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Low-temperature domain behaviour of a SrTiO3 (0 0 1) single-crystal plate
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Physica B 393 (2007) 373–381 www.elsevier.com/locate/physb
Low-temperature domain behaviour of a SrTiO3 (0 0 1) single-crystal plate A.A. Levin, P. Paufler, D.C. Meyer Institut fu¨r Strukturphysik, Technische Universita¨t Dresden, 01062 Dresden, Germany Received 30 January 2007; accepted 31 January 2007
Abstract A (0 0 1) SrTiO3 single-crystal plate was investigated in a temperature range 300–25 K by means of wide-angle X-ray scattering under vacuum conditions. Depending on the quality of surface preparation, the plate exhibited different structural characteristics and lowtemperature phase transition and domain behaviour. At the polished surface of the single-crystal plate, in a cooling cycle a cubic (C-phase, space group Pm3¯ m)–tetragonal (T-phase, space group I4/mcm) phase transformation was recorded at a temperature of approximately 105 K equal to the known C–T-phase transition temperature of bulk SrTiO3. When cooling, the formation of antiphase orientation domains of the T-phase was observed starting at a temperature of 80 K. The volume fraction of the domains changed stepwise with decrease of temperature. At the lowest temperature of 25 K, the domains developed at a time scale of several hours. The unpolished surface remained in a single-domain state down to a temperature of 25 K due to the coexistence of ideal perovskite and defect-distorted regions. Considerable change of profile parameters of the X-ray reflection (full-width at half-maximum and integrated intensity) of non-distorted C-phase were recorded below a temperature of about 90 K referred to the C–T-phase transition. The lowering of the transition temperature is attributed to oxygen deficiency of the unpolished surface. The distorted regions do not exhibit any transition-like anomalies at this temperature. r 2007 Elsevier B.V. All rights reserved. PACS: 07.20.Mc; 61.10.i; 68.35.Rh; 77.80.Dj; 83.60.a; 83.85.Hf Keywords: Strontium titanate; Low temperature; X-ray diffraction; Single-crystal plate; Domain
1. Introduction During the last decades, the perovskites ABO3 have become the most popular objects of intensive investigation due to a wide variety of important physical properties including superconductivity and ferroelectricity (FE). The parent structure of an ideal ABO3 perovskite is characterized by a cubic unit cell (space group Pm3¯ m and lattice parameter aE4.0 A˚) containing one formula unit (Z ¼ 1). The structure consists of corner-connected BO6 octahedra. The B cations (mostly, transition metals B4+) are placed in Corresponding author. Tel.: +49 35146334768; fax: +49 35146332536. E-mail address: [email protected] (A.A. Levin).
0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.01.029
the centres of the octahedra whereas the O2 atoms are situated at their corners. The A2+ cations lie in the centres of the cavities formed by the BO6 octahedra network and are characterized by 12-fold O-coordination. Usually, the ABO3 perovskite compounds adopt the cubic structure at high temperatures only, if at all, whereas at room and lower temperatures they demonstrate a distortion of the parent cubic structure. The distortion can be realized through displacements of the ions from their ideal positions in the cubic phase resulting in the appearance of a spontaneous polarization due to a phase transition of the ferrodistortive type with small change of the unit cell parameters (a, a, a and a, b, g ¼ 901 or 901). Another kind of distortions occurs in a phase transition of the non-polar antiferrodistortive (AFD) type
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due to correlated rotations of oxygen octahedra BO6 along the in a larger unit cell (lattice parameters pffiffic-axis ffi presulting ffiffiffi 2a, 2a, 2a). For a classification of the ABO3 perovskites, Goldschmidt pffiffiffi [1] introduced a tolerance factor t ¼ ðRA þ RO Þ 2ðRB þ RO Þ characterizing the compatibility of the radii R of the ions A, B and O of the perovskites. When ambient temperature decreases, the perovskites with tolerance factor t41 exhibit the ferrodistortive phase transitions whereas those with to1 are of AFD type. Among the ABO3 perovskites, SrTiO3 (STO) is a special case due to the unique combination of the A ¼ Sr and B ¼ Ti cation radii resulting in a tolerance factor of tE1.00. As a result, both, ferrodistortive and AFD phase transitions can be realized in the STO. Compared with other perovskites, a decrease of the transition temperature is expected. Indeed, STO retains cubic symmetry still at RT (C-phase, space group Pm3¯ m, a ¼ 3.905 A˚ [2]). However, the Ti atoms exhibit dynamical displacements (short-range order) off the centres of TO6 octahedra [3] unlike the static ion displacements at ferrodistortive transitions. The nonpolar AFD rotational transition to a tetragonal phase (T-phase, space group I4/mcm, a ¼ 5.507 A˚, c ¼ 7.706 A˚ [4] at T ¼ 50 K) is observed below TE105 K [5]. The temperature of AFD C–T transition is sensitive to the real structure of the STO samples. In strained epitaxial STO films, the transition temperature increases up to TE160 K [6]. For the bulk samples, annealed under reducing conditions (i.e. in the presence of oxygen vacancies), the transition temperature decreases down to TE98.7 K [7,8]. Due to the closeness to a ferroelectric transition [9], the FE in STO can be induced by an external or internal impact. The formation of a ferroelectric state at different temperatures ranging from about 25 K up to RT was detected in STO experimentally under an external electric field [10,11] or a mechanical pressure [12], in isotopic substituted SrTi16O3y18Oy [13,14], in impurity-substituted Sr1x2+MxTiO3 where M are isoelectronic (Ca2+, Ba2+, Pb2+ [15–17]) as well as non-isoelectronic (Pr3+/Pr4+ [18]) impurities, in the strained thin STO films [19,20] and in antiphase boundaries of AFD domains at a polished surface of STO single-crystal plate [21,22]. Recently, by means of wide-angle X-ray scattering (WAXS) we have observed reversible structural changes in a (0 0 1)c STO single-crystal plate in situ under the influence of an external static electric field [23] (here and later on in the text, the subscript ‘c’ means cubic indexing with respect to the STO C-phase whereas the subscript ‘t’ refers to the STO T-phase). A growth of a shoulder of 00lc X-ray reflection profiles accompanied by the formation of strains in the plate [24] was detected exclusively for the unpolished single-plate side acting as an anode. More precisely, as confirmed by further investigation, the effect is detectable for the side of the single-crystal (0 0 1)c STO plate exhibiting an asymmetry of the X-ray reflection profiles under ambient conditions in zero electric field, i.e. a contribution of intrinsic distorted areas near the plate
surface has to be taken into account. This coupling phenomenon in an external electric field was described as a tuneable and reversible formation of a significant volume of domains of Ruddlesden–Popper (RP) phases SrO(SrTiO3)n with variable n ¼ 1–3 coherently intergrown with the STO perovskite matrix [24,25]. A big influence of the quality of surface layer of about 0.1 mm thickness on the effects observed for as-cut STO single crystals is emphasized in Ref. [15]. Due to the increasing interest in STO single-crystal wafers with a good surface finish for different technological applications, STO single-crystal plates with a good surface quality have become frequently investigated objects. Polishing and acidetching are used for elimination of the distorted top skin layer of the single-crystal plates to obtain a necessary surface quality [13,26]. Recently, polished (0 0 1)c singlecrystal STO wafers were studied at low temperatures by means of WAXS (for example, Refs. [22,27]). In the present paper, we communicate the results of a low-temperature WAXS investigation of polished and unpolished surfaces of a single-crystalline (0 0 1)c STO plate similar to the wafer investigated under the influence of an external electric field [23,24] as described above. It is pointed out that the lowtemperature behaviour of the near-surface regions of the single-crystal plate depends strongly on the surface quality.
