Journal of ASTM International, Vol. 5, No. 3Paper ID JAI101161

Available online at www.astm.org

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Z. Zhao,1,2 M. Blat-Yrieix,1 J.-P. Morniroli,2 A. Legris,2 L. Thuinet,2 Y. Kihn,3 A. Ambard,1 andL. Legras1

Characterization of Zirconium Hydrides and Phase FieldApproach to a Mesoscopic-Scale Modeling of TheirPrecipitation

ABSTRACT: Zirconium alloys are currently used in nuclear power plants where they are submitted tohydrogen pick-up. Hydrogen in solid solution or hydride precipitation can affect the behavior of zirconiumalloys during service but also in long term storage and in accidental conditions. Numerical modeling atmesoscopic scale using a “phase field” approach has been launched to describe hydride precipitation andits consequences on the mechanical properties of zirconium alloys. To obtain realistic results, it should takeinto account an accurate kinetic, thermodynamic, and structural database in order to properly describehydride nucleation, growth, and coalescence as well as hydride interaction with external stresses. There-fore, an accurate structural characterization was performed on Zircaloy-4 plates and it allowed us to identifya new zirconium hydride phase called �. The � phase has a trigonal symmetry and is fully coherent with hcp�Zr. The consequences of this new zirconium hydride phase on hydride transformation process and stress-reorientation phenomenon are discussed. A first attempt to numerically model the precipitation of this newzirconium hydride phase has been undertaken using the phase field approach.

KEYWORDS: Zircaloy-4, hydride, phase identification, precipitation process, phase field

Introduction

Zirconium alloys are the main structural materials located within the fuel region of pressurized waternuclear reactors �PWRs�. They are used for fuel claddings and channels. During reactor operation, theworking environment of these components is a combination of temperature and reactive conditions such asirradiation, oxidation, and hydrogen pick-up. Hydrogen sources are mainly external, like the hydrogencathodically generated in the corrosion of the cladding by the primary side water coolant �1�, the hydrogendue to the radiolysis of the coolant water, and the H2 gas dissolved in the primary side coolant inpressurized water reactors �2�.

At the operating temperature, the zirconium cladding is expected to absorb hydrogen and to formhydrides when the hydrogen solubility limit is exceeded. The morphology, orientation, distribution, andcrystallographic aspects of hydrides in fuel cladding fabricated from Zr-based alloys play important rolesin fuel performance during all phases before and after discharge from the reactor, i.e., normal operation,transient, and accident situations in the reactor, or temporary storage and permanent storage in a wasterepository. For both fundamental aspects and safety reasons, it is important to understand the precipitationprocess and to predict the influence that various parameters such as temperature, stresses, cooling rates,and microstructure may have. Given the complexity of the precipitation process that may involve differentstructures and various types of anisotropy, an analytic analysis of the precipitation becomes too cumber-some, increasing the interest of computer simulation and modeling at the mesoscopic scale.

The achievement of a realistic mesoscopic modeling should take into account an accurate kinetic,thermodynamic, and structural database in order to properly describe hydride nucleation, growth, andcoalescence as well as hydride interaction with external stresses. Such a database relies on experimental

Manuscript received March 28, 2007; accepted for publication January 21, 2008; published online March 2008.1 EDF R&D, centre des Renardières, Ecuelles, 77818 Moret-sur-Loing Cedex, France.2 Laboratoire de Métallurgie Physique et Génie des Matériaux, USTL, ENSCL, CNRS; Bât C6, 59655 Villeneuve d’Ascq Cedex,France.3

CEMES-CNRS, 29 rue Jeanne Marvig, BP 94347, 31055 Toulouse Cedex 4.

Copyright © 2008 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.

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data that are not always available; this is the reason an accurate structural characterization was undertakenusing transmission electron microscopy �TEM� techniques.

Concerning zirconium hydrides, Gulbransen and Andrew’s �3� X-ray studies of the Zr–H phase dia-gram revealed the presence of two stable zirconium hydrides:

• the �-hydride with a face-centered cubic structure and a stoichiometric formula ZrH1.59–1.64;• the �-hydride with a face-centered tetragonal �fct� structure �c /a�1� and a ZrH1.7–2 formula.

In addition, a metastable �-hydride �ZrH� also having a fct structure with c /a�1 was reported. Inagreement with Vaughan et al. �4� and Ells et al. �5�, it is generally admitted that the hydride plateletsformed from Zr–H solid solutions with low hydrogen content correspond to the �-hydrides. The sameconclusion was reached by Schwartz and Mallett �6� using electron diffraction techniques. Bailey �7�performed a TEM study of the precipitation of zirconium hydrides in alloys with hydrogen content in therange 100 ppm to 1000 ppm. His conclusions about �-hydride formation were similar to those reported byothers authors. The role of the cooling rate on the stability of hydride phases has also been studied byBailey. It was noticed that the metastable �-hydride phase was preferentially produced in rapidly quenchedsamples, whereas a slow cooling rate promotes �-hydride phase formation. This finding was supported byNath and co-worker’s studies �8,9�. Despite of numerous papers on zirconium hydrides characteristics,there is still a lack of knowledge about them; for instance, Bailey �7� observed small needle-like hydrideprecipitates �whatever the cooling rate� from which electron diffraction patterns were difficult to obtainand interpret. From fundamental and technological points of view, the correct identification of these smallneedle-like hydride precipitates �less than 500 nm in length� is crucial since they are likely to form duringthe early stages of hydride precipitation.

