D E Soto-Parra

X Moya

L Mañosa

A Planes

H Flores-Zúñiga

F Alvarado-Hernández

R A Ochoa-Gamboa

J A Matutes-Aquino

D Ríos-Jara

Fe and Co selective substitution in Ni 2 MnGa: Effect of magnetism on relative phase stability

Keywords: phase transitions, phase transformations, martensitic transformations user supplied): Magnetic shape memory alloys, Ni2MnGa Magnetic shape memory alloys, Ni 2 MnGa, phase transitions, phase diagrams

We studied the effect of Fe and Co 3d elements selective substitution on the structural and magnetic phase transitions in the prototypical magnetic shape memory alloy Ni-Mn-Ga. We determined the phase diagram for each elemental doping substitution by means of calorimetry and ac susceptibility measurements. An effort was made to substitute each constituent element by same amounts of doping and to study the role of parameters other than electronic concentration in controlling phase stability. Specifically, selective doping with atoms of similar atomic radii but different magnetic properties allowed to investigate the role of magnetic interactions on the relative phase stability of the ternary compound. We determined the entropy change associated with the martensitic transition for each quaternary alloy to obtain further information on the effect of magnetism on the relative stability of the involved phases exhibited by these compounds.

Introduction

Ni-Mn based Heusler alloys are currently under active research due to the magnetic and structural phase transitions they exhibit [START_REF] Söderberg | Handboof of Magnetic Materials[END_REF][START_REF] Sutou | [END_REF][3][4]. In these compounds, the existence of structural phase transitions in magnetically ordered states is of great importance both from the fundamental and the application points of view and leads to very interesting phenomena such as magnetic shape memory effects [5][6][7], large magnetoresistance [8][9][10] and large magnetocaloric effects [11][12][13][14][15][16][17]. The cooccurrence of various of these effects in single alloys belonging to this family makes these compounds multifunctional materials. The interplay between structural and magnetic degrees of freedom is at the origin of such multifunctionality. Thus, a detailed understanding of the phase diagrams of these particular Heusler alloys is needed in order to improve their functional properties and to search for new applications. The most studied system so far belonging to this alloy family is the prototypical magnetic shape memory alloy Ni-Mn-Ga, for which magnetic field induced strains as large as 10% in a field of 1 T have been reported [18]. From a fundamental point of view, this alloy undergoes a complex multi-stage transformation process from a high temperature paramagnetic cubic phase to a low temperature ferromagnetic martensitic phase. At intermediate temperatures it shows precursor tweed textures which may lock into a modulated premartensitic structure via a first-order phase transition at T I (M s < T I < T C ; M s martensite start temperature, T C Curie point) [19]. This behavior is related to low resistance against distortions of {110} planes along 1 10 directions, as evidenced by the features of the low energy TA 2 acoustic phonon branch [20][21][22] and the low value of the shear elastic constant C = (C 11 -C 12 )/2 [23][24][25]. Furthermore, recent experiments have shown the opening of a pseudogap close to the Fermi energy at T I , which suggests that the premartensitic transition corresponds to a nesting feature of a single band [26]. In addition to the martensitic and premartensitic transformations, intermartensitic transformations also exist in alloys with M s near or higher than room temperature. Previous investigations have shown that such intermartensitic transformations are first-order phase transitions between different martensitic structures, with characteristic temperature T IM (< M s ) [27][28][29]. Several intermartensitic phases have been found, which have modulated lattices with different periodicity of stacking sequences of {110} planes along 1 10 directions [27][28][29][30][31][32][33]. The particular structures and transformation temperatures depend on stress and chemical composition [29,33].

Despite previous attempts of characterizing the structural transitions exhibited by these compounds, further experiments are crucial for comprehending their rich functional properties. Premartensitic and specially intermartensitic transitions have only been observed for a restricted number of magnetic shape memory alloys and are not yet fully understood. Also, a better understanding of the parameters which govern phase stability is necessary to optimize materials design and performance. Recently, we showed that selective partial substitution of 3d elements in Ni-Mn-Ga alloys is a useful tool to study the role of electron concentration on the structural and magnetic phase transitions exhibited by these materials. Specifically, we studied the effect of Fe addition on the Curie, premartensitic and martensitic transitions and we determined a detailed phase diagram of quaternary Ni-Mn-Ga-Fe alloys for low Fe concentrations [34]. Previously, the study of doping in Ni-Mn-Ga alloys had been focused only on its effect on the martensitic and the ferromagnetic phase transitions [35][36][37][38][39][40][41][42][43][44][45][46]. Here, we extend previous studies by means of investigating the dependence of all transition temperatures (M s , T I , T IM and T C ) on Fe and Co 3d transition elements doping, with concentrations up to ∼ 5% in both cases. The introduction of such elements of similar atomic radii (and therefore similar volume effects) but different magnetic properties allows study of the effect of magnetic interactions on the structural transitions. We also studied the effect of doping on the entropy change associated with the martensitic transition. Comparison of the composition dependence of ∆S for the studied quaternary compounds and the parent ternary Ni-Mn-Ga system provides further information on the role of magnetism on the relative phase stability of these alloys.

F

Experimental Details

Polycrystalline Ni-Mn-Ga-Z (Z = Fe, Co) ingots were prepared by arc melting pure metals under argon atmosphere in a water cooled Cu crucible. The ingots were melted several times for homogeneity and encapsulated under vacuum in quartz glass. They were then annealed at 1073 K for 72 hours to achieve a high degree of atomic order. Finally, the samples were quenched in ice-water. The compositions of the alloys were determined by energy dispersive x-ray photoluminescence analysis (EDX) with an estimated error less than ±0.3%. Results are collected in Table 1. The reference system was nearly stoichiometric Ni 2 MnGa, which shows a high temperature L2 1 structure (F m3m).

The alloys were grouped according to their compositions into three different families for each of the doping elements:

(1) Fe substitution: (2) Co substitution:

• Ni 52.
• Ni 50.9-x Mn 24.6 Ga 24.5 Co x (0 ≤ x ≤ 5.2), for which Ni is replaced by Co.

• Ni 50.6 Mn 25-x Ga 24.4 Co x (0 ≤ x ≤ 5.1), for which Mn is replaced by Co.

• Ni 50.6 Mn 24.4 Ga 25-x Co x (0 ≤ x ≤ 6.4), for which Co replaces Ga.

Structural transition temperatures were obtained from ac susceptibility and calorimetric measurements. Specimens cut from the ingots using a low speed diamond saw (typical size 5 × 1 × 1 mm 3 ) were used as samples for susceptibility and calorimetric studies. Magnetic susceptibility measurements were carried out in an ac susceptometer (LakeShore 7120A) in the temperature range 80 K ≤ T ≤ 320 K. The working parameters were 500 A m -1 (6.28 Oe) applied field and 375 Hz frequency. For differential scanning calorimetry (DSC) measurements, one side of the samples was ground with SiC abrasive to ensure optimal thermal contact. Calorimetric measurements were carried out by means of a high sensitivity calorimeter in the temperature range 100 K ≤ T ≤ 350 K. Typical heating and cooling rates were 2 K min -1 . Magnetic transition temperatures were determined by means of a DSC calorimeter TA 2920 suitable for higher temperatures. All transition temperatures are affected by an error of ±1 K. We also determined the entropy change associated with the martensitic transition from calorimetric measurements. The errors in entropy change are based on reproducibility and shown as errors bars in the figures.

Temperature dependent structural analysis were carried out with a Siemens D-500 x-ray diffractometer (Cu K α radiation) equipped with a low temperature stage.