2. Experimental details 2.1. Details of the specimen and of the X-ray diffraction method An as-prepared one-side-polished (0 0 1)c STO singlecrystal plate from the same delivering company (5 7 0.5 mm3, Crystec GmbH, Germany) and with similar characteristics as described in Refs. [23,24] was used for the low-temperature WAXS investigation. To obtain quantitative structural characteristics of the STO wafer, the WAXS patterns from both, polished and unpolished sides of the plate were recorded first at RT in ambient air atmosphere. Measurements were carried out in the symmetrically coupled y–2y scan mode (y and 2y are the angles of incidence and diffraction, respectively) using an X-ray diffractometer URD-6 (Seifert FPM GmbH, Germany) designed in Bragg–Brentano geometry and equipped with a scintillation detector. Characteristic radiation of a Cu anode, monochromatized by a secondary Johansson-type graphite monochromator and tuned to the Ka spectral line of the tube was used. The specimen was rotated around the holder (i.e. surface normal) axis during the measurements. To reduce statistic fluctuations of the intensities recorded, multiple scans of the 2y range between 10.51 and 1201 were performed with a step width D2y of 0.011 and 5 s sampling time per angle step. The total sampling time per angle step after summing up the individual data sets was 45 s. Additionally, the WAXS patterns from both sides of the STO plate covered by a thin
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Si powder layer (Standard Reference Material 640b of NIST) were collected. Both, polished and unpolished sides of the same (0 0 1)c STO single-crystal plate were investigated by means of WAXS at low temperatures in high vacuum (o5 104 Pa). The measurements were carried out in the coupled y–y scan mode using a D5000 diffractometer (Siemens AG, Germany; Bragg–Brentano geometry, scintillation detector, characteristic Cu Ka radiation monochromatized by Johansson-type graphite monochromator) supplied by a cryostat chamber (Anton Paar KG, Austria). The temperature was controlled by a temperature sensor (Lake Shore Cryotronics Inc., USA) in contact to the sample holder. The accuracy of temperature measurements was about 70.5 K. The WAXS patterns were recorded in the vicinity of a 004c STO reflection in the 2y range between 102.51 and 106.31 with the step width D2y of 0.011 and 1 s sampling time per angle step (about 6.4 min per individual scan). The measurements were performed in the temperature range from 300 K (RT) down to 125 K and from 115 K down to 25 K in steps of DT ¼ 25 and 5 K, respectively. To allow the temperature equilibration, a 10 min delay was realized at every temperature stage. Afterwards, a rocking curve was measured to check and correct the y–y coupling of the diffractometer. Thereafter, three scans of the X-ray reflection chosen were carried out sequentially to prove that WAXS reflection profiles measured were stable. Finally, after exposure of about 10 h at the lowest temperature of 25 K, the recording of WAXS patterns was repeated with increase of temperature starting from 25 K up to 300 K using the same temperature–time steps as described above. After finishing the low-temperature measurements, the specimen was pulverized and a WAXS pattern of the powder was recorded at RT in air atmosphere using the Xray diffractometer URD-6. Additionally, the WAXS pattern of the STO powder mixed with reference Si powder (640b, NIST) was measured. The parameters and techniques of the measurements were the same as described above for RT measurements in air atmosphere. 2.2. Details of the quantitative analysis The WAXS patterns of the samples covered/mixed with Si reference powder were used for refinement of the unit cell parameters of STO at RT by means of a program CelSiz [28] adopting the Si reflections as an internal standard. The data obtained this way were used as external standard for further analysis. The WAXS patterns recorded at RT from the (0 0 1)c single-crystal plate exhibited the STO reflections of 00lc type only. From these WAXS patterns, the lattice parameters of STO of polished and unpolished sides of the single-crystal plate at RT were extracted by a decomposition-method of fitting the whole diffraction pattern (see Ref. [29, p. 254]) as realized in the computer program TOPAS [30]. To control the possible change of
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structural parameters of STO in the bulk of the specimen, the structure of pulverized STO was refined by the Rietveld method with the program TOPAS using the WAXS powder data and an initial structure model [2] of the C-modification of STO. Pseudo-Voigt profile functions (see Ref. [29, p. 9]) were used for the simulation of the reflection profile. The values of standard uncertainties of refined structural parameters (underrated by Rietveld and X-raydiffraction-pattern-decomposition procedures of TOPAS due to serial correlations) were corrected by multiplying by the factor of about 3.5 calculated by a computer program according to a procedure described in Ref. [31]. The profiles of the STO reflection recorded at low temperatures were analyzed by means of the program ANALYZE [32].
3. Results and discussion 3.1. Lattice parameters in the bulk and at the surfaces of the STO single-crystal plate at RT For the radiation used, the crystal regions located at a depth of less than 10 mm beneath the surface of the wafer will contribute to the WAXS pattern. Thus, in case of a single-crystal plate, the unit cell parameters of the crystalline phases calculated on this basis will characterize the near-surface layer only. Due to possible defects and strains present near the plate surface, the lattice parameters of the surfaces and of the bulk cannot be assumed to be the same. Again as in Ref. [23], the WAXS pattern recorded from polished surface of the (0 0 1)c STO single-crystal plate can be fitted using one ‘ideal’ C-phase exclusively (see a section of corresponding WAXS pattern in Fig. 1a for illustration). On the other hand, the profiles of different orders of the 001c STO reflection recorded from the unpolished side can be fitted with a sufficient quality assuming two phases (with ‘ideal’ d1 and ‘distorted’ d2 C-lattices; Fig. 1b), whereas the assumption of only one phase results in deterioration of the fitting quality parameters of about 2% in comparison to those shown in Table 1. In Refs. [23,24] and in the present communication, the second STO phase is described for simplicity as a ‘distorted’ C-phase with a larger unit parameter (phase 2 or ‘distorted lattice’ d2 characterized by a ¼ 3.9084(1) A˚ in this work and a ¼ 3.9069(6) A˚ in Refs. [23,24]). According to fitting, the volume of this phase at the unpolished surface is of about 18 wt%. In Ref. [24] it is outlined, that the asymmetry of the 00lc STO reflections can be induced by a coherent intergrowth of SrO(SrTiO3)n RP phases with n ¼ 1–3 and the STO perovskite matrix. After calculation by the procedure described in Ref. [24], the amount of n ¼ 3 RP phase in the intergrowth-domains is about 2.8 wt% in this work and about 1.8% in Refs. [23,24] for the lattice parameters observed. Probably, the absence of any asymmetry of the reflection profiles of the WAXS powder pattern (Fig. 1c) shows the negligibility of the volume of this phase detectable in a thin near-surface layer of the unpolished STO plate only.
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The structure parameters of the of STO C-phase obtained by Rietveld refinement on base of WAXS powder data did not exhibited any anomaly. No observable deviation from the STO stoichiometry was found (the refined occupation factors of the atomic sites of Sr, Ti and O were 1.00(1), 1.00(1) and 0.99(1), respectively). Thus, at RT, the bulk STO as well as the polished STO single-crystal plate investigated are characterized by a lattice with unit cell parameters close to the bulk reference data (a ¼ 3.905 A˚, card 35-0734 [33]). Additionally, the unpolished STO plate contained distorted regions incorporated in the ‘ideal’ matrix. 3.2. Low-temperature behaviour of the polished (0 0 1)c STO specimen 3.2.1. Cooling cycle from RT to 25 K An example of experimental WAXS patterns at some characteristic temperatures in a range of 300–25 K recorded in the vicinity of the fourth order of the 001c (i.e. 004c) cubic STO reflection of the polished (0 0 1)c STO
Fig. 1. Sections of experimental WAXS patterns (solid lines) at angles in vicinity of the fourth order of STO 001c reflection recorded under ambient air conditions at the polished (a) and non-polished (b) sides of the wafer as well as from the pulverized specimen (c). Ka1 and Ka2 reflection contributions are resolved. Results of fitting the experimental WAXS patterns (simulated profiles and difference curves Iobserved–Icalculated) are indicated by lines of different styles marked in parts (a) and (b). For the non-polished side of the STO plate, contributions of the non-distorted (d1) and distorted (d2) lattices are shown.
Table 1 Unit cell parameters of the crystalline STO C-phases of the specimens at RT as obtained by refinement using LeBail (for surfaces of the singlecrystal plate) and Rietveld (for powder) procedures Sample
a (A˚)
Rwp (%)
Rp (%)
Polisheda Unpolishedb Phase 1 (d1) Phase 2 (d2) Powderc
3.9052(1)
4.70 11.22
3.37 4.87
3.57
2.93
3.9049(1) 3.9084(1) 3.9047(1)
The weighted profile Rwp and profile Rp factors (see Ref. [29, p. 22] for definition) are indicated as quality parameters of fitting the WAXS patterns recorded. a Polished side of the (0 0 1)c STO single-crystal plate. b Unpolished side of the (0 0 1)c STO single-crystal plate. c Powder obtained by pulverization of the (0 0 1)c STO single-crystal plate.
Fig. 2. WAXS patterns measured at angles in the vicinity of the fourth order of STO 001c reflection recorded under high-vacuum conditions at the polished side of the single-crystal (0 0 1)c STO wafer at characteristic temperatures during cooling (solid lines) and warming (dashed lines) cycles. Ka1 and Ka2 reflection contributions are resolved. The reflection indices of the crystalline phases observed are indicated. The WAXS patterns are shifted vertically for better visual investigation. The WAXS patterns at every temperature stage of cooling and warming cycles were recorded after a delay of 10 min for temperature equilibration. The measurement of the WAXS pattern at lowest temperature of 25 K in warming cycle was carried out after an exposure of 10 h at this temperature.