In the present work, an accurate phase identification of those needle-like hydrides was carried out.Then, the first steps of the modeling of hydrides precipitation using a phase field approach were under-taken.

Materials

The present investigation was carried out on Zircaloy-4 thin sheets prepared from the cold-pilgeredmaterial to an annealing treatment in the �-phase under vacuum at 625°C for 4 h. Its chemical compo-sition and microstructure are respectively indicated in Table 1 and Fig. 1. Optical micrographs of speci-mens show a fully recrystallized state with a grain size in the range 5 �m to 10 �m. Texture analysis

TABLE 1—Chemical composition of the material used in this study.

Alloying elements, wt.% Impurity elements, ppm

Sn Fe Cr Fe+Cr Nb O C H Ni Si

ASTM 1.2–1.7 0.18–0.24 0.07–0.13 0.28–0.37 — — �270 �25 — �80Tube 1.25 0.20 0.12 0.32 �0.01 1300 136 15 — —

Plate 1.28 0.21 0.10 0.31 �0.005 1265 139 �20 — �40

FIG. 1—Optical micrographs of the recrystallized Zircaloy-4 plate microstructure.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 3

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indicates that most of the basal poles are lying along a 5° to 10° disoriented direction with respect to theradial one.

Experimental Procedures

Pre-hydriding Procedure

Hydrogen charging of the Zircaloy-4 plates was carried out by cathodic hydrogen charging in a 0.1 NH2SO4 dilute solution for several hours at room temperature. For the present study, the hydrogen level isaround 200 ppm. Since the solubility limit of hydrogen at room temperature is quite null �10−4 at. % �10��,hydrides accumulate only at the specimen surface. To redistribute hydrogen in the bulk, a subsequent heattreatment under inert gas at 430°C for 24 h was performed. Two different cooling procedures to roomtemperature were selected: a slow cooling in the furnace �heat treatment F� to produce the equilibrium�-hydride and a fast cooling by water quenching �heat treatment W� to produce the metastable �-hydride.

In order to check if the hydrides obtained by the cathodic charging method were representative ofthose formed by the water corrosion process, a Zircaloy-4 plate corroded in a primary water at 360°C�static autoclave corrosion test� with a hydrogen content about 200 ppm was prepared.

Hydrogen Content Measurement

The amount of hydrogen absorbed by the specimen, in the range of 200–230 ppm, was measured by afusion method. It consists of melting the sample at 1500°C in the presence of argon, and then thehydrogen content is obtained by comparing the conductivity of the argon/hydrogen mixture with the pureargon one �Strohlein HMAT 2500 analyzer�. This method indicates the global hydrogen concentration butdoes not take into account potential concentration gradients in the thickness of specimen.

TEM Sample Preparation

Transmission electron microscopy �TEM� specimens were prepared by punching 3-mm-diameter disksfrom a 0.45-mm-thick Zircaloy-4 plate. These disks were mechanically polished down to a 80 �m thick-ness and then electropolished at 22.5 V and −20°C with a non-acid electrolyte composed of 90 %methanol and 10 % magnesium perchlorate �11�. The electrolyte was carefully selected to avoid anyhydride formation during electropolishing. Complementary investigations were also performed on thinfoils prepared on as-received material with this selected electrolyte. No formation of artifact hydrides dueto electropolishing was observed. Moreover, in order to be totally sure to avoid spurious effects, focusedion beam �FIB� TEM samples were also prepared and examined.

TEM examinations were performed at 300 kV with a Philips CM30 transmission electron microscope.

Electron Microdiffraction Technique [12,13]

Microdiffraction patterns are particular convergent-beam electron diffraction �CBED� patterns obtainedwith a nearly parallel �about 10−4 rad convergence semi-angle� incident electron beam focused on thespecimen. Depending on the specimen, the spot size is in the range 2–200 nm. Experimentally, a micro-diffraction pattern is usually carried out in the following way:

• a CBED pattern is obtained at first with a perfect �uvw� zone axis• then, it is transformed into a microdiffraction pattern by using a 10-�m-diameter C2 condenser

aperture. During this operation, great care must be taken to retain the perfect �uvw� zone axisdirection.

A small spot size was selected in order to get a good spatial resolution, minimizing the likehood ofsignificant thickness or orientation variations within the diffracted area. Nevertheless, this method does notallow determining accurately the diffracted intensities that are required for structure determinations.

Electron Precession Microdiffraction Technique

A limitation in electron crystallography has been the lack of practical methods for collecting intensity data

of sufficient quality for structure determination especially for inorganic crystals. Fortunately, Vincent andyright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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Midgley �14� have devised the precession technique to solve this problem. By precessing a parallel or anearly parallel and focused incident beam at a constant angle around a zone axis in combination with asimilar precession of the beam below the specimen, one obtains the equivalent of the specimen precessionused in a X-ray precession camera. During the precession movement, the reflections are swept succes-sively through the Ewald sphere and the resulting integrated intensities are recorded on a CCD camera.The integration of the intensity reduces the sensitivity to thickness and multiple-beam dynamical effectsare expected to be less than in conventional electron diffraction since the beam is always off the zone axiswhere the strongest dynamical interactions occur. In addition, more reflections are observed.