Results

In this section, we present representative results of susceptibility and calorimetric measurements for each family and doping element. These selected results illustrate the evolution of the magnetic and structural properties with each of the 3d substituted elements. From the complete set of data we determine a phase diagram for each family and doping element and the transition entropy change at the martensitic transformation. For the undoped sample (x = 0), susceptibility measurements reveal the presence of a martensitic transformation. The corresponding transition temperatures are: martensite start temperature M s = 216 K, martensite finish temperature M f = 203 K, austenite start temperature A s = 215 K and austenite finish temperature A f = 226 K. The Curie point was determined from complementary DSC measurements as T C = 374 K. In addition to the martensitic transformation, an extra feature is observed in the susceptibility curve at temperatures above the martensitic transition which is associated with the formation of the intermediate or premartensitic phase [19,24]. The transition temperature is T I = 256 K. As can be seen from the figure, when increasing the amount of Co concentration both premartensitic and martensitic transition temperatures are displaced to lower temperatures and eventually both transitions merge. This behaviour is illustrated by sample x = 2.6; for this sample, the features associated with both structural transformations are close to each other and are difficult to distinguish. Here, calorimetric measurements reveal crucial to discern both transitions. Figure 1(b) shows the calorimetric curves for this sample recorded on cooling and heating. At low temperatures, the martensitic transition is revealed by multiple peaks which are consequence of the well-known jerky character of martensitic transformations. The presence of the premartensitic transition is revealed by an additional feature observed in the calorimetric curves at temperatures above the martensitic transition, magnified in the inset of Figure 1(b) for the sake of clarity. Analogously, Figure 2 shows the ac susceptibility and calorimetric curves for selected samples of the corresponding family when substituting Fe. Note that the x = 0 samples for the Fe-doped and Co-doped alloys have different compositions. In this case, for the undoped sample (T C = 351 K), susceptibility measurements reveal the presence of a martensitic transformation on cooling at M s = 291 K and M f = 272 K. On heating, the reverse transformation takes place at A s = 274 K and A f = 295 K. At lower temperatures, there is another distinct structural transformation, namely, the intermartensitic transformation, occurring at T IM = 211 K during cooling and at 239 K during heating with a temperature hysteresis of ∼ 40 K (estimated as the temperature difference at half intermartensitic transformation). The presence of such intermartensitic transformation was confirmed by the calorimetric measurements shown in Figure 2(b). The intermartensitic transformation was first observed in Ni-Mn-Ga in some prestressed [30,31] and Mn-rich [27] samples . However, these transformations were non-thermoelastic, only occurring while cooling. Clearly, our observed intermartensitic transformation shows a complete thermoelastic behaviour. Thermoelastic intermartensitic transitions have been reported previously for Ni-Mn-Ga samples within a narrow composition range with e/a values close to 7.6 [18,28,29,32,33]. More details of the intermartensitic transition will be given in next section.

Figure 3 summarizes the results obtained when substituting Ni by Co and Fe 3d elements. Figure 3(a) shows the dependence of the transition temperatures as a function of Co concentration. It should be noted that all of the transition temperatures associated with the martensitic transformation (M s , M f , A s and A f ) follow similar x dependence. Thus, for the sake of clarity only M s temperatures are plotted. As can be seen from that figure, the martensitic transformation temperatures decrease as the amount of Co increases. In ternary Ni-Mn-Z systems (where Z is Ga, Al, Sn, In, and Sb), it is well established that martensitic transformation temperatures decrease as the valence electron concentration e/a decreases [3,4,[47][48][49][50]. When replacing Ni (3d 8 4s 2 ) by Co (3d 7 4s 2 ), e/a decreases and a drop in M s is expected. This behaviour is seen in Figure 3(a). Premartensitic transformation temperatures also decrease as the Co concentration increases but at higher rate than M s . Thus, when increasing Co concentration both structural transition temperatures M s and T I get closer and eventually meet. Note that transition temperatures for the x = 5.2 sample are in the limit of the temperature range which was accessible in our experiments. For this sample we did not observe the martensitic transition and we were only able to determine unequivocally the premartensitic transition temperature. It should be mentioned that Cong et al. observed an abrupt decrease of martensitic transition temperatures in Ni 53-x Mn 25 Ga 22 Co x for compositions x > 6, which was attributed to atomic disorder caused by the addition of large amounts of Co [51]. Atomic disorder leads to a substantial suppression of the martensitic transition temperatures also in Ni 2 MnGa [52]. All these facts are illustrated by the dashed line in Figure 3(a). We note that for Co doping, T C increases proportionally with x.

On the other hand, Figure 3(b) shows the transition temperatures as a function of Fe content for the (Ni,Fe) alloy family. Again, all transition temperatures associated with the martensitic transformation follow the same x dependence and thus only M s are included. The same criterion was applied to the intermartensitic transformation and only T IM are shown. Again, the martensitic transformation temperatures decrease as the amount of Fe increases [e/a decreases; Ni (3d 8 4s 2 ) and Fe (3d 6 4s 2 )], consistently with the behaviour of ternary Ni-Mn-Z alloys and the samples with Co substitution. Premartensitic transformation temperatures decrease as the Fe concentration increases as well but, in this case, at a lower rate than M s . Thus, when increasing Fe concentration both structural transition temperatures M s and T I move apart each other. Such behaviour is opposite to the one observed when substituting Co. Furthermore, the temperature of the ferromagnetic transition T C increases with increasing x, as in the case of Co substitution.

Figure 4 shows the entropy change at the martensitic transformation as a function of the doping concentration for both Fe and Co addition. The concentration dependence of ∆S is similar to the behavior of M s for both systems, i.e., the entropy change decreases as the amount of doping increases. Such a dependence reflects the stabilization of the cubic phase with increasing doping concentration.

Mn substitution

Figures 5(a) and (b) illustrate typical results obtained when replacing Mn by Fe and Co, respectively. Figure 5(a) shows the ac susceptibility curves for selected samples of the (Mn,Fe) family. As can be seen from that figure, when increasing the amount of Fe concentration both martensitic and intermartensitic transitions shift to lower temperatures. The presence of the intermartensitic transformation undergone by these samples was again confirmed by calorimetric measurements, as illustrated in the inset of Figure 5(a). On the other hand, Figure 5(b) shows the ac susceptibility curves for selected samples of the corresponding (Mn,Co) family. In this case, the samples show a rich behaviour when adding Co. While the undoped sample shows a premartensitic transition at T I = 256 K followed by a martensitic transformation at lower temperatures, M s = 216 K, the doped x = 2.1 sample undergoes a martensitic transformation at M s = 246 K followed by an intermartensitic transition at lower temperatures, T IM = 159 K. In the latter sample no signatures of the premartensitic transformation were observed. As follows from the present results, these alloys transform from the parent phase to a final martensitic structure through a thermally induced intermartensitic transformation. These transformations occur both while cooling and heating, thus showing thermoelastic behaviour. The small value of the intermartensitic transformation latent heat compared to the one associated with the martensitic transformation (note the large size change of the calorimetric peaks associated with martensitic and intermartensitic transformations in Figures 2 and5) illustrates the closeness of the free energies of the different martensites.

In order to confirm the presence of the intermartensitic transition in the studied samples, we carried out x-ray diffraction measurements at several temperatures across the martensitic and the intermartensitic phase transitions for one specimen. These results enabled determination of the structure of the different martensitic phases. Figure 6 shows the x-ray diffraction patterns taken at 145 K and 270 K while heating for the Ni 52.5 Mn 20.1 Ga 25.1 Fe 2.3 sample. Prior to the measurements, the sample was cooled down to ∼ 130 K, i.e., below the intermartensitic phase transition (T IM ). Such a sequence ensures that the sample fully transforms to the intermartensitic phase before the measurements take place. All the intense peaks have been indexed and labelled in Figure 6. At low temperatures, the martensite shows a monoclinic modulated 14M structure with lattice parameters a = 0.424 nm, b = 0.547 nm and c = 2.937 nm, with β = 94.3 • [Figure 6(a)]. When the temperature is increased, the diffraction pattern changes clearly indicating the existence of the reverse intermartensitic transition. The corresponding structure is (slightly) monoclinic modulated 10M with lattice parameters a = 0.418 nm, b = 0.554 nm and c = 2.106 nm, with β = 90.3 • [Figure 6(b)]. The present sequence of intermartensitic transitions is 14M → 10M → P while heating. Such sequence is in agreement with previously stress [30,31] and thermal induced [27,33] intermartensitic transitions. In the present experiments, however, a second intermartensitic transition to a low temperature non-modulated phase was not observed [33]. Such behaviour can be ascribed to the fact that intermartensitic transitions are very sensitive to internal stresses present in the samples [28,33] and this can lead to differences in the particular intermartensitic transition sequence observed [18,28,29,32,33].

