These different approaches are in fact similar, as shown by Sutton and Balluffi [6], and Kelly and Zhang [11]. They all result in the existence of pairs of diffraction vectors, the difference of which, ∆g, is perpendicular to the interface plane. Zhang and Purdy [4] showed that this property results directly from the properties of the direct and reciprocal O-lattices (or CSL). Indeed, since the reciprocal O-lattice is generated by all ∆g vectors, and since the interface must be parallel to a dense O-lattice plane, the interface is necessarily perpendicular to a set of ∆g vectors. This has been observed experimentally either in the diffraction mode (Zhang and Purdy [12], Savva et al [13]) or via the observation of Moiré fringes parallel to the interface (Duly et al [14], Luo and Dahmen [15]). Except for the ∆g concept, all theories refer to the direct lattices of the two phases. For instance, in one of the most recent versions of the edge-to-edge matching model, Zhang et al [16] propose to determine the best orientation relationships and interface planes by (a) identifying dense rows with similar atom spacing in the two phases, (b) searching for dense planes with similar inter-planar spacing containing these rows, (c) putting these planes and the dense rows parallel to each other (a small rotation of the dense planes around the dense rows is allowed at this step) and (d) putting the interface plane through the coinciding dense rows. These theories are however difficult to use for fast analysis in the course of electron microscopy observations. A new method that allows one to work in the reciprocal space only, i.e. using electron diffraction patterns, is thus proposed in this paper. It is in fact an extension of the ∆g method, able to predict the best orientations (OR) relationships and interfaces between Ti (hcp structure) and two hydride phases (one fcc, the other slightly tetragonal) which have been observed recently by transmission electron microscopy (TEM). Note that OR and interfaces have never been extensively investigated in the fcc/hcp system, according to Zhang and Kelly [5]. The different paths leading to the transformation of titanium into titanium hydride, and the compensation of the internal stresses generated by the phase transformations, are then discussed on the basis of additional experimental observations.

Ti Hydrides, a Review Metallic hydrides are very specific compounds that can be obtained in the solid state by the fast diffusion of hydrogen atoms in the metallic lattice. They are present in rather large quantities in commercial Ti and Ti alloys but their role is rather controversial. Indeed, hydrides are often considered as hard and brittle precipitates inducing rapid failure of the matrix, whereas other studies showed that they can be deformed plastically (Irving and Beevers [17], Guillot et al [18], Chen et al [19], Conforto et al [20]). A recent study has shown that the acid etching aimed at increasing the surface roughness of Ti dental implants (to improve bone anchoring) generates an hydride layer which is ductile enough to accommodate the penetration of an indentor [20]. Hydride phases play thus a very important role in the physical properties of Ti and Ti alloys for various applications. However, the difficult detection of hydrogen makes it difficult to identify Ti-hydride phases, which can lead to important misinterpretations. For instance, a so-called fcc Ti phase has been reported in interfaces (Banerjee et al [21]), after mechanical grinding of Ti (Chatterjee and Gupta [22], Manna et al [23]) and in Ti/x multilayers (Jankovki and Wall [24], Van Heerden et al [25]). However, this fcc Ti phase may in reality be an hydride phase according to several observations (Banerjee et al [21], Kasukabe et al [26], Casanove et al [27], Van Heerden et al [25]). Several hydride phases have been identified in the past, corresponding to various Ti/H ratio. The most frequently observed ones are the tetragonal TiH (a = 0.421 nm, c/a = 1.093) and the fcc TiH2-ε (a = 0.440 nm, for ε ranging between 0 and 0.1).

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The orientation relationships (OR) between Ti and tetragonal TiH have been investigated first by Numakura and Koiwa [28]. These authors have reported two OR, hereafter called OR1 and OR2, that are described in details in section 4. TiH in OR1 has also been observed in high resolution by Bourret et al [29], and TiH in OR2 has been reported by Woo et al [30]. No explanation has been provided till now for the high-index {02 2 5} or {02 2 7} interface planes, and for the 4° angle between the {0001} and {111} compact planes, observed in OR2. Much less information is available for TiH2-ε precipitates, although Ti/TiH2-ε interfaces in OR1 have been reported by Banerjee et al [21] and Zheng et al [31]. No other OR has been reported in this system, to the author’s knowledge.