Electron Energy-Loss Spectroscopy (EELS) Technique

The EELS technique is well adapted to the analysis of elements with low atomic number that are notdetectable using conventional energy dispersive X-ray spectrometry. EELS analysis is most commonlyperformed using the typical edges that result from inner shell ionizations. However, the peaks generated byplasmon excitations �collective oscillations of the valence electrons� can also prove to be useful for thecharacterization of the structure. Woo and Carpenter �15,16� have shown that zirconium hydrides may giverise to plasmon peaks at typical energies. These energies are sufficiently different from those of the parentmetal to be amenable to measurement using a standard magnetic prism spectrometer. The energy shiftcomes from a change in the density of the free valence electrons associated with hydride formation. In thepresent work, thin foils from a Zircaloy-4 plate were used to obtain the low loss regions of the EELSspectra for different hydride phases using a Philips CM20 electron microscope operating at 100 kV andequipped with a Gatan spectrometer.

Results and Discussions

Microstructure of the Zircaloy-4 Alloy After the Heat Treatment W (Water Quenched)

The water-quenched samples containing 200 ppm of hydrogen were examined under scanning electronMicroscope �SEM� as well as TEM. The important features of hydride formation and morphology aredescribed in the following sections.

SEM Examinations—SEM micrographs of hydrogenated specimens examined along the transversedirection reveal the presence of macroscopic hydrides located along the transverse planes �Fig. 2� with asize in the range 1 �m to 10 �m and a thickness in the range 70 nm to 500 nm. Their distribution through

FIG. 2—SEM micrographs of a hydrogenated Zircaloy-4 specimen after the heat treatment W (waterquenched). Note the homogeneous precipitation of small hydrides.

the thickness of the sample indicates that hydrogen has been evenly redistributed within the sample. At lowyright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 5

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magnification, all hydrides seem to have a length rather short and to be oriented mainly along the longi-tudinal direction of the sample, as shown in Fig. 2. Similar conclusions can be drawn from highermagnification observations. Since the microstructure could not be resolved at the level of the scanningmicroscope, a detailed microstructural study was carried out using transmission electron microscopy.

TEM Examinations—TEM examination of water-quenched specimens reveals mainly sharp interfacehydrides with a needle-like morphology as shown on Figs. 3�a� and 3�b�. Most of the hydrides areintragranular with a length in the range 0.1 �m to 1 �m and a width in the range 20 nm to 70 nm. Fewintergranular hydrides have also been observed displaying long needle morphology, as shown in Fig. 4.Their average length and width were about 1.5 �m and 0.1 �m, respectively. They are often surroundedby a “halo” contrast, probably due to coherency strains induced in the matrix �7�. The orientation rela-tionship between the needle-like hydrides and the �Zr matrix was determined from large-angle

convergent-beam electron diffraction patterns and yield hydrides lying along the �112̄0� directions of the

zirconium matrix, as previously reported by Bradbrook et al. �17�, and habit planes parallel to �101̄0��

lattice planes.

Microstructure of the Zircaloy-4 After the Heat Treatment F (Furnace Cooling)

Hydride formation in the slowly cooled samples was examined using SEM and TEM. The main results arepresented in the following section.

FIG. 3—(a) Needle-like intragranular hydrides formed after water quenching. (b) Focusing on a typicalsmall hydride having a sharp interface.

FIG. 4—Long needle hydrides in a water-quenched specimen.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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SEM Examinations—A typical SEM micrograph is given in Fig. 5�a� showing the typical macroscopiclong strings of hydrides precipitated in the longitudinal direction. The hydride length is in the range20 �m to 150 �m and the width in the range 2 �m to 3.5 �m. When the structure of a long string ofmacroscopic hydrides �such as those in Fig. 5�b�� is examined at high magnification, one can often see thatthe hydride string actually consist of many shorter hydrides closely aligned in a slightly different orien-tation.

TEM Examinations—In the slowly cooled samples, in addition to intragranular hydrides, both inter-granular and transgranular hydrides are also observed.

The small intragranular hydrides are presented in Fig. 6. Their size distribution is heterogeneous andthey have a length in the range 80–500 nm and a width between 40 nm and 100 nm. Strong contrastscertainly due to misfit strain are visible �18�. Their density inside the grains seems to be lower than for thewater-quenched specimen.

The intergranular hydrides have a platelet shape and are perpendicular or parallel to the grain bound-

FIG. 5—SEM micrograph at different magnifications showing (a) macroscopic strings of hydrides precipi-tated after furnace cooling; (b) macroscopic hydrides actually constituted by stake of smaller hydrides.

FIG. 6—Intragranular hydrides in a furnace cooled sample.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 7

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aries �Figs. 7�a� and 7�b��. They are larger than the intragranular ones �2 �m� length�5 �m and100 nm�width�500 nm�. The transition from a needle to a platelet shape is probably connected with theemission of dislocations, as illustrated in Fig. 7�a�, and was already noticed by Bailey for instance �7�. Thedislocation density close to the hydrides seems to strongly depend on the precipitate size and morphology.