The variation of transition temperatures with both Co and Fe concentration for these families are collected in Figures 7(a) and (b), respectively. Several interesting features come up from these phase diagrams. As can be seen from Figure 7(a), M s increases when increasing the amount of Co concentration, as expected due to the increase of e/a when replacing Mn (3d 5 4s 2 ) by Co (3d 7 4s 2 ). On the other hand, both premartensitic T I and intermartensitic T IM transition temperatures decrease with increasing the doping concentration and T C slightly increases with x. From our data, it appears that only when the premartensitic transition disappears, i.e., meets the martensitic transformation, the intermartensitic transformation develops. In fact, this was also pointed out in the phase diagram plotted in Figure 3(b) for the quaternary Ni-Mn-Ga-Fe. This behaviour seems to be intimately related to the mechanisms of the structural transitions. Indeed, the appearance of the different structural phases is related to the anomalous instability of the crystal lattice with respect to atomic displacements of {110} planes along 1 10 directions and manifests in different modulations of stacking planes in such directions.

Figure 7(b) shows the dependence of the transition temperatures on the amount of Fe substitution. Here, the martensitic transition temperature decreases when increasing Fe concentration, i.e., increasing e/a. This behaviour is unexpected from the scaling of the martensitic transition temperatures with the electronic concentration. However, our present results agree with those reported in most of the literature [35,39,44]. Interestingly, a similar behaviour has been recently reported in Ni-Mn-Sn alloys: while a decrease of martensitic transition temperatures when increasing e/a has been observed when replacing Mn by Fe [53], an increase of the transition temperatures with increasing the electron per atom concentration has been reported when substituting Ni by Fe [54]. These results indicate that other parameters than e/a affect phase stability. In particular, our results suggest that magnetic interactions play an important role. The intermartensitic transformation temperatures behave in a similar way and also decrease with increasing Fe content. No intermartensitic transformations were detected for Fe substitution higher than ∼ 4%, as illustrated by the dashed line. It should be noted that a decrease of thermoelastic intermartensitic transformation temperatures with the electron concentration has also been previously reported in Ni-Mn-Fe-Cu-Ga system [55]. Moreover, the Curie point increases with x.

Figure 8 shows the dependence of the entropy change at the martensitic transformation on the amount of Fe and Co addition. As can be seen from that figure, 3d element substitution does not substantially modify the values of the entropy change at the martensitic transition when replacing Mn by Fe and/or Co. It should be mentioned that it was not possible to evaluate properly ∆S for the (Mn,Co) x = 5.1 sample due to the broadening of the martensitic transition and therefore this value is not included in the plot.

Ga substitution

Finally, we discuss the results obtained for the (Ga,Fe) and (Ga,Co) families. Figure 9 shows calorimetric curves for selected samples from each family. In this case, due to the high values of the transformation temperatures only calorimetric data are discussed. As can be seen from that figure, martensitic transformation temperatures strongly increase when substituting both 3d doping elements. This is clearly seen in Figure 10, where we plotted the phase diagrams of these two families. Such strong x dependence is consistent with the rapid increase of e/a when Fe and/or Co are substituted for Ga [Ga (4s 2 4p 1 ), Fe (3d 6 4s 2 ) and Co (3d 7 4s 2 )]. By contrast, the Curie point shows a different behaviour as a function of x for each family. On the one hand, in the Co doped samples the Curie point is almost independent of the doping concentration when the ferromagnetic transition takes place in the austenitic state, while T C decreases with increasing x when the ferromagnetic transition occurs within the martensitic state. On the other hand, for the (Ga,Fe) samples T C increases with increasing doping concentration over the entire studied range, the slope of the increase being larger when the martensitic and the ferromagnetic transition meet each other. This behaviour is ascribed to the coupling between the magnetic and the structural transitions and the significant increase of M s with x [56] and has been previously observed in Ga substituted for Ni and Mn ternary alloys [57][58][59]. Finally, notice that no signatures of either premartensitic or intermartensitic transitions were observed in these families.

The entropy change at the martensitic transition as a function of Fe and Co concentration is collected in Figure 11. As can be seen from this figure, ∆S parallels the behaviour of the martensitic transformation temperatures and increases as the amount of doping increases, pointing out the stabilization of the the low temperature phase due to Fe and Co substitution.

Discussion

In this paper we have studied the effect of Fe and Co 3d elements substitution on the relative phase stability of the prototypical magnetic shape memory alloy Ni-Mn-Ga for compositions close to the 2-1-1 stoichiometry. to selectively substitute each constituent element by same amounts of doping. In this way, we were able to systematically study the effect of substitution at a particular site for each doping element. The complete set of results for magnetic and structural transition temperatures obtained from calorimetric and ac-susceptibility measurements are shown as a function of the electron concentration e/a in Fig. 12. This representation shows that e/a is a convenient parameter for reducing both magnetic and structural transition temperatures and confirms that phase stability in shape-memory Heusler materials is controlled by electronic degrees of freedom to a large extent [47,48]. However, the scatter of the data points which is higher than that observed in the phase diagrams corresponding to the three studied composition related families (see Figs. 3, 7 and 10) already suggests that additional parameters other than electron concentration affect phase stability. In this sense, it is known that the ground state of Ni-Mn-Z alloys (Z as Ga, In, Al, ...) shows the same sequence of phases when e/a is increased [50]. However, for a given value of e/a the corresponding M s transition temperature displays a strong dependence on the Z element [4,61]. Khan et al. [62] specifically studied the effect of isoelectronic substitution of Ga by In in Ni 2 MnGa and concluded that the effect of Z on M s mainly arise from the change of unit cell volume which modifies the relative position of the Brillouin zone boundary and Fermi surfaces. The role of volume effects on the martensitic transition has been further studied via doping of Ni-Mn-Ga with several other elements and use of electron density to parametrize structural transition temperatures has been suggested [63,64]. The effect of magnetism on the martensitic transition, however, has been studied in less detail. Recently, Roy et al. [65] have shown that substitution of Mn by non-magnetic Cu has considerable influence on phase stability. Cu gives rise to delocalization of the Mn magnetism which is accompanied by an increase of Ni-covalency and a reinforcement of the Ni-Ga bonds [65]. The result in this case is a decrease of the Curie temperature and an increase of stability of the martensitic phase with respect to the parent compound.

In order to compare our present results for Fe-and Co-doped alloys to the behaviour of the ternary system, the phase diagram of Ni-Mn-Ga is indicated in Fig. 12 by dashed lines. Such comparison is useful to obtain information about the effect of magnetism on the structural transitions due to our selection of doping atoms with similar atomic radii but different magnetic properties. The general trends of all three systems are similar: M s and T I increase as e/a increases, whereas T IM and T C decrease. Notice that for intermartensitic transitions, only data belonging to thermoelastic transformations have been taken into account. In the case of the Fe substituted system, at constant e/a, we find that the addition of Fe to Ni-Mn-Ga shifts the structural transition temperatures M s , T I and T IM to lower values, whereas T C shifts to higher temperatures. On the other hand, when Co is added to the ternary system the effect of doping on the phase transition temperatures is more complex. While for low values of e/a M s are displaced to lower values, for higher e/a the martensitic transition temperatures are shifted to higher values. Additionally, M s and T I are suppressed for values of e/a 7.50. Such behaviour differs from the linearity observed in both ternary and Ni-Mn-Ga-Fe systems. As mentioned before, Cong et al. observed an abrupt decrease of the martensitic transition temperature in Co-doped systems, which was attributed to atomic disorder caused by the addition of large amounts of Co [51]. However, from the comparison of both quaternary compounds, it can be seen that the Fe-doped system does not show such a dramatic suppression of M s and T I for similar amounts of doping (and thus similar e/a values). Due to the similar atomic radii and concentration of doping atoms considered, the differences between both quaternary systems observed here should be ascribed to the different magnetic properties of Fe and Co. Notice that the Curie temperatures values for these Co-doped samples are significantly higher than the corresponding T C values for the Fe-doped samples, which suggests that the strengthening of the magnetic interactions stabilizes the austenitic phase. This behaviour is in agreement with the rapid decrease of M s accompanied by considerable increase of T C observed in the results from Cong et al. [51] and also in recent results from Kanomata and co-workers [68]. On the other hand, the scarce T IM data does not allow a detailed determination of the effect of Co addition on the intermartensitic transformation, although from comparison with both ternary and Fe-doped systems one expects T IM to decrease when increasing e/a. Regarding the Curie point, T C shifts to higher values when the magnetic transition occurs within the austenitic state (low e/a), while it is slightly displaced to lower values when takes place within the martensitic state (high e/a values).