Experimental Procedure All observations were made in commercially-pure titanium samples submitted to a sand-blasting (~ 250 µm-sized Al2O3 particles) followed by an acid (HCl/H2SO4 hot solution) etching treatment, called SLA [20]. The acid etching releases large amounts of hydrogen ions that can easily penetrate into the substrate bulk. This results in the formation of a several microns-thick fcc TiH2-ε hydride layer. The concentration of hydrogen decreases at the transition zone between the TiH2-ε layer and the Ti substrate, where various precipitates of TiH2-ε and TiH nucleate and growth. Some of the observations reported in this article were made at the transition zone, and others were made in the pure TiH2-ε layer. Cross-sectional samples were prepared by mechanical polishing and ion milling, and observed by transmission electron microscopy (TEM). The instruments were a Philips EM-430, operated at 300KV, and a Jeol 2010HC, operated at 200KV.

Orientation Relationships and Interfaces Rules of Orientation A set of very simple rules can be established on the basis of the different models described in introduction, which yield favorable orientation relationships and interfaces. They are based on the analysis of lattice node positions at the interface, with no consideration to the detailed transformation process (geometrical matching approach). The fact that dense rows always lie along the intersections of dense planes, i.e. dense rows are zone axes of the reciprocal lattice, is used throughout this analysis. Although these rules do not replace a more rigorous analysis by the Bollman theory, they are very convenient for a first and rapid investigation in the electron microscope. They can be expressed as follows: (i) The interface should contain parallel dense atomic rows of the two phases. In the reciprocal lattice, this means that two parallel zone axes should be observed when the interface is edge on. (ii) The distances δ between these dense rows should be equal or in a simple ratio. According to fig. 1a,b, this means that dense planes containing these dense rows should be continuous across the interface, namely that diffraction spots should be aligned perpendicularly to the interface. This corresponds to the ∆g condition mentioned in the introduction. (iii) The distance between adjacent atoms of these dense rows should be equal or in a simple ratio. According to fig. 2, this condition requires the existence of at least another pair of dense rows (or zone axes) verifying the same properties (i) and (ii) above. Fig. 2a illustrates the rather loose fit when the distances are in a simple ratio, whereas fig. 2b illustrates the almost perfect fit

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when the distances are equal. In both cases, the interface contains additional rows also verifying (i) and (ii). The angle between the two main pairs of rows is called θ.

Figure 1. Schematic description of dense planes and corresponding diffraction patterns across a

favorable interface. a,b) general case. c,d) case of a coincidence along the y axis.

Figure 2. Schematic description of atomic positions in a low-energy interface. a) loose fit. b) perfect fit.

Under such conditions, the most general condition to obtain a “good” interface is: Condition (a): “A good interface should contain two sets of parallel zone axes of the two phases,

and be perpendicular to the ∆g vectors of the diffraction patterns taken along them.”

It can be noted that condition (a) implies that the interface plane is a dense plane of the two structures. However, as illustrated in fig. 2, dense rows and dense planes are not necessarily those with the lowest indexes. It can also be noted that the two pairs of dense rows must make the same angle θ in the two phases. θ is then restricted to simple values common to the two structures, most often θ = 90°. In addition, one can note that the condition on ∆g vectors is straightforwardly satisfied in the case of fig. 1c,d, namely when the interface contains two coinciding g vectors along direction y. The only condition to find this situation is that the interface must be a dense plane (y,z) containing two coinciding diffraction vectors along y. As a matter of fact, direction z which is at

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the intersection of two dense planes is necessarily a dense row, namely a zone axis of the two structures. Then, conditions (a) can sometimes be replaced by one of the two following alternative ones: Condition (b): “If the OR involves two parallel zone axes that are also a direction of coincidence

of the two reciprocal lattices, the interface should be a dense plane perpendicular to the ∆g vectors of the diffraction pattern taken along this direction.”

Condition (c): “If the OR involves two sets of parallel zone axes, perpendicular to each other,

which are also directions of coincidence of the reciprocal lattices, the interface should be parallel to these two directions.”

