Paulus H S Kwakman

L Boer

Carolien P Ruyter-Spira

Tineke Creemers-Molenaar

Johannes P F G Helsper

Christina M J E Vandenbroucke-Grauls

Dr Sebastian A J Zaat

A A Velde

Leonie De Boer

Hans Helsper

Anje A Te Velde

Creemers -Molenaar

Christina M J E Vandenbroucke- 9 Grauls

Medical-grade honey enriched

Keywords: Antibacterial agents, Antimicrobial peptides, honey, MRSA, E. coli ESBL Antibacterial agents 22 Antimicrobial peptides 23

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Introduction

Line 36 -The variation usually seen in the activity of different types of honey is predominantly due to the floral source of the honey. What is the floral source of this honey? This is important if this honey is intended for medicinal use. AUTHOR: different honeys show large variation in activity, which is not solely a result of floral origin; despite the identical floral source, different batches of Manuka honey show a very large variation in activity. As mentioned above, RS honey is different from regular honeys in that it is produced under standardized conditions. Details of this production platform are proprietary information of the manufacturer. Since the honey has been granted CE-certification for application on wounds there is no problem regarding its medical use.

As the antibacterial peptides feature extensively in this work it would be worth briefly introducing them in this section. AUTHOR: a paragraph briefly describing the activity of antimicrobial peptides has been added to the 'Introduction' section (pag. 5, line 4-13).

Methods

Line 41 -how were the bacterial strains identified and stored? AUTHOR: details regarding bacterial isolates have been added (pag. 6, line [START_REF] Matsuzaki | Why and how are peptide-lipid interactions utilized for 15 self-defense? Magainins and tachyplesins as archetypes. 16[END_REF][START_REF] Devine | Cationic peptides: distribution and 18 mechanisms of resistance[END_REF][START_REF] Naiemi | Widespread 2 transfer of resistance genes between bacterial species in an intensive care 3 unit: implications for hospital epidemiology[END_REF]. Strains were identified and stored according to general medical microbiological practice. We consider this common knowledge among the readership of EJCMID, and did not add this to the text.

Results

Quite a bit of material that would be more appropriate for either the Introduction or Discussion sections is included here. While this may be appropriate for this journal it adds unnecessary length to this manuscript, making it repetitive. E.g. page 10 lines 29 -34, 54-58; page 11 lines 5-9, 18-31; page 12 lines 16-24, etc. Some of the figure legends contain too much information, in particular explicitly stating results that are clearly shown in the figures is redundant. AUTHOR: unneccesary repetitive phrases in results section and in figure legends were removed (e.g. phrases on page 11 lines 5-9 in the original manuscript are removed and the legends of fig. 5 & 6 are now condensed).

It would have been worth including a sugar control in these experiments as the concentrations of RS honey needed to inhibit the test organisms seem quite high compared to those one would expect from other medical grade honeys (see further comment in Discussion section). AUTHOR: discussed in reply to the 'General' comments of this reviewer. Page 11, line 43 -from figure 5 it does not look like there is a substantial improvement in activity against VREF, although it does look like there is one for MRSE. Is the figure mislabelled? This statement is also made in the Discussion. AUTHOR: data for VREF and MRSE were indeed mixed up, and is now corrected, thank you. Page 12, line 38 -the controls with just honey seem to have produced different results from those in the previous experiment when comparing figures 5 and 6. AUTHOR: in figure 5 & 6, the LC99.9 (the lowest concentration that results in at least 1000-fold reduction in numbers of CFU) is indicated for 2-fold dilution series of honey. Minor inter-experiment variation can thus result in an apparent 2-fold change in activity when survival of bacteria is near the cut-off for the LC99.9. Indeed, the differences in activity of honey in figure 5 & 6 never exceed one dilution step. Page 12, line 43 -same comment as for Page 11, line 43 above, are MRSE and VREF mixed up? AUTHOR: data for VREF and MRSE were indeed mixed up, and is now corrected, thank you.

Discussion

Much of the Discussion is a repeat of the Results adding unnecessary length to the manuscript. The whole section could be more concise. For example, the MGO paragraph is rather long considering MGO was not tested here. AUTHOR: we have condensed the paragraph on MGO, and also removed unnecessary repetition.

It would be of interest to name the organisms referred to in reference 13, i.e. which "other bacteria" (page 13 line 34) does RS honey have rapid activity against? AUTHOR: the ' other bacteria' refers to results of the current manuscript, and not to reference 13 as assumed by the reviewer. The text has been modified for clarity, and the bacteria are now named explicitly (pag. 14, lines 10-14).

No sugar controls were included and the RS honey activity appears be predominantly due to the osmotic effect of the sugars. This honey does not appear to have been selected based on its floral source, as other medical grade honeys generally are, so RS may not have an inherently high level of activity. AUTHOR: the reviewer has indicated this point previously; see our reply in the 'General' comments section of this reviewer. needs a reference. Also this is the first time Manuka is mentioned, for those not well acquainted with the field of antibacterial honey some explanation as to the relevance of discussing it here would be helpful. AUTHOR: Manuka honey is now briefly described in the introduction (pag. 4, lines [START_REF] Mavric | Identification and 12 quantification of methylglyoxal as the dominant antibacterial constituent of 13 Manuka (Leptospermum scoparium) honeys from New Zealand. 14[END_REF][START_REF] Postmes | The sterilization of 16 honey with cobalt 60 gamma radiation: a study of honey spiked with spores 17 of Clostridium botulinum and Bacillus subtilis[END_REF][START_REF] Kwakman | 21 eradicates skin colonization[END_REF][START_REF] Kwakman | How honey kills 4 bacteria[END_REF][17]. The statement regarding lack of rapid activity of MGO has been removed in the act of condensation of the paragraph on MGO in the Discussion section, so no reference is required.

Page 16 line 14 -the abbreviation AMP is introduced without definition AUTHOR: this abbreviation was indeed not clarified in the Discussion section, this is now corrected.

Page 17 line 7 -it is not appropriate to say that B. cepacia is "highly" susceptible to the RS honey. Quite high concentrations were used here, see sugars comment above. AUTHOR: we have modified this phrase, now stating that B. cepacia is relatively susceptible to honey compared to other bacteria (pag. 17, lines [START_REF] Mavric | Identification and 12 quantification of methylglyoxal as the dominant antibacterial constituent of 13 Manuka (Leptospermum scoparium) honeys from New Zealand. 14[END_REF][START_REF] Postmes | The sterilization of 16 honey with cobalt 60 gamma radiation: a study of honey spiked with spores 17 of Clostridium botulinum and Bacillus subtilis[END_REF][START_REF] Kwakman | 21 eradicates skin colonization[END_REF]. Purpose. Honey has potent activity against both antibiotic-sensitive and -resistant 3 bacteria and is an interesting agent for topical antimicrobial application to wounds. 4

As honey is diluted by wound exudate, rapid bactericidal activity up to high dilution 5 is a prerequisite for its successful application. 6

Methods. We investigated the kinetics of killing of antibiotic-resistant bacteria by 7 RS honey, the source for production of Revamil ® medical-grade honey, and we 8 aimed to enhance the rapid bactericidal activity of RS honey by enrichment with its 9 endogenous compounds or addition of antimicrobial peptides. 10

Results. RS honey killed antibiotic-resistant isolates of Pseudomonas aeruginosa, 11

Staphylococcus epidermidis, Enterococcus faecium and Burkholderia cepacia 12 within 2 hours, but lacked such rapid activity against methicillin-resistant 13

Staphylococcus aureus (MRSA) and extended-spectrum beta-lactamase-14 producing (ESBL) Escherichia coli. It was not feasible to enhance the rapid activity 15 of RS honey by enrichment with endogenous compounds, but RS honey enriched 16 with 75 μM of the synthetic peptide Bactericidal Peptide 2 (BP2) showed rapid 17 bactericidal activity against all species tested, including MRSA and ESBL E. coli, 18 at up to 10-20-fold dilution. 19

Conclusions. RS honey enriched with BP2 rapidly killed all bacteria tested and 20 had a broader spectrum of bactericidal activity than either BP2 or honey alone. 21

INTRODUCTION 1 2

Antibiotic-resistant bacteria pose a very serious threat to public health. For all 3 antibiotic classes, including the major last resort drugs, resistance is increasing 4 worldwide [START_REF] Walsh | Antibiotics: Actions, Origins, Resistance[END_REF]2]. Even more alarming, very few new antibiotics are being developed 5

[1,3], so alternative antimicrobial strategies are urgently needed. 6

The potent in vitro activity of honey against antibiotic-resistant bacteria [4] 7 and its successful application in treatment of chronic wound infections not 8 responding to antibiotic therapy [START_REF] Efem | Clinical Observations on the Wound-Healing 13 Properties of Honey[END_REF] resulted in a revival of the interest in honey as 9

antibacterial agent [START_REF] Bonn | Sweet solution to superbug infections?[END_REF][START_REF] Dixon | Bacteria can't resist honey[END_REF][START_REF] Lusby | Honey: a potent agent 18 for wound healing?[END_REF]. Important prerequisites for application of honey as 10 antimicrobial agent are reproducible and rapid bactericidal activity [START_REF] Simon | 1 Medical honey for wound care--still the 'latest resort'? 2[END_REF] and 11 knowledge of its mechanism of action. 12 Honeys collected from the natural environment including Manuka honey, 13 which is used for production of most currently available medical-grade honeys, 14

show large variation in antibacterial activity [10,[START_REF] Allen | A survey of the antibacterial 6 activity of some New Zealand honeys[END_REF]. Manuka honey can contain 15 very high levels of MGO, which is regarded the major antibacterial compound in 16 this honey [START_REF] Adams | Isolation by HPLC and 9 characterisation of the bioactive fraction of New Zealand manuka 10 (Leptospermum scoparium) honey[END_REF][START_REF] Mavric | Identification and 12 quantification of methylglyoxal as the dominant antibacterial constituent of 13 Manuka (Leptospermum scoparium) honeys from New Zealand. 14[END_REF]. The honey used as a source for Revamil ® medical-grade honey 17 (RS honey) is produced under standardized conditions in greenhouses, and is 18 sterilized by gamma-irradiation to kill potentially present bacterial spores. Gamma 19 irradiation is known not to affect honey bactericidal activity [START_REF] Postmes | The sterilization of 16 honey with cobalt 60 gamma radiation: a study of honey spiked with spores 17 of Clostridium botulinum and Bacillus subtilis[END_REF]. Revamil ® has 20 broad-spectrum, batch-to-batch reproducible bactericidal activity in vitro. It has 21 been shown that it can strongly diminish microbial colonization of the human skin 22 [START_REF] Kwakman | 21 eradicates skin colonization[END_REF]. We have recently identified all major bactericidal factors in RS honey, i.e. its 23 high sugar concentration, H 2 O 2 , low pH, methylglyoxal (MGO) and the cationic 1 antimicrobial peptide bee defensin-1 [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. 2 3 Antimicrobial peptides are known for their potent, rapid broad-spectrum 4 microbicidal activity. Their supposed mechanism of action is direct targeting of 5 microbial membranes [17], although AMPs may also have intracellular targets 6 [18,19]. A cationic domain of these peptides specifically interacts with the 7 negatively charged outer surfaces of micro-organisms and a hydrophobic domain 8 is required for membrane perturbation or penetration, either causing membrane 9 disruption or translocation into the cell [START_REF] Epand | Diversity of antimicrobial peptides and 13 their mechanisms of action[END_REF][START_REF] Matsuzaki | Why and how are peptide-lipid interactions utilized for 15 self-defense? Magainins and tachyplesins as archetypes. 16[END_REF]. Some bacteria have evolved 10 mechanisms to reduce their outer surface negative charge to reduce susceptibility 11

to AMPs [START_REF] Devine | Cationic peptides: distribution and 18 mechanisms of resistance[END_REF]. Since this involves complex biosynthetic pathways, the risk for rapid 12 resistance-development against AMPs is considered low [START_REF] Devine | Cationic peptides: distribution and 18 mechanisms of resistance[END_REF]. 13

In the current study we show that RS honey has potent bactericidal activity, 14 but this requires prolonged exposure of the target organisms. RS honey lacks rapid 15 bactericidal activity against several important antibiotic-resistant wound pathogens, 16 including methicillin-resistant Staphylococcus aureus. We were not able to 17 augment the bactericidal activity of RS honey by enrichment with endogenous 18 honey bactericidal compounds, but addition of the synthetic antimicrobial peptide 19 BP2 did result in broad-spectrum rapid bactericidal activity. Oxacillin susceptibility of S. aureus and S. epidermidis and vancomycin 21 susceptibility of E. faecium were determined by Etest (AB Biodisk) according to the 22 manufacturers' instructions. ESBLs were identified as described by Al Naiemi [START_REF] Naiemi | Widespread 2 transfer of resistance genes between bacterial species in an intensive care 3 unit: implications for hospital epidemiology[END_REF].

7 1

Determination of H 2 O 2 concentration in honey 2

Hydrogen peroxide concentrations in honey were determined quantitatively using a 3 modification of a method described by White & Subers [START_REF] White | Studies on honey inhibine. 2. A 5 chemical assay[END_REF]. Undiluted and ten-fold 4 diluted samples of honey (40 µl) were mixed in wells of microtiterplates with 135 µl 5 reagent, consisting of 50 g/ml o-dianisidine (Sigma) and 20 g/ml horseradish 6 peroxidase type IV (Sigma) in 10 mM phosphate buffer pH 6.5. o-Dianisidine was 7 freshly prepared as a 1 mg/ml stock in demineralized water and peroxidase was 8 diluted from a 10 mg/ml stock in 10 mM phosphate buffer pH 6.5 stored at -20 °C. 9

After 5 min. of incubation at room temperature, reactions were stopped by addition 10 of 120 l 6 M H 2 SO 4 and absorption at 540 nm was measured. Hydrogen peroxide 11 concentrations were calculated using a calibration curve of 2-fold serial dilutions of 12 H 2 O 2 ranging from 2200 to 2.1 M. [START_REF] Mavric | Identification and 12 quantification of methylglyoxal as the dominant antibacterial constituent of 13 Manuka (Leptospermum scoparium) honeys from New Zealand. 14[END_REF] 14

Liquid bactericidal assay 15

Bactericidal activity was quantitatively assessed in low protein binding 16 polypropylene microtiterplates (Costar Corning). Bacteria from logarithmic phase 17 cultures in trypticase soy broth (TSB; BD Difco) were washed twice with incubation 18 buffer containing 10 mM phosphate buffer pH 7.0 supplemented with 1% (v/v) TSB 19 and were suspended at a concentration of 5x10 6 CFU/ml, based on optical density. 20 A 50% (v/v) stock solution of honey was freshly prepared in incubation buffer. For 21 enrichment with antimicrobial peptides, an aliquot of 1.2 mM LL-37 or BP2 stock 22 solutions was added to 50% honey solutions to obtain 37.5 µM of peptide, thus 23 corresponding to enrichment of undiluted honey with 75 µM of the respective 1 peptides. Eighty microliter of diluted honey was mixed with 20 µl of a bacterial 2 inoculum containing 5x10 6 CFU/ml, and plates were incubated at 37°C on a rotary 3 shaker at 150 rpm. At indicated time points, duplicate 10 µl aliquots of undiluted 4 and 10-fold serially diluted suspensions were plated on blood agar. The dilutions 5

were prepared in incubation buffer containing 0.025% sodium 6 polyanetholsulphonate (SPS; Sigma), which neutralizes cationic bactericidal 7 components [START_REF] Dankert | Involvement of bactericidal factors from thrombin-stimulated 8 platelets in clearance of adherent viridans streptococci in experimental 9 infective endocarditis[END_REF]. Bacterial survival was quantified after overnight growth at 37 °C. 8

The detection level of this assay is 100 CFU/ml. 9

To determine the LC99.9 values of LL-37 and BP2, 25 µl aliquots of 2-fold serially 10 diluted peptide in incubation buffer were prepared in polypropylene microtiterplates 11 (Costar Corning) and to each of the wells 25 µl of a bacterial suspension 12 containing 2x10 6 CFU/ml was added. After 2 h of incubation on a rotary shaker at 13 150 rpm at 37°C, triplicate 10 µl aliquots were plated on blood agar plates. The 14 plates were inspected for growth after 24 h. LC99.9 was defined as the lowest 15 concentration of peptide which killed >99.9% of the inoculum of 10 6 CFU/ml after 2 16 h. 17 18

Partial purification of bee defensin-1 19

We previously demonstrated that bee defensin-1 is the only bactericidal 20 factor in the >5 kDa fraction of RS honey [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. To prepare a >5 kDa fraction, 15 ml 21 of 20% (v/v) honey was centrifuged in a 5 kDa molecular weight cut-off Amicon 22

Ultra-15 tube (Millipore) at 4000 x g for 45 min. at room temperature. The >5 kDa 23 retentate was subsequently washed three times in the filter tube with 15 ml of 1 demineralized water and concentrated to 0.3 ml. 2 3 10 RESULTS 1 2

Kinetics of bactericidal activity of RS honey 3

We determined the kinetics of bactericidal activity of different dilutions of RS 4 honey against various antibiotic-resistant pathogens. RS honey at a concentration 5 of 40% (v/v) reduced survival of methicillin-resistant Staphylococcus epidermidis 6 (MRSE), vancomycin-resistant Enterococcus faecium (VREF), enhanced-spectrum 7 beta-lactamase-producing (ESBL) Pseudomonas aeruginosa and Burkholderia 8 cepacia to undetectable levels within 2 hours, while similar activity against 9 methicillin-resistant Staphylococcus aureus (MRSA) and ESBL Escherichia coli 10 required 6 hours of incubation (Fig. 1). RS honey at a concentration of 20% killed 11 B. cepacia within 4 hours of incubation, while activity against all other bacteria 12 required 24 hours of incubation (Fig. 1). RS honey diluted to 10% killed MRSA and 13 MRSE after 24 hours but lacked activity against all other bacteria tested (Fig. 1). 14

Even in undiluted RS honey, survival of MRSA was not affected within 2 15 hours (supplemental Fig. 2) of incubation and numbers of CFU of E. coli ESBL 16 were only reduced by 2.3-log. After 24 hours incubation in undiluted honey, 17 survival of E. coli was reduced to undetectable levels but numbers of CFU of 18 MRSA were only reduced by 1-log (supplemental Fig. 2). In summary, RS honey 19 did not rapidly kill MRSA and E. coli ESBL, and rapid activity against all other 20 species tested was abolished upon dilution of the honey to ≤ 20%. Since MRSA and E. coli ESBL were not rapidly killed by RS honey, we 2 assessed whether the endogenous concentrations of bactericidal compounds in 3 RS honey might be too low for rapid activity. Dilution of RS honey to 30% was 4 optimal for H 2 O 2 accumulation, resulting in maximal concentrations of 22.5 ± 1.3 5 µg/ml and 148.4 ± 27.8 μg/ml H 2 O 2 after 2 and 24 hours, respectively (Fig. 3a) [START_REF] Bonn | Sweet solution to superbug infections?[END_REF] incubations not containing honey but only H 2 O 2 , 3200 µg/ml H 2 O 2 was required to 7 kill MRSA within 2 hours (Fig. 3b). This is 142 times the concentration of H 2 O 2 that 8 maximally accumulated in RS honey after a similar 2 hours incubation period, 9

indicating that the H 2 O 2 concentration in honey is far too low for rapid activity 10 against MRSA. In view of possible toxicity (see discussion), it is not feasible to 11 increase the concentration of H 2 O 2 in honey to the level required for rapid killing. 12 For similar reasons we did not assess enrichment of RS honey with MGO. 13 14 15

Bee defensin-1 concentration required for rapid killing of MRSA 16

Next, we assessed the contribution of bee defensin-1 to rapid bactericidal 17 activity of RS honey. At the concentration present in undiluted RS honey, bee 18 defensin-1 effectively killed Bacillus subtilis, a highly bee defensin-1-susceptible 19 organism [START_REF] Kwakman | How honey kills 4 bacteria[END_REF], within 2 hours (Fig. 4a). However, this peptide had no substantial 20 activity against MRSA, E. coli ESBL or VREF (Fig. 4a). Even at an 8-fold higher 21 concentration, bee defensin-1 reduced numbers of CFU of MRSA after 2 hours by 22 only 1-log (Fig. 4b), indicating that it also was not feasible to enhance the rapid 1 bactericidal activity of RS honey by increasing the concentration of bee defensin-1. 2 3 4

Enhanced rapid bactericidal activity of LL-37-enriched honey 5

We subsequently assessed the potential of LL-37, a broad-spectrum human 6 antimicrobial peptide expressed in neutrophils and various epithelial cells [START_REF] Sorensen | The human antibacterial cathelicidin, hCAP-18, is synthesized in 12 myelocytes and metamyelocytes and localized to specific granules in 13 neutrophils[END_REF][START_REF] Frohm | The human cationic antimicrobial protein 16 (hCAP18), a peptide antibiotic, is widely expressed in human squamous 17 epithelia and colocalizes with interleukin-6[END_REF], 7

to enhance the rapid bactericidal activity of honey. RS honey was enriched with 8 tenfold excess (75 µM) of the concentration LL-37 required to reduce survival of 9 MRSA to undetectable levels (Fig. 5a). The lethal concentration of LL-37 for 10 99.9% of the inocula (LC99.9) of MRSA and E. coli in 2 hour incubations were 7.5 11 and 1.9 µM, respectively (Fig. 5a). Enrichment of RS honey with LL- 37 12 substantially improved the activity against E. coli ESBL and VREF but not against 13 other bacteria tested (Fig. 5b). LL-37-enriched honey retained bactericidal activity 14 against E. coli ESBL and VREF up to 20-fold dilution, which was a major 15 improvement compared to non-enriched honey (Fig. 5b). The LC99.9 of LL-37 in 16 honey however was 4-fold higher than in incubation buffer (Fig. 5b), indicating that 17 honey inhibited LL-37. Inhibition was even more clear from the tests with MRSA, 18 MRSE and P. aeruginosa. Enrichment with LL-37 did not substantially improve the 19 activity of honey while LL-37 alone effectively killed these bacteria (Fig. 5b). 20 21 22

Enhanced bactericidal activity of BP2-enriched honey 23

The synthetic antimicrobial peptide Bactericidal Peptide 2 (BP2) has potent 1 activity in physiological salt concentrations and in plasma, and is effective in vivo in 2 a mouse model of biomaterial-associated infection [START_REF] Kwakman | The tandem of free radicals and methylglyoxal. 1[END_REF]. The LC99.9 concentrations 3 of BP2 for MRSA and E. coli in 2 hour incubations were 1.9 and 3.8 µM, 4 respectively (Fig. 6a). RS honey enriched with tenfold excess (75 µM) of the 5 concentration BP2 required to reduce survival of MRSA to undetectable levels (Fig. 6 6a) retained bactericidal activity against all bacteria tested up to 20-fold dilution, 7 except for P. aeruginosa (Fig. 6b), which was killed by up to a 10-fold dilution of 8 this enriched RS honey (Fig. 6B). Non-enriched RS honey lacked rapid bactericidal 9 activity for all bacteria tested when diluted more than 2.5-fold. 10

The activity of BP2 against E. coli ESBL and VREF was not inhibited in 11 honey (Fig. 6b). Killing of MRSA, MRSE and P. aeruginosa ESBL required 2-4 fold 12 higher concentrations of BP2 in honey than in buffer (Fig. 6b). This indicates a 13 slight reduction of BP2 activity in honey, but markedly less than the observed 14 inhibition of LL-37 in honey. We conclude that enrichment with 75 µM BP2 15 markedly enhanced the rapid bactericidal activity of RS honey. 16

DISCUSSION 1 2

The potent activity against antibiotic-resistant pathogenic bacteria makes 3 honey an interesting agent to treat topical infections not responding to antibiotics. 4

Ideally, honey used for such applications should have rapid and broad-spectrum 5 bactericidal activity. In addition, honey should remain active upon dilution, since 6 honey will rapidly be diluted at the wound interface due to its hygroscopic 7 characteristics and the presence of wound exudate. 8 RS honey has reproducible, broad-spectrum bactericidal activity in vitro and 9 effectively reduces microbial colonization of human skin [START_REF] Kwakman | 21 eradicates skin colonization[END_REF]. Our present results, 10 however, show that the activity of this honey against the major wound-infecting 11 pathogens MRSA and E. coli ESBL is not rapid. Honey does have rapid activity 12 against P. aeruginosa, E. faecium and S. epidermidis but this activity is lost when 13 RS honey becomes diluted. Of note, B. cepacia, an otherwise notoriously antibiotic 14 resistant pathogen, proved to be the most honey-susceptible organism. 15

Enhancement of activity of RS honey with its endogenous microbicidal compounds 16

appeared not to be feasible, but addition of the cationic antimicrobial peptide BP2 17 did increase the activity to the desired levels. 18

19

We recently identified all bactericidal factors in RS honey using an approach 20 of successive neutralization of individual factors combined with activity-guided 21 isolation of factors responsible for residual bactericidal activity [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. Thus, we 22 determined that the high sugar concentration, H 2 O 2 production, MGO, the low pH 23 and bee defensin-1 were responsible for bactericidal activity of RS honey. In order 1 to enhance the rapid bactericidal activity of RS honey, we first assessed the 2 potential of H 2 O 2 and of bee defensin-1. Upon dilution of honey, H 2 O 2 is produced 3 by the glucose oxidase enzyme from the bees [START_REF] White | Studies on honey inhibine. 2. A 5 chemical assay[END_REF]29]. Production of H 2 O 2 was 4 highest in RS honey diluted to 30%, in which 22.5 and 148 µg/ml accumulated 5 after 2 and 24 hours, respectively. In a study with 90 different honeys, 12 ± 19 6 µg/ml hydrogen peroxide (range 0 -72 µg/ml) accumulated in honey diluted to 20% 7 (w/v) after 4 hours [START_REF] White | Studies on honey inhibine. 2. A 5 chemical assay[END_REF], indicating that RS honey produces relatively high levels of 8 H 2 O 2 . 9

MRSA is highly susceptible to H 2 O 2 -mediated killing by RS honey upon 10 incubation for 24 hours [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. Killing of MRSA within 2 hours by H 2 O 2 in absence of 11 honey required a concentration as high as 3200 µg/ml H 2 O 2 (corresponding to a 12 0.32% (w/v) solution). Wound cleansing with a 3% (w/v) solution of H 2 O 2 has been 13 a clinical practice, but at this concentration H 2 O 2 is toxic to human cells and skin 14 tissue and tissue exposure can result in delayed wound healing [30][31][32] . Although 15 the concentration of H 2 O 2 required to kill MRSA was about 10-fold lower than the 16 concentration used for wound cleansing, we did not consider increasing the levels 17 of H 2 O 2 as a possibility to improve the rapid bactericidal activity of RS honey. 18

Bee defensin-1 (also referred to as royalisin [33]) is a 51-residue 19 antimicrobial peptide identified in honey bee hemolymph, royal jelly and in honey 20 [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]33,34]. Because of its complicated folding with three intramolecular cysteine 21 bonds, synthetic production of bee defensin-1 is not possible and recombinant 22 production would be highly challenging. Bee defensin-1 effectively kills B. subtilis 23 but lacks activity against all other bacteria tested at a concentration equivalent to 1 that in undiluted honey. Even at an 8-fold higher concentration, bee defensin-1 2 only slightly reduced survival of MRSA. The narrow spectrum of its bactericidal 3 activity renders bee defensin-1 unsuited for enhancement of the bactericidal 4 activity of honey. 5

MGO is present in RS honey at a relatively low concentration (0.25 mM) 6 compared to the concentrations reported for Manuka honey (up to 16.1 mM) [START_REF] Adams | Isolation by HPLC and 9 characterisation of the bioactive fraction of New Zealand manuka 10 (Leptospermum scoparium) honey[END_REF]. 7

MGO is a reactive metabolite that can exert toxic effects by direct inhibition of 8 enzymes, by genomic modifications resulting in carcinogenesis and by protein 9 modifications resulting in the formation of advanced glycation endproducts [35]. 10

The latter are believed to be main determinants for pathological effects related to 11 diabetes [36,[START_REF] Stitt | The role of advanced glycation in the pathogenesis of 5 diabetic retinopathy[END_REF]. Because of the concerns regarding potential toxicity of MGO we 12 did not pursue to augment the activity of RS honey with this compound. 13

Other honey bactericidal factors are the high sugar concentration and low 14 pH. Honey is a super-saturated sugar solution, so it is not possible to further 15 increase its sugar concentration. RS honey has a pH of 3.2, which is at the lower 16 end of the pH range found for honeys (3.2 -4.5) [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. Even such a low pH only 17 contributed to the activity against B. subtilis after 24 hours of incubation, and not to 18 the activity against other bacterial species [START_REF] Kwakman | How honey kills 4 bacteria[END_REF]. Therefore, the sugar concentration 19 and low pH were not suited as factors for enhancement of the bactericidal activity 20 of honey. 21

In contrast to bee defensin-1, most antimicrobial peptide (AMPs) have 1 broad-spectrum bactericidal activity. The human α-helical AMP LL-37 is one of the 2 best characterized AMPs [START_REF] Zanetti | Cathelicidins: a novel protein 7 family with a common proregion and a variable C-terminal antimicrobial 8 domain[END_REF][START_REF] Lehrer | Cathelicidins: a family of endogenous 10 antimicrobial peptides[END_REF][START_REF] Niyonsaba | Protective roles of the skin against 12 infection: Implication of naturally occurring human antimicrobial agents 13 [beta]-defensins, cathelicidin LL-37 and lysozyme[END_REF][START_REF] Putsep | Deficiency of 16 antibacterial peptides in patients with morbus Kostmann: an observation 17 study[END_REF]. Despite its potent activity in incubation buffer, 3 LL-37 was strongly inhibited in the presence of honey. BP2 is a synthetic AMP with 4 very rapid broad-spectrum microbicidal activity, which is retained in plasma and in 5 physiological salt solution [START_REF] Kwakman | The tandem of free radicals and methylglyoxal. 1[END_REF]. BP2 also effectively kills S. epidermidis in vivo, in a 6 murine model of biomaterial-associated infection [START_REF] Kwakman | The tandem of free radicals and methylglyoxal. 1[END_REF], indicating its potential for 7 clinical application. The activity of BP2 against E. coli ESBL and VREF was not 8 inhibited in honey, and activity against MRSA, MRSE and P. aeruginosa ESBL 9 required only slightly higher (2-4 fold) concentrations in honey than in buffer. Thus, 10 BP2 certainly was suited for enrichment of honey. 11 B. cepacia is notorious for its intrinsic resistance against antibiotics [START_REF] Govan | Microbial pathogenesis in cystic fibrosis: 1 mucoid Pseudomonas aeruginosa and Burkholderia cepacia[END_REF][START_REF] Clore | Three-dimensional structure of interleukin 8 in solution[END_REF] and 12

AMPs [START_REF] Turner | Activities 7 of LL-37, a cathelin-associated antimicrobial peptide of human neutrophils[END_REF] and is indeed not susceptible to LL-37 [START_REF] Turner | Activities 7 of LL-37, a cathelin-associated antimicrobial peptide of human neutrophils[END_REF] or to BP2 [START_REF] Kwakman | The tandem of free radicals and methylglyoxal. 1[END_REF]. Our results 13 demonstrate however that B. cepacia is relatively susceptible to honey compared 14 to other tested bacteria, which is in accordance with findings of Cooper et al. [START_REF] Cooper | Susceptibility of 10 multiresistant strains of Burkholderia cepacia to honey[END_REF]. 15

Not surprizingly, addition of BP2 to RS honey did not enhance the bactericidal 16 activity against B. cepacia (not shown). 17

6 7 BP2 14 15

 671415 Unprocessed Revamil source (RS) honey was kindly provided by Bfactory Health 4 Products (Rhenen, The Netherlands). 5Peptides (GKWKLFKKAFKKFLKILAC) and LL-37 were synthesized at Pepscan 8 Systems (Lelystad, The Netherlands) using solid-phase Fmoc (9-9 fluorenylmethoxycarbonyl) chemistry with a free amine at the N-terminus and a 10 free amide at the C-terminus. Peptides were HPLC-purified and purity (>95%) and 11 mass were confirmed by ionspray mass spectrometry. The lack of disulphide 12 formation between free cysteines of BP2 was confirmed by Q-TOF/MS analysis. 13MicroorganismsBactericidal activity was assessed against clinical isolates of methicillin-resistant 16Staphylococcus aureus (MRSA), methicillin-resistant Staphylococcus epidermidis 17 (MRSE), vancomycin-resistant Enterococcus faecium (VREF), extended-spectrum 18 beta-lactamase producing Escherichia coli (E. coli ESBL) and Pseudomonas 19 aeruginosa ESBL and against the Burkholderia cepacia ATCC 25416 type strain. 20

21 11 H

 11 2 O 2 concentration required for rapid killing of MRSA 1

24 Funding 1 ofFig. 1 7 Fig. 2 13 14Fig. 3 21 Fig. 4 8 Fig. 5 18 Fig. 6 21 logFigure 6

 24117213321485186216 FIGURE LEGENDS 1

Conflict of interest 5

None to declare 6


come

The reversible stress-induced magnetization (inverse magnetostriction or Villari effect) has been measured in a polycrystalline Ni-Fe-Ga-Co ferromagnetic martensite. The samples were mechanically excited using longitudinal resonant oscillations at frequencies close to 100 kHz, and experiments were performed over the temperature range 170 -350 K under variable polarizing fields. It has been found that the reversible inverse magnetostriction changes its sign under low polarizing fields over a certain temperature range with its upper limit close to the Curie temperature. We argue that the variations of sign of the reversible inverse magnetostriction effect are related in the present experiments with the change of the sign of magnetostriction, as has additionally been verified in test measurements performed for pure Ni and Fe. The observed peculiarity of magnetoelastic coupling is also reflected in the temperature dependence of electrical resistance and even produces a minor effect in calorimetry scans. Possible origins of these features of magnetoelastic coupling are discussed.

.H\ZRUGV ferromagnet; shape memory alloy; martensite; magnetostriction Magnetically ordered alloys undergoing a thermoelastic martensitic transformation have been attracting considerable attention due to the possibility of inducing large strains by magnetic field [START_REF] Ulakko | SSO 3K\V /HWW[END_REF][START_REF] Murray | SSO 3K\V /HWW[END_REF] and producing high magnetocaloric effect [START_REF] Zhou | [END_REF]4]. These alloys demonstrate a number of structural modifications, both in the martensitic and parent phases, like magnetic anomalies [START_REF] Pakhomov | UDQVDFWLRQV RQ 0DJQHWLFV 2718[END_REF][START_REF] Murakami | [END_REF][7][8][9] and intermartensitic transformations [10][11][12][13][14] a clear physical origin for which is still lacking. The above mentioned anomalies have been studied by means of measurements of the electrical resistance, calorimetry, elastic and anelastic properties as well as variety of magnetic characteristics.

Recently, a technique for mechanomagnetic spectroscopy has been designed, based on measurements of the reversible inverse magnetostriction effect under periodic stress simultaneously with elastic and anelastic properties of ferromagnetic materials over wide ranges of temperatures, mechanical stress amplitudes and under variable polarizing magnetic field [START_REF] Kustov | SSO 3K\V /HWW[END_REF]. The designed technique is a new development of previous experimental works in which periodic stress/strain induced magnetization of ferromagnetic materials has been studied [START_REF] Pravdin | 6RYLHW -RXUQ 1RQ[END_REF][17][18][START_REF] Hatafuku | QJLQHHULQJ LQ -DSDQ[END_REF]. In the present work, the following experimental facilities have been introduced in the experimental studies of the reversible inverse magnetostriction: i) determination of the phase of the stress-induced induction (in contrast to just rms values registered before); ii) simultaneous study of magnetic and anelastic properties; and, the most important, iii) possibility to perform the experiments over wide temperature ranges, whereas previously the measurements were made only at ambient temperatures. This technique has already been applied to compare the dynamics of elastic and magnetic domain boundaries in Ni-Fe-Ga polycrystalline ferromagnetic martensites [START_REF] Kustov | SSO 3K\V /HWW[END_REF]. In the present work we focus our attention on two aspects related to i) methodology of studying magnetoelastic effects, and ii) specific experimental results revealing so far unknown peculiarities of magnetoelastic coupling in ferromagnetic martensites. As far the first aspect is concerned, it should be reminded that the differential direct and inverse magnetostriction effects are linked [START_REF] Bozorth | [END_REF] through the Maxwell relations:

¥ % + O O       ∂ ∂ =       ∂ ∂ σ σ 1 , (1)
where O, +, % and σ are the length of the sample, magnetic field, induction and stress, respectively.

Applying a method similar to the one used in determining the magnetocaloric effect, one easily obtains from (1) the magnetostriction λ ∆OO upon application of a field + as a function of differential inverse magnetostriction:

G+ % G+ + O O + ¦ ¦ ¦ ∫ ∫       ∂ ∂ =       ∂ ∂ = * * 0 0 * 1 ) ( σ λ σ .
(

) 2
It should be noted here that the experimental method used in the present work yields a periodic magnetic response of the crystal with induction amplitude 0 % to a periodic mechanical stress with an amplitude 0 σ , the action of the latter being equivalent to application of a certain anisotropy field + σ . Estimations have shown that the magnitude of the stress anisotropy field is of the order of only 10 A/m for characteristic stress amplitudes of around 1 MPa [START_REF] Kustov | SSO 3K\V /HWW[END_REF]. Therefore, in the presence of a static bias field up to 20 kA/m, the periodic stress produces a small oscillatory anisotropy field superimposed on the biasing field. The stress-induced induction in the studied Ni-Fe-Ga-Co alloy is essentially linear with respect to stress amplitude within the range of 0 σ employed, 0 0 σ ∝ % , very much like in the ternary Ni-Fe-Ga system [START_REF] Kustov | SSO 3K\V /HWW[END_REF]. Therefore, their ratio, following Bozorth notation [START_REF] Bozorth | [END_REF],

0 0 σ % = Λ
, is stress-amplitude independent and in the presence of static biasing field should be treated as reversible inverse magnetostriction 0

0 lim 0 0 σ σ % = Λ → .
Maxwell-type relations are also fully applicable to the reversible direct and inverse magnetostriction effects, as has been confirmed experimentally for steel [START_REF] Pravdin | [END_REF] and nickel polycrystals [23], reflecting the relationship between the "motor" and "generator" coefficients of a ferromagnet [START_REF] Jiles | FWD 0DW[END_REF]. Therefore, measured stress-induced magnetization reflects not only the reversible inverse magnetostriction, but also, through the Maxwell-type relation, the reversible direct magnetostriction. Thus, plots of 0 0 σ % versus +, or 0 0 σ % versus 7 (or simply % § + and % § 7 if the stress amplitude σ § is kept constant) reflect correspondingly the field and temperature dependences of the reversible magnetostriction of the material, so that one can equally well use both these terms to characterize the observed magnetoelastic effects. Reversible and differential characteristics (direct and inverse magnetostriction, permeability) are equal only under hysteresis-free conditions. In that case

∫         = * 0 0 0 * ) ( ¨¨G+ % + σ λ . ( 3
)
In the presence of hysteresis the reversible magnetostriction differs notably from the differential one [START_REF] Bozorth | [END_REF] and (3) breaks. Moreover, experiments show that the reversible inverse magnetostriction measured in the ultrasonic frequency range is substantially lower than the static one [START_REF] Pravdin | 6RYLHW -RXUQ 1RQ[END_REF]. Nevertheless, we will use [START_REF] Zhou | [END_REF] later on to evaluate the magnetostriction from reversible inverse magnetostriction in the case of quenched Ni-Fe-Ga-Co samples which demonstrate a very low value of coercive field. Similar estimations will be done also for reference samples of Fe and Ni in order to check the signs and compare the magnitudes of the magnetostriction obtained in these materials using the present technique.

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Ultrasonic resonant oscillations of a four component oscillator (two quartz transducers, intermediate non-magnetic bar produced from low-damping Al-Mg alloy and the sample) were generated by means of the equipment described elsewhere [START_REF] Kustov | [END_REF]. Each element of the composite oscillator, operating at a frequency of around 100 kHz, was measuring half ultrasonic wave length in the corresponding material.

The stress-induced induction produced in the sample by an oscillatory stress/strain in a standing wave was detected by a small pickup coil (with a height of 2 mm) placed around the oscillatory stress antinode in the middle of the sample. The magnitude (modulus) and the phase of the stress-induced induction were determined using an EG&G 5208 lock-in amplifier with an upper frequency limit of 200 kHz. The reference signal was produced from the AC voltage drop on an active resistance by the current flowing through the gauge quartz, which is proportional to and is in phase with the velocity at the end of the transducer [27] (which has the same value for each element of the composite oscillator due to the continuity property). Measurements of the modulus and the phase of the magnetization were performed for a fixed value of applied magnetic field as a function of temperature and also for different fixed temperatures under cyclic polarizing field. In these experiments the oscillatory amplitude of the sample was typically kept constant at 1×10 -5 or 2×10 The Curie and the DSC peak temperature of the direct martensitic transformation for the SC samples were found to be 327 and 360 K. Quenching produces a strong martensite stabilization effect in the present alloy [28]. The major feature of the stabilization effect is a substantial shift to higher temperatures of the first reverse transformation after the thermomechanical treatment, which usually disappears in the second and subsequent reverse transformations. In the present alloy the first reverse transformation is displaced to around 570 K. The direct and reverse transformation temperatures registered after the first reverse transformation (when the stabilization effect is removed) return to their values of around 340 and 350 K, respectively. According to the results previously obtained for the present alloy [28], water quenching and slow cooling produce samples with low and high degrees of the long-range atomic ordering, respectively. Quenching results also in a rather diffuse para-ferromagnetic transition, for which the Curie temperature can be estimated as 277 K. Magnetoelastic properties were studied in three WQ and two SC samples, which showed a good reproducibility of data.

Polycrystalline samples of 99.99% purity iron and nickel, for which magnetostriction data are well documented were used as a reference material. Samples were annealed in an evacuated quartz tube for 7 hrs at 1170 K (Fe) and 3 hrs at 1270 K (Ni) and slowly cooled. ±+© is an obvious effect, related to a change of the direction of preferential magnetic moments alignment without applied stress. As it is well known [29,30], applied stress σ induces uniaxial anisotropy: if 0 > λσ , where λ is the magnetostriction coefficient, the stress direction is an easy axis and magnetic moments tend to align along the applied stress (along the easy axes closest to the stress direction in anisotropic materials), if 0 < λσ , the stress creates an easy plane perpendicular to the stress axis. Thus, for different directions of the internal field (i.e. preferential domain alignment), the same positive (tensile) stress in the case of positive magnetostriction λ will tend to additionally align magnetic moments along the sample axis in opposite directions and therefore will produce the flux variations of different signs through the pickup coil. The same is true for the compressive stress in the case of negative magnetostriction.

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The λ+ dependence obtained for the initial quarter of cycle from the demagnetized state of a sample using ( 3) is also shown in figure 1(c). The data thus derived demonstrate a maximum at around 13 kA/m and a change of the sign at around 16 kA/m. Such behaviour of the fractional length change with applied field is a " signature" of polycrystalline iron, related to the interplay of contributions of positive 100 λ and negative 111 λ magnetostriction constants and corresponds well with the results of classical works [29,30]. The real part of the reversible inverse magnetostriction and calculated fractional length change for a Ni sample are shown in figure 2. In full agreement with available data [29,30] λ+ demonstrates no change of the sign of magnetostriction, which is opposite to the sign obtained for Fe in low fields, the absolute values of the magnetostriction being nearly an order of magnitude higher with respect to Fe.

The absolute values of magnetostriction calculated from the reversible inverse magnetostriction are substantially lower than the well established data on static fractional change of the length [29,30]. This discrepancy, as discussed in the Introduction section, should be attributed to the existence of the magnetic hysteresis in both materials and using rather high frequencies of around 100 kHz. However, despite the difference in absolute values of magnetostriction obtained from (3) and static fractional length change, the method used detects perfectly qualitative peculiarities of λ+ dependences in both test materials used (e.g., different signs of magnetostriction in polycrystalline Ni and Fe, substantial difference in their absolute values and the change of the sign of λ(H) in Fe for increasing fields). As a summary, test experiments with reference Fe and Ni samples successfully detect characteristic features of magnetostriction behaviour in these materials despite the restrictions imposed on application of (3) as discussed above in the Introduction section, and, thus, confirm the applicability of this technique to study qualitative peculiarities of magnetoelastic coupling.

)HUURPDJQHWLF 1L)H*D&R DOOR\ Figure 3 shows the temperature spectra of low-field susceptibility for a WQ and SC samples of the Ni-Fe-Ga-Co alloy. The para-ferromagnetic transition is well defined in SC sample, possessing a high degree of long-range atomic order, with a sharp peak at 318 K, just below the Curie temperature of 327 K, determined from the maximum slope of the permeability versus temperature. Such peak in permeability is often referred to as Hopkinson peak and is observed in a variety of ferromagnetic materials, see e.g. [31,32]. On the contrary, the transition is rather diffuse in a disordered WQ sample.

The Hopkinson-type peak cannot be detected and the Curie temperature, determined in the same way as in SC sample, is around 277 K. to the para-ferromagnetic transition closely remind the data on low-field susceptibility, figure 3: the transition as detected by the inverse magnetostriction is sharp and is also accompanied by the Hopkinson-type peak at 318 K for SC samples, whereas the para-ferromagnetic transition is diffuse in WQ samples. Above the 7© , the inverse magnetostriction gradually decreases with increasing temperature, much like the permeability does. However, one immediately notices an essential difference between the permeability and inverse magnetostriction spectra, which consists in the presence of several minima in the stress-induced magnetization: the first one being situated just above the Curie temperature, the second one well in the ferromagnetic state of the material at around 210-240 K. Figure 4(b) evidences that each minima of the inverse magnetostriction, as in the case of iron samples, figure 1, corresponds to a change of the phase of the stress-induced induction by approximately 180°. In other words, the reversible inverse/direct magnetostriction in Ni-Fe-Ga-Co alloy changes its sign twice: just above the Curie temperature and at lower temperatures in the ferromagnetic state.

Figure 4(c) indeed demonstrates that the real part of the stress-induced magnetization, calculated from the modulus and the phase data, crosses the temperature axis twice. In each zero-crossing point, the magnetization of the sample is not affected by the applied periodic stress. The points, wherein the magnetization of a ferromagnet looses its sensitivity to applied stress are known as Villari critical points [29]. In the case of a small periodic excitation and reversible magnetostriction, such points have been referred to as differential reversible Villari critical points [START_REF] Pravdin | 6RYLHW -RXUQ 1RQ[END_REF]. The sign of the stress-induced induction at high and low temperature sides of the temperature spectra is the same as in Fe sample for low values of polarizing field. That means that the reversible direct/inverse magnetostriction is positive at high and low temperatures and is negative in the intermediate temperature range. However, observations of change of the sign of reversible inverse magnetostriction in temperature spectra does not necessarily imply the change of the sign of magnetoelastic coupling: the change of the sign of reversible inverse magnetostriction corresponds just to passing through an extremum in %σ (or λ+) dependence if it is not monotonous and the position of the extremum is temperature-dependent. Studying the reversible inverse magnetostriction as a function of + allows one to clarify whether or not the static magnetostriction λ also changes its sign. Figure 5 (a) to (d) shows the magnitude of the stress-induced induction registered in a WQ sample at different temperatures under cyclic polarizing field. The results demonstrate a dramatic variation of these magnetic " signatures" in the vicinity of zeros of the inverse magnetostriction. The magnetic field dependences show different types of behaviour, with (for example, for temperatures from T=231 to T= 273 K) or without (T=200, 215 K) several minima/maxima, which change qualitatively upon relatively small variations of temperature. Analysis of the in phase component of magnetization, figure 6 (a) to (d), allows one to clarify different tendencies. Over the temperature range from 200 to 266 K the hysteresis loops are very narrow: the hysteresis is even difficult to distinguish in figure 6 (a) and (b). With increasing temperature the loops turn to rotate clockwise (corresponding thus to lower absolute values of magnetoelastic coupling), and, in addition, a dip appears at low polarizing fields whose minimum position is temperature-dependent and which displace the stress-induced induction into the 2 nd and 4 th quadrants from the 1 st and 3 rd ones. The positioning of the hysteresis loops in the 2 nd and 4 th quadrants means that Λ becomes negative. The minimum value of % § in the 2 nd quadrant and the maximum in the 4 th one are reached at around 250 K, figure 6(b). At higher temperatures, between 250 and 275 K, figure 6(c), the hysteresis loops displace backwards to their initial positions in the 1 st and 3 rd quadrants. In that case, however, the position of the minima/maxima along the field axis is essentially unchanged. Interestingly, this transformation of hysteresis loops is accompanied by appearance of a notable hysteresis at low applied fields. Between 273 and 288 K, figure 6(d), the motion of the loops towards the 1 st and the 3 rd quadrants continues. Finally, somewhat above 275 K the loops return completely to their initial positions in the 1 st and the 3 rd quadrants. Thus, a reversible change of the sign of the inverse and, hence, direct reversible magnetostriction effect takes place over a certain temperature range, which depends on the magnitude of the polarizing field. For high values of polarizing field, the magnetostriction always remains in the 1 st and the 3 rd quadrants, i.e., it always remains positive.

For the external field of 4.25 kA/m these transitions occur around 240 and 275 K, in full agreement with data of figure 3, although the temperature spectra and hysteresis loops shown in figure 6 correspond to different samples.

The very narrow (in the limit, disappearing) hysteresis in WQ samples implies that the reversible inverse/direct magnetostriction becomes closer to the differential one:

σ λ σ σ       ∂ ∂ =       ∂ ∂ ≈ = Λ + % % 0 0 .
Therefore, integration of ) ( 0 0 + % σ loops according to (3) yields in that case a very reasonable estimation for the qualitative behaviour of the field dependence of the static magnetostriction λ+. The results of such integration are depicted in figure 7. We mention first of all that the magnetostriction is positive (like in iron at room temperature and low fields) at high and low temperatures. For the intermediate temperatures and relatively small values of polarizing field (below approximately 18 kA/m) the magnetoelastic coupling changes its sign. The values of polarizing field for which the λ+ dependences change their sign are the Villari (in that case not differential) critical points, wherein the magnetization looses its sensitivity to stress. Figure 8 depicts similar % § + hysteretic loops for one of the SC samples. Two plots, figures 8(b) and 8(d), again reflect the behaviour of the alloy close to the two differential Villari critical points. The most striking difference between WQ and SC samples is that the hysteresis is practically absent in the former below the Curie temperature, figure 6, whereas the hysteresis is quite wide in the latter. However, similar to the WC samples, the hysteresis loops change their positions in the vicinity of the two differential Villari points from the 1 st and 3 rd quadrants to the 2 nd and the 4 th and vice versa. Existence of the hysteresis facilitates observation of the fact that simultaneously with such rotation of the loops, the change of the direction of the circulation along the loops takes place. This effect can be illustrated by figure 8(b). One sees that on lowering temperature from 262.4 K to 250 K a " neck" appears in the middle part of the loop, the direction of the circulation being the same. In between 250 and 244 K the two parts of the formed " neck" collapse and switch their positions. This results in the inversion of the circulation direction along the central part of the loop, keeping, however, the former direction of the circulation close to the extremities of the loops. The latter completely disappears upon further cooling by just a few degrees down to 240 K. Figures 8(d) and 6(d) demonstrate that, despite the substantial difference in the coercive force between SC and WQ samples below the Curie temperature, the behaviour of the loops close to the differential Villari point just above 7© is essentially the same. The presence of a significant magnetic hysteresis in SC samples does not allow one to obtain the λ+ dependences similar to those for WQ samples, figure 7. Nevertheless, we believe that the similarity of the temperature spectra (figure 4) and of the effect of temperature and magnetic field on the % § + dependences (figure 8) give a clear evidence of a similar change of the sign of magnetoelastic coupling in SC samples as in the WQ ones.

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The present results, as shown in figure 7, indicate that the magnetostriction λ in the Ni-Fe-Ga-Co alloy is negative over certain temperature-polarizing field domain and positive otherwise. Thus, a Villari critical line can be drawn on the +7 plane, separating domains with positive and negative magnetostriction, as is shown in figure 9. The high-temperature limit of the region of negative magnetostriction is close to the Curie temperature, just where the magnetic domain structure is being formed. This fact is confirmed by the simultaneous shift of this high-temperature limit together with the 7© for WQ and SC samples, in which the Curie temperatures are substantially different. In general, one should not be surprised that certain magnetoelastic coupling can be detected above the 7© . For example, the exchange magnetostriction can be detected in Ni at least some 150 K above the 7© [33].

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A very narrow hysteresis of magnetoelastic coupling registered in quenched samples and a broad one in slowly cooled ones look strange, since quenched samples contain more defects, which are expected to impede the mobility of domain walls. Indeed, the studies of magnetization loops for a Ni 50 Mn 27 Ga 23 alloy reveal an opposite tendency: the coercivity is higher for disordered samples than for ordered ones [34]. In this respect, it is worthwhile to comment, first of all, that the width of domain walls in ferromagnetic materials is rather high. The magnetization vector rotates in a 180° degree Bloch wall over the distance [START_REF] Bertotti | +\VWHUHVLV LQ 0DJQHWLVP[END_REF] 0 0 µ ∼1 T, one obtains /∼100 Å. On the other hand, quenched ferromagnetic shape memory alloys possess a low degree of long-range L2 1 order and very small ordered domain size, with a characteristic dimension in ternary Ni-Fe-Ga alloys of the order of only 100-300 Å [START_REF] Oikawa | [END_REF]. Ordered samples, on the contrary, possess high degree of atomic order and ordered domains ∼ 2000 Å [START_REF] Oikawa | [END_REF]. Antiphase domain boundaries are known as efficient pinners of the magnetic domain walls [34,38]. However, the size of ordered domains in WQ samples is of the same order of magnitude as the width of the magnetic domain wall. That means that, statistically, all positions of a magnetic domain wall with respect to the antiphase boundaries are equivalent, meaning that the pinning effect is absent.

On the contrary, in ordered samples the ordered domain size is much higher than the magnetic domain wall width and antiphase boundaries represent efficient obstacles for domain walls. Another interesting observation, related to the abovementioned interpretation is that WQ and SC samples demonstrate similar hysteresis above the Curie temperature, where the magnetic domains are not as yet formed and only short-range magnetic ordering exists. Under these circumstances, i.e. somewhat above the 7© , the coercive force for WQ samples becomes even much higher than well in the ferromagnetic state, cf. figures 6(c) and 6(a), although the magnitude of magnetoelastic coupling is very low above the 7© as compared to the ferromagnetic state. Opposite effects of the degree of ordering on the magnetic hysteresis obtained in the present work and reported in [34] are probably related to substantially larger antiphase domains in Ni-Mn-Ga than in Ni-Fe-Ga alloys. Indeed, even in WQ Ni-Mn-Ga samples the domain size can be estimated as being of the order of 100 nm [START_REF] Venkateswaran | FWD PDWHULDOLD[END_REF], whereas in ordered samples the domain size exceeds ~ 10 3 nm. Under these circumstances, antiphase domain boundaries become efficient pinners even in WQ samples. Since WQ samples have higher density of antiphase boundaries (which are now efficient pinners) than ordered samples, the coercivity of disordered samples is higher than that of the ordered ones.

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The observed variations of sign of magnetoelastic coupling are limited to the range of rather low applied fields. Therefore, they can be detected by magnetic as well as by any other type of measurements only under low magnetic fields, whereas any possible anomaly should disappear for measurements under high fields. This is exactly the feature of the anomalies observed in the temperature dependence of the magnetic susceptibility in ternary Ni-Fe-Ga martensite over similar temperature range [9]. From this point of view, one can speculate that the observed peculiarities of the magnetoelastic coupling in ferromagnetic martensites can be the driving force for the variety of the abovementioned structural/microstructural rearrangements [START_REF] Pakhomov | UDQVDFWLRQV RQ 0DJQHWLFV 2718[END_REF][START_REF] Murakami | [END_REF][7][8][9][10][11][12][13][14] detected by calorimetry, resistivity and internal friction measurements, since these experiments are performed typically under zero applied field. Additional calorimetry and AC impedance measurements have been performed in order to verify this hypothesis.

Figure 10 shows the temperature spectra of the real part of the AC impedance of the SC sample. The data in figure 10 were obtained for a low frequency of 21.7 Hz, making negligible the contribution of skin-effect to the real part of the AC impedance [START_REF] Corró | m; SC sample #2: oscillatory strain amplitude of 1×10 -5 , polarizing field 2.8 kA/m. For WQ sample #1 and SC sample#1 data for cooling and heating scans are shown to demonstrate reversibility of the data[END_REF]. Therefore, the resistance in figure 10

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Although the polycrystalline ferromagnets are isotropic through compensation, the isotropic treatment of magnetostriction is not appropriate. For example, for crystals with cubic symmetry the anisotropic saturation magnetostriction of a polycrystalline aggregate without texture, obtained by averaging of strain over each crystallite, is a linear combination of two magnetostriction coefficients, 2 , γ λ and 2 , ε λ [30]. If these coefficients have different signs, the magnetostriction of a polycrystalline aggregate can demonstrate non-monotonous dependence or even a change of sign, for example as a function of applied field [29]. Polycrystalline iron is a classical example of such situation [29,30]. Thus, changes of the sign of magnetoelastic coupling in a temperature domain, observed in the present work, can be attributed to a similar mechanism, assuming that some of the magnetostriction coefficients in low-symmetry martensitic phase have opposite signs and demonstrate different temperature dependence. This hypothesis implies that just a smooth variation with temperature and applied magnetic field of the linear combination of the magnetostriction constants occurs, which produces the change of the sign of net magnetostriction in polycrystalline aggregates. However, according to this scenario, no anomalies are expected in the resistivity and DSC data, which actually point to substantial structural/microstructural rearrangements occurring at the Villari critical line. Therefore, one cannot discard another interpretation of the observed peculiarity of magnetoelastic coupling, related to possible changes of signs of magnetoelastic constants themselves. Namely, the contributions of two-and single-ion coupling to anisotropic magnetoelastic coupling coefficients can be of the same order of magnitude and have opposite signs, and in that case, the anisotropic magnetostriction coefficients can demonstrate extrema or changes of sign [30].

Unfortunately, low symmetry of martensite and polyvariant structure of samples makes difficult the use of single crystalline samples to distinguish between the two possible mechanisms discussed. However, we believe that observation of sharp minima in temperature spectra of inverse magnetostriction in the austenitic phase of a polycrystalline ternary Ni-Fe-Ga alloy [START_REF] Kustov | SSO 3K\V /HWW[END_REF] reflects the existence of similar variation of sign of magnetoelastic coupling in the austenitic cubic phase as well. Therefore, investigation of austenitic single crystals of different orientation should provide a key to identify the specific origin of the observed peculiarity of magnetoelastic coupling. This work is ongoing.

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-Measurement of the inverse magnetostriction effect is an efficient and convenient method of investigations of the magnetoelastic coupling in ferromagnetic materials.

-The inverse and direct magnetostriction in a polycrystalline Ni-Fe-Ga-Co ferromagnetic shape memory alloy demonstrates a variation of its sign over a certain temperature range. The variation of the sign of magnetoelastic coupling is restricted to low values of polarizing field. We suggest that the observed peculiarity of the magnetoelastic coupling might be at the origin of as yet not well understood structural/microstructural effects detected in ferromagnetic shape memory alloys by calorimetry, internal friction, resistivity and also in magnetic properties at low polarizing fields.

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The authors are grateful to Prof. D.N. Beshers (Columbia University) for fruitful discussions.

1 3HFXOLDULWLHV¤ 1

 11 Departament de Física, Universitat de les Illes Balears, Cra. Valldemossa, km 7.5, 07122, Palma de Mallorca, Spain 2 Departamento de Física, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain Sergey.Kustov@uib.cat

Figure 1

 1 Figure 1 depicts the data on stress-induced induction obtained at 293 K for a test sample of polycrystalline iron. Figure 1(a) shows the magnitude of the magnetic signal under cyclic polarizing field. Full symbols stand for the initial quarter cycle measured for the demagnetized state of the sample, open symbols demonstrate the hysteresis registered in the second cycle of polarizing field. One sees two well-defined minima of the signal for each half cycle of applied field with different polarity. The registered phase of the induction signal with respect to mechanical stress is represented in figure 1(b) by a cycle A-B-C-D-E-F-G-H-I-J. The instantaneous jumps B-C, E-F and H-I of the phase by 360 degrees reflect the change of the range of the measuring device. In addition to these 360 degrees jumps, six rather rapid variations of the phase by ∼180°, enumerated from 1 to 6 in figure 1(b), can be observed for each period of applied field. Figure 1(b) depicts also a continuous curve (after correcting the measured data by eliminating the 360 degrees jumps related to the change of the range of lock-in amplifierbetween -180 and +180 degrees) in which these six variations of phase are clearly visible. Variations of the phase by 180 degrees reflect the change of the sign of the magnetic response to applied stress and coincide with the minima of the induction magnitude, figure1(a). Two of the phase shifts by 180°, 1 and 4, occur with a large hysteresis, whereas four others -2,3 and 5,6 -form two pairs of fairly reversible phase variations. The real part of the induction, calculated from the modulus and the phase signal, is represented in figure1(c). The imaginary part of the stress-induced induction in iron, as well as in the Ni-Fe-Ga-Co alloy studied, remains quite small with respect to the real one, and will be disregarded in the present paper. Two variations of the sign of magnetic induction occur at the points of the loop corresponding to the coercive field +© . They correspond to the phase variations, 1 and 4, figure 1(b), which occur with a strong hysteresis. Change of the sign of the inverse magnetostriction in points +© and

Figure 4 (

 4 Figure 4(a) represents the temperature spectra of the magnitude of stress-induced induction registered under constant polarizing field and oscillatory strain amplitude for several WQ and SC Ni-Fe-Ga-Co samples. According to figure 4(a), certain features of the behaviour of the magnetoelastic coupling close

  O is the exchange length, 0 s and . 1 are the saturation magnetization and anisotropy constant, respectively. Taking the magnetocrystalline anisotropy constant for a Ni-Fe-Ga-Co alloy of similar composition . 1 ∼ 1×10 5 kJ/m 3[START_REF] Morito | SSO 3K\V /HWW[END_REF] and the characteristic values of the exchange length O ∼30 Å[START_REF] Bertotti | +\VWHUHVLV LQ 0DJQHWLVP[END_REF],

  , although measured with AC, asymptotically reflects the direct current resistance. The parts of the temperature spectrum below ∼ 230 K and above this temperature up to the 7© can very well be fitted by straight lines, with a change of the slope close to the Villari critical point. Two different samples showed similar behaviour, reproducible on cooling and heating, much like the observed anomaly of the magnetoelastic coupling. Thus, resistivity data clearly demonstrate a change of the temperature coefficient of the resistance just at the Villari critical point.

Figure 11

 11 Figure 11 shows the results of the calorimetry tests performed for a SC sample. Similar data were obtained for 5 different SC samples. One can distinguish small peculiarities of the heat flow at temperatures of around 320 and 240 K, which correspond to the 7© and the observed Villari critical point. In fact, since the high-temperature Villari critical point is close to the 7© temperature, they cannot be separated in the DSC results. One can notice even a slight change of the slope of the DSC curve both at 240 and 320 K, pointing to a change of the heat capacity value. It is tempting thus, based on the results of DSC and AC impedance studies, to conclude that the observed variations of the sign of magnetoelastic coupling slightly affect also transport and thermodynamic properties of the Ni-Fe-Ga-Co alloy.

  The work was supported by FEDER and DGI, Spain, through the projects MAT2006-28193-E, MAT2008-01587 and MAT 2009-07928.

Figure 1 .

 1 Figure 1. Stress-induced induction of a polycrystalline sample of Fe (ultrasonic strain amplitude of 1×10 -5 , temperature T=293 K) versus cyclic polarizing field with a frequency of 0.002 Hz: a) absolute value of the

Figure 2 .

 2 Figure 2. Real part of the amplitude of the stress-induced induction in a polycrystalline Ni sample (ultrasonic strain amplitude 3×10 -7 , temperature 293 K) versus cyclic polarizing field with a frequency of 0.002 Hz. Empty symbols stand for the second cycle of polarizing field, full symbols -for the first quarter cycle starting from demagnetized state. Solid line shows the result of the integration, according to (3), of the real part of the % § /σ § ratio for the first quarter cycle of polarizing field starting from the demagnetized state of the sample.

20

 20

Figure 3 . 21 Figure 4 . 8 Figure 5 .Figure 6 .

 3214856 Figure 3. Temperature spectra of the low-field susceptibility for water quenched (WQ) and slowly cooled (SC) samples of a polycrystalline Ni 53.5 -Fe 16.5 -Ga 27 -Co 3 alloy.

Figure 7 .

 7 Figure 7. Field dependences of the direct/inverse magnetostriction for several temperatures, as obtained by integration of first quarter cycles of hysteresis loops from figure 6.

Figure 8 .

 8 Figure 8. Real part of the stress-induced induction versus cyclic polarizing field for a slowly cooled sample

Figure 9 .

 9 Figure 9. Schematic representation of the position of Villari critical line separating regions of positive and negative magnetostriction on +7 plane.

Figure 10 . 29 Figure 11 .

 102911 Figure 10. Temperature dependence of the resistance (in arbitrary units) of a slowly cooled sample of a Ni-Fe-Ga-Co alloy. Thin lines show fittings of the two parts of the dependence (below 240 K and between 240 K and the Curie temperature, 7© , by linear functions.

a Ni-Fe-Ga-Co alloy (ultrasonic strain amplitude of 2×10 -5 ) versus cyclic polarizing field with a frequency of 0.002 Hz for temperatures 200-231 K (a), 231-266 K (b), 266-273 K (c) and 273-288 K (d). Arrows show directions of the circulation along the loops.


O J Durá

E Bauer

L Vázquez

M A López

M A López De La Torre

Depressed thermal

come

Introduction

The improvement of thermal barrier coatings (TBCs) for combustors and turbine blades in gas turbine engines, which would enable them to operate at higher temperatures, is essential to increase their overall efficiency [1,2]. TBCs are thick films of a refractory ceramic material that protect the metal from the high gas temperature. Yttria-Stabilized Zirconia (YSZ) is the standard material used in high temperature thermal barrier coatings technology, due to its good chemical Confidential: not for distribution. Submitted to IOP Publishing for peer review 18 December 2009 stability and excellent thermal and mechanical properties [3]. The prospect of improving even more its performance is the reason of the interest in studying the thermal transport properties of nanostructured YSZ [4,5]. In dielectric materials the principal way of conductive heat transfer is through acoustic phonons. The kinetic theory establishes that thermal conductivity κ can be expressed in the form:

vl C V 3 1 = κ (1)
where C V is the specific heat at constant volume, ν is the sound speed and l is the phonon mean free path [START_REF] Tritt | Thermal Conductivity[END_REF]. The low thermal conductivity of YSZ, even in single-crystalline samples, is due to the strong phonon scattering by the oxygen vacancies, characteristic of its fluorite structure, resulting in a reduced mean free path [START_REF] Klemens | [END_REF]. A straightforward strategy to decrease even more the thermal conductivity of thermal insulators consists in introducing into their structure a sufficiently high density of point defects, so that they cause inelastic phonon scattering, thus decreasing the phonon mean free path and the thermal conductivity. A possible alternative is to reduce the grain size down to the nanocrystalline scale. For grain sizes smaller than the phonon mean free path a significant reduction of the thermal conductivity is naturally expected [8]. On the other hand, for grain sizes well in the nanometer range, the additional thermal scattering due to grain boundaries can give rise to a noticeable thermal resistance, the so-called Kapitza resistance [9]. Other authors have interpreted the low values of thermal conductivity in nanostructured insulators as a result of localization of short-wavelength phonons inside the grains. In this model, the thermal transport occurs by phonon hopping through grain boundaries (the phonon hopping model) [10].

In this work we present an experimental study of the thermal conductivity dependence on the grain size in mechanically alloyed 10 mol% YSZ nanocrystalline samples. Assuming that thermal transport is determined by scattering at grain boundaries, we will compare the results of two alternative analyses mentioned above: i) the Kapitza thermal resistance model (KRM), and ii) the phonon hopping model (PHM).

Experimental details

Compact 10 mol%. YSZ samples with different grain sizes were obtained by cold uniaxial compaction and two steps sintering [11] of mechanically alloyed powders. More details about the compaction and sintering procedures can be found in reference [12]. In this work we study a set of four samples with grain sizes in the nanometer range. An extra microcrystalline sample was obtained by means of a conventional sintering process. A complete X-ray diffraction analysis using the Warren-Averbach method (W.A.) was carried out in order to confirm the fluorite structure corresponding to YSZ and to obtain information about grain sizes for the nanocrystalline samples [12]. Atomic Force Microscope experiments were performed in tapping mode with silicon cantilevers (nominal radius of 10 nm) in ambient conditions with a Nanoscope IIIa equipment (Veeco). These measurements allowed us to obtain the grain size of the microcrystalline sample and confirmed the grain sizes values obtained from the W. A. analysis. The density of the compact samples was determined using the Archimedes method, with water as fluid. Information about sintering temperatures, densities and grain sizes for each sample is summarized in table I.

The thermal conductivity κ of each sample was determined from separate measurements of the thermal diffusivity α, specific heat C p , and density ρ, using the relationship

κ =α•C p •ρ (2)
Thermal diffusivity was measured with a commercial Anter Flashline 3000 system. All samples were covered with a graphite screen to ensure full absorption of the flash light at the front surface and highest emissivity from the backside. Thermal diffusivity was measured from 173 K to 773 K in inert atmosphere. Several measurements were performed under the same conditions to check that there were no changes in samples or damage of the graphite screen during the experiment. Thermal diffusivity values were obtained from the raw data by applying the Clarke and

Taylor correction [13], which takes into account radiative losses that occur in nonadiabatic conditions. Heat capacity was measured between 173 K and 773 K with a Netzsch Jupiter 404 Differential Scanning Calorimeter (DSC), using platinum crucibles in helium atmosphere. A single crystalline sapphire sample was used as reference. The thermal conductivity values were corrected to account for the porosity,

Results and Discussion

In first place, we will describe the microstructure of the five samples studied in this work. Accurate determination of grain sizes is not an easy task for nanocrystalline materials. The simple but very common analysis of XRD patterns in terms of Scherrer relation can lead to underestimated grain size values. For that reason we have performed careful X-ray profile analyses, and checked the results with those obtained from AFM images. The samples obtained by cold com-paction and two steps sintering of the mechanically alloyed powders display grain sizes d ranging from the 17 nm (green sample) to about 100 nm (see table I), as determined from a Warren-Averbach line profile analysis of X-ray diffraction patterns [12]. Atomic Force Microscope (AFM) experiments were performed in order to confirm these values. In Figure 1 we show a typical AFM image of the sample with d = 53 nm from XRD. The figure displays a uniform and isotropic distribution of grain sizes around an average value d = 50 ± 3 nm, as deduced from treatment of images using WSxM2.2 software from Nanotec [15], in very good agreement with the value obtained from XRD analysis. In the case of the microcrystalline sample, the grain size cannot be obtained from X-ray analysis, and d ≈ 1 µm was determined from AFM images. The images reveal relatively low porosity, consistent with the density values, higher than 90 % of the theoretical X-Ray density (ρ theor = 5.93 g cm -3 ), except in the case of the sample with smallest grain size, 17 nm, that shows ρ ≈ 84 % ρ theor .

As we have already mentioned the thermal conductivity κ values were calculated from specific heat, diffusivity and density measurements. In figure 2 (a) we present temperature dependence of molar specific heat C P between 173 K and 773 K for each sample. The specific heat points reach a value higher than that predicted by Dulong and Petit law (72.75 J mol -1 K -1 ) at high temperature. Moreover, the values present a slightly positive slope instead of reaching the expected plateau. This phenomenon has been reported in previous works for this material [16]. The authors interpreted this result as a possible contribution of lattice defects to the specific heat. On the other hand, the observed differences between the C p values of our samples are smaller than the equipment accuracy, ±3%, included as error bars in figure 2 (a). Thus, we can conclude that C p does not depend significantly on grain size, at least for 10 mol% YSZ samples with grain sizes varying from the micrometer range down to 17 nm. In figure 2 (b) we display thermal diffusivity as a function of temperature between 173 K and 773 K, for all the samples studied in this work. In contrast to specific heat, in this case we do observe a clear grain size dependence of thermal diffusivity, which strongly decreases with decreasing grain size. In the case of the microcrystalline sample, the diffusivity values are more than two times higher than those corresponding to the nanocrystalline samples.

In figure 3 we show the temperature dependence of thermal conductivity κ between 173 K and 773 K for the samples studies in this work. As explained above, the raw data were corrected in order to take into account the sample's porosity. For this purpose, different corrections formulas can be found in the literature. In our case, as different methods render similar results, we decided to use the usual Klemens relation [START_REF] Klemens | High Temps[END_REF]17]. The thermal conductivity shows weak temperature dependence above T ~400 K, tending to saturate at a constant value at high temperature. On the other hand, as it is observed for diffusivity measurements, κ is strongly depen-dent on grain size. All the nanocrystalline samples display a significant reduction of thermal conductivity values respect to that of the microcrystalline sample.

As a matter of fact, these κ values are lower than the reported theoretical values calculated using an Einstein model for disordered crystals [18]. Similar results in YSZ thin film samples [19], polycrystalline alloys [20] and compounds [21,22] have been previously reported and tentatively explained by different authors as a consequence of a higher additional thermal resistance due to contact between grain boundaries, the so called Kapitza resistance. For polycrystalline materials, values of Kapitza resistance can be obtained from κ values measured as a function of grain size [22] using the following expression:

d R κ κ κ + = 0 1 1 (4)
where R k is the Kapitza resistance, d is the grain size and κ 0 is the conductivity that correspond to the single crystal. Nan and Birringer [20] used an effective medium approach to develop a similar relationship. In the present study, we have used (4) to obtain the Kapitza resistance (R k ) and bulk conductivity (κ 0 ) from fits of 1/κ versus 1/d. In figure 4 we display these fits for different temperatures. Only the experimental points corresponding to the microcrystalline sample (d = 1 µm), which exhibit a clear deviation from the linear alignment of the rest of the data, have not been included in the fits. We want to point out that, using analogous analyses, other authors have observed the same trend, that is, the analysis in terms of a constant R K is valid only for the nanocrystalline samples [21,22]. The R K values obtained for our YSZ nanocrystalline bulk samples are displayed in figure 5 (a). The Kapitza resistance R K decreases with increasing temperature, approaching a plateau at R K = 9.5•10 -9 (m 2 K/W) for T > 350, of the same order than previously reported values [19,23]. In figure 5 (b) we present the κ 0 values obtained from fits of 1/κ versus 1/d to expression (4) for different temperatures. These κ 0 are significantly lower than those from literature and than κ(T) for our own microcrystalline sample. As a result of the same type of analysis of their data for nanocrystalline YSZ thick coatings, Yang et al. [19] obtained also reduced κ 0 values, what they interpreted as a consequence of the reduced grain size. However, it is necessary to point out that, although the previous analysis in terms of Kapitza resistance at grain boundaries seems fairly satisfactory, it is based on hypotheses and approximations that can be considered, at least, somewhat crude. It has been suggested, for example, that theoretical treatments based on the validity of Fourier equations could break down for grain sizes well in the nanometer scale, similar to the phonon wavelength [19,[START_REF] Majumdar | Microscale Energy Transport[END_REF]. In that case, it is also doubtful that thermal transport could be described in terms of coherent movement of phonons through the lattice [10].

To explain the peculiarities of high temperature heat transport in nanocrystalline and porous materials, Braginski et al. proposed an alternative model, based on phonon hopping through grain boundaries [10]. In the framework of the PHM, κ(T) for a given material can be calculated using the following expression:

dx S B(x)t T k d a k S B(x)t T k T D B i B i B Φ + Φ = - θ κ κ κ / 1 0 2 1 ) ( h (5) being 2 2 4 4 1 ) 1 ( 2 9 )
( - - = θ θ x e e x x B x x .
The other parameters in expression ( 5) are: κ i , the conductivity of single-crystal YSZ, d the grain size, T D the Debye temperature, θ D =T/T D , a is the lattice parameter, S the main area of interface, is a factor relevant to the disorder, and t is the unique fitting parameter, which describes the interface transparency for the phonon hopping. The different lines in figure 3 are fits to this expression for the high temperature data (T ≥ 300 K), using T D = 650 K, estimated from our specific heat measurements (see figure 2 (a)), in good agreement with the results obtained for YSZ by other authors [START_REF] Tojo | [END_REF]26]. We have used κ i = 2.2 W/mK for the intrinsic thermal conductivity of 10 mol% YSZ in this temperature range. In the fits to expression (5), the grain boundary transparency t is the only free parameter. It is important to remark that t is much higher for the microcrystalline sample, which has been also observed in other systems [27]. It has been proposed that, in practice, the Kapitza analysis is a limit of the PHM, and that t is proportional to the Kapitza conductance [28]. Besides of this, it can be considered that, compared to the simple analysis in terms of a phenomenological constant Kapitza resistance, the PHM describes the interfacial thermal resistance in terms of phonon localization induced by the enhanced phonon scattering at grain boundaries.

An interesting possibility is that this phonon localization effect might be due to changes in vibrational anharmonicity induced by grain size reduction. As a matter of fact, in glasses and in disordered crystals it has been proposed that vibrational anharmonicity might regulate both the thermal conductivity [29] and ultrasonic attenuation for T > 100 K [30,31], although there is some controversy about the issue [32]. The possibility suggested above seems quite reasonable, because even for single crystal YSZ the thermal conductivity below room temperature and the low temperature specific heat (T <10 K) exhibit features typical of glassy systems [33,18]. Thus, low temperature specific heat and thermal conductivity measurements on the present samples are desirable for a better understanding of the thermal properties in this system.

From the theoretical point of view, a marked grain size effect on the thermal conductivity is naturally expected [START_REF] Klemens | [END_REF]10]. Klemens and Gell have demonstrated a reduction up to 60% for a grain size of 10 nm in 7%wt YSZ. On the other hand, from the experimental point of view, there is some controversy about the existence of this grain size effect on the thermal conductivity of YSZ. It is important to point out that our work has been performed on bulk isotropic nanocrystalline samples. Previous works, showing similar but not so patent grain size effects, were performed on nanocrystalline YSZ coatings [4,19] that usually display columnar structure, which could explain their higher conductivity values. On the other hand, Raghavan et al. have discarded the effect of the grain size, proposing instead that the reduction of thermal conductivity is only a consequence of the porosity effect in bulk nanocrystalline samples [5]. But they only discard grain size effects above 100 nm. As a matter of fact, their results show a depressed thermal conductivity for d ≤ 100 nm. In any case, our analysis indicates that the extremely low thermal conductivity observed in our samples is a genuine grain size effect.

Conclusions

In this work we present the results of thermal conductivity measurements on a set of samples, with grain sizes between 17 nm and 1 µm. We observe a substantial reduction in thermal conductivity respect to the bulk values. Two alternative analyses in terms of the Kapitza resistance and the phonon hopping models allow us to conclude that there is a genuine grain size effect on the thermal conductivity in nanocrystalline YSZ. It is quite reasonable to interpret our results in terms of a phonon localization effect could be related to changes in vibrational anharmonicity.

The results reported in this work could open the possibility of technological applications in the field of high temperature thermal barrier coatings, if a way of impeding grain growth to preserve the nanometric grain size were found.

Figure 1 .

 1 Figure 1. Atomic Force Microscope Image (500 x 500 nm 2 ) for the sample with 53 nm grain size.

Figure 2 .

 2 Figure 2. (a) Molar specific heat C p and (b) thermal diffusivity of 10 mol% YSZ samples studied in this work as a function of temperature. Different symbols correspond with samples with different grain-size. Errors bars (±3 % for C p and ±5% for ) are included in both cases. Solid line is a Debye function with T D =650 K.

Figure 3 .

 3 Figure 3. Temperature dependence of thermal conductivity κ for the samples studied in this work. Lines are the results of fits to expression (5) (phonon hopping model[10], see text). Error bars for κ (±8%), are included.

Figure 4 .

 4 Figure 4. κ -1 vs. d -1 plots for different temperatures. The points are experimental data while the solids lines are fits of the experimental data to equation (4), excluding the points corresponding to d = 1 µm which show a clear discrepancy.

Figure 5 .

 5 Figure 5. (a) Kapitza resistance, R k , and (b) values of κ 0 , obtained from the fits of our experimental data to equation (4) shown in figure 4.

Figure 1 13Figure 2 (a) 14 Figure 2

 12142 Figure 1

figure 5 (a)

figure 5 (b)

Acknowledgements

We acknowledge financial support by Junta de Comunidades de Castilla-La Mancha, through project PCI08-0091-9017 and Ministerio de Educación y Ciencia through project FIS2006-12253-C06-03. We thank the technical staff at Solid State Physics Institute (TuWien) for their support during sample preparation for thermal conductivity measurements.