Preceding results indicate that in both Fe-and Co-doped Ni-Mn-Ga alloys, magnetic effects play a certain role in controlling relative phase stability. In the region where the martensitic transition occurs in the ferromagnetic phase below the Curie point, the increase of T C with respect to Ni-Mn-Ga suggests that both Feand Co-addition give rise to a strengthening of magnetic exchange coupling and this seems to be responsible for lowering structural transition temperatures. Additional information on the effect of magnetism on the martensitic transition can be obtained from the e/a dependence of the entropy difference ∆S between the high temperature cubic phase and the low temperature martensitic phase. Due to the diffusionless nature of the martensitic transition, the distribution of atoms in the parent phase is inherited by the martensitic phase and ∆S should only contain vibrational, electronic and magnetic contributions. Fig. 13 shows the entropy change at the martensitic transformation as a function of electron concentration per atom e/a for (a) Ni-Mn-Ga-Fe and (b) Ni-Mn-Ga-Co systems. Like in the ternary Ni-Mn-Ga, in both quaternary systems ∆S increases as the electron per atom concentration increases. In the case of Ni-Mn-Ga, the large concentration dependence of the entropy change was attributed by Khovailo et al. to changes of the magnetic contributions [67]. Actually, when the martensitic transition occurs above the Curie point, the magnetic contribution to the entropy change should be very small and the entropy change is expected to be largely provided by the lattice vibrational contribution. In contrast, when the transition occurs below the Curie temperature a magnetic contribution to the entropy of opposite sign to the vibrational contribution is expected. This magnetic contribution is responsible for the increase of ∆S with increasing e/a. In the case of Fe and Co substituted alloys the entropy changes for a given value of e/a are lower than those in the corresponding ternary Ni-Mn-Ga system. This drop confirms the suggested strengthening of magnetic exchange coupling when adding Fe and Co which results in a decrease of the free energy difference between the parent and martensite phases when the alloy orders magnetically [34], and therefore stabilization of the high temperature phase. The reduction of entropy change at a given electron concentration is considerably larger in Co-doped alloys which means that Co has a stronger effect on magnetic exchange coupling than Fe. Such stronger effect is consistent with the abrupt decrease of martensitic (and premartensitic) transition temperatures shown in Figure 12(b), and further indicates that the strengthening of magnetic interactions stabilizes the high temperature cubic phase.

Conclusions

We studied the effect of Fe and Co selective substitution on the magnetic and structural phase transitions exhibited by Ni-Mn-Ga alloys. We determined the phase diagrams and the entropy changes at the martensitic transition of the resulting quaternary systems. Similarities between ternary Ni-Mn-Ga and quaternary Ni-Mn-Ga-Fe and Ni-Mn-Ga-Co systems reaffirm that electronic concentration qualitatively controls phase stability in these compounds. However, differences between these systems show that additional parameters affect phase stability and therefore e/a can only be used for examining systematic changes of structural and magnetic properties within a single-alloy system. In particular, differences between both quaternary systems indicate that relative phase stability is strongly modified by the strengthening of magnetic exchange coupling induced by Fe-and Co-doping and evidence that magnetic interactions affect the structural and magnetic phase transitions exhibited by Heusler magnetic shape memory alloys. Squares stand for M s , circles stand for T I , up and down triangles stand for T C and T IM , respectively. Red dashed lines depict the (fitted) transition lines of the related Ni-Mn-Ga ternary system (data compiled from reference [60]). The open red circles stand for the thermoelastic intermartensitic transformation temperature in Ni-Mn-Ga [18,29,32,33].

  5-x Mn 23 Ga 24.5 Fe x (0 ≤ x ≤ 5.2), for which Ni is replaced by Fe. • Ni 52.5 Mn 22.3-x Ga 25.2 Fe x (0 ≤ x ≤ 5.2), for which Mn is replaced by Fe. • Ni 52.7 Mn 22.1 Ga 25.2-x Fe x (0 ≤ x ≤ 5.3), for which Fe replaces Ga.

Figure 1

 1 Figure1(a) shows the ac susceptibility curves for selected samples of the family which results when replacing Ni by Co. For the undoped sample (x = 0), susceptibility measurements reveal the presence of a martensitic transformation. The corresponding transition temperatures are: martensite start temperature M s = 216 K, martensite finish temperature M f = 203 K, austenite start temperature A s = 215 K and austenite finish temperature A f = 226 K. The Curie point was determined from complementary DSC measurements as T C = 374 K. In addition to the martensitic transformation, an extra feature is observed in the susceptibility curve at temperatures above the martensitic transition which is associated with the formation of the intermediate or premartensitic phase[19,24]. The transition temperature is T I = 256 K. As can be seen from the figure, when increasing the amount of Co concentration both premartensitic and martensitic transition temperatures are displaced to lower temperatures and eventually both transitions merge. This behaviour is illustrated by sample x = 2.6; for this sample, the features associated with both structural transformations are close to each other and are difficult to distinguish. Here, calorimetric measurements reveal crucial to discern both transitions. Figure1(b)shows the calorimetric curves for this sample recorded on cooling and heating. At low temperatures, the martensitic transition is revealed by multiple peaks which are consequence of the well-known jerky character of martensitic transformations. The presence of the premartensitic transition is revealed by an additional feature observed in the calorimetric curves at temperatures above the martensitic transition, magnified in the inset of Figure1(b) for the sake of clarity.Analogously, Figure2shows the ac susceptibility and calorimetric curves for selected samples of the corresponding family when substituting Fe. Note that the x = 0 samples for the Fe-doped and Co-doped alloys have different compositions. In this case, for the undoped sample (T C = 351 K), susceptibility measurements reveal the presence of a martensitic transformation on cooling at M s = 291 K and M f = 272 K. On heating, the reverse transformation takes place at A s = 274 K and A f = 295 K. At lower temperatures, there is another distinct structural transformation, namely, the intermartensitic transformation, occurring at T IM = 211 K during cooling and at 239 K during heating with a temperature hysteresis of ∼ 40 K (estimated as the temperature difference at half intermartensitic transformation). The presence of such intermartensitic transformation was confirmed by the calorimetric measurements shown in Figure2(b). The intermartensitic transformation was first observed in Ni-Mn-Ga in some prestressed[30,31] and Mn-rich[27] samples . However, these transformations were non-thermoelastic, only occurring while cooling. Clearly, our observed intermartensitic transformation shows a complete thermoelastic behaviour. Thermoelastic intermartensitic transitions have been reported previously for Ni-Mn-Ga samples within a narrow composition range with e/a values close to 7.6[18,28,29,32,33]. More details of the intermartensitic transition will be given in next section.Figure3summarizes the results obtained when substituting Ni by Co and Fe 3d elements. Figure3(a)shows the dependence of the transition temperatures as a function of Co concentration. It should be noted that all of the transition temperatures associated with the martensitic transformation (M s , M f , A s and A f ) follow similar x dependence. Thus, for the sake of clarity only M s temperatures are plotted. As can be seen from that figure, the martensitic transformation temperatures decrease as the amount of Co increases. In ternary Ni-Mn-Z systems (where Z is Ga, Al, Sn, In, and Sb), it is well established that martensitic transformation temperatures decrease as the valence electron concentration e/a decreases[3,4,[47][48][49][50]. When replacing Ni (3d 8 4s 2 ) by Co (3d 7 4s 2 ), e/a decreases and a drop

Figure 1 .

 1 Figure 1. Ni 50.9-x Mn 24.6 Ga 24.5 Co x family. (a) Magnetic susceptibility versus temperature for samples of selected compositions. (b) Calorimetric curves for the sample with x = 2.6 showing the martensitic and intermediate (magnified in the inset) transformations. Vertical arrows show the position of the premartensitic transition temperature, T I . Horizontal arrows in panel (b) indicate direction of temperature change.

Figure 2 .

 2 Figure 2. Ni 52.5-x Mn 23 Ga 24.5 Fe x family. (a) Magnetic susceptibility versus temperature for samples of selected compositions. (b) Calorimetric curves for the sample with x = 0 showing the martensitic and intermartensitic (magnified in the inset) transformations. Vertical arrows in panel (a) show the position of the intermartensitic transition temperature, T IM (sample with x = 0), and the premartensitic transition temperature, T I (samples with x = 1.4 and 2.2). Horizontal arrows in panel (b) indicate direction of temperature change.

Figure 3 .

 3 Figure 3. (a) Evolution of the transition temperatures of Ni 50.9-x Mn 24.6 Ga 24.5 Co x as a function of Co concentration. (b) Evolution of the transition temperatures of Ni 52.5-x Mn 23 Ga 24.5 Fe x as a function of Fe concentration. Lines are guides to the eye.