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Fig. 3. Thermal evolution of the interplanar distances corresponding to reflections indicated calculated for polished (a) and non-polished (b) sides of the single-crystal (0 0 1)c STO wafer. The data obtained during cooling and warming cycles are drawn by open and solid symbols, respectively. In (b), the data determined for non-distorted (d1) and distorted (d2) lattices are represented by triangles and squares, respectively. Linear fittings in appropriate characteristic temperature ranges are drawn. Insets show the low-temperature sectors in an enlarged scale.
wafer is presented in Fig. 2. As to be seen in Fig. 2, with decrease of temperature from RT down to 85 K, the shape of the reflection profile does not change significantly. The centre of gravity of the reflection only shifts to higher diffraction angles as an outcome of usual contraction of the lattice parameters due to refrigeration. According to precise results of the quantitative analysis, the thermal dependence of the interplanar spacing d (Fig. 3a) in temperature ranges 300–200 and 200–125 K is represented by linear segments with different slopes. The linear thermal expansion coefficients a obtained by means of least-square fitting are equal to 8.6(1) 106 and 7.4(1) 106 K1, respectively, i.e. consistent with values known for STO from literature (a ¼ 8.9 106 K1 [34] in the temperature range 300–200 K and a ¼ 8.753 106 K1 [35] at the temperature of 300.3 K). At a temperature of 80 K, an asymmetry of the reflection profile shape appeared forming a well-distinguishable shoulder at a temperature of 65 K. Finally, a new reflection was resolved starting from a temperature of 45 K.
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Fig. 4. Thermal evolution of the integrated intensities (a) and FWHM (b) corresponding to reflections calculated for polished side of single-crystal (0 0 1)c STO wafer. The data obtained during cooling (solid lines) and warming (dashed lines) cycles are drawn by open and solid/half-solid symbols, respectively. The lines are guides for eyes.
The low-temperature behaviour of the polished (0 0 1)c STO platelet can be apparently linked to C–T AFD transition known to occur for bulk STO at a temperature of about 105 K [5]. The same value of the transition temperature for the polished STO plate under investigation can be derived from inspection of the thermal dependencies of the interplanar spacing d (Fig. 3a) and the integrated intensity (Figs. 4a and 5) extracted from the experimental X-ray reflection profiles. Below the AFD transition temperature, in the absence of special constraints, twin domains are formed in a singlecrystal specimen due to the transformation of the structure from cubic to tetragonal modification [36]. As a result of twin domain growth and reorientation in the single-crystal plate starting at a temperature of 80 K in the cooling cycle, new reflections develop. According to indexing, the reflections of the AFD T-phase with indices 008t and 440t are formed (Fig. 2) representing two domains with antiphase orientation growing near the surface of the plate, i.e. domains with normals oriented parallel to the caxis of the tetragonal unit cell ([0 0 1]t domains) and perpendicular to it ([1 1 0]t domains). It should be noted here, that directions [0 0 1]t and [1 1 0]t coincide with
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temperatures higher than the AFD transition temperature were about 153(2) nm. The volume fraction of the domains changed continuously with stepwise decrease of temperature as to be concluded from temperature-dependent evolution of the reflection profile shape in Fig. 2. After start of the domain manifestation at a temperature of 80 K, with further cooling the integrated intensity of 440t T-phase reflection increased considerably correlated with a quick decrease of the intensity of 008t T-reflection (Fig. 4a) reflecting a corresponding change of population of the [1 1 0]t and [0 0 1]t T-domains, respectively. The total integrated intensity of both, 008t and 440t, reflections grows after the AFD transition reached a maximum value at a temperature of about 65 K (Fig. 5). Further cooling down to 25 K resulted in a moderate decrease of the total intensity of the profile measured.
Fig. 5. Thermal evolution of the integrated intensity of the experimental reflections calculated for polished (a) and unpolished (b) sides of the single-crystalline (0 0 1)c STO wafer. The data obtained during cooling (solid lines) and warming (dashed lines) cycles are drawn by open and solid symbols, respectively. The lines are guides for eyes.
directions [0 0 1]c and [1 0 0]c, respectively, facilitating the formation of corresponding antiphase T-domains. According to the Scherrer equation (Ref. [29, p. 141]), the mean size of the twin domain t (or mean size of mosaic blocks in case of single-crystal C-phase) can be estimated from full-width at half-maximum (FWHM) of corresponding Bragg reflections as t¼
l , FWHM cos y
where l is the wavelength of the X-ray radiation used and y is the Bragg angle of the reflection. Thus, at first stages of 440t reflection formation during the cooling cycle at temperatures of 80–70 K, the [0 0 1]t and [1 1 0]t domains are characterized by typical mean sizes of 174(2) and 135(1) nm, respectively. With subsequent cooling down to 25 K, the 008t reflection exhibited a slow broadening whereas the FWHM of 440t reflection decreased abruptly at 65 K first and then showed a slow increase too (Fig. 4b). As a result, in the temperature range 65–25 K the sizes of both kinds of domains reached more close values of 165(2) and 149(2) nm ([0 0 1]t and [1 1 0]t domains, respectively). The mosaic block sizes of the C-phase estimated from the FWHM of the 004c C-reflection at
3.2.2. Ageing at 25 K A drastic change of the volume fraction of both types of domains present beneath the polished surface of the plate occurred after exposure for about 10 h at 25 K, the lowest temperature during the experiments (Figs. 4a and 5). It gave rise to an inverse intensity ratio of 440t and 008t T-phase STO reflections in comparison to the initial state. Whereas the intensity of the 440t reflection increased distinctly at 20%, the intensity of the 008t reflection decreased considerably (more than by a factor of 2) becoming smaller than 440t. Thus, the volume fraction of the [1 1 0]t T-domain increased moderately accompanied by a drastic decrease of the [0 0 1]t domain population. Nevertheless, the mean size of [0 0 1]t domains as calculated from a change of FWHM of reflections (Fig. 4b) was maintained (the typical extension of about 165(2) and 164(2) nm at 25 K in the initial state and after 10 h ageing, respectively) while the [1 1 0]t domains grew up to a higher value of about 157(2) nm (in comparison to 149(2) nm in the initial state at 25 K). In spite of significant modifications of domain sizes and relative populations, the corresponding interplanar distances do not change in limits of estimated standard deviations. Presumably, the changes observed were caused by [0 0 1]t and [1 1 0]t domain creation, growth and annihilation processes after long-time ageing at a low temperature. 3.2.3. Warming cycle from 25 K up to RT However, the changes observed proved reversible with warming. After temperature equilibration of about 10 min at every temperature level, the central-angle position of the reflections (i.e. interplanar distances and, consequently, the unit cell parameters) completely recovered at once (Figs. 2 and 3a). The process of recovering the reflection intensity (i.e. volume fractions of the different domains in case of T-phase) and the FWHM of the reflections (i.e. domain sizes) is more gradual demonstrating a hysteresis (Figs. 4 and 5). Nevertheless, with increase of the temperature up to 55 K, the reflection profiles were
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found close to that observed at this temperature during the cooling cycle (small hysteresis), whereas in the temperature range of 200–300 K they were indistinguishable (no hysteresis). The thermal hysteresis of the integrated intensity and FWHM of the reflection profiles are attributed to the existence of lattice defects remaining in regions near the polished STO surface and hindering the motion of domain walls [27]. 3.2.4. Comparison with literature reports on lowtemperature investigations of polished (0 0 1)c STO plates Thus, the polished (0 0 1)c STO single-crystal plate investigated is characterized by a lattice with unit cell parameters close to bulk reference data (a ¼ 3.905 A˚). In the temperature range 300–200 K, the plate exhibited a linear coefficient of thermal expansion a ¼ 8.6 101 K1 close to a known value from literature. The STO plate under study showed a reversible AFD phase transition at a temperature of 105 K equal to the known bulk value. At a lower temperature of 80 K, a beginning formation of [0 0 1]t and [1 1 0]t antiphase domains was observed resulting in asymmetry and broadening of the reflection profile recorded in the vicinity of the 004c STO C-phase reflection. Significant amounts of the domains were developed (probably due to growth and reorientation of the domains) at a temperature of about 45 K giving rise to well-resolved X-ray reflections attributed to these domains. A similar reversible low-temperature behaviour with a delay of formation of detectable domains was observed in Ref. [27] during X-ray investigation of a comparable polished (0 0 1)c STO plate. Despite of the C–T transition temperature of 104.2 K estimated for the sample by a quantitative analysis of the X-ray diffraction data, the broadening of the reflection profile measured in vicinity of the 002c STO C-phase reflection started at a lower temperature of 94 K whereas the new X-ray reflections referred to three T-domains were formed at a temperature of 54 K. In distinction to the results of the present investigation, a good reversibility of the reflection profile shape (with very small thermal hysteresis of the integrated intensity, only) during cooling and warming cycles was observed at all low temperatures investigated. The dissimilarity arises probably from the difference in the time–temperature procedure used (no long-time exposure at a low temperature was made in Ref. [27]). In conclusion, the polished (0 0 1)c STO plate under study showed characteristics close to bulk reference STO material and exhibited a low-temperature behaviour similar to the behaviour known from literature. The differences observed are attributed to peculiarities of the low-temperature processing as well as to different morphological details (surface quality, near-surface layer constraints of a large single-crystal plate, etc.) of the specimen investigated.