Few transgranular hydrides running across several �Zr grains �Fig. 8� have been detected in the slowlycooled specimens. Due to the presence of many dislocations in the grains containing theses hydrides, onecan conclude that the elastic strains induced by these precipitates have been relaxed. Note the differencewith the intergranular hydrides of Fig. 7�a�, where a network of dislocations is observed around theprecipitates. On the contrary, the transgranular hydrides are surrounded by many dislocations evenlydistributed in the different involved �-phase grains in Fig. 8, which means that the whole �Zr grains weresubmitted to a plastic deformation.

Finally, a sample charged in hydrogen by a corrosion process in autoclave �primary water at 360°C�

FIG. 7—Intergranular hydrides in a furnace cooled samples. (a) A hydride precipitated almost perpen-dicular to a grain boundary; (b) A hydride precipitated along the grain boundary.

FIG. 8—Transgranular hydride in a furnace cooled sample.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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was also examined in order to check if the hydrides obtained by cathodic charging were actually repre-sentative of those formed by a water corrosion process. Its hydrogen content is similar to that of artificiallycharged samples. Some TEM results about the hydride distribution and morphology of corroded samplesare presented in Table 2. At the scale of our observations �SEM, TEM�, no significant differences can beobserved between corroded specimen and pre-hydrided one. Such a result is not surprising since in bothcases most hydrides precipitated during cooling. Indeed, on the one hand the cathodic charged specimenswere submitted to a heat treatment �430° during 24 h�, leading to a total dissolution of hydride, therefore,hydrides precipitated during the cooling. On the other hand, the corrosion test was carried out at 360°Ccorresponding to a hydrogen solubility close to 140 ppm: in this case almost hydrides precipitate duringthe cooling.

New Hydride Phase Identification

As a first conclusion, whatever the cooling rate or the hydriding method, TEM observations show smallhydrides with a length less than 500 nm and a needle-like morphology. The diffraction patterns of theseneedle-like hydrides did not correspond to any previously known hydride structure. The needle-like hy-drides were therefore studied by electron precession microdiffraction, electron energy loss, andab initio electronic structure calculations. The connected results are reported in this section and this newhydride phase is named � �zeta�. It is important to emphasize that exactly the same hydrides with the samemorphology and the same diffraction patterns were observed in the TEM samples whatever the procedureused to prepare thin foils �electropolishing or FIB�. This clearly indicates that the following observationscorrespond to hydrides formed during the heat treatment and are not due to “artifact” hydrides hypotheti-cally produced during the electropolishing of conventional TEM samples.

Electron Precession Microdiffraction Results—In order to obtain information about their crystallo-graphic structure, electron precession microdiffraction patterns have been performed on the needle-likehydrides. These patterns display weak extra spots with respect to the corresponding patterns from the �Zrmatrix and these extra spots are not in agreement with any of the previously known and reported zirconiumhydride structures. Taking into account this fact, a systematic observation of some typical zone axes

located around the �0001� �Zr zone axis was undertaken. To this aim, the �112̄6� and �11̄04� zone axis

TABLE 2—TEM micrographs showing the similarity of different morphology of hydrides precipitated from slow cooled samples andfrom corroded samples.

patterns �ZAPs� were selected. For each of them, two precession microdiffraction patterns were recordedyright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 9

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�Figs. 9�a�–9�d��, the first one with the electron beam located in the matrix very close to the studiedhydride and the second one with the beam located inside the hydride. The corresponding patterns arearranged in Figs. 10�a� and 10�b� with respect to the 6mm �Zr symmetry so that their mutual orientationsare kept. The same strong “fundamental” spots are displayed by each zone axis from both the matrix andthe hydride. In addition, the patterns from the hydride contain weak extra spots �in Fig. 9�b�, these spots

are marked with circles whose radius increases with the spot intensity�. One notices, on the �112̄6� ZAPs�Fig. 10�a��, that the couple of extra spots located on each side of the �Zr mirrors m1, m2, and m3 showa difference of intensity, which proves that m1, m2, and m3 are no longer mirrors for the hydride. The threeother mirrors �m4, m5, and m6� remain, meaning that the �Zr sixfold rotation axis is transformed into athreefold rotation axis. As a result, the 6mm symmetry, typical of the hexagonal �Zr, is reduced to a 3msymmetry for the hydride. Therefore, this new hydride belongs to the trigonal crystal system and not to thehexagonal one.

In order to deduce the hydride reciprocal and direct lattices, the reciprocal nodes that correspond tothese extra spots were put inside the zirconium reciprocal lattice. As shown in Fig. 11, all of them arelocated on additional �0001�* layers inserted in between the �0001�* �Zr layers at the levels 1 /2,−1 /2,3 /2,−3 /2,5 /2. . .. The corresponding reciprocal and direct lattices are easily deduced from theselayers as well as the following lattice parameters based on the �Zr structure with aZr=0.33 nm and cZr

=0.515 nm �19�:

ahyd = a�Zr = 0.33 nm

chyd = 2*c�Zr = 1.029 nm

Thus, the direct lattice of the hydride is hexagonal and it is two times larger along the c axis than the

FIG. 9—Precession microdiffraction patterns (a) from the �11̄04� zone axis of �Zr matrix; (b) from thestudied small hydride exhibiting extra spots (encircled ones) with respect to the �Zr matrix — these extraspots are not in agreement with any of the previously known and reported zirconium hydride structures; (c)

from the �112̄6� zone axis of �Zr matrix. (d) Diffraction pattern from the hydride.

hexagonal �Zr lattice.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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EELS Results—The amount of hydrogen atoms present in this hydride has been determined relying onthe plasmon EELS results reported previously by Woo and Carpenter �16� and summarized in Table 3. Theneedle-like hydrides yield plasmon energy-loss values in the range 17.3–17.5 eV, whereas the two other�- and �-hydrides give 18,3 eV and 19 eV, respectively �see Fig. 12� in excellent agreement with theprevious results �Table 3� �15,16�. The H /Zr ratio range of the new hydride phase has been determined

FIG. 10—(a) Microdiffraction precession patterns of zone axes around [0001] of �Zr from a small needle-like hydride. The presence of the superlattice spots (encircled diffraction spots, with a big radius for thebrightest ones) with respect to the �Zr matrix reveals a trigonal symmetry. (b) Microdiffraction precessionpatterns of zone axes just around [0001] of �Zr clearly showing a hexagonal symmetry. The lattice vectorsof the matrix have been used to index some axes in both figures.

using the following plasmon energy relationship:yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 11

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FIG. 11—Scheme showing the extra spots putting inside the zirconium reciprocal lattice located in a layerat level 1 /2.

TABLE 3—Reported and experimental measured plasmon energy-loss values of each zirconium hydride phases.

Plasmon energy loss, eV

Reported values �16� Present work

Zirconium matrix 16.80.2 16.7–16.8

�-hydrides �ZrH� 18.30.2 18.3

�-hydrides ZrH1.5−1.66 19.20.2 19

�-hydrides ZrH0.25−0.5 — 17.3–17.5

FIG. 12—EELS plasmon spectrums of Zr, �-hydrides, and �-hydrides; plasmon loss peaks at 16.6, 18.3,

and 17.3–17.5 eV, respectively.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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�E = � p �1�

where �E is the energy-loss value due to plasmon excitations, p is the oscillation frequency of theplasmon, and � Planck’s constant. Equation 1 shows the �E dependence on the p, which has thefollowing expression:

p =4��ee2

me�2�

where �e represent the charge density of the free valence electrons in the system, and e and me are thecharge and mass of the electrons, respectively. Hence, the energy loss is a function of the charge densityof the free valence electrons that we suppose are close to that of the matrix �4 valence electrons 4s2 3d2for each Zr atom�. The presence of H induces a small perturbation to that value. As a result, the plasmonenergy-loss value depends strongly on the number of hydrogen atoms contained in the analyzed phase.Since the new hydride phase displays a lower plasmon energy-loss value than the �- and �-hydrides, itshould contain less hydrogen atoms. According to its plasmon energy-loss value, the composition of thenew hydride phase is located in the range ZrH0.25−0.5. Statistical EELS measurements on many needle-likehydrides have been carried out and most of them display a �E equal to 17.5 eV, so that the ZrH0.5

composition was selected.

Ab Initio Electronic Structure Calculations Results—Selecting the Zr2H composition, we performedelectronic structure calculations in order to determine the arrangement of the hydrogen and zirconiumatoms in the hydride unit cell. This arrangement should be consistent with previous experimental andtheoretical work �20–24�, which proves that, whatever the composition and the crystal structure, thehydrogen atoms always occupy the tetrahedral sites in Zr-H alloys. Taking into account the hydride unitcell, which is two times larger along the c axis than the zirconium unit cell and the H /Zr=1 /2 ratio, wehave to locate two hydrogen atoms into eight tetrahedral sites. Among all the possible arrangements, onlyseven of them give different atomic structures. Starting from the geometrical positions, these seven pos-sible atomic structures were fully relaxed �the unit cell parameters and the atomic positions� using theVienna ab-initio package VASP �25–27�, an electronic structure calculation code based on the densityfunctional theory. The calculations were performed using the same parameters as in Refs. �21,22� withinthe framework of the generalized gradient approximation scheme. The total energy of the seven possiblestructures was carefully calculated and it appears that the � structure illustrated in Fig. 13 has the lowestenergy, and should be, at least at low temperature, the most stable structure for the considered composition.

Simulated electron diffraction patterns—To check the validity of our calculations, the proposed struc-

ture model was used as an input to simulate the theoretical �112̄6� and �11̄04� ZAPs. Dynamical calcula-tions were performed with a version of the JEMS software from Stadelmann �28,29� dedicated to electronprecession. As shown in Fig. 14, the theoretical patterns are in excellent agreement with the experimentalones �Fig. 10�a�� and they support the proposed hydride structure.

To summarize the presented results at this point, a new metastable phase, designated �-hydride phase,was found in the Zircaloy-4 alloy. Whatever the charging methods and cooling rate, this new needle-like�-hydride phase has been detected and identified having space-group symmetry P3m1. The c /a ratio of the�-hydride is approximately 3.12 with estimated values a=0.33 nm and c=1.029 nm, according to �19�.

Discussion

�-hydride Precipitation

This new �-hydride phase is in agreement with the assumption made by previous studies �7,30,31�, whichsuggested the existence of a metastable hydride phase that forms before the �-hydride. The first authormentioning the existence of a fully coherent zirconium hydride phase was Hägg �31�. Unfortunately, hisobservation was not confirmed by subsequent work. Later, Carpenter �30�, who proposed a mechanism forthe precipitation of �-hydride in zirconium, assumed the formation of a metastable cluster of interstitial

hydrogen atoms in the hcp matrix that gives rise to the precipitation of the �-hydride. Finally, Bailey �7�yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 13

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studied the precipitation of zirconium hydride in alloys with various hydrogen content using TEM tech-niques. He pointed out that electron diffraction patterns from thin needle-like precipitates were difficult toobtain and interpret. The identification of our coherent precipitate ��-hydride�, which can be associated tothe metastable cluster of interstitial H atoms guessed by Carpenter �30�, gives support to the precipitationsequence he proposed, which we briefly recall. Following the precipitation of a coherent hydride, the

emission of Shockley partial dislocations with a 1 /3�101̄0� Burgers vector on alternate �0001� planes maychange the stacking in the hydride and produce an fcc-like one �Fig. 15�. A shuffling of Zr atoms shouldachieve the transformation to the face-centered tetragonal �fct� structure of the �-hydrides. During thedeformation process, the precipitate should absorb more H atoms to reach the ZrH composition. It isimportant to point out that the �-hydride is more than simply a metastable cluster of H atoms as imaginedby Carpenter but it constitutes a new phase, since we observed needles as long as 500 nm having the�-hydride structure. Hence, the hydride precipitation process in zirconium alloys should start by thenucleation and growth of the �-hydride, which should transform on growing into the �-hydride accordingto the mechanism proposed by Carpenter �30�. Nevertheless, a direct transformation �−� cannot beexcluded at low cooling rates since Nath et al. �8� demonstrated that �- and/or �-hydride formationdepends strongly on the cooling rate. It is important to mention at this point that the �-hydrides wereobserved on samples cooled to room temperature, we cannot, however, exclude that such phase mayprecipitate at the PWR’s working temperature �350°C�.

Orientation of the �-hydride

According to Northwood et al. �32�, the hydride orientation is dictated by the nucleation process. Once

FIG. 13—Illustration of the �-hydride crystal structure with a space group P3m1 and having the lowesttotal energy determined using ab initio electronic structure calculations.

nucleated, the hydride orientation is maintained during subsequent growth. Many factors may control theyright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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shape and orientation of the precipitates: interface excess-energy anisotropy, elastic anisotropy, and finallyinterface mobility anisotropy. Furthermore, in presence of external stresses, the elastic interaction betweenthe precipitation-induced strain and the applied stress may have an influence on the orientation of theprecipitates. TEM observations have shown a significant elastic strain field characterized by a halo ofcontrast line around these needles-like �-hydrides, whereas �- or �-hydrides often have an array of dislo-cation surrounding them �Fig. 7�a��. This fact probably means that the elastic strain energy concentratedaround the precipitates has been partially or totally relaxed by the plastic deformation of the matrix.

FIG. 14—Simulated microdiffraction patterns of zone axes around [0001] of �Zr obtained from the �Zr.Note the presence of the same superlattice spots than the ones obtained experimentally (encircled diffrac-tion spots, with a big radius for the brightest ones) indicating a trigonal symmetry. The lattice vectors ofthe � phase were used to index the zone axes.

FIG. 15—Scheme illustrating the passage of partial dislocation with a 1 /3 �101̄0� Burgers vector on

alternate (0001) planes to form, finally, an fcc-like structure.yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 15

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Hence, an external stress may interact strongly with the local elastic strain around �-hydrides �withpossible reorientation of the hydrides�, while the interaction with �- or �-hydrides seems mosthypothetical.

�-hydride Precipitation Modeling

Work by Previous Researchers

It is well known that hydride precipitation is influenced by temperature and stress fields. Kim et al. �33�,for instance, produced magnificent micrographs of hydrides at the tip of a crack following the iso-tensile-stress lines. Domizzi et al. �34� showed that a cold spot allowed the growth of a blister. These are just acouple of examples that illustrate that modeling hydride precipitation may address industrial concerns suchas hydride reorientation during transportation, delayed hydride cracking in a cask storage, and blistergrowth in a spalled rod �see Chung �35� for an overview�.

Numerous models were developed to describe these phenomena. Their roots can be found in the worksof Sawastzky �36�. They have in common two major hypotheses: �i� hydrogen fluxes are generated bystress field and temperature gradients �see, for instance, Sagat et al. �37�, Varias et al. �38�, Shi �39� or Puls�40��; �ii� only the hydride growth is described in these models and the influence of the external parameterson the nucleation stage is not taken into account. On the contrary, some authors pointed out the importanceof the nucleation stage �41,33� to redistribute the hydrides. Chan �41�, for instance, assumes that theorientation of the hydrides is kept constant through the growth process and dictated by nucleation. Hedescribes the influence of an external stress in a relatively simple way by adding a P�V term in the criticalactivation energy �P is the hydrostatic component of the stress tensor and �V the expansion due to thehydride�. Although useful to describe the particular situations for which they were developed, these modelslack generality in a sense, and they are not able, for instance, to explain the experimentally observedreorientation of hydrides under an applied homogeneous stress �35�.

Given the hexagonal symmetry of zirconium alloys and the fact that �-hydrides are coherent with thematrix, the complete description of hydrides’ morphology and reorientation under stress should require oneto take into account the anisotropic elastic interaction between precipitation-induced strain and the appliedstress, the anisotropy of the precipitation-induced strain, the anisotropy of the excess free energy ofinterfaces between the Zr matrix and hydrides, and probably the anisotropy of interface mobility, amongother possible effects. Given the complexity of the task, analytical models seem a priori excluded and thephase field modeling, which is able to encompass the various effects mentioned, appears as an appealingway to model the precipitation.

Generalities of Phase Field Method

In a phase field model, the microstructure is described by a set of order parameters that depend on spatialcoordinates and time. Two different types of order parameters are considered, one that has to obeyconservation laws �conservative parameter� and the other that is not submitted to any constraint �non-conservative�. In the present situation, the conserved parameter is the hydrogen molar fraction or compo-sition, c�r , t�. The non-conserved parameter is ��r , t�. It is related to the crystal structure of the solidsolution �supposed to have the pure zirconium symmetry� and to that of the �-hydride �trigonal symmetry�;thus, it is called the structural order parameter. It is equal to zero in the hydrogen solid solution and isstrictly positive in the hydrides �supposed, with no loss of generality, equal to 1�. The knowledge of c�r , t�and ��r , t� at any time enables us to follow the evolution of the microstructure.

In the phase field approach, a kinetic equation is written for each order parameter: the compositionevolution equation is often referred to as the Cahn-Hilliard equation 2 �42�, and the long range orderparameter evolution equation is referred to as the time-dependent Ginzburg-Landau equation or as theCahn-Allen equation 1 �43�,

���r,t�= − L

�F+ ��r,t� �3�

�t ���r,t�yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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�c�r,t��t

= M�2 �F

�c�r,t�+ ��r,t� �4�

where M and L are the diffusion mobility and ordering kinetic coefficient, respectively, ��r , t� and ��r , t�are the Langevin noise terms associated with � and c, respectively, and F represents the total free energyof the system. ��r , t� and ��r , t� represent the fluctuations terms. In order to account for nucleation in ametastable system, it is necessary to consider fluctuations in the local driving forces for the reaction tooccur. In the following, dealing with growth, these terms are neglected.

In the phase field formalism, F is a functional of the order parameters. In evaluating the free energy,three effects are incorporated:

• non-ideal thermodynamics of the solution;• gradients in c and �’s;• elastic interaction between transformed areas of the microstructure.The non-ideal thermodynamics of the solution and the gradients in c and �’s are taken into account in

the local “chemistry” �Fchem� term 6. The elastic interaction is taken into account in the Eelas term 7.

F = Fchem + Eelas �5�

Fchem = �Vm

� � � fhom�c�r,t�,��r,t�� +�

2����2 +

�

2��c�2 dV �6�

Usually, fhom�c ,�� represents the free energy volume density of a homogenous phase and it is approxi-mated by a Landau expansion, which reproduces qualitatively the correct thermodynamic behavior of thesystem. Interfacial energies are accounted for by adding terms proportional to ��c�2 and ����2.

For the elastic contributions 7, the Khachaturyan Green’s function solution �44� for homogeneouselasticity is used. Assuming a homogeneous elastic medium �i.e., elastic constants are the same in the solidsolution and in the precipitates�, Eelas has a relatively simple expression in Fourier space:

Eelas =Vm

2�q�0

B�q���q��*�q� − Vp�ija �ij

0 �7�

with �ij0 the stress-free self-strain of the precipitate that measures the macroscopic deformation of a piece

of matrix that transforms into a hydride in the absence of external stresses. For the � phase, it wasdetermined from ab initio calculations, and reads �ij

0 =�ii0�ij, with �11

0 =�220 =9.4�10−3 and �33

0 =4.1�10−2.�ij

a is the applied stress �if any�, Vp is the total volume of precipitate, and q is a vector of the reciprocalspace limited to the first Brillouin zone of the spatial grid. B�q� carry all information of the elasticproperties of the hydride/Zr system.

The parameters entering the expression of fhom were fitted in order to reproduce the experimentalsolubility limit at 600 K, the � and � coefficients were chosen in order to give isotropic interfacial excessfree energy of about 100 mJ /m2. The interface mobility L was supposed higher than the atomic mobilityM chosen to reproduce the experimental diffusion coefficient at 600 K.

Results and Discussion

Using the model with the previously described parameters in a 2D simulation domain, we studied the

growth of an initially circular precipitate located either in the basal or in a prismatic �101̄0� plane im-mersed in a saturated solid solution containing 2 % atomic H at 600 K. A series of snapshots of the resultsis shown in Fig. 16. The simulations were performed on a square grid containing 128 by 128 points atT=600 K. In Fig. 16�a�, the growth of a disk in the basal plane was performed turning on �top panel� oroff �bottom panel� the elastic contribution to the free energy. Comparison of both cases shows growth isdelayed in the presence of the elastic effects but is qualitatively the same in each situation: the initial diskremains circular during the simulation. The weak deviation from a circular shape at the end of thesimulation, more visible when the elastic effects are turned off, is probably due to non-physical effectscaused by the relatively small size of the simulation box.

The situation is slightly different when the growth takes place in the prismatic plane, the disk becom-

ing narrow parallel to the c axis as time increases �Fig. 16�b��. This behavior can be qualitatively under-yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

ZHAO ET AL. ON CHARACTERIZATION OF ZIRCONIUM HYDRIDES 17

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stood. For symmetry reasons, an isotropic elastic response is expected in the basal plane and a hinderedgrowth parallel to the c axis, which is the stiff direction and along which the highest value of thestress-free strain is reached.

In three dimensions, an initially spherical precipitate should become a revolution ellipsoid with asymmetry axis and a narrow dimension parallel to the c axis. This kind of shape is partially at odds with

the observed needles with a prismatic �101̄0�-habit plane. This means that other ingredients not includedin the present version of the model may play an important role in the control of the precipitate shape.

Ab initio calculations are currently undertaken to investigate the eventual anisotropy of the interface

excess free energy that may favor a growth parallel to the compact �112̄0� directions. Another possibility,more difficult to compare with experimental observations, is the occurrence of an interface mobilityanisotropy that could favor a faster growth along the compact directions. Another point that may bechecked with the present model is the influence of an externally applied stress or the use of an inhomo-geneous elastic model to describe the matrix and the precipitates.

Our results differ strongly from those of Ma et al. �45� who, when modeling the precipitation of�-hydrides, obtained precipitates similar to ours but with the narrow direction in the basal plane andperpendicular to the compact axis, which gives to the precipitates the aspect of needles when they areprojected on the basal plane. In this case, the morphology of the precipitates is only due to elastic effectsassociated to the stress-free strain tensor of the �-hydride that is different from that of the �-hydride. The�-hydride having a fct structure, one may question, however, the validity of the coherent precipitationassumption that constitutes the starting hypothesis of the elastic models describing strain effects inducedby precipitation.

In spite of the open issue concerning the shape of the hydrides discussed so far, the present modelseems promising in order to reach a better understanding of the complex interactions between appliedstress and hydride reorientation. Keeping the coherency with the matrix, �-hydrides will be able to interact

FIG. 16—(a) Growth of a disk in the basal plane taking (top panel) and without taking (bottom panel) intoaccount the elastic effects. The snapshots were taken at t�25 000, 50 000, 75 000, and 100 000 �t, with�t�0.1t0�3.3�10�10 s. The bar below on the left represents 10 nm. (b) Growth of a disk: a prismatic{10-10} plane taking (top panel) and without taking (bottom panel) into account the elastic effects. Thesnapshots were taken at t�25 000, 50 000, 75 000, and 100 000 �t, with �t�0.1t0�3.3�10�10 s. Thebar below on the left represents 10 nm. The c axis is horizontal and the a axis is vertical in this case.

with the external stress through the precipitation-induced strain. This interaction should in principle van-yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.

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ish, if the precipitate becomes incoherent by emitting misfit dislocations that will relax the elastic energyassociated to the precipitation.

Conclusion1. A new metastable zirconium hydride with formula Zr2H, designated as �-hydride, was identified

and characterized in a Zircaloy-4 alloy submitted to hydrogen cathodic charging and autoclavecorrosion. This new hydride was observed on TEM samples prepared by electropolishing proce-dures as well as on samples produced using the FIB technique. The hydride phase with latticeparameters a=0.33 nm and c=1.029 nm has a hexagonal lattice. It belongs to the trigonal crystalsystem with space group P3m1. Its crystal structure was obtained by combining TEM experimen-tal results and theoretical calculations. Thanks to electron precession microdiffraction, it waspossible to identify slight differences of intensity between some weak extra-reflections and todeduce the hexagonal direct lattice and the trigonal crystal system of the hydride. The hydrogencomposition of the hydride was inferred from observations of plasmons peaks on EELS patterns.Finally, a structural model of the hydride was deduced from ab initio structure calculations and itsvalidity was confirmed by kinematical simulation of the diffraction patterns. We feel that this workis a nice example of structure determination involving complementary experimental and calculatedresults.

2. Based on this new �-hydride phase, the hydride precipitation process described by Carpenter �30�seems appealing. It consists on the nucleation and growth of the �-hydride phase whatever the heattreatment submitted to the alloys. Then, according to the cooling rate, the �-hydride phase trans-forms to give rise either to the metastable �-hydride phase �fast cooling rate� or to the stable�-hydride phase �slow cooling rate�. Because of the presence of a strong strain field around the�-hydride, it is likely that this new hydride phase should play an important part in the stress-reorientation phenomenon.

3. Using a phase field model, a 2D simulation of the growth of an initially circular precipitate located

either in the basal or in a prismatic �101̄0� plane has been carried out. The main simulation resultsare:

• whatever the simulation time, an initial disk remains a disk in the basal plane either with orwithout elastic effects;

• whereas in prismatic plane and in the presence of elastic effects, the disk becomes thinner in thec-direction as the time increases.

To obtain a needle-like shape, other ingredients not included in the present version of the model shouldplay an important role. Further studies investigating the interface excess free energy anisotropy, theinterface mobility anisotropy, and the inhomogeneous elasticity role in precipitate shape will be under-taken.

References

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yright by ASTM Int'l (all rights reserved); Sun Mar 6 23:26:14 EST 2011nloaded/printed byur Moses Thompson Motta (Pennsylvania State Univ) pursuant to License Agreement. No further reproductions authorized.