Figure 4 .

 4 Figure 4. Entropy change at the martensitic transformation as a function of doping concentration (Fe or Co) for Ni substitution. Solid lines are linear fits to the experimental data.

Figure 5 .

 5 Figure 5. (a) Ni 52.5 Mn 22.3-x Ga 25.2 Fe x family. Magnetic susceptibility versus temperature for samples of selected compositions. Inset illustrates the martensitic and the intermartensitic transformations for the sample x = 2.3 detected by calorimetry. (b) Ni 50.6 Mn 25-x Ga 24.4 Co x family. Magnetic susceptibility versus temperature for selected samples. Vertical arrows show the position of the intermartensitic transition temperature, T IM . Horizontal arrows in the inset of panel (a) indicate direction of temperature change.

Figure 6 .

 6 Figure 6. X-ray diffraction patterns illustrating the change of the martensitic structure through the intermartensitic transition for the Ni 52.5 Mn 20.1 Ga 25.1 Fe 2.3 sample. (a) Monoclinic 14M structure (T < T IM ) and (b) 10M (slightly) monoclinic structure (T < M s ).

Figure 7 .

 7 Figure 7. (a) Evolution of the transition temperatures of Ni 50.6 Mn 25-x Ga 24.4 Co x as a function of Co concentration. (b) Evolution of the transition temperatures of Ni 52.5 Mn 22.3-x Ga 25.2 Fe x as a function of Fe concentration. Lines are guides to the eye.

Figure 8 .

 8 Figure 8. Entropy change at the martensitic transformation as a function of doping concentration (Fe or Co) for Mn substitution. Solid lines are guides to the eye.

Figure 9 .Figure 10 .

 910 Figure 9. Calorimetric curves for samples of selected compositions of (a)-(b) Ni 52.7 Mn 22.1 Ga 25.2-x Fe x and (c)-(d) Ni 50.6 Mn 24.4 Ga 25-x Co x families. Vertical arrows show the Curie point, T C . Horizontal arrows indicate direction of temperature change.

Figure 11 .

 11 Figure 11. Entropy change at the martensitic transformation as a function of doping concentration (Fe or Co) for Ga substitution. Solid lines are guides to the eye.

Figure 12 .

 12 Figure 12. (Color online) (a) Phase diagram of Ni-Mn-Ga-Fe system as a function of electron concentration per atom e/a. Filled symbols stand for Ni 52.5-x Mn 23 Ga 24.5 Fe x family; half-filled symbols stand for Ni 52.5 Mn 22.3-x Ga 25.2 Fe x family; open symbols stand for Ni 52.7 Mn 22.1 Ga 25.2-x Fe x family. (b) Phase diagram of Ni-Mn-Ga-Co system as a function of electron concentration per atom e/a. Filled symbols stand for Ni 50.9-x Mn 24.6 Ga 24.5 Co x ; half-filled symbols stand for Ni 50.6 Mn 25-x Ga 24.4 Co x family; open symbols stand for Ni 50.6 Mn 24.4 Ga 25-x Co x family. Lines are fits to the experimental data.Squares stand for M s , circles stand for T I , up and down triangles stand for T C and T IM , respectively. Red dashed lines depict the (fitted) transition lines of the related Ni-Mn-Ga ternary system (data compiled from reference[60]). The open red circles stand for the thermoelastic intermartensitic transformation temperature in Ni-Mn-Ga[18,29,32,33].

Figure 13 .

 13 Figure 13. (Color online) (a) Entropy change at the martensitic transformation of Ni-Mn-Ga-Fe system as a function of electron concentration per atom e/a. Filled symbols stand for Ni 52.5-x Mn 23 Ga 24.5 Fe x family; half-filled symbols stand for Ni 52.5 Mn 22.3-x Ga 25.2 Fe x family; open symbols stand for Ni 52.7 Mn 22.1 Ga 25.2-x Fe x family. (b) Entropy change at the martensitic transformation of Ni-Mn-Ga-Co system as a function of electron concentration per atom e/a. Filled symbols stand for Ni 50.9-x Mn 24.6 Ga 24.5 Co x ; half-filled symbols stand for Ni 50.6 Mn 25-x Ga 24.4 Co x family; open symbols stand for Ni 50.6 Mn 24.4 Ga 25-x Co x family. Solid lines are linear fits to the experimental data. Red dashed lines depict the (fitted) entropy change of the related Ni-Mn-Ga ternary system (data compiled from references[66,67]).

  Figure 7 71x105mm (600 x 600 DPI)

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Table 1 .

 1 Compositions of the Ni-Mn-Ga-Co and Ni-Mn-Ga-Fe samples determined by EDX. For each element doping, different specimens are grouped into three distinct families, depending on the element that is substituted (elements within parenthesis, first and seventh column, respectively). Samples displayed in the first row are the undoped reference Ni-Mn-Ga samples. The estimated error in the compositions is less than ±0.3 %. Values of valence electron concentration per atom, e/a, are also given.

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Acknowledgement(s)

This work received financial support from the CICyT (Spain), Project No. MAT2007-61200, and from CONACYT (44786-SEP-CONACYT 2003). X. M. acknowledges support from Comissionat per a Universitats i Recerca (CUR) del Departament d'Innovació, Universitats i Empresa de la Generalitat de Catalunya.


Asier Minondo
email: aminondo@ud-ss.deusto.es

Exports' productivity and growth across Spanish regions

Keywords: Spain, exports, productivity, growth Exportproduktivität und Wachstum verschiedener spanischer Regionen Aktuellen Studien zufolge wachsen Länder, die sich auf Güter mit hohem Produktivitätsniveau spezialisiert haben, rascher als Länder, die sich auf Güter mit niedrigem Produktivitätsniveau spezialisiert haben. In diesem Beitrag analysieren wir, ob diese Beziehung auch auf regionaler Ebene zutrifft. Mit Hilfe einer eindeutigen, hochgradig desaggregierten, regionalen Handelsdatenbank berechnen wir das Produktivitätsniveau der Exporte spanischer Provinzen und analysieren, ob Provinzen mit produktiveren Exporten höhere Wachstumsraten verzeichnen. Unsere Ergebnisse lassen darauf schließen, dass auch auf regionaler Ebene eine Verbindung zwischen Exportproduktivität und Wachstum besteht Spanien Exporte Produktivität Wachstum JEL Classification: F14; O40

According to recent studies, countries specialised in goods associated with high productivity levels grow faster than countries specialised in goods associated with low productivity levels.

In this paper we analyse whether that relationship also takes place at the regional level. Using a unique, highly-disaggregated, regional trade database, we calculate the productivity level associated to Spanish provinces' exports and analyse whether provinces that latch on more productive exports have achieved higher rates of growth. Our results show that there is also a positive link between exports' productivity and growth at a regional level.

3 La productividad de las exportaciones y el crecimiento a través de las regiones españolas Estudios recientes muestran que los países especializados en productos asociados a una alta productividad crecen más rápido que los países especializados en productos asociados a una baja productividad. En este artículo analizamos si esta relación también se produce a nivel regional. Utilizando una base de datos regional altamente desagregada, calculamos el nivel de productividad asociado a las exportaciones de las provincias españolas y analizamos si las provincias que se han especializado en productos asociados a una alta productividad han logrado un mayor crecimiento económico. Nuestros resultados muestran que también existe una relación positiva entre la especialización en productos asociados a una alta productividad y el crecimiento económico a nivel regional. There is long standing argument in the literature that specialising in some goods is more growth promoting than specialising in others. Back in the 1950s, in separated articles, [START_REF] Prebisch R | The Economic Development of Latin America and its principal problems[END_REF]SINGER, 1950, argued that there was a secular decline of the net barter terms of trade between primary products and manufactures. Due to this deterioration, countries that specialised in primary products would have a declining capacity to import manufactures, and among them capital goods, which would reduce their growth possibilities.

Due to different reasons, other authors have also pointed out that specialising in natural resources may have depressing effects on economic growth [START_REF] Gylfason | Natural resources, education, and economic development[END_REF]SACHS AND WAGNER, 2001). According to this line of research, known as the natural resource curse, countries that specialise in primary products are prone to suffer Dutch disease problems and rent-seeking behaviour; moreover, wealth obtained from natural resources imbue people with a false sense of security that hinders the introduction of growth promoting policies, such as investment in human capital. Other authors have also argued that some sectors, due to learning by doing externalities, have a higher growth potential than others (YOUNG, 1991;[START_REF] Matsuyama | Agricultural Productivity, Comparative Advantage and Economic Growth[END_REF]. According to those authors, countries that specialise in sectors where productivity can be enhanced due to learning by doing (equated with manufacturing or hightech sectors) will grow faster than those countries that specialise in sectors in which productivity is not improved through experience (equated with agriculture or low-tech sectors).