Fig. 6. Same as Fig. 2 for the unpolished side of the single-crystalline (0 0 1)c STO plate.
3.3. Low-temperature behaviour of the unpolished side of (0 0 1)c STO wafer Contrary to the WAXS patterns recorded from the polished (0 0 1)c STO single-crystal plate, no new reflection was observed in the WAXS patterns of the unpolished side of the plate at any temperature down to 25 K (see Figs. 2 and 6 for comparison). With cooling, the position of the reflection present at RT (004c C-phase) shifted only to a higher value of the diffraction angle and became broader (Fig. 6). Unlike with the polished STO plate, a long-time ageing for 10 h at the lowest temperature and a further warming-up cycle did not give rise to any noticeable hysteresis of the reflection profiles. To a first approximation, the thermal evolution of calculated interplanar distances of both, phase 1 and phase 2 contributing to the apparent reflection profile (correspondingly, the C-lattice regions with non-distorted and larger unit cell parameters at RT; see Table 1 and Fig. 1b) followed a linear law in the whole temperature range of 25–300 K investigated (Fig. 3b). However, a thorough inspection of the calculated interplanar distances d(T) at different temperatures revealed changes of the slope dd/dT, which are comparatively more moderate in the whole temperature range than in the case of polished STO. During cooling, the first two successive modifications of the majority phase 1 occurred at the same temperature of 200 and 125 K like for the C-phase of polished STO.
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Fig. 7. Same as Fig. 4 for non-polished side of the single-crystalline (0 0 1)c STO plate. The data obtained for non-distorted (d1) and distorted (d2) lattices are represented by triangles and squares, respectively.
Furthermore, the linear thermal expansion coefficients showed about 12% smaller magnitude (a ¼ 7.7(2) 106 K1 and a ¼ 6.4(6) 106 K1 in the temperature ranges of 300–200 and 200–125 K, respectively). As referred to the minority phase 2 with a distorted lattice, when cooling down from 300 to 115 K, the corresponding calculated interplanar distance showed a linear decrease with a similar rate (a ¼ 7.5(3) 106 K1) like the phase 1 in the temperature range 300–200 K. In contradiction to the polished STO-side, further cooling did not lead to a long-range ordering of the TiO6 libration at a temperature of 105 K resulting in an AFD C–T transition at this temperature like at the polished STO-side. Contrary to that, in case of the unpolished STO plate-side, a linear decrease of the interplanar distances is found for both phases down to 50 K. However, a noticeable broadening of the X-ray reflection of the phase 1 accompanied by reducing its integrated intensity as well as of the sum integrated intensity of the experimental X-ray reflection profile is detected at temperatures below 90 K (Figs. 5b and 7). From the point of view of X-ray diffraction, the unpolished STO plate-side remained in a single-domain state (neglecting the contribution of the minority phase 2 present at RT yet), but the size of mosaic
blocks of the dominating phase 1 decreased from 85(1) nm above 90 K down to 73(1) nm at 50–25 K. Note that the size of mosaic blocks of phase 1 of the unpolished side at RT is approximately twice less than that observed at the polished STO plate (Section 3.2.1). The distorted lattice (phase 2) contained smaller mosaic blocks (about 54(2) nm at RT and 50(2) nm at 25 K, as estimated from the larger FWHM (Fig. 7b) of the corresponding reflection profiles). Apparently, the finer mosaic blocks of the STO phases at the unpolished side of the plate reflect the presence of defects (cation and oxygen vacancies) preventing the formation of larger regions with ideal lattice. Presumably, the noticeable change of the FWHM and of the integrated intensity at 90 K can be attributed to an AFD C–T transformation of the C-like phase 1 which is a dominating phase near the surface of the unpolished-side of STO. The decrease of the transition temperature down to 90 K is caused probably by the presence of oxygen vacancies [7,8]. Recently [6], a similar C–T transition manifested by a drastic change of the reflection intensity but not by the lattice parameters was detected in STO films and referred to a clamping effect of the substrate. As it was mentioned in the introduction, regions containing a coherent intergrowth of STO and RP phases SrO(SrTiO3)n (n ¼ 1–3) were found near the unpolished surface of a STO plate [24] comparable to the specimen under investigation. Presumably, in the single-crystal plate studied the extended regions of the defect lattice hinder the formation of twin AFD domains and act as clamping centres resulting in the absence of any anomaly of d(T) of phase 1 while passing the C–T transition temperature at a temperature of 90 K. After the transition, the 004c reflection of the dominating (matrix) C-type phase 1 transforms to 008t reflection of the T-phase. Probably due to the other structure type (intergrowth of STO and RP phases) or higher amounts of defects, the distorted phase 2 does not show any phase transition at 90 K as to be concluded from the absence of remarkable anomalies of profile parameters of this distorted lattice (Figs. 3b and 7). 4. Conclusion The quality of the surface of STO single-crystal wafers plays a crucial role for the physical and structural properties of the wafer. Already at RT under ambient conditions, an additional contribution of lattice regions with distorted structure was detected at the unpolished side of the wafer reflected by quite a different behaviour of the polished and unpolished STO plates at low temperatures (as well as under influence of an external electric field [23,24]). Acknowledgement Financial support by Deutsche Forschungsgemeinschaft (DFG) in the framework of the research unit FOR 520 is kindly acknowledged.
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References [1] V.M. Goldschmidt, Acad. Oslo Math.-Natur 2 (1926) 7. [2] J. Hutton, R.J. Nelmes, J. Phys. Chem. 14 (1981) 1713. [3] Yu.A. Abramov, V.G. Tsirelson, V.E. Zavodnik, S.A. Ivanov, I.D. Brown, Acta Crystallogr. B 51 (1995) 942. [4] W. Jauch, A. Palmer, Phys. Rev. B 60 (1999) 2961. [5] H. Unoki, T. Sakudo, J. Phys. Soc. Jpn. 23 (1967) 546. [6] F. He, B.O. Wells, Z.-G. Ban, S.P. Alpay, S. Grenier, S.M. Shapiro, W. Si, A. Clark, X.X. Xi, Phys. Rev. B 70 (2004) 235405. [7] H. Hu¨nnefeld, T. Niemo¨ller, J.R. Schneider, U. Ru¨tt, S. Rodewald, J. Fleig, G. Shirane, Phys. Rev. B 66 (2002) 014113. [8] J.P. Buban, H. Iddir, S. O¨g˘u¨t, Phys. Rev. B 69 (2004) 180102. [9] K.A. Mu¨ller, H. Burkard, Phys. Rev. B 19 (1979) 3593. [10] J. Hemberger, P. Lunkenheimer, R. Viana, R. Bohmer, A. Loidl, Phys. Rev. B 52 (1995) 131159. [11] K. Morito, Y. Iwazaki, T. Suzuki, M. Fujimoto, J. Appl. Phys. 94 (2003) 5199. [12] H. Uwe, T. Sakudo, Phys. Rev. B 13 (1976) 271. [13] J. Dec, W. Kleeman, M. Itoh, Phys. Rev. B 71 (2005) 144113. [14] R. Wang, M. Itoh, Phys. Rev. B 64 (2001) 174104. [15] J.G. Bednorz, K.A. Mu¨ller, Phys. Rev. Lett. 52 (1984) 2289. [16] V.V. Lemanov, E.P. Smirnova, E.A. Tarakanova, Phys. Solid State Phys. 37 (1995) 1356 (translated from Fiz. Tverd. Tela 37 (1995) 2476). [17] V.V. Lemanov, E.P. Smirnova, E.A. Tarakanova, Phys. Solid State Phys. 39 (1997) 628 (translated from Fiz. Tverd. Tela 39 (1997) 714). [18] A. Dura´n, E. Martı´ nez, J.A. Dı´ az, J.M. Siqueiros, J. Appl. Phys. 97 (2005) 104109. [19] O. Tikhomirov, H. Jiang, J. Levy, Phys. Rev. Lett. 89 (2002) 147601.