Since two perpendicular zone axes are generally not observable in TEM (zone axes must be close to the normal to the sample plane), it is generally necessary to construct the stereographic projections of the two crystals, in order to complete the information necessary for the above analysis. These rules are now tested on several experimentally observed situations. Ti/Ti-hydride Interfaces Four different orientation relationships (OR) corresponding to four different interface planes have been observed at Ti/TiH and Ti/TiH2-ε interfaces. Some ORs can occur for both types of hydride precipitates, but others have been observed for one of them. The two first ORs, referred as 1 and 2, are those described by Numakura and Koiwa [28] for TiH precipitates, but the others are new. Data concerning the interplanar distances involved in these ORs are listed in table 1.

Table 1.Interplanar spacings in Ti and Ti hydrides Ti (hcp) TiH2-ε (fcc) TiH (fct, c/a = 1.09)

planes spacings (nm) planes spacings (nm) planes spacings (nm)01 1 0 0.256 111 0.255 111 0.251 0002 0.234 002 0.230 1 1 01 0.224 200 0.221 200 0.210 1 1 02 0.173 022 0.156 11 2 0 0.148 220 0.156 220 0.149 11 2 2 0.125 311 0.133

OR1: Many lath-shaped precipitates exhibit the first orientation described by Numakura and Koiwa [28] and are described in table 2. Fig. 3a shows a TiH precipitate embedded in the Ti matrix. The interface plane is (10 1 0) // ( 1 10) and the main growth direction is [ 1 2 1 0] // [110]. Fig. 3d,e shows the superimposed diffraction patterns in the zone axes [0001] // [001] and [ 1 2 1 3]d

1 // [112], respectively. There is a fairly good coincidence between two pairs of diffraction vectors contained in the interface plane, namely [ 1 2 1 0] ≈ [220] in (d) and [ 1 2 1 2 ] ≈ [22 2 ] in (e), as a result all the ∆g vectors are perfectly aligned in the direction perpendicular to the interface. Accordingly, one can immediately verify that the interface obeys condition (a). Several superstructure spots of the ordered tetragonal structure can be observed, e.g. [110]. The supplementary spot noted x in fig. 3e is however not a superstructure spot of the TiH phase, but a superstructure spot of the hcp titanium, of coordinates 1/2[ 1 010]. A dark field with this spot 1 The subscript d refers to a direction of the direct hcp lattice, when different from a direction of the reciprocal lattice.

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shows that the corresponding diffracting areas are thin layers located at the Ti/TiH interface (fig. 3c, to be compared with a dark field over the [11 1 ] spot of TiH in fig. 3b). This corresponds to a local ordering where every second dense planes parallel to the interface of the hcp Ti phase contain hydrogen in solution. Since TiH exhibits the same kind of order, the ordering of the hcp phase can be considered as a precursor of the Ti-TiH transformation.

Figure 3. TiH precipitates in OR1. a) dark field obtained with the [ 1 101] spot of Ti. b) dark field obtained with the [ 1 1 1] spot of TiH. c) dark field obtained with the ½[ 1 010] spot noted x. d and e) diffraction patterns across the precipitates and the substrate, along respectively [001]//[0001] and [112]//[ 1 2 1 3]d.

Fig. 4a shows precipitates with same interface plane and growth direction as the preceding ones. The corresponding diffraction patterns are similar to those shown in fig. 3 except that the coincidences [ 1 2 1 0] ≈ [220], in (c), and [ 1 2 1 2 ] ≈ [22 2 ], in (d), are less perfect, as a result the other diffraction spots are not perfectly aligned in the direction perpendicular to the interface plane. One can however consider that condition (a) is still approximately satisfied. According to table 1, precipitates in fig. 4 are made of the fcc TiH2-ε phase. OR2: Since nothing new has been obtained concerning this orientation reported for TiH precipitates by Numakura and Koiwa [28], we just recall the main orientation relationships: [ 1 2 1 0] ≈ [220], as in the preceding orientation, and interface plane (20 2 5) // (1 1 0). Note however that the alignment of the ∆g vectors in the direction perpendicular to the interface plane (fig. 3 of [28]) was not mentioned by the authors. OR3: This new orientation relationship has been observed by Conforto et al [20], and more recently in the case of the very thin precipitate of the TiH2-ε phase shown in dark field in fig. 5a.