Recently, HAUSMANN, HWANG and RODRIK, 2007 (henceforth HHR) put forward another link between specialisation and economic growth. They argue that some commodities have a higher implied productivity level than others; in particular, HHR assert that According to HHR if countries latch on high-productivity commodities they will grow faster than if they specialise in low-productivity commodities. A key contribution by HHR is the development of a quantitative index to rank commodities in terms of their implied productivity; based on this index, they also calculate the productivity-level associated to a country's exports. Equipped with this latter indicator they empirically test their model and, as expected, they find that countries specialised in high-productivity goods, relative to their income per capita, grow faster than countries specialised in low-productivity goods.

In the HHR model, growth occurs when resources are transferred from lower productivity products to higher productivity products 1 . In that model, specialisation patterns are not entirely predictable, because, along with fundamentals (labour, capital, natural resources and the quality of institutions), idiosyncratic factors also play a role in determining countries' comparative advantage. Hence, each country has a range of products, that differ in their implied productivity, in which it can specialise. However, the country does not know the exact commodity-composition of that range; it has to "discover" it. If entrepreneurs "discover" the high-productivity products within that range, economic growth will (temporarily) occur as resources are transferred to more productive activities.

In line with the HHR model, regional studies also have a large tradition of analysis on how specialising in some goods is more growth promoting than specialising in others. As explained by CAPELLO, 2007 since the late 1930s authors, such as Clark and Fischer, stressed that the process of regional growth was linked to the sectoral composition of the economy. The stages theory argued that regions moving from agriculture to industry would et al., 2006 note that specialisation in manufacturing also plays a large role in the Keynesian theories of regional divergence. For example, in Kaldor's approach, a region could achieve a higher productivity growth in manufacturing than in agriculture, because the former sector opens more possibilities to learn from experience. As PIKE at al, 2006 highlight specialisation in manufacturing is also important in Myrdal's circular and cumulative causation model of regional divergence. In this approach, manufacturing activities lead to agglomeration economies, which reinforce the advantage of regions that industrialise first.

Myrdal's ideas can also be found in more recent economic geography models. For example, KRUGMAN, 1991 shows that regional specialisation is path-dependant, as the effect of economies of scale and external economies make some regions to get lock-in some industries.

Based on those ideas, some economist have argued that public policy can play a role in the development of high-value industries characterised by external economies at a regional level.

In particular, the nurturing of those industries' first activities through trade protection or tax incentives would put in motion the increasing returns that would reinforce the regional advantage [START_REF] Pike | Local and Regional Development[END_REF].

The aim of this paper is to analyse whether the link between trade specialisation and economic growth found by HHR at the country level also takes place at the regional level. In particular, we aim to investigate whether Spanish provinces (NUTS III) that have specialised in high-productivity goods have grown faster than provinces that have specialised in lowproductivity goods. As a preliminary to our conclusion, we also find a positive link between provinces' exports productivity level and subsequent growth. The remaining of the paper is organised as follows. The next section explains the construction of the quantitative index to measure Spanish provinces exports' productivity level. Section 3 presents data on Spanish provinces' exports productivity level. Section 4 studies the relationship between provinces' exports productivity and subsequent growth. The final section summarizes the paper's main findings.

The construction of an exports' productivity index

Following HHR, to construct the productivity-level associated to a province's exports indicator (EXPY), two steps are followed. Firstly, we compute the income level associated to each exported commodity. This indicator, denominated PRODY, is calculated as follows:

(1) *

j j j j ij j ij i y X x X x PRODY ∑ ∑       =
where ij x denotes country j exports of product i, Xj country j total exports and yj country j GDP per capita. The numerator of the weight,

j ij X x
, is the share of product i in j country's total exports; the denominator of the weight, ∑ HHR, if this weight is used the PRODY indicator will be biased towards large countries' GDP per capita, because large countries export more than small countries. In order to overcome this limitation, the authors suggest the use of revealed comparative advantage as weight.

Secondly, the exports' productivity index, EXPY, is calculated as a weighted average of each exported commodity's PRODY, where the weights are the shares of each product in the country's total exports. Algebraically,

* ∑       = i j ij i j X x PRODY EXPY (2)
As HHR recognise, a shortcoming of PRODY, and hence of EXPY, is that it does not correct for differences in quality within a product category. For example, as [START_REF] Rodrik | What's so Special about Chinese Exports?[END_REF] shows, even at the Harmonised System (HS) 6-digit disaggregation level, which distinguishes more than 5000 product categories, there are large differences in terms of quality. Moreover, SCHOTT, 2004 points out that those differences are related with countries GDP per capita level. He shows that, within narrowly defined manufactures, there is a clear vertical differentiation across countries, with low GDP per capita countries specialised at the lower end of the quality spectrum and large GDP per capita countries specialised at the higher end of the quality spectrum.

If EXPY coefficients do not correct for differences in quality, we may overvalue or undervalue regional exports' productivity level. This under or overvaluation, on its hand, may compromise the validity of the econometric results. In order to control for quality differences For each product, we calculate each country's exports unit value. Then, we sort unit values from the lowest to the highest value. In order to minimise the impact of measurement errors, we remove unit values which are below or equal to the first percentile as well as unit values that are equal or above to the 99th percentile. From the remaining unit values, we select the 33rd percentile unit value and the 67th percentile unit value. Exports whose unit value falls between the minimum unit value and the 33rd percentile are considered as low quality varieties; those exports whose unit value falls between the 33rd percentile and 67th percentile are considered as medium quality varieties, and finally, those exports whose unit value falls between the 67th percentile and the maximum unit value are considered as high quality varieties. We only calculate varieties PRODY if we have, at least, five unit value observations per each product.

Once we establish, for each product, the unit value ranges for each quality level, we calculate the PRODY value associated to each variety:

∑ ∑                 = j j j j j qi j j qi qi y X x X x PRODY * , , (3)
where j qi

x , denotes country j exports of product i's q variety, where q can be low, medium or high. As before, Xj denotes j country's total exports and yj is j country's GDP per capita. Now, the numerator of the weight,

j j qi X x ,
, is the share of product i's q variety in total exports; the x , , aggregates the shares of product i's q variety in total exports across countries. Hence, the weight reflects j country's revealed comparative advantage in product i's q variety. qi PRODY is, therefore, the average of exporting countries GDP per capita, weighted by each country's revealed comparative advantage in product i's q variety.

The EXPY indicator will now be calculated as follows: 3. The productivity-level of Spanish provinces' exports Table 1 presents Spanish provinces ' quality-adjusted EXPY in 1994' quality-adjusted EXPY in , in 2005 and the average annual growth rate between those years. In 2005 the average of Spanish provinces' qualityadjusted EXPY was 15612$.The Spanish province with the highest quality-adjusted EXPY was Huelva: 18870$. That province was followed by Ávila (18752$), Girona (18671$), Soria (18606$) and Huesca (18369$). In the bottom of the ranking we find Las Palmas (9431$), Almería (10209$), Tenerife (10259$), Cáceres (12211$) and Zamora (12640$). We can observe that the ratio between the province with the highest quality-adjusted EXPY (Huelva) and the province with the lowest quality-adjusted EXPY (Las Palmas) is around 2. With respect to 1994, we can observe that Tenerife was the province in the top of the ranking, followed by Salamanca, Ourense, León and Palencia; at the bottom of the ranking we find Ávila, Zamora, Almería, Granada and Badajoz.

qi i high medium low q j j qi j PRODY X x EXPY ∑ ∑ =         = , , , (4)

[TABLE 1 AROUND HERE]

Differences in EXPY across Spanish provinces are explained by trade specialisation.

Provinces that are located at the top of the ranking are characterised by a large specialisation in products with high productivity levels, such as motor vehicles, parts and accessories of motor vehicles, chemical products and medicaments. On the contrary, provinces that are In principle, a larger specialisation in products associated with high productivity should be related with a higher GDP per capita: provinces that command a high GDP per capita should export goods associated with high productivity levels, whereas provinces that command a low GDP per capita should export goods associated with low productivity levels. If that were not the case, we would find an unbalance between provinces' income level and the productivity associated to their exports. For example, as the HHR model predicts, if a province exports goods associated to a productivity level that is higher that the one predicted by its GDP per capita, the province's GDP per capita will grow until a balance between EXPY and the income level is reached; on the contrary, if the province exports goods associated to a productivity level below its GDP per capita, the province ought to move its resources to more productive activities in order to keep its income level.

