Publications by Mike Glazer


Confusion over the description of the quartz structure yet again

Journal of Applied Crystallography International Union of Crystallography 51 (2018) 915–918-

AM Glazer

In a recent paper [Huang, Gog, Kim, Kasman, Said, Casa, Wieczorek, Hönnicke and Assoufid (2018). J. Appl. Cryst. 51, 140–147], a description of the structure of quartz was given that is incorrect. There is a long history of such errors in publications describing the quartz structure. This was fully and correctly discussed in 1978 [Donnay and Le Page (1978). Acta Cryst. A34, 584–594], and yet these errors still persist. In the present paper the description by Huang et al. is corrected and the seminal work of Donnay and Le Page revisited.


Probing the intrinsic and extrinsic origins of piezoelectricity in lead zirconate titanate single crystals

Journal of Applied Crystallography International Union of Crystallography 51 (2018) 1396-1403

N Zhang, S Gorfman, H Choe, T Vergentev, V Dyadkin, H Yokota, D Chernyshov, B Wang, A Glazer, W Ren, Z-G Ye

The physical origin of the piezoelectric effect has been the focus of much research work. While it is commonly accepted that the origins of piezoelectricity may be intrinsic (related to the change of lattice parameters) and extrinsic (related to the movement of domain walls), their separation is often a challenging experimental task. Here in situ high-resolution synchrotron X-ray diffraction has been combined with a new data analysis technique to characterize the change of the lattice parameters and domain microstructure of a PbZr1−xTixO3 (x = 0.45) crystal under an external electric field. It is shown how `effective piezoelectric coefficients' evolve upon the transition from purely `intrinsic' effects to `extrinsic' ones due to domain-wall motion. This technique and corresponding data analysis can be applied to broader classes of materials and provide important insights into the microscopic origin of their physical properties.


Local-scale structures across the morphotropic phase boundary in PbZr1-xTixO3

IUCrJ International Union of Crystallography 5 (2017)

N Zhang, H Yokota, A Glazer, DA Keen, S Gorfman, PA Thomas, W Ren, ZG Ye

Lead zirconate-titanate (PZT) is one of the most widely discussed piezoelectric materials, mainly because of its "mysterious" relationship between the so-called Morphotropic Phase Boundary (MPB) and its strong piezoelectric coupling factor. Here we discuss, using results from a Pair Distribution Function analysis, how the complex local structure in PZT affects the long-range average structure across the MPB. A monoclinic MC type structure is discovered in PZT. A first-order transformation between the monoclinic MA and MC components in both the average and local structures explains the sudden change in piezoelectric effect around these compositions. The role of polarization rotation in the enhancement of the piezoelectric properties is discussed with respect to the composition of PZT. The structure-property relationship that is revealed by this study explains the unique property of PZT, and may be applicable in the design of new MPB-type functional materials.


Local structures and temperature-driven polarization rotation in Zr-rich PbZr1-xTixO3

Applied Physics Letters AIP Publishing 113 (2018) 012901-

Z Wang, N Zhang, H Yokota, AM Glazer, Y Yoneda, W Ren, Z-G Ye

PbZr1-xTixO3, which has abundant structural variations in the corresponding physical properties, has been used in a large variety of applications. To understand the effect of the structure on its high-performance piezoelectric properties, its local and average structures are studied. Total scattering data have been obtained from high-energy synchrotron powder diffraction experiments at 20 K and 300 K. Using the reverse Monte Carlo method, information on cation displacements has been extracted from X-ray Pair Distribution Function data. This suggests that the local disorder of the B cations is mainly driven by thermal motion, while the local disorder of Pb is most likely caused by more complex factors, such as displacive disorder. Both rhombohedral and monoclinic local polarizations are observed in Zr-rich PZT, whose directions depend on temperature.


Monoclinic distortion, polarization rotation and piezoelectricity in the ferroelectric Na0.5Bi0.5TiO3

IUCrJ International Union of Crystallography 5 (2018) 417-427

H Choe, J Bieker, N Zhang, AM Glazer, PA Thomas, S Gorfman

The relationship between crystal structure and physical properties in the ferroelectric Na0.5Bi0.5TiO3 (NBT) has been of interest for the last two decades. Originally, the average structure was held to be of rhombohedral (R3c) symmetry with a fixed polarization direction. This has undergone a series of revisions, however, based on high-resolution X-ray diffraction, total neutron scattering, and optical and electron microscopy. The recent experimental findings suggest that the true average symmetry is monoclinic (space group Cc), which allows for a rotatable spontaneous polarization. Neither polarization rotation nor its potentially important real role in enhanced piezoelectricity is well understood. The present work describes an in situ investigation of the average monoclinic distortion in NBT by time-resolved single-crystal X-ray diffraction under external electric fields. The study presents a high-resolution inspection of the characteristic diffraction features of the monoclinic distortion – splitting of specific Bragg reflections – and their changes under a cyclic electric field. The results favour a model in which there is direct coupling between the shear monoclinic strain and the polarization rotation. This suggests that the angle of polarization rotation under a sub-coercive electric field could be 30° or more.


Relationship between the structure and optical properties of lithium tantalate at the zero-birefringence point

JOURNAL OF APPLIED PHYSICS 121 (2017)

S Huband, DS Keeble, N Zhang, AM Glazer, A Bartasyte, PA Thomas


Crystallographic and optical study of LiNb1 - xTaxO3.

Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials 73 (2017) 498-506

S Huband, DS Keeble, N Zhang, AM Glazer, A Bartasyte, PA Thomas

Powders of lithium niobate-tantalate across the full compositional range have been made and crystals grown using a lithium vanadate flux growth technique. The Li-content of a lithium tantalate crystal has been determined using the zero-birefringence temperature and Curie measurements, confirming the Li content is between that of congruent and stoichiometric crystals. X-ray diffraction measurements show the Nb/Ta displacement and octahedral tilt both decrease as the Ta content is increased. This also results in a decrease in the lattice parameters from lithium niobate to lithium tantalate. Birefringence measurements on the crystals as a function of temperature have been used to determine the point that the crystals become zero-birefringent, and by comparison with the structural studies have confirmed that it is not related to a phase transition and the structures remain polar through the zero-birefringence points.


Crystallographic and optical study of PbHfO3 crystals.

Journal of applied crystallography 50 (2017) 378-384

S Huband, AM Glazer, K Roleder, A Majchrowski, PA Thomas

The symmetry of the intermediate high-temperature phase of PbHfO3 has been determined unambiguously to be orthorhombic using a combination of high-resolution X-ray diffraction and birefringence imaging microscopy measurements of crystal plates. While lattice parameter measurements as a function of temperature in the intermediate phase are consistent with either orthorhombic or tetragonal symmetry, domain orientations observed in birefringence imaging microscopy measurements utilizing the Metripol system are only consistent with orthorhombic symmetry with the unit cell in the rhombic orientation of the pseudocubic unit cell.


X-ray white beam topography of self-organized domains in flux-grown BaTiO3 single crystals

Physical Review B American Physical Society 94 (2016) 024110

D Walker, AM Glazer, S Gorfman, J Baruchel, P Pernot, RT Kluender, F Masiello, C DeVreugd, PA Thomas

The phenomenon of self-organization of domains into a “square-net pattern” in single-crystal, flux-grown BaTiO3 several degrees below the ferroelectric to paraelectric phase transition was investigated using in situ synchrotron x-ray topography. The tetragonal distortion of the crystal was determined by measuring the angular separation between the diffraction images received from 90° a and c domains in the projection topographs, and shows a rapid decrease towards 110 °C, the onset temperature for self-organization. The onset of self-organization is accompanied by bending of the {100} lattice planes parallel to the crystal surface, which produces a strain that persists up to and beyond the Curie temperature, where the crystal becomes cubic and the self-organized domains disappear. At the Curie point, the bending angle α100 = 8.1(±0.3) mrad is at a maximum and corresponds to the radius of curvature of the surface being 16.3(±0.6) mm.


Reconsidering the origins of Forsbergh birefringence patterns

Physical Review B American Physical Society 94 (2016) 024109

A Schilling, A Kumar, RGP McQuaid, A Glazer, PA Thomas, JM Gregg

In 1949, Forsbergh, Jr. reported spontaneous spatial ordering in the birefringence patterns seen in flux-grown BaTiO3 crystals under the transmission polarized light microscope [Phys. Rev. 76, 1187 (1949)]. Stunningly regular square-net arrays were often only found within a finite temperature window and could be induced on both heating and cooling, suggesting genuine thermodynamic stability. At the time, Forsbergh rationalized the patterns to have resulted from the impingement of ferroelastic domains, creating a complex tessellation of variously shaped domain packets. However, no direct evidence for the intricate microstructural arrangement proposed by Forsbergh has subsequently been found. Moreover, there are no robust thermodynamic arguments to explain the finite region of thermal stability, its occurrence just below the Curie temperature, and the apparent increase in entropy associated with the loss of the Forsbergh pattern on cooling. Despite decades of research on ferroelectrics, this ordering phenomenon and its thermodynamic origin have hence remained a mystery. In this paper, we reexamine the microstructure of flux-grown BaTiO3 crystals, which show Forsbergh birefringence patterns. Given an absence of any obvious arrays of domain polyhedra or even regular shapes of domain packets, we suggest an alternative origin for the Forsbergh pattern in which sheets of orthogonally oriented ferroelastic stripe domains simply overlay one another. We show explicitly that the Forsbergh birefringence pattern occurs if the periodicity of the stripe domains is above a critical value. Moreover, by considering well-established semiempirical models, we show that the significant domain coarsening needed to generate the Forsbergh birefringence is fully expected in a finite window below the Curie temperature. We hence present a much more straightforward rationalization of the Forsbergh pattern than that originally proposed in which exotic thermodynamic arguments are unnecessary


Crystallography: A Very Short Introduction

Oxford University Press, 2016

AM Glazer

A. M. Glazer. A. M. Glazer CRYSTALLOGRAPHY A Very Short Introduction 1 Great Clarendon Street, Oxford, OX26DP, United Kingdom Oxford University Press Crystallography: A Very Short Introduction.


FOURIER2D and FOURIER3D : programs to demonstrate Fourier synthesis in crystallography

Journal of Applied Crystallography International Union of Crystallography 49 (2016) 2276-2278

AM Glazer


There ain't nothing like a Dame: a commentary on Lonsdale (1947) 'Divergent beam X-ray photography of crystals'.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 373 (2015)

AM Glazer

Prof. Dame Kathleen Lonsdale was one of the two first female Fellows of the Royal Society, having originally been a student of that great British scientist and Nobel Laureate William Henry Bragg. She came to fame initially for her solution of the crystal structure of hexamethyl benzene, thus demonstrating that the benzene ring was flat, of considerable importance to organic chemistry, where it had been proposed before but without proof. This was at a time when the solution of crystal structures was in its infancy, and in its day this work was considered a triumph. As a rare example then of a female physicist, Lonsdale became interested in various aspects of the diffraction of X-rays, and in particular published an important paper on a form of diffraction in which a strongly divergent source was used rather than the usual highly collimated beam. The photographs thus obtained showed a series of arcs and circles, whose positions were so sensitive that they could be used to determine the quality of crystals such as diamond, and even to calculate their lattice dimensions, and hence carbon-carbon bond lengths, to hitherto extraordinary precision. Lonsdale also became known not just as a scientist but as a peace activist and an active member of the Society of Friends. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.


Celebrating the Braggs - a Personal Account

INTERDISCIPLINARY SCIENCE REVIEWS 40 (2015) 329-339

AM Glazer


A neutron diffuse scattering study of PbZrO3 and Zr-rich PbZr1-xTixO3

JOURNAL OF APPLIED CRYSTALLOGRAPHY 48 (2015) 1637-1644

N Zhang, M Pasciak, AM Glazer, J Hlinka, M Gutmann, HA Sparkes, TR Welberry, A Majchrowski, K Roleder, Y Xie, Z-G Ye


Crystal Clear The Autobiographies of Sir Lawrence and Lady Bragg

Oxford University Press, USA, 2015

AM Glazer, P Thomson

The Autobiographies of Sir Lawrence and Lady Bragg Patience Thomson. CRYSTAL CLEAR 1 CRYSTAL CLEAR The Autobiographies of Sir Lawrence and Lady.


Phase Transitions in Materials. By Brent Fultz. Cambridge University Press, 2014. Pp. 583. Price GBP 60, US$ 90. ISBN 9781107067240.

Acta crystallographica Section B, Structural science, crystal engineering and materials 71 (2015) 122-123

AM Glazer


Phase transitions and thermal-stress-induced structural changes in a ferroelectric Pb(Zr0.80Ti0.20)O3 single crystal.

Journal of physics. Condensed matter : an Institute of Physics journal 27 (2015) 025901-

J Frantti, Y Fujioka, A Puretzky, Y Xie, Z-G Ye, C Parish, AM Glazer

A single crystal of lead-zirconate-titanate, composition Pb(Zr0.80Ti0.20)O3, was studied by polarized-Raman scattering as a function of temperature. Raman spectra reveal that the local structure deviates from the average structure in both ferroelectric and paraelectric phases. We show that the crystal possesses several, inequivalent complex domain boundaries which show no sign of instability even 200 K above the ferroelectric-to-paraelectric phase transition temperature TC. Two types of boundaries are addressed. The first boundary was formed between ferroelectric domains below TC. This boundary remained stable up to the highest measurement temperatures, and stabilized the domains so that they had the same orientation after repeated heating and cooling cycles. These domains transformed normally to the cubic paraelectric phase. Another type of boundary was formed at 673 K and exhibited no signs of instability up to 923 K. The boundary formation was reversible: it formed and vanished between 573 and 673 K during heating and cooling, respectively. A model in which the crystal is divided into thin slices with different Zr/Ti ratios is proposed. The physical mechanism behind the thermal-stress-induced structural changes is related to the different thermal expansion of the slices, which forces the domain to grow similarly after each heating and cooling cycle. The results are interesting for non-volatile memory development, as it implies that the original ferroelectric state can be restored after the material has been transformed to the paraelectric phase. It also suggests that a low-symmetry structure, stable up to high temperatures, can be prepared through controlled deposition of layers with desired compositions.


Seitz symbols for crystallographic symmetry operations.

Acta crystallographica. Section A, Foundations and advances 70 (2014) 300-302

AM Glazer, MI Aroyo, A Authier

The aim of this report is to describe the Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography. The established notation follows the existing crystallographic conventions in the descriptions of symmetry operations.


Local structure of Pb(Zr0.53Ti0.47)O-3

JOURNAL OF APPLIED CRYSTALLOGRAPHY 47 (2014) 1688-1698

KZ Baba-Kishi, AM Glazer

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