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The interface plane and the main growth direction have been deduced from observations under various tilting conditions, to be respectively (0001) // (1 1 2) and [ 1 2 1 0] // [110]. For geometrical reasons, no diffraction pattern could be obtained with the interface plane parallel to the electron beam, in order to check condition (a). However, two sets of coinciding diffraction vectors, perpendicular to each other, can be seen in fig. 5c: [ 1 2 1 0] ≈ [220], as in the two preceding orientations, and [ 1 010] ≈ [ 1 11]. Since these two directions lie in the interface plane, rule (c) is obeyed.

Figure 4. TiH2-ε precipitate in OR1. a) dark field obtained with the [10 1 0] spot of Ti. b) dark field obtained with the [ 1 1 1] spot of TiH2-ε. c,d) diffraction patterns over the precipitate and the substrate, along respectively [001]//[0001] and [112]//[ 1 2 1 3]d.

OR4: This new orientation is close to OR2, but clearly different, because i) it concerns a large TiH2-ε precipitate instead of a small TiH one, and ii) the interface plane (seen edge-on in fig. 6b) is ( 1 01 1 ) // ( 1 11). The alignments of the ∆g vectors in the direction perpendicular to the interface plane, and favored by the near-coincidence [ 1 2 1 0] ≈ [220] (same as in the three preceding orientations) can be seen in fig. 6c.

Table 2. Orientation relationships between Ti and Ti hydrides OR1 OR2 OR3 OR4 common coincidence

[220]≈[ 1 2 1 0]

coincidences ⊥ common one

[002] ≈ [0002] [1 1 0] // [10 1 0]

[1 1 1 ] ≈ [10 1 0] [1 1 2] // [0002]

[002] ≈ [ 1 011]

Interface plane (1 1 0) // (10 1 0) (1 1 0) // (20 2 5) (1 1 2) // (0001) (1 1 1 ) // (10 1 1)

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Figure 5. TiH2-ε precipitate in OR3. a,b) dark field obtained with the [ 1 1 1] spot of TiH2-ε , where picture (b) is an enlargement of (a). c) diffraction pattern over one precipitate and the matrix, along zone axis [1 1 2]//[0001], i.e. when the interface is in the picture plane.

Figure 6. TiH2-ε precipitate in OR4. a) bright field, inclined interface. b) bright field, edge-on interface. c) diffraction pattern corresponding to (b), across the interface, and along zone axis [1 1 2]//[ 1 012]d.

Discussion of the Observed Ti/Ti-hydride OR and Interfaces All OR can be deduced from each other by a rotation around the common direction of coincidence (or near-coincidence) [ 1 2 1 0] ≈ [220]. A partial agreement with the rules established in §4-1 has been sometimes mentioned. This is now investigated in more details.