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[20] J.H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y.L. Li, S. Choudhury, W. Tian, M.E. Hawley, B. Craigo, A.K. Tagantsev, X.Q. Pan, S.K. Streiffer, L.Q. Chen, S.W. Kirchoefer, J. Levy, D.G. Schlom, Nature 430 (2004) 758. [21] A.K. Tagantsev, E. Courtens, L. Arzel, Phys. Rev. B 64 (2001) 224107. [22] L. Arzel, B. Hehlen, F. De´noyer, R. Currat, K.-D. Liss, E. Courtens, Europhys. Lett. 61 (2003) 653. [23] D.C. Meyer, A.A. Levin, S. Bayer, A. Gorbunov, W. Pompe, P. Paufler, Appl. Phys. A 80 (2005) 515. [24] D.C. Meyer, A.A. Levin, T. Leisegang, E. Gutmann, P. Paufler, M. Reibold, W. Pompe, Appl. Phys. A 84 (2006) 31. [25] M. Bobeth, N. Farag, A.A. Levin, D.C. Meyer, W. Pompe, A.E. Romanov, J. Ceram. Soc. Jpn. 114 (2006) 1029. [26] J. Dec, W. Kleeman, M. Itoh, Appl. Phys. Lett. 85 (2004) 5328. [27] S. Doi, I. Takahashi, Philos. Mag. A 80 (2000) 1889. [28] Program Celsiz, Version 1.1 (1995), freeware available via Homepage of International Union of Crystallography. [29] R.A. Young (Ed.), The Rietveld Method, Oxford University Press, Oxford, 1995. [30] TOPAS (version 2.0), Software Package, Bruker AXS GmbH, 2000. [31] J.-F. Be´rar, P. Lelann, J. Appl. Crystallogr. 24 (1991) 1. [32] Programm ANALYZE, Rayflex Version 2.285, Rich. Seifert & Co., 2000. [33] Powder diffraction file (PDF), Release 2001, International Centre for Diffraction Data (ICSD), 2001. [34] A. Okazaki, M. Kawaminami, Ferroelectrics 7 (1974) 91. [35] K. Munakata, A. Okazaki, Acta Crystallogr. A 60 (2004) 33. [36] E. Sawaguchi, A. Kikuchi, Y. Kodera, J. Phys. Soc. Jpn. 18 (1963) 459.
Physica B 393 (2007) 373–381 www.elsevier.com/locate/physb
Low-temperature domain behaviour of a SrTiO3 (0 0 1) single-crystal plate A.A. Levin, P. Paufler, D.C. Meyer Institut fu¨r Strukturphysik, Technische Universita¨t Dresden, 01062 Dresden, Germany Received 30 January 2007; accepted 31 January 2007
Abstract A (0 0 1) SrTiO3 single-crystal plate was investigated in a temperature range 300–25 K by means of wide-angle X-ray scattering under vacuum conditions. Depending on the quality of surface preparation, the plate exhibited different structural characteristics and lowtemperature phase transition and domain behaviour. At the polished surface of the single-crystal plate, in a cooling cycle a cubic (C-phase, space group Pm3¯ m)–tetragonal (T-phase, space group I4/mcm) phase transformation was recorded at a temperature of approximately 105 K equal to the known C–T-phase transition temperature of bulk SrTiO3. When cooling, the formation of antiphase orientation domains of the T-phase was observed starting at a temperature of 80 K. The volume fraction of the domains changed stepwise with decrease of temperature. At the lowest temperature of 25 K, the domains developed at a time scale of several hours. The unpolished surface remained in a single-domain state down to a temperature of 25 K due to the coexistence of ideal perovskite and defect-distorted regions. Considerable change of profile parameters of the X-ray reflection (full-width at half-maximum and integrated intensity) of non-distorted C-phase were recorded below a temperature of about 90 K referred to the C–T-phase transition. The lowering of the transition temperature is attributed to oxygen deficiency of the unpolished surface. The distorted regions do not exhibit any transition-like anomalies at this temperature. r 2007 Elsevier B.V. All rights reserved. PACS: 07.20.Mc; 61.10.i; 68.35.Rh; 77.80.Dj; 83.60.a; 83.85.Hf Keywords: Strontium titanate; Low temperature; X-ray diffraction; Single-crystal plate; Domain
1. Introduction During the last decades, the perovskites ABO3 have become the most popular objects of intensive investigation due to a wide variety of important physical properties including superconductivity and ferroelectricity (FE). The parent structure of an ideal ABO3 perovskite is characterized by a cubic unit cell (space group Pm3¯ m and lattice parameter aE4.0 A˚) containing one formula unit (Z ¼ 1). The structure consists of corner-connected BO6 octahedra. The B cations (mostly, transition metals B4+) are placed in Corresponding author. Tel.: +49 35146334768; fax: +49 35146332536. E-mail address: [email protected] (A.A. Levin).
0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.01.029
the centres of the octahedra whereas the O2 atoms are situated at their corners. The A2+ cations lie in the centres of the cavities formed by the BO6 octahedra network and are characterized by 12-fold O-coordination. Usually, the ABO3 perovskite compounds adopt the cubic structure at high temperatures only, if at all, whereas at room and lower temperatures they demonstrate a distortion of the parent cubic structure. The distortion can be realized through displacements of the ions from their ideal positions in the cubic phase resulting in the appearance of a spontaneous polarization due to a phase transition of the ferrodistortive type with small change of the unit cell parameters (a, a, a and a, b, g ¼ 901 or 901). Another kind of distortions occurs in a phase transition of the non-polar antiferrodistortive (AFD) type
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due to correlated rotations of oxygen octahedra BO6 along the in a larger unit cell (lattice parameters pffiffic-axis ffi presulting ffiffiffi 2a, 2a, 2a). For a classification of the ABO3 perovskites, Goldschmidt pffiffiffi [1] introduced a tolerance factor t ¼ ðRA þ RO Þ 2ðRB þ RO Þ characterizing the compatibility of the radii R of the ions A, B and O of the perovskites. When ambient temperature decreases, the perovskites with tolerance factor t41 exhibit the ferrodistortive phase transitions whereas those with to1 are of AFD type. Among the ABO3 perovskites, SrTiO3 (STO) is a special case due to the unique combination of the A ¼ Sr and B ¼ Ti cation radii resulting in a tolerance factor of tE1.00. As a result, both, ferrodistortive and AFD phase transitions can be realized in the STO. Compared with other perovskites, a decrease of the transition temperature is expected. Indeed, STO retains cubic symmetry still at RT (C-phase, space group Pm3¯ m, a ¼ 3.905 A˚ [2]). However, the Ti atoms exhibit dynamical displacements (short-range order) off the centres of TO6 octahedra [3] unlike the static ion displacements at ferrodistortive transitions. The nonpolar AFD rotational transition to a tetragonal phase (T-phase, space group I4/mcm, a ¼ 5.507 A˚, c ¼ 7.706 A˚ [4] at T ¼ 50 K) is observed below TE105 K [5]. The temperature of AFD C–T transition is sensitive to the real structure of the STO samples. In strained epitaxial STO films, the transition temperature increases up to TE160 K [6]. For the bulk samples, annealed under reducing conditions (i.e. in the presence of oxygen vacancies), the transition temperature decreases down to TE98.7 K [7,8]. Due to the closeness to a ferroelectric transition [9], the FE in STO can be induced by an external or internal impact. The formation of a ferroelectric state at different temperatures ranging from about 25 K up to RT was detected in STO experimentally under an external electric field [10,11] or a mechanical pressure [12], in isotopic substituted SrTi16O3y18Oy [13,14], in impurity-substituted Sr1x2+MxTiO3 where M are isoelectronic (Ca2+, Ba2+, Pb2+ [15–17]) as well as non-isoelectronic (Pr3+/Pr4+ [18]) impurities, in the strained thin STO films [19,20] and in antiphase boundaries of AFD domains at a polished surface of STO single-crystal plate [21,22]. Recently, by means of wide-angle X-ray scattering (WAXS) we have observed reversible structural changes in a (0 0 1)c STO single-crystal plate in situ under the influence of an external static electric field [23] (here and later on in the text, the subscript ‘c’ means cubic indexing with respect to the STO C-phase whereas the subscript ‘t’ refers to the STO T-phase). A growth of a shoulder of 00lc X-ray reflection profiles accompanied by the formation of strains in the plate [24] was detected exclusively for the unpolished single-plate side acting as an anode. More precisely, as confirmed by further investigation, the effect is detectable for the side of the single-crystal (0 0 1)c STO plate exhibiting an asymmetry of the X-ray reflection profiles under ambient conditions in zero electric field, i.e. a contribution of intrinsic distorted areas near the plate
surface has to be taken into account. This coupling phenomenon in an external electric field was described as a tuneable and reversible formation of a significant volume of domains of Ruddlesden–Popper (RP) phases SrO(SrTiO3)n with variable n ¼ 1–3 coherently intergrown with the STO perovskite matrix [24,25]. A big influence of the quality of surface layer of about 0.1 mm thickness on the effects observed for as-cut STO single crystals is emphasized in Ref. [15]. Due to the increasing interest in STO single-crystal wafers with a good surface finish for different technological applications, STO single-crystal plates with a good surface quality have become frequently investigated objects. Polishing and acidetching are used for elimination of the distorted top skin layer of the single-crystal plates to obtain a necessary surface quality [13,26]. Recently, polished (0 0 1)c singlecrystal STO wafers were studied at low temperatures by means of WAXS (for example, Refs. [22,27]). In the present paper, we communicate the results of a low-temperature WAXS investigation of polished and unpolished surfaces of a single-crystalline (0 0 1)c STO plate similar to the wafer investigated under the influence of an external electric field [23,24] as described above. It is pointed out that the lowtemperature behaviour of the near-surface regions of the single-crystal plate depends strongly on the surface quality.
