Low Temperature Crystal Structure Behaviour of Complex Yttrium

Vol. 124 (2013) ACTA PHYSICA POLONICA A No. 2

Special Anniversary Issue: Professor Jan Czochralski Year 2013 Invited Paper Low Temperature Crystal Structure Behaviour of Complex

Yttrium Aluminium Oxides YAlO3 and Y3Al5O12 A. Senyshyna,∗ and L. Vasylechkob aForschungs-Neutronenequelle Heinz Maier-Leibnitz FRM-II, Technische Universität München Lichtenbergstrasse 1, D-85748 Garching b. München, Germany bLviv Polytechnic National University, 12 Bandera Str, 79013 Lviv, Ukraine

Crystal structures of two yttrium aluminium oxides, namely YAlO3 and Y3Al5O12, were investigated in the temperature range 3.4300 K by high-resolution neutron powder diraction. Neither traces of phase transforma- tions nor discontinuous changes of physical properties were observed. Thermal expansion of yttrium aluminium oxides was evaluated in terms of 1st order Grüneisen approximation, where the Debye temperatures and the Grüneisen parameters have been estimated for both compositions. Anomalies in the thermal expansion of yttrium aluminium perovskite have been observed and modelled using the Einstein oscillator with negative Grüneisen parameter. Extended bond length analysis revealed signicant thermally-driven modications of the aluminium oxygen framework. DOI: 10.12693/APhysPolA.124.329 PACS: 61.66.Fn, 61.05.F−, 65.40.De, 65.60.+a, 63.70.+h

1. Introduction Practical applications of Y3Al5O12 and YAlO3 as laser matrices and substrate materials for thin lms epitaxy Yttrium aluminium perovskite YAlO (YAP) and yt- 3 make thermal behaviour issue of crystal structures in trium aluminium garnet Y Al O (YAG) are exten- 3 5 12 a wide temperature range a relevant task. In partic- sively studied during the last ve decades due to their ular, coecient of thermal expansion (TEC, ) is one great technological relevance, where their use as host α of the key thermo-optical properties of cryogenically materials in solid-state lasers of dierent kinds [19] is cooled solid-state lasers, along with thermal conduc- the most widespread areas of application for both com- tivity and thermal coecient of refractive index [7, 8]. pounds. Since the discovery of YAG:Nd laser in 1964 [1], Consequently, rst examination of thermal expansion of the Nd doped Y Al O remains one of the most popu- 3 5 12 Y Al O [2426] appears in 1970, shortly after rst pub- lar laser materials and the large single crystals are grown 3 5 12 lications on YAG:Nd laser performance. Since then a on a commercial base. The Yb-doped Y Al O is con- 3 5 12 lot of reports on TEC determination in nominally pure sidered as prospective materials for cryogenically cooled and doped YAG by various experimental techniques have (80100 K) solid-state lasers, which promise a revolution been published (see, for example Refs. [79, 27] and ref- in power scalability while maintaining a good beam qual- erences herein). According to the literature, the value ity [79]. Single crystals of yttrium aluminium perovskite of TEC of YAG at room temperature (RT) varies from YAlO , doped with Nd, Tm, Er and Ho are also well 3 −6 to −6 K−1. Low-temperature (77 known as active and passive laser media [25, 10, 11]. 6.1 × 10 7.3 × 10 300 K) and high-temperature (3031073 K) dependences YAP doped with Yb2+ or V4+ was proposed as mate- of the TEC of pure and doped YAG crystals were re- rial for tunable solid-state lasers [12, 13], whereas optical ported in Refs. [7, 8, 27] and [28], respectively. Recently, properties of YAlO :Mn crystals are suitable for holo- 3 lattice dynamics and rst principle simulations have been graphic and optical storage devices [14]. Besides the laser applied for a calculation of TEC in Y Al O as a func- applications, both materials are used as phosphors and 3 5 12 tion of pressure and temperature up to 1500 (1600 K) scintillators of - and -radiation, cathodoluminescence α β [29, 30]. However, all these publications are limited screens, and X-ray imaging screens [1517]. Variously mainly to the study of the lattice expansion and thermal doped YAG materials have been proposed as optical pres- expansion coecient. To our best knowledge, there is no sure sensors up to very high pressure (ca. 180 GPa) [18]. information in the literature on the detailed investigation Single crystalline substrates of YAlO are used for the 3 of the thermal behaviour of the principal structural pa- epitaxy of thin lms of HTSC [19, 20], manganites with rameters of Y Al O such as interatomic distances and colossal magnetoresistive eect [21] and TbMnO mul- 3 5 12 3 angles, atomic displacement parameters, etc. tiferroic lms [22]. Jourdan et al. [23] reported on the epitaxial growth of the heavy fermion superconductor Study of the thermal behaviour of YAlO3 perovskite UNi Al on the (112)-oriented YAlO substrates. structure starts in 1972 by using holographic interfer- 2 3 3 ometry for the measurement of the thermal expansion coecients of YAG:Nd and YAP:Nd crystals [31]. The high-temperature behaviour of the pure and variously