Figure 1 analyses the relationship between Spanish provinces' EXPY and GDP per capita. As can be seen in the figure, although there is a positive correlation between both variables, it is not very strong. If we run a simple regression, GDP per capita will only explain 13per cent of the variation in EXPY across Spanish provinces. This explanatory capacity is much lower than the one found by HHR between countries' GDP per capita and EXPY; however in that latter study the variability in GDP per capita across countries' was much larger than the variability in GDP per capita across Spanish provinces. Notwithstanding these differences, we should ask ourselves why GDP per capita has a lower capacity to explain differences in EXPY across Spanish provinces. The answer seems to lie in the share of primary products in Spanish provinces' total exports. As developing countries have comparative advantage in [FIGURE 1 AROUND HERE] Table 1's last column presents EXPY's average annual growth rate between 1994 and 2005. It is important to note that during all the period varieties' PRODY values are fixed. Hence, changes in provinces' quality-adjusted EXPY can only occur through changes in the relative share of each variety in provinces' exports. As can be seen in the bottom of the table, the average annual growth rate in the 1994-2005 period was 0.46%. There are 33 provinces that improve their quality-adjusted EXPY and 17 provinces that deteriorate their quality-adjusted EXPY. Ávila is the province that presents the highest annual average growth (6.67%), followed by Granada (3.31%), Zamora (2.67%), Málaga (2.44%) and Cuenca (1.98%). On its hand, Tenerife is the province with the largest drop in quality-adjusted EXPY (-6.51), followed by Las Palmas (-5.24), Salamanca (-2.45), León (-1.79%) and Ourense (-0.77%). At the end of table we analyse whether differences in growth rates across Spanish provinces are governed by a convergence process in EXPY. Firstly, we compute the standard deviation of the (log) EXPY in 1994 and 2005. The evolution of this variable tells us whether there has been a reduction in the dispersion of EXPY across Spanish provinces, or σconvergence. We can see that there is a reduction in the dispersion of the EXPY across Spanish provinces in the 1994-2005 period as the standard deviation drops from 0,180 to 0,159. Secondly, we compute β-convergence, which analyses the relationship between initial (log) EXPY and subsequent EXPY growth. The coefficient is negative and statistically significant, which shows that, as average, provinces that started with a lower EXPY achieved a higher EXPY growth than provinces that started with a higher EXPY. Hence, according to these results, there has been a convergence in EXPY across the Spanish provinces in the 1994-2005 period. In this section we analyse econometrically whether regions specialised in high-productivity exports have grown faster than regions specialised in low-productivity exports. In order to control for differences in employment rate across provinces, we use value added per worker growth, instead of GDP per capita growth, as our dependent variable. We estimate the following regression equation:

) log( ) log( ) log( _ 3 2 1 0 i i i i h y EXPY growth y β β β β + + + = (5)
where y i _growth is the average annual growth rate of value added per worker in province i, EXPY the initial exports' quality-adjusted productivity, y i the initial value added per worker and h i the initial human capital level. Value added per worker is included in the equation because, according to the HHR model, it is the productivity level of exports relative to value added per worker which determines provinces' growth opportunities. In particular, provinces with an EXPY which is higher than the one predicted by their value added per worker will have opportunities to transfer resources from less productive activities to more productive activities. Finally, following HHR, human capital is also introduced in the equation. These authors show that differences in EXPY across countries are related to differences in human capital; on the other hand, human capital can also affect a country's growth prospects. 1994-2004. In order to increase the number of observations in the regression analysis, we divide the 10 year period in two five-years growth intervals.

Table 2 presents the results of the regression analyses. In Column (1) we estimate a pool OLS model with the observations of the two five-years intervals. The coefficient for qualityadjusted EXPY is positive, which denotes that those Spanish regions that specialise in more productive goods, relative to labour productivity, achieve higher rates of growth. However, by a very small margin, the coefficient is not statistically significant at 10 per cent. The coefficient for the initial value added per worker is negative and statistically significant and the coefficient for human capital, although positive, is not statistically significant. At the bottom of the column, we include the p-value of the Moran's I statistic to test for spatial autocorrelation of the residuals. According to this coefficient we cannot reject the null hypothesis of no spatial autocorrelation of the residuals.

[ As can be seen in Column (3) the fixed effects model estimation yields a positive and statistically significant quality-adjusted EXPY coefficient. This result is in line with the one obtained in the pool estimate and confirms HHR model's prediction on the positive association between a country's EXPY and subsequent growth. Moreover, in this last estimation, the coefficient for human capital is positive and statistically significant. To sum up, both the pool and the fixed effects estimations find a positive link between Spanish provinces exports' initial productivity-level and subsequent growth. According to these results, Spanish provinces that have specialised in more productive goods have achieve higher growth rates than Spanish provinces specialised in less productive goods. There is a long standing argument in the literature that specialising in some goods is more growth promoting than others. Recently, [START_REF] Hausmann | The Structure of the Product Space and the Evolution of Comparative Advantage[END_REF] have developed a model that establishes a new link between specialisation and economic growth. These authors argue that products differ in their implied level of productivity and show that countries specialised in high-productivity products, relative to their GDP per capita, grow faster than countries specialise in low-productivity products. The aim of this paper has been to test whether this relationship also takes place at the regional level. In particular, we analyse whether Spanish provinces specialised in high-productivity exports have grown faster than provinces specialised in low-productivity exports. In order to do that, firstly, we calculate the productivity level associated to each province exports, controlling for quality differences within a product category. Our calculations show that there are large differences in exports' productivity-level across Spanish provinces; however, during the last decade there has been a convergence process in exports' productivity level across Spanish provinces. Provinces that are located at the top of the ranking are characterised by a large specialisation in products with high productivity levels, such as motor vehicles, parts and accessories of motor vehicles, chemical products and medicaments. On the contrary, provinces that are located at the bottom of the ranking are characterised by a large specialisation in commodities with low productivity levels, such as agricultural products and minerals.

Secondly, we regress the average growth rate in labour productivity on the initial exports' productivity level and other control variables. Using different estimation techniques, our results show that there is a positive association between a province's exports' productivity level and subsequent economic growth. According to our results, Spanish provinces that have show that the relationship between exports' productivity and growth also holds at a regional level. In order to compare a commodity's unit value across years and countries, all unit values should be calculated with the same quantity unit. For each commodity we analyse which is the quantity unit (kilograms, items, litres,...) that maximises the number of observations. In the majority of cases the weight in kilograms is the quantity unit chosen. This procedure obliges us to remove from the sample some observations that allow the calculation of a unit value but do not use the quantity measure that has been chosen for the product. The removal of those observations raises the percentage of exports for which a valid unit value cannot be computed to 18.4 per cent of total sample's exports. Finally, in order to minimise measurement errors, we remove observations where the unit value is below or equal to the 1st percentile and equal or above In order to calculate provinces' EXPY we assign each HS 6 digit export observation to the low, medium or high variety, depending on which quality range the unit value falls. In order to overcome the effect of the evolution of prices and exchange rates on the calculation of unit 1 HAUSMANN and KLINGER, 2007 show that there are differences across countries in their possibilities to upgrade from lower productivity products to higher productivity products.

2 As in HHR, we use three years in order to attenuate the biases generated by observations driven by yearspecific circumstances.

3 This analysis poses the additional question of how some Spanish provinces can be competitive in agricultural exports that are associated with a low productivity level. The answer seems to be linked to the European Union's (EU) protectionist policy on agricultural products. As the EU imposes border barriers on some agricultural products, some EU members can still be competitive in exporting agricultural commodities with a low EXPY to other EU members.