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Considering the existence of the common coincidence [ 1 2 1 0] ≈ [220] along two parallel zone axes, conditions (b) or (c) can be tentatively used to determine the best interfaces. It is just necessary to either check the ∆g conditions along the common zone axis [ 1 2 1 0] // [110], and apply rule (b), or find another direction of coincidence perpendicular to the first one, and check if rule (c) can be used. Atoms have the same average spacing of 0.297nm along the direction [ 1 2 1 0] // [110]. To check conditions (b) or (c), it is necessary to analyze the diffraction patterns along the zone axis [ 1 2 1 0] // [110]. These diffraction patterns could not be observed in the above examples. They are thus represented schematically in fig. 7, in the particular case of fcc TiH2-ε precipitates. - For OR1, fig. 7a shows that there is a near-coincidence, [0002] ≈ [002], along a direction which is also a zone axis of the two phases, and which is perpendicular to [ 1 2 1 0] ≈ [220]. According to rule (c), the best interface is then (10 1 0) // (1 1 0), namely that observed experimentally. One can subsequently verify that that several ∆g vectors are perpendicular to the interface plane, not only on fig. 7a, but also in figs. 4c,d. Since the coincidences [ 1 2 1 0] ≈ [220] and [0002] ≈ [002] are the most closely satisfied with TiH (see table 1), the interface energy is probably the lowest for TiH precipitates. All atoms in one side of the interface fit with those in the opposite side (fig. 7b). - For OR2, fig. 7c shows that there is no second coincidence that would allow one to use condition (c). However, one can note that several ∆g vectors are parallel to each other, and perpendicular to (10 1 3) // (1 1 0) which is accordingly a favorable interface plane. This plane is close to (20 2 5) // (1 1 0) observed by Numakura and Koiwa [28]. The occurrence of such a complex interface plane, and the presence of a 4° angle between (0001) and (111) close packed planes, are thus readily explained. It is subsequently verified that the interface plane goes through the zone axis direction [ 3 032]d 2// [001]. The direction of the direct lattice [ 3 032]d is not very dense, as the corresponding distance between atoms is as large as 1.77 nm, namely 4 times that between adjacent atoms along [001] (fig. 7d). For this reason, and although there is a 1/1 atomic correspondence along [ 1 2 1 0] // [110], the interface plane (10 1 3) is not very dense too. This shows that the best OR and interface plane are the result of a compromise leading to the “best possible” solution. - For OR3, fig. 7e shows that there is a second direction of near-coincidence, [10 1 0] ≈ [1 1 1 ], perpendicular to [ 1 2 1 0] ≈ [220], which is also a zone axis direction of the two phases. According to condition (c), the best interface is (0001) // (1 1 2), as observed experimentally. Note that the periodicity of atomic fit along the dense row [10 1 0] // [1 1 1 ] is 6 times larger than the interatomic distance between (1 1 1 ) and (10 1 0) planes, namely 1.53 nm (fig. 7f). - For OR4, fig. 7g shows that there is a direction of coincidence [ 1 011] ≈ [002]. However, since the direction [ 1 011] of the reciprocal lattice is not a dense direction of the direct hcp lattice, condition (c) cannot be used. However, one can notice that several ∆g’s are perpendicular to (10 1 1) // (1 1 1 ) which is, according to condition (b), a favorable interface plane. This interface plane is that observed in experiments. It is subsequently verified that [ 1 012]d 3// [1 1 2] are dense directions of the direct hcp lattice. The periodicity of atomic matching along [ 1 012]d // [1 1 2] is 2 One can check that [ 3 032]d yields a nil scalar product with [10 1 3] and [ 1 2 1 0]. 3 One can check that [ 1 012]d yields a nil scalar product with [10 1 1] and [ 1 2 1 0].

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12 times the interatomic distance between (2 2 4) planes, namely 1.08 nm (fig. 7h). This analysis confirms that OR4 is definitely different from OR2, and that the coexistence of these two OR is justified by energetic reasons.

TiH-TiH2-ε Transformation and Hydride-hydride Interfaces Several types of hydride-hydride interfaces develop, during the transformation from TiH into TiH2-ε, and during the coalescence of TiH2-ε precipitates. Fig. 8 shows an hydride precipitate during its transformation from the TiH phase to the TiH2-ε one. Fig. 8a is a diffraction pattern taken along the zone axis [0001] // [001], which corresponds the superposition of figs. 3d and 4c. It indicates that both phases are present, and that TiH transforms into TiH2-ε keeping the same OR1 orientation with the matrix. No intermediate phase has been observed between TiH and TiH2-ε. Fig. 8 also shows dark fields taken with the [020] spot of TiH, in (b), and the [020] spot of TiH2-ε, in (c). The TiH phase is concentrated near the interface with the Ti matrix, whereas the interior is made essentially of TiH2-ε. The remaining TiH phase has the shape of many small clusters with no preferential interface plane with the surrounding TiH2-ε. This indicates that Ti-TiH2-ε interfaces probably have a very low energy. The presence of a remaining TiH layer is consistent with a density of hydrogen atoms decreasing from the interior of the hydride precipitate to the Ti matrix.

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Figure 7. The four OR seen along [110]//[ 1 2 1 0], in the reciprocal space, and in the direct space (where the misfit has been taken equal to zero). The most favorable interface planes are perpendicular to ∆g vectors. Full circles in the projected structures correspond to Ti atoms in the figure plane, and open circles correspond to Ti atoms at height ±1/2[110] = ±1/6[ 1 2 1 0]. Hydrogen atoms are not represented.