∗corresponding author; e-mail: [email protected] doped YAlO3 have been studied in situ applying neutron [32], X-ray [33] and X-ray synchrotron [34] powder

(329) 330 A. Senyshyn, L. Vasylechko

diraction techniques. It was shown that YAlO3 reveals Treatment of powder diraction data was carried out a strong anisotropy of thermal expansion in dierent using the Rietveld technique implemented into the soft- crystallographic directions. The anisotropy of thermal ware package FullProf [39]. The peak prole shape was expansion of YAlO3 was conrmed by recent investiga- described by a pseudo-Voigt function. The background tions of high-temperature thermal behaviour of TEC of of the diraction pattern was tted using a linear inter- Tm- and Ho-doped YAP crystals performed in [35, 36]. polation between selected data points in non-overlapping Low-temperature examinations of structural behaviour regions. The scale factor, lattice parameter, fractional of YAlO3 performed in situ by using neutron and X-ray coordinates of atoms and their isotropic displacement pa- synchrotron powder diraction techniques revealed pro- rameters (the anisotropic displacement parameters were nounced anomalies in b-direction, which occur in both rened for Y3Al5O12 case), zero angular shift, prole Mn and Nd-doped crystals [34]. shape parameters, and half width (Caglioti) parameters In the present manuscript we report the results of were allowed to vary during the tting. thorough examination of low-temperature behaviour of 3. Results and discussion yttrium aluminium garnet Y3Al5O12 and yttrium alu- In contrast to observations from the X-ray pow- minium perovskite YAlO3 two most important tech- der diraction indicating the structural purity of the nological crystals in the rich family of group III metal- obtained materials, the high-resolution neutron pow- -aluminium oxides. der diraction revealed some weak traces of corundum 2. Experimental present, which were further conrmed by X-ray exam- Single crystals of YAG and YAP:Nd were grown by ination on neutron irradiated samples. After numerous the Czochralski method in Scientic Research Company cross checks the traces of corundum have been attributed Carat (Lviv, Ukraine) [37]. The YAP:Nd crystals were to the contaminations from the milling materials (and pulled in the [010] direction in P bnm setting. For crys- not to residue amount of Al2O3 used for crystal growth) tal growth experiments, a stoichiometric mixture made and have been included as an independent phase to the of pure Y2O3 and Al2O3 (99.99 w/w% of main compo- Rietveld renement model. nents) was used. The Nd O dopant was introduced di- 2 3 3.1. Yttrium aluminium garnet rectly into the crucible before charge melting in 1 w/w% amount. Constant temperature gradients in the growth The best Rietveld t to the powder diraction pattern direction as well as a at solidliquid interface during collected at 3.4 K was obtained with parameters listed growth process have been ensured with a special design in Table and the graphical representation of the Rietveld of the heat-insulating unit [37]. renement is shown in Fig. 1, accordingly.Thermal evolu- For powder diraction studies a part of the single crys- tion of Y3Al5O12 lattice parameters is shown in Fig. 2a, talline ingot was crushed, ground using corundum mill where cell dimensions smoothly and nonlinearly grow on and homogenized in size. Short check with X-ray pow- heating. The lattice of Y3Al5O12 is characterized by a der diraction reveals only the Bragg reections con- very weak structural response on temperature, i.e. tem- sistent with GdFeO type of structure for YAlO and perature dierence of ca. 300 K results in the increase 3 3 of lattice parameter by 0.0118 Å (about 0.1%), which Al2Ca3Si3O12 structure type for Y3Al5O12. Elastic co- herent neutron scattering experiments were performed correspond to a linear thermal expansion coecient of on the high-resolution powder diractometer SPODI at 6.4(5) × 10−6 K−1 at room temperature (calculated as the research reactor FRM-II (Garching, Germany) [38]. αl(T ) = d ln l(T )/dT ). Monochromatic neutrons (λ = 1.5482 Å) were obtained at a 155◦ take-o angle using the (551) reection of a vertically-focused composite Ge monochromator. The vertical position-sensitive multidetector (300 mm eective height) consisting of 80 3He tubes and covering an angular range of 160 deg 2θ was used for data collection. Measurements were performed in the DebyeScherrer ge- ometry. The powder sample (ca. 2 cm3 in volume) was lled into a thin-wall (0.15 mm) vanadium can of 13 mm in diameter and then mounted in the top-loading closed- -cycle refrigerator. Helium 4.6 was used as a heat trans- mitter. The instantaneous temperature was measured using two thin lm resistance cryogenic temperature sensors Cernox and controlled by a temperature controller TM from LakeShore . Two dimensional powder diraction data were collected at xed temperatures in the range of 3.4300 K upon heating and then corrected for geomet- Fig. 1. Results of Rietveld renements of neutron pow- rical abberations and curvature of the DebyeScherrer der diraction data for Y3Al5O12 at 3.4 K. rings as described in Ref. [38]. Low Temperature Crystal Structure Behaviour . . . 331

