The crystal structure of ZrO2 and HfO2

Adam, J.; Rogers, M. D.

doi:10.1107/s0365110x59002742

Cited by 172 publications

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“…The single-crystal benchmark unit-cell dimensions are taken from Adam & Rogers (1959). The structural parameters are from Smith & Newkirk (19655 (14) (5.3406 (13) 0.004 ( 1 ) 0(2) …”

Section: Results Of the Rietveld Refinements: Unit-cell Constants mentioning

confidence: 99%

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂

Gualtieri¹,

Norby²,

Hanson³

et al. 1996

J Appl Crystallogr

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The results of Rietveld refinements using synchrotron X-ray powder diffraction data collected in transmission mode with a new flat imaging-plate (IP) technique agree with those obtained from other techniques, m-ZrO2 was chosen as test compound because it was the standard selected by the Commission on Powder Diffraction of the International Union of Crystallography for a round robin of Rietveld refinement using data obtained by different techniques and from different laboratories [Hill & Cranswick (1994). J. Appl. Cryst. 27, 802-844]. For comparison, new data were also collected using a gas-filled position-sensitive detector. Powder diffraction using a flat IP detector requires a modification to the geometric term of the Lorentz factor and the zero-shift correction. Other factors that were accurately taken into account are the polarization of the synchrotron beam, the angle-dependent variations induced by the use of a flat detector and the absorption.

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“…The single-crystal benchmark unit-cell dimensions are taken from Adam & Rogers (1959). The structural parameters are from Smith & Newkirk (19655 (14) (5.3406 (13) 0.004 ( 1 ) 0(2) …”

Section: Results Of the Rietveld Refinements: Unit-cell Constants mentioning

confidence: 99%

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂

Gualtieri¹,

Norby²,

Hanson³

et al. 1996

J Appl Crystallogr

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“…While several structural determinations for m-HfO 2 can be found in the literature [1,11], corresponding results for the tetragonal and cubic phases are relatively sparse [12]. Nor has there been much theoretical work on hafnia; most important is the recent work of Ref.…”

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confidence: 99%

“…For m-HfO 2 , the parameters given in Ref. [11] were used as the starting point of our relaxation procedures, while for t-and c-HfO 2 we started the relaxation from the zirconia experimental structures. It can readily be seen that both the LDA and GGA agree reasonably well with the previous work, but that the LDA yields a better overall agreement.…”

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confidence: 99%

First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

2002

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Crystalline structures, zone-center phonon modes, and the related dielectric response of the three low-pressure phases of HfO2 have been investigated in density-functional theory using ultrasoft pseudopotentials and a plane-wave basis. The structures of low-pressure HfO2 polymorphs are carefully studied with both the local-density approximation (LDA) and the generalized gradient approximation (GGA). The fully relaxed structures obtained with either exchange-correlation scheme agree reasonably well with experiment, although LDA yields better overall agreement. After calculating the Born effective charge tensors and the force-constant matrices by finite-difference methods, the lattice dielectric susceptibility tensors for the three HfO2 phases are computed by decomposing the tensors into the contributions from individual infrared-active phonon modes.PACS numbers: 77.84.Bw Hafnia (HfO 2 ) is technologically important because of its extraordinary high bulk modulus, high melting point, and high chemical stability, as well as its high neutron absorption cross section. HfO 2 resembles its twin oxide, zirconia (ZrO 2 ), in many physical and chemical properties. The resemblance is attributable to the structural similarity between the two oxides, which can in turn be explained by the chemical similarity of Hf and Zr, which have similar atomic and ionic radii (i.e., ionic radii for Hf 4+ and Zr 4+ of 0.78 and 0.79Å, respectively [1]) as a result of the so-called lanthanide contraction. Under ambient pressure, both oxides are monoclinic (m, space group P 2 1 /c) at low temperature, and transform to a tetragonal structure (t, space group P 4 2 /nmc) and then to a cubic structure (c, space group F m3m) as the temperature increases, as illustrated in Fig. 1.High-K metal-oxide dielectrics have recently been the focus of substantial ongoing efforts directed toward finding a replacement for SiO 2 as the gate dielectric in complementary metal-oxide-semiconductor (CMOS) devices. HfO 2 , ZrO 2 and their SiO 2 mixtures show promise for this purpose [2,3]. Thus, a systematic theoretical investigation of the structural and dielectric properties of these dielectrics, in both bulk and thin-film form, is clearly desirable. As a first step in this direction, we have, in a previous paper [4], investigated the bulk structures and lattice dielectric response of ZrO 2 polymorphs. We found that the dielectric responses vary dramatically with the crystal phase. Specifically, we found that the monoclinic phase has a strongly anisotropic lattice dielectric tensor and a rather small orientationally-averaged dielectric constant owing to the fact that the mode effective charges associated with the softest modes are relatively weak.This report presents the corresponding work on HfO 2

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“…mined by McCullough & Trueblood (1959) using a single crystal of baddeleyite and by Adam & Rogers (1959) using synthetic ZrO 2 powder. The discrepancy between the two sets of data is very slight but results in significant differences in calculated interplanar spacings at low diffraction angles.…”

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Direct high-temperature single-crystal observation of orientation relationship in zirconia phase transformation

Wolten¹

1964

Acta Cryst

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SHORT COMMUNICATIONS 763 fl-Bet7Ti 2 is a relatively simple one, in which the [010]T direction becomes the [0001]~ direction. Some titanium atoms must change from a = 0 to a = ½-positions, or vice versa, to complete the symmetry, and the removal of 7 Be atoms from the unit cell involves a small decrease in the atomic spacing in this direction, from 7.36 to about 7.30 A. The removal of 7 atoms without disrupting the near-hexagonal symmetry displayed by the tetragonal arrangement in Fig. 2 appears difficult to accomplish. Removal of the two smaller layers is simple but results in a loss of 8Be atoms. This raises the question of how accurately the composition of Be~TTi~ is known and whether a composition BesTi is possible.The other two hexagonal structures of Table 1 can be derived from this transformation, l~aeuchle & Rundle's disordered hexagonal structure has the same c parameter as the fl-Be~TTi2 structure and four times the a parameter; the a-Be17Ti~ structure has the same a parameter and approximately 1.5 times the c parameter.

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The crystal structure of ZrO2 and HfO2

Cited by 172 publications

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Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂

First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Direct high-temperature single-crystal observation of orientation relationship in zirconia phase transformation

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The crystal structure of ZrO2 and HfO2

Cited by 172 publications

References 0 publications

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO2

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO2

First-principles study of structural, vibrational, and lattice dielectric properties of hafnium oxide

Direct high-temperature single-crystal observation of orientation relationship in zirconia phase transformation

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Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂

Rietveld Refinement using Synchrotron X-ray Powder Diffraction Data Collected in Transmission Geometry using an Imaging-Plate Detector: Application to Standardm-ZrO₂