The misfit along the main directions of coincidence increases during the TiH-TiH2-ε transformation (tables 1 and 2). This generates supplementary stresses that are partly relaxed by a dislocation mechanism described elsewhere (Conforto et al, to be published). Other mechanisms contributing to an optimum spatial distribution of misfit stresses are described in the next section. When TiH2-ε precipitates have grown sufficiently to coalesce, new interfaces develop between the different variants of each OR, and between different OR’s. These interfaces should also obey the rules discussed in §4-1. Fig. 9 shows several TiH2-ε precipitates with different OR, separated by parallel interface planes seen edge-on. Three families are present, noted A, B, and C. They are imaged in dark field in figs. 9 a, b, and c, respectively. Precipitates A and C are two variants in OR3 with the Ti substrate, and precipitates B are close to OR1. This configuration has been described in details by Conforto et al [20]. Here, it is sufficient to note that the diffraction pattern taken over the three families exhibits rows of spots perpendicular to the interface (fig. 9d). At least one of the conditions on ∆g vectors imposed by rule (a) is accordingly satisfied.

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Figure 8. TiH2-ε precipitate containing some amount of TiH at its interface with the Ti matrix. a) diffraction pattern along zone axis [001]//[0001]. b) dark field with the [020] spot of TiH. c) dark field with the [020] spot of TiH2-ε. d) diffraction pattern over an area containing the three variants of similar precipitates.

Discussion Validity of the Method The practical method used in this study to determine the best OR and interface planes between two different phases appears simple and efficient. It has been able to predict the 4 different situations observed in the same sample. In particular, the origin of OR2, which involves an unexpected misorientation angle of 4° between the close packed planes of the two structures, has been explained straightforwardly. The occurrence of a high-index interface plane has also been explained considering that interfaces must be parallel to dense planes, but not necessarily very dense ones. In the same way, dense rows fitting with each other can be moderately dense, and the atomic fit along them can be rather loose, as shown in fig. 7d, f, h. The method is sufficiently accurate to make a clear distinction between OR2 and OR4, that have markedly different interface planes, although they can be deduced from each other by a rotation of only 5°. The occurrence of some OR’s for only one of the two hydride phases has also been justified, in spite of the close resemblance between the two corresponding lattices. Ti-hydride Transformation Paths The conditions for low-energy interfaces between Ti and Ti-hydride precipitates are not satisfied with the same degree of accuracy for TiH and TiH2-ε (except for the coincidence [ 1 2 1 0] ≈ [220] which is always better satisfied with TiH). This determines some preferences that are detailed below and yields some information on the various possible transformation paths of titanium into titanium hydride.

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Figure 9. Three families of adjacent TiH2-ε precipitates, in dark field contrast in (a), (b), (c) respectively. d) corresponding diffraction pattern showing that diffraction spots are aligned perpendicularly to the interface plane, seen edge on.

i) The condition [0002] ≈ [002] for OR1 is much better satisfied for TiH precipitates than for TiH2-ε ones (table 1). TiH precipitates are thus likely to nucleate with this orientation, the Ti-TiH transformation being preceded by an ordering of the hydrogen atoms in solution in the hcp Ti phase (fig. 3c). They subsequently transform into the TiH2-ε phase, keeping the same orientation (fig. 8). Since a remaining TiH phase has been observed at the interface between TiH2-ε and the Ti matrix (fig. 8b), the TiH-TiH2-ε transformation is likely to be initiated at the centre of the TiH precipitates, and to extend in the direction of the interfaces with the Ti matrix (§4-4 above). A remaining layer of the TiH phase also allows to keep the favorable TiH/Ti interface even after the transformation of TiH into TiH2-ε.

ii) A close inspection of fig. 3 of Numakura and Koiwa [28] shows that the conditions for OR2 are almost perfectly satisfied for TiH precipitates, and for the exact interface plane mentioned by the authors, namely (20 2 5). All ∆g’s are indeed parallel and perpendicular to this plane. The fit would obviously be less good for TiH2-ε , which explains why OR2 has been observed only in case of Ti-TiH interfaces.

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iii) The condition [10 1 0] ≈ [1 1 1 ] for OR3 is much better satisfied with TiH2-ε than with TiH (see table 1). Then, OR3 is probably the only way to nucleate directly TiH2-ε precipitates in the Ti matrix. This result is in very good agreement with our observations of very thin TiH2-ε precipitates with this orientation (fig. 5). Our earlier observations show that these small precipitates are able to grow keeping the same OR [20]. iv) The condition [ 1 011] ≈ [002] for OR4 is slightly in favor of TiH2-ε precipitates (see table 1), in agreement with observations. Because of the small rotation angle between OR2 and OR4, it is proposed that TiH precipitates in OR2 rotate to OR4 during their transformation into TiH2-ε, when the hydrogen concentration increases. It is striking that the most “natural” OR between hcp and fcc structures, for which the main interface is parallel to the (0001) basal plane and to one family of {111} planes, has not been observed here. In fact, this OR has been observed in the only case of very thin TiH laths present in the untreated Ti substrate (unpublished work). It seems thus that this OR is incompatible with the large precipitates observed after SLA treatment. In summary, Ti can transform into TiH2-ε via several paths which depend on the plane where the first hydride nucleus appears, and which induces the smallest misfit as a function of the degree of tetragonality. This transformation occurs in a strong concentration gradient of hydrogen atoms, coming from the surface and flowing in the bulk towards the growing precipitates. Tetragonal TiH nucleates in OR1 and OR2 that are favored by excellent crystallographic coincidences (OR1 being preceded by an ordering of H atoms in the Ti matrix, and OR2 being possibly preceded by the neighboring “natural” {111}/{0001} orientation). The occurrence of either OR1 or OR2 is probably influenced by the local stress, as shown below. TiH subsequently transforms into TiH2-ε , either keeping the OR1 orientation or rotating a few degrees from OR2 to OR4. TiH2-ε can also nucleate directly and grow in OR3, for which good coincidences are realized. Stress compensation between TiH2-ε precipitates Since Ti atoms cannot diffuse over long distances at room temperature, they presumably keep all their first neighbors during the transformation. Under such conditions, fig. 7 shows that the volume expansion (of the order of 15% for the nucleation of TiH, and 21% for that of TiH2-ε), takes place mainly in the direction perpendicular to the interface, by the transformation of: i) (10 1 0) planes into two (2 2 0) ones in OR1, ii) (10 1 3) planes into (2 2 0) ones in OR2, iii) (0002) planes into three (2 2 4) ones in OR3, and iv) (10 1 0) planes into (1 1 1 ) ones in OR4. Assuming that all the misfit is relaxed, the corresponding anisotropic expansions are schematized in fig. 10. The nucleation of several variants of the same OR allows to distribute the different expansions along several directions. This has been observed repeatedly, for instance in fig. 8d where three variants of OR1 yield the star-like diffraction pattern, and in fig. 9 where two variants of OR3 are present. This process has also been observed at the transition zone between the Ti substrate and the TiH2-ε layer. For instance, the mixture of OR3 and near-OR1 orientations observed in fig. 9 contributes (as well as the presence of two variants of OR3) to a more isotropic distribution of the volume expansion.

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It is also important to note that the formation of TiH2-ε precipitates in OR1 generates a pronounced shrinking (-5.1%) along the direction [0001] // [001] parallel to the interface plane (fig. 10a). This results from the transformation of the original (0002) planes in the (002) ones which have a smaller interplanar distance. Such zones in extension enhance the nucleation of precipitates that tend to compress the matrix along the same direction. OR3 precipitates should be especially favored, according to fig. 10c. The nucleation of OR2 and OR4 precipitates with orientations close to OR3 should also be enhanced (fig. 10 b, c). This explains why the [0002] diffraction spot of Ti is very often surrounded by <002> and <111> diffraction spots of hydride precipitates, in agreement with a mixture of OR1, OR2 and OR4 orientations (see fig. 11b). Closer to the sample surface, where the hydride precipitates have coalesced to form a pure TiH2-ε layer, the <002> and <111> spots are still coupled, as shown in fig. 11c. These considerations show that internal stresses produced by the growth of the first-nucleated precipitates strongly influence the nature of the OR for the subsequently-nucleated ones. This results in an energetically favorable mixture of all OR’s, and explains why the grain size of the TiH2-ε layer is much smaller than that of Ti substrate.

Figure 10. Distribution of the volume expansions due to the nucleation of the four types of hydride precipitates. All the misfit stresses are assumed to be relaxed.

Figure 11. Diffraction patterns on a) the Ti matrix between two adjacent precipitates, b) the Ti matrix and a large number of hydride precipitates, and c) the neighboring TiH2-ε layer where all Ti has been transformed.

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