4 HHR also include the quality of the institutions in the growth regression as it may also explain the differences in EXPY across countries. As the quality of institutions differ mildly within regions we do not include this variable in the regression. 5 As there are no GDP deflators for provinces, we use autonomous communities' (NUTS 2) GDP deflators to transform current values into constant values. It is important to note that during the period of analysis there have been changes in the methodology used to calculate provinces GDP (1986GDP ( 's methodology, 1995's methodology 's methodology Page 29 of 30 http://mc.manuscriptcentral.com/cres Email: regional.studies@newcastle.ac.uk In order to control for those changes, and taking into account that in some years provinces' GDP figure is available in more than one methodology, we calculate the real growth rates during the years that compose the 1995's methodology period and the 2000's methodology period. Afterwards, we use those growth rates to extend the 1986's methodology period's GDP figures. 6 Following the same reasoning, in the case of Balearic Islands, we also exclude aircraft exports.

Regional

Page 30 of 30 http://mc.manuscriptcentral.com/cres Email: regional.studies@newcastle.ac.uk

Regional Studies

  rich countries are associated with high productivity levels, whereas commodities exported by poor countries are associated with low productivity levels.

  of growth, due to the larger labour productivity in the latter sector. PIKE

  and EXPY indicators, we follow the methodology developed by[START_REF] Minondo | Exports' quality-adjusted productivity and economic growth[END_REF]

  which is a weighted average of each variety's PRODY, where the weights are the shares of each variety in total exports.In order to calculate varieties' PRODY we use a sample of countries that reported export and GDP per capita data in2002, 2003 and 2004 2 . Exports' data are total country's exports at the HS 6-digit disaggregation; these data are obtained from the UN Comtrade database; GDP per capita in PPP constant dollars are obtained from the World Bank's World Development Indicators database. The sample is composed by 115 countries. In order to reduce measurement errors, following[START_REF] Co | Factors That Account for the Large Variations in U.S. Export Prices[END_REF][START_REF] Hallak | Estimating Cross-Country Differences in Product Quality[END_REF][START_REF] Hallak | Estimating Cross-Country Differences in Product Quality[END_REF], we drop from the analysis those observations where the value of exports is below 10000$. The sample accounts for 89 per cent of total world merchandise exports in the 2002-2004 period. We use Agencia Tributaria database's export data to calculate Spanish provinces' EXPY. The Data we treat data in order to calculate the quality-adjusted PRODY and EXPY indicators.

  bottom of the ranking are characterised by a large specialisation in commodities with low productivity levels, such as agricultural products and minerals.

  these commodities' PRODY is low. Hence, those Spanish provinces specialised in primary products have an EXPY which is lower than the one expected from their GDP per capita; this gap will be specially severe when Spanish provinces export varieties of primary products in which developing countries' command a large comparative advantage. As shown in the figure, the gap between the expected EXPY and the actual EXPY is very pronounced for provinces such as Las Palmas, Tenerife and Almería, that in 2005 were specialised in varieties of agricultural products, such as tomatoes or cucumbers, where developing countries command a large comparative advantage. If we control for the share of primary products in provinces' total exports, the explanatory capacity of the model raises to almost 40 per cent 3 .

  figures and, hence, to large drops in CanaryIslands' provinces EXPY between 1994 and[START_REF] Lall | The "Sophistication" of Exports: A New Measure of Product Characteristics[END_REF]

  productive goods, relative to their labour productivity, have grown faster than Spanish provinces that have specialised in less productive goods. Hence, our results

  the end of Section 2, we use a sample of countries that reported export and GDP per capita data in2002, 2003 and 2004 to calculate varieties' PRODY. In order to obtain average values for the 2002-2004 period, we have to transform current exports' values into constant exports' values. To perform this operation, ideally, we would like to have exports' price indexes for each country and each HS product included in the sample. Since we do not have those data, we decide to use the US Harmonised System import price index in order to proxy the evolution of export prices in the world; these data were obtained from the Bureau of Labour Statistics. For each country and HS product, we add up the2002, 2003 and 2004 (constant) exports and quantity data. With this procedure we only allow each country to have one variety per each product. Not all exports' observations provide a quantity measure that allows the calculation of the unit value; for example, in our sample such observations account for 7.5 per cent of total sample's exports. The Comtrade database offers export observations that, in most cases, report a net weight figure, which allows a $ per kilogram unit value calculation. In other cases, a supplementary quantity figure is reported as well.

  . The removal of those observations further raises the number of excluded exports to 19.8 per cent of total exports. This figure also includes those exports that are dropped from the sample because there were not enough unit value observations per product to calculate varieties' PRODY. Spanish regions' exports data are obtained from the Agencia Tributaria's database. The database offers annual data on international trade, disaggregated by Spanish provinces and in the Common Nomenclature (CN) classification. The CN is an 8 digit extension of the HS classification used by European Union countries. Hence, there are no difficulties, at first hand, to transform NC products into HS products. However, the Agencia Tributaria reports trade data in the NC classification's revision, and hence in the HS classification's revision, that is in use in each year. This fact introduces some limitations in the calculation of provinces' EXPY.As explained above, we use the 1992 version of the HS classification to calculate the varieties' PRODY. In order to avoid biases, we only calculate provinces' EXPY figures with those products whose classification does not change between 1994 and 2005. Those products represent 90% of total provinces' exports.

Figure 1 .

 1 Figure 1. Relationship between Spanish provinces' GDP per capita and quality-adjusted EXPY, 2005

  Other studies, such as[START_REF] Lall | The "Sophistication" of Exports: A New Measure of Product Characteristics[END_REF], use the share of country j's exports of product i in total world exports of product i as weight in the PRODY calculation. However, as noted by

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		j	j ij X x	, aggregates the shares of product i in y
	total exports across countries. Hence, the weight reflects j country's revealed comparative
	advantage in product i.	i PRODY is, therefore, the average of exporting countries GDP per
	capita, weighted by each country's revealed comparative advantage in product i.
				8

  de Investigaciones Económicas (Ivie) database (www.ivie.es). Human capital is proxied by the percentage of occupied population that have upper-secondary or tertiary studies. Those data are also obtained from the Ivie database. The period of analysis is

	the Instituto Valeciano
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	to avoid the EXPY coefficient from getting human capital's explanatory power, this latter
	variable is also included in the model 4
		16

Value added per province data are obtained from Spanish Statistical Institute's (INE) Regional Economic Accounts database (www.ine.es) 5 . Data on occupied population is obtained from

TABLE 2

 2 which affect, in turn the regression analysis. When we introduce a dummy variable to control for the special behaviour of Canary Islands' provinces (Column (2)), there is an increase in the value of the quality-adjusted EXPY coefficient and it becomes statistically significant at 5 per cent.The conclusions of the pooled OLS model are valid as long as there are not province-level effects. At the end of Column (3) we test whether there are time-invariant province-level characteristics that may affect the validity of the estimation. The F-test shows that we can reject the null hypothesis that all province-level effects are zero. According to this result, we should use a fixed-effects model to analyse whether there is a relationship between a province initial quality-adjusted EXPY and subsequent growth. However, we should stress that the weakness of the FE model is that there is a large reduction in the degrees of freedom compared to the pool estimate.

	AROUND HERE]

Islands' tomatoes unit values are in the medium-quality/high-quality border and small changes in the unit values lead to large swings in the Las Palmas' and Tenerife's quality-adjusted

Table 1 .

 1 values, as explained before, we use the US import price index to transform current values into 2000 constant values. Observations that lack a valid unit value enter the EXPY calculation multiplying their value by the non quality-adjusted PRODY. Finally, in the calculation of Spanish regions' EXPY we do not include some products with a high PRODY, such as sailboats and motorboats, that have a second-hand export market. In most of the cases those produced in Spain; however, as some of them are sold as second-hand products in foreign countries, their inclusion in the EXPY calculation could bias some provinces' sophistication index 6 . We also exclude Badajoz's exports of natural gas; those exports are assigned to Badajoz because the gas pipeline crosses this province in its way to Spanish provinces quality-adjusted EXPY (2000 constant PPP $) : statistically significant at 1%. Source: authors' calculation based on Comtrade and Agencia Tributaria databases.

	products are not Portugal.
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*

Column (3) -Column (6) regressions include period dummies. Robust t-statistics in parentheses. *** statistically significant at 1%; ** statistically significant at 5%; * statistically significant at 10%.

Acknowledgments: I would like to thank the Basque Institute of Competitiveness and the Education, Universities and Research Department of the Basque Government for the financial support to undertake this research. I am grateful to Patricia Canto, two anonymous referees and participants at the XI Encuentro de Economía Aplicada for many helpful suggestions.

Any errors or omissions remains the author's own responsibility.

F14 -Country and Industry Studies of Trade < F1 -Trade < F -International Economics, O40 -General < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and Growth, R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics