric properties in SrTiO3[END_REF][START_REF] Kang | Thermopower-conductivity relation for distinguishing transport mechanisms: Polaron hopping in CeO2 and band conduction in SrTiO3[END_REF] This affords an estimate of shell. All data at 450 K.In all cases, 0.3 volume % fraction shell is assumed, corresponding to a 50 nm thick shell and cube shaped grains of 10  10  10 m 3 . 2.5% estimated uncertainties on the measures S and  values.

	y	Smeasured (V K -1 )	measured (m cm)	core (m cm)	shell ( cm)
	0	-205(5)	126(3)	1.8(1)	41.4(1)
	0.05	-284(7)	29(1)	4.7(2)	8.1(1)
	0.10	-234(6)	32(1)	2.8(1)	9.7(1)
	0.15	-247(6)	80(2)	3.0(1)	25.7(1)

Acknowledgements

The EPSRC (EP/N01717X/1) and Leverhulme Trust (RPG-2012-576) are acknowledged for support and the STFC for provision of beam time at ISIS. Raw data underpinning this work is available from the Heriot-Watt data repository.

Supplementary Information

Crystallographic information from Rietveld analysis of laboratory X-ray and neutron powder diffraction; laboratory X-ray powder diffraction patterns; Scanning Electron Microscopy data; additional immittance spectroscopy data and Arrhenius fits to the near room temperature DC electrical resistivity data. Representations

Table 2. Symmetry-allowed atomic displacements (phonon character) at lower symmetry lines of the Brillouin Zone (BZ) for a Pm-3m ABO3 perovskite structure. The "X" indicates that displacements of that atom type are allowed by symmetry for that irreducible representation (IR).

Note that motions of both A and B are now often symmetry allowed within an IR, leading to coupling between A, B and O site motions. Labels for the IRs are as tabulated in the web-based program ISODISTORT based on the Pm-3m perovskite structure with A 1a (0,0,0), B 1b (½, ½, ½), O 3c (0, ½, ½).


Prof Sergey A A N Malykhin

Prof Jonathan A Houard

Prof Rinat R A N Ismagilov

Anton S Orekhov

Angela Vella

Alexander N Obraztsov

Obraztsov

Vella

Luminescent Characteristics of Needle-Like Single Crystal Diamonds

Keywords: cathodoluminescence, chemical vapor deposition, diamond, needle-like crystals, photoluminescence

Luminescent properties of needle-like single crystal diamonds are investigated in a wide range of wavelength. The luminescent spectra with zero phonon lines centered at 389, 442, 468, 534, 563, 575, and 738 nm are detected using excitation by photons and electrons. Obtained photo-and cathodo-luminescent (PL and CL) spectra indicate presence in the singlecrystal diamond needles of nitrogen-and silicon-vacancy centers as well as substitutional or/and interstitials related to these atomic impurities. The dependencies of PL intensities of the 575 and 738 nm lines (related, correspondingly, to nitrogen-and silicon-vacancy centers) on excitation wavelength are determined. Time-resolved measurements are performed for the 575 nm PL line. The luminescence decay behavior for this line demonstrates the presence of recombination processes with characteristic times of about 28 ns (on 200 ns time scale) and 2.8 ns (on 20 ns time scale).

Introduction

Diamond is an amazing material that combines record hardness and thermal conductivity, biocompatibility, optical transparency, and other properties attractive for numerous applications. [1,2] Development of methods for synthesis of diamond with highpressure-high-temperature (HPHT) [3] and chemical vapor deposition (CVD) techniques [4] provides expansion of industrial usage of diamond. [5] Crystalline qualities of synthetic diamonds (which may be better than the best natural diamonds at present time [6] ) are critical for many applications as well as properties of particular structural defects. This stimulates investigations of structural peculiarities and defects in diamond. Many of these defects attract attention because of their optical and luminescent properties. More than 500 types of the color-centers are known in diamond. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] Luminescent characteristics of some of them allow consideration of diamond as promising material for different optical and quantum optical applications. [START_REF] Babinec | [END_REF]9] Important advantage of CVD techniques consists in ability to produce diamond crystallites of needle-like shape [10,11] which may be usable for some applications. In particular diamond needles are considered for creation of optical probes and sensors. These applications require comprehensive investigation and deeper understanding of the luminescent properties of particular color-centers in this type of diamond material. In this work, we perform study of the diamond needle-like single crystals to reveal their photo-and cathode-luminescent characteristics in a wide range of wavelength, never explored before for this kind of samples. Results of preliminary investigations of these properties have been reported in Refs. [12,13]. Here we present results of our studies of the diamond needle-like single crystals aimed to further revealing peculiarities of their photo-and cathodeluminescent characteristics.

Experimental Details

Materials

The needle-like single crystal diamonds (SCD) were obtained by combination of the CVD and selective oxidation techniques. [10] Home built direct current plasma enhanced CVD allowed creation of the carbon films composed of the pyramid shaped needle-like single crystal diamonds surrounded by a matrix of graphite, nanodiamond, and amorphous carbon. The films were grown on silicon wafer substrate. A selective oxidation at 650 C in air atmosphere for about 24 h was applied to remove the lowordered and graphitic part of CVD film and, thus, to obtain the pyramid-shaped diamond crystals in form of powdered material. This powder was used to prepare ethanol-based suspension containing SCD needles. The well-separated diamond crystallites were deposited on the substrates (e.g., on silicon wafers) by subsequent precipitation and drying the drops of the suspension. Detailed description of used methods and facilities are presented elsewhere. [14]

Cathodoluminescent Measurements

The cathodoluminescent (CL) investigations were made using specially prepared samples of SCD. Individual diamond crystallites in these samples were disposed on silicon substrates and fixed by local Pt deposition to prevent their uncontrollable moving by electrostatic forces appeared due to charging of dielectric particles by electron beam. The localization and Pt deposition were made with use of Versa 3D dualbeam (FEI) facility equipped by micromanipulators. The samples with different orientation of the diamond crystallites were prepared for these CL investigations. Scanning electron microscope (SEM) images of some of the samples and simplified scheme of their positioning are presented in Figure 1. It is worth noting that the bottom part of the needle in Figure 1(b) is not fixed on the right side, but it has not got any effects on further investigations. Surface purity of the samples was analyzed by energy-dispersive X-ray spectroscopy (EDS) using INCA EDS analyzer attached to JEOL 7001F scanning electron microscope. Obtained EDS maps did not indicate any detectable impurities on the facets of the SCD samples which were investigated.

The CL measurements were performed using GATAN MONO CL3 attachment to JEOL JSM7001F scanning electron microscope at room temperature (300 K) and with cooling down to temperature of about 81 K. The electron beam accelerating voltage was varied from 3 to 30 kV and the beam current was changed from 500 pA to 150 nA. The electron beam was focused in the area less than 10 nm in diameter as it was estimated from sample contrast on the SEM images obtained in secondary electrons mode. The diffraction grating with 1200 lines per mm (sensitivity maximum on 500 nm wavelength) was used in spectrometer for CL spectra detection. The optimal values of signal to noise ratio and spectral resolution were achieved at 15 kV voltage and 80 nA current of the electron beam. These parameters of the electron beam were used for detection of all CL spectra presented in this work.

Photoluminescent Measurements

The needle-like single crystal diamonds were also investigated with photoluminescence (PL) technique. A simplified optical scheme of used facility assembled on optical table is presented in Figure 2. A titanium-sapphire tunable pulsed laser (Chamaleon Ultra from Coherent) with wavelength varied from 690 to 1080 nm and 80 MHz frequency was used as a source of excitation irradiation. A pulse picker was used to reduce the laser retention rate at 4 MHz. Laser irradiation was passed through the second and third harmonic generation block (SHG/THG in Figure 2). To pick out needed wavelength from the generated set of laser radiation color filter was used (excitation filter in Figure 2). Selected laser beam, after passing through the 50/50 ultraviolet beam splitter (BS UV 50/50 in Figure 2) and reflective objective, irradiated the sample. The PL radiation emitted by the sample was collected by the same reflective objective and directed to the imaging camera (if optical image of the sample is required) or to the spectrometer analyzing collected light radiation. An additional optical filter (imaging filter in Figure 2) was installed before the spectrometer to remove intensive scattered radiation of the laser beam or its harmonics. A streak camera (model C5680 from Hamamatsu with slow sweep and an ultimate timing resolution of about 20-30 ps) situated after the spectrometer also was used for decay time determinations.

The PL investigations were performed under room temperature (300 K) and with cooling down to 24 K and to 4 K temperatures. Wavelength of excitation radiation was varied from 260 to 515 nm. Power of the irradiation beam measured before reflective objective was varied from 50 to 800 mW. PL spectra were obtained by focusing laser beam at different areas along an individual needle-like diamond crystal.

Results and Discussion

The advanced experimental techniques used in this study allow obtaining much more details about CL and PL spectra in comparison with our preliminary investigations reported in Refs. [12,13]. These details include spectral characteristics of the luminescence, dependence of the spectral lines on temperature and excitation wavelength, their decay time dependence, and phonon vibronic bands characteristics. In the preliminary investigation, we have established that luminescent characteristics of SCD indicate on nitrogen and silicon impurities contaminations. [12,13] While the nitrogen-related color centers are distributed more or less homogeneously in the crystallites, the silicon centers are concentrated predominantly at their apexes. The CL and PL investigations were performed in different areas of SCD (near the apex, in the middle, and near the base). The same luminescence lines in all of these points were observed. In this study, we focused mostly on the analysis of crystallite luminescent properties on the whole. The spectra discussed in this work were observed near the middle of the SCD and are used here as the most representative for the whole crystallite while spectra variations along the needles are discussed in other our works. [12,13]

Main Luminescence Lines

The luminescent spectra were obtained in wavelength range of 225-900 nm with CL technique and (depending on the excitation wavelength) in the range of 260-880 nm for PL. The spectra in the range of 350-800 nm are presented in Figures 3 and4.

Typical CL spectra measured in the middle part of SCD at room temperature and with cooling down to 81 K are presented in Figure 3. Figure 4 presents the PL spectra obtained at room temperature and at cryogenic temperature (24 K). At low temperatures, luminescence intensity increases, the width of the lines and, especially, the width of the broad bands related to structural defects in diamond reduces markedly. Overall signalto-noise ratio is increased with temperature decrease that allows appearance of more details in the spectra.

The most intensive sharp lines distinguished in the spectra are centered at 389, 442, 468, 534, 563, 575, and 738 nm. The line at 778 nm presenting in the CL spectra is a second order diffraction of 389 nm line. The spectral shape of low temperature PL spectrum in 650-730 nm wavelength range is due to transmission characteristics of the imaging optical filter. Previous investigations [15][16][17] allow assignment of observed luminescent line at 389 nm (3.188 eV) to a zero phonon line (ZPL) of nitrogen-related centers in diamond. Intensity of this 389 nm line was changed significantly during CL signal accumulation for electron beam accelerating voltage above few kV. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] It may explain variation of relative intensity of this line in the spectra shown in Figures 3 and4. The intensity of similar 389 nm line have been increased strongly after diamond annealing at temperature from 600 to 800 C. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] Such annealing may occur during oxidation of the CVD diamond film at 650 C. The nitrogen-related centers proposed for this line may include: defects that contains interstitial nitrogen atoms [18] ; pseudomolecules C-N formed by single substitutional nitrogen atom shifted along the h111i axis [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] or C2N [19] ; defects containing substitutional nitrogen atom bound to interstitial carbon atoms. [20] The 442 nm (2.807 eV) line obtained at 24 K with excitation wavelength of 260 nm has been assigned also to nitrogen impurities and represents a ZPL observed in the PL spectra. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] Moreover this line can be observed in low temperature CL spectra but it is too weak for detailed analysis. The line is not visible in PL and CL spectra measured at room temperature probably due to large background noise. In accord with previous investigations, the luminescent centers responsible for appearance of 442 nm line can contain interstitial carbon atoms. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] The 468 nm (2.651 eV) line has been observed in high-quality single-crystal CVD diamond films. This line has been assigned to the centers containing nitrogen and interstitial atoms. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF]17] However, in some reports this type of centers was associated also with silicon impurities that appeared in CVD diamond grown on Si substrates. [15,19] Clarification of this contradictory assignments requires high-temperature annealing of diamond in vacuum which was unavailable for us in this work. Obtained spectra demonstrate different shape of 468 nm line because of vibronic bands which will be discussed in the next section. Intensity of 468 nm line shows a significant increase in both CL and PL spectra at low temperatures. On the whole 468 nm line demonstrates greater relative intensity in photo-luminescence in comparison with cathode-luminescence.

The 534 nm (2.322 eV) line is supposed to be associated with the centers containing nitrogen atoms or nitrogen-vacancy complexes in its structure. [15] Usually the line is observed as a part of ZPL doublet containing also 531 nm line. But in perfect homoepitaxial CVD diamond films, this line has been observed as a single ZPL line instead. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] Only single line can be resolved in all spectra obtained in our work (see Figure 3 and4). This may be considered as an evidence of the high-quality single crystal structure of the needle-like diamonds in consistency with previously reported results. [21] The 534 nm line is better resolved in CL spectra. It may be due to less intensity of the vibronic bands of 468 nm line that results to less intensive background.

The 563 nm line can be detected in PL and sometimes in CL spectra but this line is weaker in comparison with the nearest 575 nm band. Moreover other lines in this spectral range relate to different defects in diamond. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] The 575 nm (2.156 eV) line in the luminescence spectra corresponds to the nitrogen-vacancy centers in uncharged state (NV 0 ). [22] The properties and structural features of NV 0 are investigated in details (see e.g., Ref. [23]). Intensity of vibronic bands associated with 575 nm line is significantly reduced and the zero phonon line becomes much more pronounced at low temperatures (see Figure 3 and4).

The decay time of 575 nm line was investigated with excitation by pulsed laser radiation at 370 nm. Figure 5(a) shows detected time dependence of PL intensity after pulse irradiation on long time scale of 200 ns. The decay time of neutral nitrogen-vacancy color centers luminescence calculated from this data is about 28 AE 1 ns. This value is in agreement with previously reported values of about 29-32 ns for the decay time of 575 nm line. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF]24] However, our measurements indicate that in short time scale (20 ns) a fast decay of luminescence intensity with characteristics time of 2.8 AE 0.3 ns also occurs (see Figure 5(b)). Similar characteristics decay time has been previously observed in diamonds. [25] The 738 nm (1.681 eV) line has been assigned to another wellknown color center in diamond related to silicon impurities (so called silicon or silicon-vacancy (SiV) color center). [26] Investigations of this center in recent year have been mostly stimulated by its potential usage in quantum optical devices. [27] Atomic structure of SiV center has been supposed as interstitial silicon atom between two substitutional vacancies. [28] The center is known to exist in neutral and negative charge states. The line at 738 nm corresponds to its negatively charged state. Only single ZPL line may be resolved in CL and PL spectra obtained in our work.

The intensities of the lines at 575 and 738 nm were found to be dependent on wavelength of excitation radiation. The dependencies obtained for the ratios of PL line amplitude to base signal are shown in Figure 6. For the 738 nm line, the relative intensity increases linearly with the laser wavelength, suggesting that excitation of these centers with longer wavelength (around 500 nm) is preferable. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] The linear intensity dependence is in consistency with PL excitation spectra reported in previous studies. [29] In contrast, the 575 nm line shows a non-monotonic (parabolic) variation of excitation efficiency, which increases of a factor three from 400 to 500 nm. Similar strong dependencies of 575 nm line on excitation wavelength has been explained by increasing of absorption efficiency in the range near 415 nm (3 eV). [30]

Vibronic Bands

Besides of the ZPL lines the luminescent spectra of SCD contains pronounced phonon replications (or vibronic) bands for most of the color centers. Figure 7 presents dependencies of the spectra in vicinity of the ZPL lines with phonon replications on the phonon energy. The phonon energies were calculated from wavelength in luminescent spectra (similar to that shown in Figures 3 and4) considering phonon energy equal to zero for the wavelength of corresponding ZPL lines. The spectra presented in Figure 7 were normalized on intensity of corresponding ZPL lines and shifted in vertical direction for clarity.

The most of the vibronic bands detected in spectra shown in Figure 7 are in well consistency with previous investigations. The observed vibronic bands of 389 nm ZPL line are appeared in PL and CL spectra at 80 AE 6, 159 AE 6, and 236 AE 6 meV that corresponds to electron transitions with local vibrational modes associated with 75 meV transverse acoustic (TA) phonon [31] and 165 meV longitudinal optical (LO) phonon. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] Interaction of 389 nm transition with both of these phonons can explain appearance of 236 AE 6 meV feature in the spectra. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] The observed vibronic bands of 442 nm line (Figure 7 Four phonon bands can be resolved for 468 nm line in its side band (Figure 7(c)). Predominant interaction with 76 AE 4 meV phonon (similar to that described in Ref. [7]) corresponds to the bands observed at 148 AE 5 and 220 AE 4 meV for two-and threephonon processes, respectively. However, the line corresponding to phonon with 43 AE 6 meV was also detected in some spectra for this optical center. This line can be either additional vibrational band of 442 or 468 nm lines or independent luminescence line with wavelength about 477 nm. For 534 nm line one vibrational band can be resolved. It corresponds to phonon with energy of 79 AE 8 meV that in consistence with previous researches. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF] The phonon interactions with energies of 46 AE 6 and 90 AE 6 meV that corresponds to two-phonon process with 46 AE 6 meV can be resolved in spectral range of 575 nm line (Figure 7(d)) similar to previous reports. [START_REF] Dischler | Handbook of Spectral Lines in Diamond[END_REF] Some difference between CL and PL spectra (Figures 3(a) and 4(a)) can be seen for vibronic bands of 575 nm ZPL line. The PL spectrum looks wider and more intensive around 640 nm wavelength. Subtraction of normalized CL spectrum from PL spectrum (see Figure 8) produces dependence with shape similar to spectrum of negatively charged nitrogen-vacancy center in diamond with 637 nm wavelength. This is in well agreement with previous reports indicating that negatively charged nitrogen-vacancy center is not detectable by CL technique. [START_REF] Zaitsev | Optical Properties of Diamond[END_REF]

Conclusion

The 389, 442, 468, 534, 563, 575, and 738 nm luminescent lines of the color centers in needle-like single crystal diamond were observed. Single zero phonon line at 534 nm, strong luminescence at 468 nm, and the vibration modes observed in the spectra demonstrate high structural quality of manufactured needle-like single diamond crystals. The presence of 389 and 468 nm luminescent lines indicates that these structures also contain interstitial and/or substitutional atoms. The luminescent lines at 389, 468, 534, and 575 nm demonstrate a nitrogen atoms content. The 738 nm line is an evidence of silicon atom impurities presence. Pronounced vibronic bands in the luminescent spectra of nitrogen-vacancy centers correspond to interactions with: 80 AE 6 and 159 AE 6 meV phonons for 389 nm line, 58 AE 4 and 96 AE 4 meV phonons for 442 nm line;

Figure 1 .

 1 Figure 1. SEM images (a and b) and schematic representation (c) of the samples prepared for CL investigations. Scale bars correspond to 10 μm.

Figure 2 .

 2 Figure 2. Scheme of the PL setup used for investigation of the diamond needles (see description in text).

Figure 3 .

 3 Figure 3. Typical cathodoluminescent spectra obtained at 300 K (a) and at 81 K (b). Energy of irradiated electrons is 15 keV, beam current is 80 nA.

Figure 4 .

 4 Figure 4. Typical photoluminescent spectra: (a) spectrum measured at sample temperature of 300 K and with wavelength of excitation radiation of 300 nm; (b) spectrum measured at sample temperature of 24 K and with wavelength of excitation radiation of 260 nm.

Figure 5 .

 5 Figure 5. Time dependences of photoluminescent 575 nm line decay on long (a) and short (b) time scale. Excitation wavelength is 370 nm, beam power is 400 mW. Red lines correspond to exponential decay adjustments in semi-logarithmic (a) and linear scale (b).

Figure 6 .

 6 Figure 6. Photoluminescent intensity dependence for 575 and 738 nm on excitation wavelength measured for the area located near the apex of diamond needle.

  (b)) correspond to phonon energies of 58 AE 4 and 96 AE 4 meV.

Figure 7 .

 7 Figure 7. Vibronic bands for 389 nm (a), 442 nm (b), 468 nm (c), and 575 nm (d) centers. Blue lines (CL LT) correspond to cathodoluminescent spectra measured at 81 K, red lines (CL RT) correspond to cathodoluminescent spectra measured at room temperature, black lines (PL LT) correspond to photoluminescence spectra measured at low temperatures (24 K for (a) and (b), 4 K for (c) and (d)), green lines (PL RT) correspond to photoluminescence spectra measured at room temperature.

Figure 8 .

 8 Figure 8. Spectral dependence obtained by subtraction of normalized CL spectrum from PL spectrum (shown in Figure 3(a) and 4(a), respectively) indicated by black dots. The red line corresponds to smoothed data.

Acknowledgments

This work was supported by the French "l'Agence Nationale de la Recherche (ANR)," through the program "Investissements d'Avenir" (ANR-10-LABX-09-01), LabEx EMC3, ASAP project. SAM and ANO are grateful for support from Russian Science Foundation (grant no. 15-02-30041).

Conflict of Interest

The authors declare no conflict of interest.