Experimental structural parameters of Y3Al5O12 and YAlO3 at T = 3.4 K. Numbers in parentheses TABLE give statistical deviations in the last signicant digits.

Y3Al5O12, space group Ia-3d (No. 230), a = 11.99954(17) Å Atom Wycko x/a y/b z/c [Å2] [Å2] [Å2] [Å2] [Å2] [Å2] [Å2] site symbol [frac. un.] [frac. un.] [frac. un.] uiso u11 u22 u33 u12 u13 u23

Y1 24c 1/8 0 1/4 0.0047(3) 0.0059(4) 0.0041(2) u22 0 0 0.0002(3) Al1 16a 0 0 0 0.0043(3) 0.0043(3) u11 u11 −0.0005(6) u12 u12 Al2 24d 3/8 0 1/4 0.0039(6) 0.0025(9) 0.0045(5) u22 0 0 0 O1 96h −0.03070(4) 0.05088(5) 0.14895(5) 0.0053(3) 0.0059(3) 0.0062(3) 0.0039(3) 0.0009(2) 0.00006(19) 0.0013(2) 2 Fit residuals: Rp = 4.30%, Rwp = 5.81%, Rexp = 1.76%, χ = 10.9

YAlO3, space group P bnm (No. 62), a = 5.17242(9) Å, b = 5.32659(9) Å, c = 7.36085(13) Å Atom Wycko x/a y/b z/c [Å2] [Å2] [Å2] [Å2] [Å2] [Å2] [Å2] site symbol [frac. un.] [frac. un.] [frac. un.] uiso u11 u22 u33 u12 u13 u23 Y1 4c 0.01241(12) 0.55406(9) 1/4 0.00150(13) Al1 4a 0 0 0 0.0016(2) O1 4c −0.08385(15) −0.0220(1) 1/4 0.00070(16) O2 8d 0.2047(1) 0.29483(9) 0.04427(7) 0.00177(13) 2 Fit residuals: Rp = 3.21%, Rwp = 4.08%, Rexp = 1.30, χ = 9.88

As it has been shown in numerous works [4042] the elongation is compensated by the tilting and distortion obtained thermal dependences of lattice parameters can of the coordination polyhedra. be modelled in the frame of the rst order Grüneisen approximation γ V (T ) = V0 + U(T ) KT " # 3Z θD/T 3 γ T x (1) = V0 + 9NkBT x dx , KT θD 0 e − 1 where V0 denotes the hypothetical cell volume at zero temperature, γ is the Grüneisen constant, KT is the bulk modulus, and U is the internal energy of the system. Both γ and KT are assumed to be temperature independent. The use of the Debye approximation for the internal energy U in Eq. (1) with characteristic temperature θD provides a reasonable description. The least-square minimization t of experimental temperature dependence of cell volumes by Eq. (1) yields 1727.8(1) Å3, 618 × 10−14 ± 108 × 10−14 Pa−1 and 534 ± 112 K for V , γ/K ratio and θ , respectively. Fig. 2. Thermal dependence of lattice parameter and 0 T D thermal expansion coecient in Y Al O (a); evolu- The t was characterized by a high coecient of deter- 3 5 12 tion of YO (b) and AlO (c) interatomic distances mination 0.99939 and the graphical results are shown in and isotropic displacement parameters (d). Lines in (a) Fig. 2a by dashed lines. The rst-order Grüneisen ap- correspond to the modelling using Eq. (1) and lines in proximation delivers γ/KT ratio and the determination (b)(d) denote linear ts and are shown as guides for of the Grüneisen constant requires the knowledge of bulk the eyes. modulus, which has been determined for Y3Al5O12 by Hofmeister and Campbell [43] from measured infrared vi- Three types of the vortex-shared cation coordination brational frequencies (KT = 220 GPa), by Stoddart et al. polyhedra are forming the Y3Al5O12 structure, namely [44] and by Alton and Barow [45] using a combination YO8, AlO4, and AlO6. The yttriumoxygen coordina- of the Brillouin scattering and refractive index measure- tion polyhedron in Y3Al5O12 has a form of distorted ments (KT = 189 GPa and 185.2 GPa, respectively), by cube, which is built on two distinct yttriumoxygen dis- Xu and Ching [46] using rst-principles local-density cal- tances undergoing dierent thermal behaviour (Fig. 2b). culations (KT = 221.1228.6 GPa). Approximately 17% The shorter YO interatomic distance (YO1)a remains uncertainty in the value of γ/KT ratio along with 10% nearly independent on temperature in the whole range discrepancy for literature values of bulk modulus dene investigated, whereas the longer one (YO1)b increases the Grüneisen constant in the range 0.951.66, indicat- linearly upon heating. ing weak anharmonicity of the lattice vibrations and, as The metal cations in regular octahedral (AlO6) and a consequence, relatively low thermal expansivity. Low tetrahedral (AlO4) coordination are yet another struc- lattice expansion seems to be quite typical for materials tural feature of garnets. Thermal dependences of with garnet structure [47], where bond-length thermal AlO interatomic distances display dierent character 332 A. Senyshyn, L. Vasylechko

(Fig. 2c). The intraoctahedral AlO distances weakly has been attributed to the coupling of crystalline electric increase on heating, whereas the tetrahedral one re- eld (CEF) levels of 4f ions to the lattice and, conse- mains nearly temperature-independent (or even show- quently, was not expected to occur in YAlO3. Despite its ing some tendency to contract with increasing temper- weakness, the possible reasons for this eect are unclear atures). Such thermal rigidity often occurs in tetrahe- and require to be characterized explicitly. dral oxygen coordinations [48] and on the rst glance it can be attributed to the increase of the covalent part in the tetrahedral bonding leading to shorter AlO bond length etc. Hence, performed bond valence calculations revealed 3.125(2), 2.636(2), 2.686(2), −1.892(1) bond valence sums for Y, Al1, Al2 and O sites at 3.4 K, respectively, indicating similar type of AlO bonding for both Al1 and Al2. On the other hand, the bond valence calculations already utilize R0 values adapted to special coordinations and so forth. This general problem is not trivial and more light on it can be shed by careful and es- pecially dedicated theoretical research, which is beyond the scope of the current contribution and, therefore, will not be considered here in detail. The isotropic displacement parameters for structural sites of Y3Al5O12 are shown in Fig. 2d. At 3.5 K the uiso(Al2) ≈ uiso(O) > uiso(Y) ≈ uiso(Al1) have been found and the heating up to room temperature leads to an increase of for all constituents with the slope ful- uiso Fig. 3. Results of Rietveld renements of neutron pow- lling the relationship u (Y) > u (O) > u (Al1) ≈ iso iso iso der diraction data for YAlO3 at 3.4 K. uiso(Al2). Assuming the root mean square displacement Recently, Fortes et al. [50] found that the lattice pa- to be proportional to the mass of constituent the observed rameters (and not only the cell volume) of α-MgSO4 can behaviour can be attributed to a little static disorder be tted by a modied Eq. (1) on the Al2 site along with temperature-driven disorder (2) of Y inside the distorted cubic coordination. Analysis of l(T ) = l0 + x1UD(T ), where corresponds to lattice parameter, denotes its components of the anisotropic displacement tensor indi- l l0 hypothetical value at zero temperature and is the t- cated that the orientation of principal axes of the ellipsoid x1 ting parameter (in the case of using cell volumes it be- remain nearly constant within the limits of uncertain- comes the meaning of the ratio). Therefore, t- ties and the axes components smoothly increase upon γ/KT ting of obtained thermal dependences of a and c lattice heating with u11(Y) > u22(Y) = u33(Y), u11(Al1) = , parameters as well as cell volume has been performed u22(Al1) = u33(Al1) u11(Al2) < u22(Al2) = u33(Al2) using the protocol previously described for Y Al O . and . 3 5 12 u11(O) ≈ u22(O) > u33(O) The best results (shown by lines) have been obtained 3.2. Yttrium aluminium perovskite with the parameters displayed in Figs. 4ac. Beyond

Graphical result of the Rietveld renement of neutron the meaningless x1 values obtained from the tempera- powder diraction pattern for YAlO3 collected at 3.5 K ture evolution of a and c lattice parameters the obtained is shown in Fig. 3 and the best t has been obtained Debye temperatures 466(91) K and 440(87) K were quite with the parameters listed in Table. The data analysis consistent and are in agreement with the θD from the revealed the GdFeO3 type of structure in the whole tem- nonlinear t of cell volumes (θD = 545(134) K) as well perature range considered, where structural parameters as to the data from Ref. [51], where temperature-driven smoothly react on the temperature change. Similar to the shifts of zero phonon lines (R lines) of YAlO3 appar- rare-earth alluminates [34] thermal expansion of YAlO3 ent at low temperature have been considered and the has been found anisotropic, where lattice parameters a θD = 465±15 K has been estimated. The γ/KT ratio has and c nonlinearly and smoothly increase upon heating been determined as 510(134) × 10−14 Pa−1, which using and the lattice parameter b shows a well-pronounced min- theoretical value of 188 GPa [52] and experimental one imum around 160 K. Thermal expansion coecients in a of 192(2) GPa [53] gives a spread for the Grüneisen pa- and c directions of the orthorhombic lattice follow the rameter from 0.7 to 1.25. The observed range of values is nonlinear increasing trend and are very similar in magni- in agreement with the Grüneisen parameter determined tude, whereas the αb coecient possesses negative values for Y3Al5O12 and isostructural rare-earth containing per- in the temperature range 3.5160 K with the minimum ovskites [5456]. around 75 K. The observed negative thermal expansion As it has been shown in Ref. [50], Eq. (2) is not suitable in b-direction of GdFeO3-type structure is not new. It for description of the negative thermal expansion occur- has been already established for the series of perovskite- ring in the b-direction of the β-MgSO4 lattice. Taking -type rare-earth alluminates [34] and gallates [41, 49] and into account that the total thermal expansion coecient, Low Temperature Crystal Structure Behaviour . . . 333

where YO2 distances appear twice. It makes overall 12 YO bonds and their temperature dependences are shown in Fig. 5a. Among twelve yttriumoxygen dis-

tances the (YO1)3, (YO1)2 and 2 × (YO2)1 are the longest one and do not entirely belong to the rst coordination sphere of yttrium. This may cause a reduction of an eective coordination number for YO coordination polyhedron from 12 to 10, 9 or even eight. The genuine coordination number of AO coordination polyhedron in

ABX3 perovskites was the matter of signicant discussion in the past [34, 5860] and still remains sometimes an issue. It can be determined by the analysis of coordination polyhedron and bond-length distortion, bond valence sums as well as analysis of thermally-induced bond- -lengths elongation. The absolute elongation of yttrium oxygen bonds shown in Fig. 5b (using the same colour Fig. 4. Thermal dependence of the lattice parameters scheme as in Fig. 5a), from which the thermally-driven (a)(c) and cell volume (d) of YAlO3 as well as corre- contraction for (YO1)2 and 2 × (YO2)1 bonds is obvi- sponding thermal expansion coecients. Lines corre- ous. These selected longest interatomic distances do not spond to the modelling using Eq. (1)(3). take part in the thermal expansion, which might indicate an eective coordination number of 9 for yttriumoxygen similar to heat capacity, is an additive property, one more environment in YAlO3. term, describing the lattice contraction, was introduced by Fortes et al. [50]:

l(T ) = l0 + x1UD(T ) + x2UE(T ) 3NkBθE = l0 + x1UD(T ) + x2 , (3) exp(θE/T ) − 1 where the x2 tting parameter is constrained as strictly negative, i.e. x2 < 0, and corresponds to a negative Grüneisen parameter. It has also been proposed in

Ref. [50] to use the Einstein model UE as a single mode with xed frequency (with negative mode Grüneisen parameter), corresponding to a xed Einstein temperature θE. This approach was found successful in simulations of negative thermal expansion occurring in the b-direction of the β-MgSO4 lattice [50], Li2B4O7 [57] as well as in Pr-containing rare earth gallates [41, 49]. Similar to the observations from Ref. [41], the least- -square t of b lattice parameters by Eq. (3) yields much higher Debye temperature θD = 909(50) K in compari- son to these obtained from the nonlinear t of a, c lattice parameters and cell volume. This might be related to the limited temperature range considered, which along with the superposition of two eects results in overestimated for the -direction of the orthorhombic lattice. The Fig. 5. Thermal evolution of YO (a) interatomic dis- θD b tances and their relative expansion (b), evolution of θE = 231(128) K was determined for YAlO3, which is AlO (c) interatomic distances and their relative ex- in line with values for Pr(Nd)GaO3 pseudo-binary sys- pansion (d), thermal dependence of AlOAl interocta- tem [41]. Observed agreement might indicate a similar- hedral angles (e), isotropic displacement parameters in ity in the nature for negative thermal expansion in yt- YAlO3 upon heating (f). Lines in (a)(f) denote linear/ trium aluminate and praseodymium-based gallates with polynomial ts and are shown as guides for the eyes. perovskite structure and, consequently, requires an extended bond-length analysis. The perovskite-structure for ABX3 type compounds In contrast to Y3Al5O12, the nominal oxygen coor- can also be presented as a framework of corner-shared dination number for yttrium in YAlO3 is twelve and BX6 octahedra forming the primitive perovskite cell. has a form of distorted cubooctahedron. It is built on In contrast to garnet and the ideal perovskite, the oc- eight distinct types of distances from yttrium to oxy- tahedral distortion is a typical feature in the GdFeO3 gens (O1 and O2), which range from 2.25 Å to 3.27 Å, type of structure. It reects into three distinct types of 334 A. Senyshyn, L. Vasylechko

BX (or specically AlO) distances, namely (AlO1)1, and aluminates. This indicates that the softening of the (AlO2)1, (AlO2)2, where each of them is doubly de- low lying optical phonons, possibly originated from yt- generated. In contrast to yttriumoxygen coordination trium motion, might play a more crucial role in the an- the spread of AlO distances is much lower (1.894(2) harmonicity as expected. Hence, due to the weakness of 1.922(2) Å at 3.5 K). Thermal evolution of AlO bond the anomalous thermal expansion, its origin and struc- lengths is shown in Fig. 5c showing their low expansi- tural mechanism cannot be elucidated with enough con- tivities. View of the absolute elongation of aluminium dence and requires further research. oxygen bond lengths (Fig. 5d) indicated their dierent Thermal dependences of lattice parameters were thermal behaviour: the (AlO1)1 and (AlO2)2 intraoc- treated using rst order Grüneisen approximation, where tahedral distances increase in a similar way upon heating, anomalous thermal expansion has been simulated using whereas (AlO2)1 one shows some tendency for contrac- the Einstein oscillator with negative Grüneisen parame- tion. This eect makes the distorted AlO6 octahedra ter. On the basis of that the Debye temperatures for both in YAlO3 stier to temperature changes as compared to Y3Al5O12 and YAlO3 have been determined. Using lit- these in Y3Al5O12. Solely contraction tendency of one erature data for bulk modules the Grüneisen parameters AlO bond length is not enough to explain the nega- were estimated for both Y3Al5O12 and YAlO3. tive thermal expansion in GdFeO -type perovskite. In 3 Acknowledgments Ref. [41] it has been shown that a distortional mechanism of lattice contraction may occur under decrease of This work was supported in parts by the German Fed- eral Ministry of Education and Research (BMBF project mean hBX2i distance upon heating. Temperature de- 03FU7DAR) and by the Ukrainian Ministry of Education pendence of hAlO2i distance shown in Fig. 5e displays nearly constant temperature behaviour, which along with and Sciences (project Neos). the increase of AlO2Al interatomic angles (Fig. 5e) give References neither clear evidence for rotational nor distortion mech- [1] J.E. Geustic, H.M. Marcos, L.G. Van Uitert, Appl. anism of negative thermal expansion in YAlO3. Taking Phys. Lett. 4, 182 (1964). into account an extremely small magnitude of the ob- [2] M.J. Weber, M. Bass, K. Andringa, Appl. Phys. served anomaly, its origin, most probably, cannot be re- Lett. 15, 342 (1969). solved using diraction methods as the current study was [3] M. Bass, M.J. 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