2. Experimental details 2.1. Details of the specimen and of the X-ray diffraction method An as-prepared one-side-polished (0 0 1)c STO singlecrystal plate from the same delivering company (5 7 0.5 mm3, Crystec GmbH, Germany) and with similar characteristics as described in Refs. [23,24] was used for the low-temperature WAXS investigation. To obtain quantitative structural characteristics of the STO wafer, the WAXS patterns from both, polished and unpolished sides of the plate were recorded first at RT in ambient air atmosphere. Measurements were carried out in the symmetrically coupled y–2y scan mode (y and 2y are the angles of incidence and diffraction, respectively) using an X-ray diffractometer URD-6 (Seifert FPM GmbH, Germany) designed in Bragg–Brentano geometry and equipped with a scintillation detector. Characteristic radiation of a Cu anode, monochromatized by a secondary Johansson-type graphite monochromator and tuned to the Ka spectral line of the tube was used. The specimen was rotated around the holder (i.e. surface normal) axis during the measurements. To reduce statistic fluctuations of the intensities recorded, multiple scans of the 2y range between 10.51 and 1201 were performed with a step width D2y of 0.011 and 5 s sampling time per angle step. The total sampling time per angle step after summing up the individual data sets was 45 s. Additionally, the WAXS patterns from both sides of the STO plate covered by a thin
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Si powder layer (Standard Reference Material 640b of NIST) were collected. Both, polished and unpolished sides of the same (0 0 1)c STO single-crystal plate were investigated by means of WAXS at low temperatures in high vacuum (o5 104 Pa). The measurements were carried out in the coupled y–y scan mode using a D5000 diffractometer (Siemens AG, Germany; Bragg–Brentano geometry, scintillation detector, characteristic Cu Ka radiation monochromatized by Johansson-type graphite monochromator) supplied by a cryostat chamber (Anton Paar KG, Austria). The temperature was controlled by a temperature sensor (Lake Shore Cryotronics Inc., USA) in contact to the sample holder. The accuracy of temperature measurements was about 70.5 K. The WAXS patterns were recorded in the vicinity of a 004c STO reflection in the 2y range between 102.51 and 106.31 with the step width D2y of 0.011 and 1 s sampling time per angle step (about 6.4 min per individual scan). The measurements were performed in the temperature range from 300 K (RT) down to 125 K and from 115 K down to 25 K in steps of DT ¼ 25 and 5 K, respectively. To allow the temperature equilibration, a 10 min delay was realized at every temperature stage. Afterwards, a rocking curve was measured to check and correct the y–y coupling of the diffractometer. Thereafter, three scans of the X-ray reflection chosen were carried out sequentially to prove that WAXS reflection profiles measured were stable. Finally, after exposure of about 10 h at the lowest temperature of 25 K, the recording of WAXS patterns was repeated with increase of temperature starting from 25 K up to 300 K using the same temperature–time steps as described above. After finishing the low-temperature measurements, the specimen was pulverized and a WAXS pattern of the powder was recorded at RT in air atmosphere using the Xray diffractometer URD-6. Additionally, the WAXS pattern of the STO powder mixed with reference Si powder (640b, NIST) was measured. The parameters and techniques of the measurements were the same as described above for RT measurements in air atmosphere. 2.2. Details of the quantitative analysis The WAXS patterns of the samples covered/mixed with Si reference powder were used for refinement of the unit cell parameters of STO at RT by means of a program CelSiz [28] adopting the Si reflections as an internal standard. The data obtained this way were used as external standard for further analysis. The WAXS patterns recorded at RT from the (0 0 1)c single-crystal plate exhibited the STO reflections of 00lc type only. From these WAXS patterns, the lattice parameters of STO of polished and unpolished sides of the single-crystal plate at RT were extracted by a decomposition-method of fitting the whole diffraction pattern (see Ref. [29, p. 254]) as realized in the computer program TOPAS [30]. To control the possible change of
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structural parameters of STO in the bulk of the specimen, the structure of pulverized STO was refined by the Rietveld method with the program TOPAS using the WAXS powder data and an initial structure model [2] of the C-modification of STO. Pseudo-Voigt profile functions (see Ref. [29, p. 9]) were used for the simulation of the reflection profile. The values of standard uncertainties of refined structural parameters (underrated by Rietveld and X-raydiffraction-pattern-decomposition procedures of TOPAS due to serial correlations) were corrected by multiplying by the factor of about 3.5 calculated by a computer program according to a procedure described in Ref. [31]. The profiles of the STO reflection recorded at low temperatures were analyzed by means of the program ANALYZE [32].
3. Results and discussion 3.1. Lattice parameters in the bulk and at the surfaces of the STO single-crystal plate at RT For the radiation used, the crystal regions located at a depth of less than 10 mm beneath the surface of the wafer will contribute to the WAXS pattern. Thus, in case of a single-crystal plate, the unit cell parameters of the crystalline phases calculated on this basis will characterize the near-surface layer only. Due to possible defects and strains present near the plate surface, the lattice parameters of the surfaces and of the bulk cannot be assumed to be the same. Again as in Ref. [23], the WAXS pattern recorded from polished surface of the (0 0 1)c STO single-crystal plate can be fitted using one ‘ideal’ C-phase exclusively (see a section of corresponding WAXS pattern in Fig. 1a for illustration). On the other hand, the profiles of different orders of the 001c STO reflection recorded from the unpolished side can be fitted with a sufficient quality assuming two phases (with ‘ideal’ d1 and ‘distorted’ d2 C-lattices; Fig. 1b), whereas the assumption of only one phase results in deterioration of the fitting quality parameters of about 2% in comparison to those shown in Table 1. In Refs. [23,24] and in the present communication, the second STO phase is described for simplicity as a ‘distorted’ C-phase with a larger unit parameter (phase 2 or ‘distorted lattice’ d2 characterized by a ¼ 3.9084(1) A˚ in this work and a ¼ 3.9069(6) A˚ in Refs. [23,24]). According to fitting, the volume of this phase at the unpolished surface is of about 18 wt%. In Ref. [24] it is outlined, that the asymmetry of the 00lc STO reflections can be induced by a coherent intergrowth of SrO(SrTiO3)n RP phases with n ¼ 1–3 and the STO perovskite matrix. After calculation by the procedure described in Ref. [24], the amount of n ¼ 3 RP phase in the intergrowth-domains is about 2.8 wt% in this work and about 1.8% in Refs. [23,24] for the lattice parameters observed. Probably, the absence of any asymmetry of the reflection profiles of the WAXS powder pattern (Fig. 1c) shows the negligibility of the volume of this phase detectable in a thin near-surface layer of the unpolished STO plate only.
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The structure parameters of the of STO C-phase obtained by Rietveld refinement on base of WAXS powder data did not exhibited any anomaly. No observable deviation from the STO stoichiometry was found (the refined occupation factors of the atomic sites of Sr, Ti and O were 1.00(1), 1.00(1) and 0.99(1), respectively). Thus, at RT, the bulk STO as well as the polished STO single-crystal plate investigated are characterized by a lattice with unit cell parameters close to the bulk reference data (a ¼ 3.905 A˚, card 35-0734 [33]). Additionally, the unpolished STO plate contained distorted regions incorporated in the ‘ideal’ matrix. 3.2. Low-temperature behaviour of the polished (0 0 1)c STO specimen 3.2.1. Cooling cycle from RT to 25 K An example of experimental WAXS patterns at some characteristic temperatures in a range of 300–25 K recorded in the vicinity of the fourth order of the 001c (i.e. 004c) cubic STO reflection of the polished (0 0 1)c STO
Fig. 1. Sections of experimental WAXS patterns (solid lines) at angles in vicinity of the fourth order of STO 001c reflection recorded under ambient air conditions at the polished (a) and non-polished (b) sides of the wafer as well as from the pulverized specimen (c). Ka1 and Ka2 reflection contributions are resolved. Results of fitting the experimental WAXS patterns (simulated profiles and difference curves Iobserved–Icalculated) are indicated by lines of different styles marked in parts (a) and (b). For the non-polished side of the STO plate, contributions of the non-distorted (d1) and distorted (d2) lattices are shown.
Table 1 Unit cell parameters of the crystalline STO C-phases of the specimens at RT as obtained by refinement using LeBail (for surfaces of the singlecrystal plate) and Rietveld (for powder) procedures Sample
a (A˚)
Rwp (%)
Rp (%)
Polisheda Unpolishedb Phase 1 (d1) Phase 2 (d2) Powderc
3.9052(1)
4.70 11.22
3.37 4.87
3.57
2.93
3.9049(1) 3.9084(1) 3.9047(1)
The weighted profile Rwp and profile Rp factors (see Ref. [29, p. 22] for definition) are indicated as quality parameters of fitting the WAXS patterns recorded. a Polished side of the (0 0 1)c STO single-crystal plate. b Unpolished side of the (0 0 1)c STO single-crystal plate. c Powder obtained by pulverization of the (0 0 1)c STO single-crystal plate.
Fig. 2. WAXS patterns measured at angles in the vicinity of the fourth order of STO 001c reflection recorded under high-vacuum conditions at the polished side of the single-crystal (0 0 1)c STO wafer at characteristic temperatures during cooling (solid lines) and warming (dashed lines) cycles. Ka1 and Ka2 reflection contributions are resolved. The reflection indices of the crystalline phases observed are indicated. The WAXS patterns are shifted vertically for better visual investigation. The WAXS patterns at every temperature stage of cooling and warming cycles were recorded after a delay of 10 min for temperature equilibration. The measurement of the WAXS pattern at lowest temperature of 25 K in warming cycle was carried out after an exposure of 10 h at this temperature.
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Fig. 3. Thermal evolution of the interplanar distances corresponding to reflections indicated calculated for polished (a) and non-polished (b) sides of the single-crystal (0 0 1)c STO wafer. The data obtained during cooling and warming cycles are drawn by open and solid symbols, respectively. In (b), the data determined for non-distorted (d1) and distorted (d2) lattices are represented by triangles and squares, respectively. Linear fittings in appropriate characteristic temperature ranges are drawn. Insets show the low-temperature sectors in an enlarged scale.
wafer is presented in Fig. 2. As to be seen in Fig. 2, with decrease of temperature from RT down to 85 K, the shape of the reflection profile does not change significantly. The centre of gravity of the reflection only shifts to higher diffraction angles as an outcome of usual contraction of the lattice parameters due to refrigeration. According to precise results of the quantitative analysis, the thermal dependence of the interplanar spacing d (Fig. 3a) in temperature ranges 300–200 and 200–125 K is represented by linear segments with different slopes. The linear thermal expansion coefficients a obtained by means of least-square fitting are equal to 8.6(1) 106 and 7.4(1) 106 K1, respectively, i.e. consistent with values known for STO from literature (a ¼ 8.9 106 K1 [34] in the temperature range 300–200 K and a ¼ 8.753 106 K1 [35] at the temperature of 300.3 K). At a temperature of 80 K, an asymmetry of the reflection profile shape appeared forming a well-distinguishable shoulder at a temperature of 65 K. Finally, a new reflection was resolved starting from a temperature of 45 K.
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Fig. 4. Thermal evolution of the integrated intensities (a) and FWHM (b) corresponding to reflections calculated for polished side of single-crystal (0 0 1)c STO wafer. The data obtained during cooling (solid lines) and warming (dashed lines) cycles are drawn by open and solid/half-solid symbols, respectively. The lines are guides for eyes.
The low-temperature behaviour of the polished (0 0 1)c STO platelet can be apparently linked to C–T AFD transition known to occur for bulk STO at a temperature of about 105 K [5]. The same value of the transition temperature for the polished STO plate under investigation can be derived from inspection of the thermal dependencies of the interplanar spacing d (Fig. 3a) and the integrated intensity (Figs. 4a and 5) extracted from the experimental X-ray reflection profiles. Below the AFD transition temperature, in the absence of special constraints, twin domains are formed in a singlecrystal specimen due to the transformation of the structure from cubic to tetragonal modification [36]. As a result of twin domain growth and reorientation in the single-crystal plate starting at a temperature of 80 K in the cooling cycle, new reflections develop. According to indexing, the reflections of the AFD T-phase with indices 008t and 440t are formed (Fig. 2) representing two domains with antiphase orientation growing near the surface of the plate, i.e. domains with normals oriented parallel to the caxis of the tetragonal unit cell ([0 0 1]t domains) and perpendicular to it ([1 1 0]t domains). It should be noted here, that directions [0 0 1]t and [1 1 0]t coincide with
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temperatures higher than the AFD transition temperature were about 153(2) nm. The volume fraction of the domains changed continuously with stepwise decrease of temperature as to be concluded from temperature-dependent evolution of the reflection profile shape in Fig. 2. After start of the domain manifestation at a temperature of 80 K, with further cooling the integrated intensity of 440t T-phase reflection increased considerably correlated with a quick decrease of the intensity of 008t T-reflection (Fig. 4a) reflecting a corresponding change of population of the [1 1 0]t and [0 0 1]t T-domains, respectively. The total integrated intensity of both, 008t and 440t, reflections grows after the AFD transition reached a maximum value at a temperature of about 65 K (Fig. 5). Further cooling down to 25 K resulted in a moderate decrease of the total intensity of the profile measured.
Fig. 5. Thermal evolution of the integrated intensity of the experimental reflections calculated for polished (a) and unpolished (b) sides of the single-crystalline (0 0 1)c STO wafer. The data obtained during cooling (solid lines) and warming (dashed lines) cycles are drawn by open and solid symbols, respectively. The lines are guides for eyes.
directions [0 0 1]c and [1 0 0]c, respectively, facilitating the formation of corresponding antiphase T-domains. According to the Scherrer equation (Ref. [29, p. 141]), the mean size of the twin domain t (or mean size of mosaic blocks in case of single-crystal C-phase) can be estimated from full-width at half-maximum (FWHM) of corresponding Bragg reflections as t¼
l , FWHM cos y
where l is the wavelength of the X-ray radiation used and y is the Bragg angle of the reflection. Thus, at first stages of 440t reflection formation during the cooling cycle at temperatures of 80–70 K, the [0 0 1]t and [1 1 0]t domains are characterized by typical mean sizes of 174(2) and 135(1) nm, respectively. With subsequent cooling down to 25 K, the 008t reflection exhibited a slow broadening whereas the FWHM of 440t reflection decreased abruptly at 65 K first and then showed a slow increase too (Fig. 4b). As a result, in the temperature range 65–25 K the sizes of both kinds of domains reached more close values of 165(2) and 149(2) nm ([0 0 1]t and [1 1 0]t domains, respectively). The mosaic block sizes of the C-phase estimated from the FWHM of the 004c C-reflection at
3.2.2. Ageing at 25 K A drastic change of the volume fraction of both types of domains present beneath the polished surface of the plate occurred after exposure for about 10 h at 25 K, the lowest temperature during the experiments (Figs. 4a and 5). It gave rise to an inverse intensity ratio of 440t and 008t T-phase STO reflections in comparison to the initial state. Whereas the intensity of the 440t reflection increased distinctly at 20%, the intensity of the 008t reflection decreased considerably (more than by a factor of 2) becoming smaller than 440t. Thus, the volume fraction of the [1 1 0]t T-domain increased moderately accompanied by a drastic decrease of the [0 0 1]t domain population. Nevertheless, the mean size of [0 0 1]t domains as calculated from a change of FWHM of reflections (Fig. 4b) was maintained (the typical extension of about 165(2) and 164(2) nm at 25 K in the initial state and after 10 h ageing, respectively) while the [1 1 0]t domains grew up to a higher value of about 157(2) nm (in comparison to 149(2) nm in the initial state at 25 K). In spite of significant modifications of domain sizes and relative populations, the corresponding interplanar distances do not change in limits of estimated standard deviations. Presumably, the changes observed were caused by [0 0 1]t and [1 1 0]t domain creation, growth and annihilation processes after long-time ageing at a low temperature. 3.2.3. Warming cycle from 25 K up to RT However, the changes observed proved reversible with warming. After temperature equilibration of about 10 min at every temperature level, the central-angle position of the reflections (i.e. interplanar distances and, consequently, the unit cell parameters) completely recovered at once (Figs. 2 and 3a). The process of recovering the reflection intensity (i.e. volume fractions of the different domains in case of T-phase) and the FWHM of the reflections (i.e. domain sizes) is more gradual demonstrating a hysteresis (Figs. 4 and 5). Nevertheless, with increase of the temperature up to 55 K, the reflection profiles were
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found close to that observed at this temperature during the cooling cycle (small hysteresis), whereas in the temperature range of 200–300 K they were indistinguishable (no hysteresis). The thermal hysteresis of the integrated intensity and FWHM of the reflection profiles are attributed to the existence of lattice defects remaining in regions near the polished STO surface and hindering the motion of domain walls [27]. 3.2.4. Comparison with literature reports on lowtemperature investigations of polished (0 0 1)c STO plates Thus, the polished (0 0 1)c STO single-crystal plate investigated is characterized by a lattice with unit cell parameters close to bulk reference data (a ¼ 3.905 A˚). In the temperature range 300–200 K, the plate exhibited a linear coefficient of thermal expansion a ¼ 8.6 101 K1 close to a known value from literature. The STO plate under study showed a reversible AFD phase transition at a temperature of 105 K equal to the known bulk value. At a lower temperature of 80 K, a beginning formation of [0 0 1]t and [1 1 0]t antiphase domains was observed resulting in asymmetry and broadening of the reflection profile recorded in the vicinity of the 004c STO C-phase reflection. Significant amounts of the domains were developed (probably due to growth and reorientation of the domains) at a temperature of about 45 K giving rise to well-resolved X-ray reflections attributed to these domains. A similar reversible low-temperature behaviour with a delay of formation of detectable domains was observed in Ref. [27] during X-ray investigation of a comparable polished (0 0 1)c STO plate. Despite of the C–T transition temperature of 104.2 K estimated for the sample by a quantitative analysis of the X-ray diffraction data, the broadening of the reflection profile measured in vicinity of the 002c STO C-phase reflection started at a lower temperature of 94 K whereas the new X-ray reflections referred to three T-domains were formed at a temperature of 54 K. In distinction to the results of the present investigation, a good reversibility of the reflection profile shape (with very small thermal hysteresis of the integrated intensity, only) during cooling and warming cycles was observed at all low temperatures investigated. The dissimilarity arises probably from the difference in the time–temperature procedure used (no long-time exposure at a low temperature was made in Ref. [27]). In conclusion, the polished (0 0 1)c STO plate under study showed characteristics close to bulk reference STO material and exhibited a low-temperature behaviour similar to the behaviour known from literature. The differences observed are attributed to peculiarities of the low-temperature processing as well as to different morphological details (surface quality, near-surface layer constraints of a large single-crystal plate, etc.) of the specimen investigated.
Fig. 6. Same as Fig. 2 for the unpolished side of the single-crystalline (0 0 1)c STO plate.
3.3. Low-temperature behaviour of the unpolished side of (0 0 1)c STO wafer Contrary to the WAXS patterns recorded from the polished (0 0 1)c STO single-crystal plate, no new reflection was observed in the WAXS patterns of the unpolished side of the plate at any temperature down to 25 K (see Figs. 2 and 6 for comparison). With cooling, the position of the reflection present at RT (004c C-phase) shifted only to a higher value of the diffraction angle and became broader (Fig. 6). Unlike with the polished STO plate, a long-time ageing for 10 h at the lowest temperature and a further warming-up cycle did not give rise to any noticeable hysteresis of the reflection profiles. To a first approximation, the thermal evolution of calculated interplanar distances of both, phase 1 and phase 2 contributing to the apparent reflection profile (correspondingly, the C-lattice regions with non-distorted and larger unit cell parameters at RT; see Table 1 and Fig. 1b) followed a linear law in the whole temperature range of 25–300 K investigated (Fig. 3b). However, a thorough inspection of the calculated interplanar distances d(T) at different temperatures revealed changes of the slope dd/dT, which are comparatively more moderate in the whole temperature range than in the case of polished STO. During cooling, the first two successive modifications of the majority phase 1 occurred at the same temperature of 200 and 125 K like for the C-phase of polished STO.
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Fig. 7. Same as Fig. 4 for non-polished side of the single-crystalline (0 0 1)c STO plate. The data obtained for non-distorted (d1) and distorted (d2) lattices are represented by triangles and squares, respectively.
Furthermore, the linear thermal expansion coefficients showed about 12% smaller magnitude (a ¼ 7.7(2) 106 K1 and a ¼ 6.4(6) 106 K1 in the temperature ranges of 300–200 and 200–125 K, respectively). As referred to the minority phase 2 with a distorted lattice, when cooling down from 300 to 115 K, the corresponding calculated interplanar distance showed a linear decrease with a similar rate (a ¼ 7.5(3) 106 K1) like the phase 1 in the temperature range 300–200 K. In contradiction to the polished STO-side, further cooling did not lead to a long-range ordering of the TiO6 libration at a temperature of 105 K resulting in an AFD C–T transition at this temperature like at the polished STO-side. Contrary to that, in case of the unpolished STO plate-side, a linear decrease of the interplanar distances is found for both phases down to 50 K. However, a noticeable broadening of the X-ray reflection of the phase 1 accompanied by reducing its integrated intensity as well as of the sum integrated intensity of the experimental X-ray reflection profile is detected at temperatures below 90 K (Figs. 5b and 7). From the point of view of X-ray diffraction, the unpolished STO plate-side remained in a single-domain state (neglecting the contribution of the minority phase 2 present at RT yet), but the size of mosaic
blocks of the dominating phase 1 decreased from 85(1) nm above 90 K down to 73(1) nm at 50–25 K. Note that the size of mosaic blocks of phase 1 of the unpolished side at RT is approximately twice less than that observed at the polished STO plate (Section 3.2.1). The distorted lattice (phase 2) contained smaller mosaic blocks (about 54(2) nm at RT and 50(2) nm at 25 K, as estimated from the larger FWHM (Fig. 7b) of the corresponding reflection profiles). Apparently, the finer mosaic blocks of the STO phases at the unpolished side of the plate reflect the presence of defects (cation and oxygen vacancies) preventing the formation of larger regions with ideal lattice. Presumably, the noticeable change of the FWHM and of the integrated intensity at 90 K can be attributed to an AFD C–T transformation of the C-like phase 1 which is a dominating phase near the surface of the unpolished-side of STO. The decrease of the transition temperature down to 90 K is caused probably by the presence of oxygen vacancies [7,8]. Recently [6], a similar C–T transition manifested by a drastic change of the reflection intensity but not by the lattice parameters was detected in STO films and referred to a clamping effect of the substrate. As it was mentioned in the introduction, regions containing a coherent intergrowth of STO and RP phases SrO(SrTiO3)n (n ¼ 1–3) were found near the unpolished surface of a STO plate [24] comparable to the specimen under investigation. Presumably, in the single-crystal plate studied the extended regions of the defect lattice hinder the formation of twin AFD domains and act as clamping centres resulting in the absence of any anomaly of d(T) of phase 1 while passing the C–T transition temperature at a temperature of 90 K. After the transition, the 004c reflection of the dominating (matrix) C-type phase 1 transforms to 008t reflection of the T-phase. Probably due to the other structure type (intergrowth of STO and RP phases) or higher amounts of defects, the distorted phase 2 does not show any phase transition at 90 K as to be concluded from the absence of remarkable anomalies of profile parameters of this distorted lattice (Figs. 3b and 7). 4. Conclusion The quality of the surface of STO single-crystal wafers plays a crucial role for the physical and structural properties of the wafer. Already at RT under ambient conditions, an additional contribution of lattice regions with distorted structure was detected at the unpolished side of the wafer reflected by quite a different behaviour of the polished and unpolished STO plates at low temperatures (as well as under influence of an external electric field [23,24]). Acknowledgement Financial support by Deutsche Forschungsgemeinschaft (DFG) in the framework of the research unit FOR 520 is kindly acknowledged.
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