Henk J Wisselink
email: henk.wisselink@wur.nl

Conny B Van Solt-Smits

Derk Oorburg

Dick Van Soolingen

Pieter Overduin

Judith Maneschijn-Bonsing

Norbert Stockhofe-Zurwieden

Herma Buys-Bergen

Bas Engel

Bert A P Urlings

Jelle E R Thole

Serodiagnosis of Mycobacterium avium infections in pigs

A c c e p t e d M a n u s c r i p t 2

Abstract

The aim of this study is the development and evaluation of a serodiagnostic assay for Mycobacterium avium (MA). After screening MA lipid fractions in an ELISA format, a polar lipid fraction was selected as antigen because of its superior recognition by serum antibodies in experimentally infected pigs. The resulting MA-ELISA was evaluated as an alternative for detection of MA infection by traditional pathological examination of pig lymph nodes for granulomatous lesions by meat inspectors. By comparing with bacteriological examination, the MA-ELISA showed significantly better sensitivity (69%) as compared to pathological examination (31%) in experimentally infected pigs. The MA-ELISA also appeared significantly more specific in a set of serum samples from MA negative pigs: only 1 out of these 153 serum samples reacted positive, whereas 99 (65%) of these had displayed false positive results by detection of lymph nodes lesions that appeared not to be associated with MA [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF].

The MA-ELISA was subsequently evaluated using serum samples from two farms with pigs known to be infected with MA. Bacteriological examination of the sub-maxillary and mesenteric lymph nodes showed that 56% (103/184) and 35% (41/117) of the pigs, respectively were positive for MA in these farms. In the first farm, 16% (29/184) of the pigs tested positive in MA-ELISA and 31% (57/184) by pathological examination. On the contrary, in the second farm, more pigs tested positive 17% (15/117) in MA-ELISA with 8% (9/117) positivity by pathological examination. Taking the results on both farms together, the sensitivity of the MA-ELISA was 14% and the specificity 83%, whereas the sensitivity of the pathological examination was 31% and the specificity 86%.

For practical reasons use of a serological test as the MA-ELISA may be preferred over pathological or bacteriological examination. Our studies in experimentally infected and negative "field" sera indicate that the MA-ELISA is significantly more specific and more sensitive than detection by classical pathological examination. However, the studies in two MA infected farms show a variable picture with pathological examination overall performing better. Study in a wider range of "positive" farms will be needed to provide a more comprehensive view of the quality of both tests for detection of MA in infected farms. At the same time further optimization of MA-ELISA with use of lipid antigens from a broader range of serotypes may improve its performance in the face of infections with different MA serotypes.

A c c e p t e d M a n u s c r i p t

Introduction

Mycobacterium avium (MA) is an important pathogen in both animals and humans which belongs to the Mycobacterium avium complex (MAC). To date, 28 MAC serotypes have been identified from which the serotypes 1-6, 8-11 and 21 belong to Mycobacterium avium subsp. avium (MAA). The serotypes 1, 2 and 3 are isolated from birds and have been designated as the MAA "bird" serotypes whereas the serotypes 4-6, 8-11 and 21 are identified as the "non-bird" serotypes [START_REF] Dvorska | Study of Mycobacterium avium complex strains isolated from cattle in the Czech Republic between 1996 and 2000[END_REF]. The "non-bird" serotypes are isolated from humans and pigs and for these reasons [START_REF] Mijs | Molecular evidence to support a proposal to reserve the designation Mycobacterium avium subsp. avium for bird-type isolates and 'M. avium subsp. hominissuis' for the human/porcine type of M. avium[END_REF] proposed to name these serotypes M. avium subsp. hominissuis (MAH). These "non-bird" serotypes are also found in the environment, especially in soil [START_REF] Dvorska | Study of Mycobacterium avium complex strains isolated from cattle in the Czech Republic between 1996 and 2000[END_REF].

MA is a potential zoonotic pathogen as it can produce disease in immunocompromised individuals with acquired immunodeficiency syndrome and pulmonary disease in immunocompetent adults [START_REF] Biet | Zoonotic aspects of Mycobacterium bovis and Mycobacterium avium-intracellulare complex (MAC)[END_REF][START_REF] Wagner | Nontuberculous mycobacterial infections: a clinical review[END_REF]). An infection with MA in pigs develops mostly subclinically leading to granulomatous lesions in the lymph nodes. Most of the lesions are formed in the sub-maxillary and mesenteric lymph nodes and disseminated lesions are occasionally observed in the liver, spleen and lungs [START_REF] Thoen | Tuberculosis[END_REF].

Sources of MA infections in humans are still uncertain. Results of high resolution genotyping methods showed that humans and pigs can be infected with the same MAC strains [START_REF] Komijn | Prevalence of Mycobacterium avium in slaughter pigs in The Netherlands and comparison of IS1245 restriction fragment length polymorphism patterns of porcine and human isolates[END_REF]. The authors discussed the possibilities that humans and pigs share common sources of infection or that contaminated meat originating from pigs is a potential source for infection in susceptible humans. To exclude pigs as a reservoir for infection in man, regulations in European Union legislation (2004/854/EC) are prescribed for special handling of pig carcasses in slaughter houses in which evidence of an MA infection is observed.

Diagnosis of MA infections in pigs is based on detection of granulomatous lesions in lymph nodes of pigs by palpation and incision at slaughter [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF][START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF]. Because MA has been isolated from lymph nodes without lesions, and, on the other hand, non mycobacterial species such as Rhodococcus equi have been frequently isolated from granulomatous lesions, sensitivity and specificity of the current detection method have been questioned [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF][START_REF] Dvorska | Isolation of Rhodococcus equi and atypical mycobacteria from lymph nodes of pigs and cattle in herds with the occurrence of tuberculoid gross changes in the Czech Republic over the period of 1996-1998[END_REF][START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF][START_REF] Offermann | The prevalence of Salmonella, Yersinia and Mycobacteria in slaughtered pigs in Switzerland[END_REF]. In this study, we describe a serodiagnostic test that may provide a more reliable tool for detecting MA infected pig herds.

Based on earlier observations that indicate that MA-derived lipid preparations contain dominant antigens of MA, we focused on the applicability of antigenic lipid fractions for the development of an antibody A c c e p t e d M a n u s c r i p t 4 based immunodiagnostic test for detection of MA infections in 26-weeks old slaughter pigs [START_REF] Brennan | Structure of the specific oligosaccharides from the glycopeptidolipid antigens of serovars in the Mycobacterium avium-Mycobacterium intracellulare-Mycobacterium scrofulaceum complex[END_REF][START_REF] Inderlied | The Mycobacterium avium complex[END_REF][START_REF] Kitada | Serodiagnosis of pulmonary disease due to Mycobacterium avium complex with an enzyme immunoassay that uses a mixture of glycopeptidolipid antigens[END_REF][START_REF] Kitada | Use of glycopeptidolipid core antigen for serodiagnosis of Mycobacterium avium complex pulmonary disease in immunocompetent patients[END_REF]. Using serum samples of pigs that were experimentally infected with MA, lipid fractions of MA were evaluated for applicability, and a polar lipid fraction was selected for developing an ELISA for MA. The ELISA was validated using serum samples from pigs, experimentally and naturally infected with MA. Bacteriological examination of the lymph nodes for MA was used as reference to indicate the true infection status and the outcome of the ELISA was compared to the traditional method of detecting lesions in lymph nodes [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF].

Materials and Methods

Bacterial strain

In this study MAH serotype 4 strain 17404 was used. This strain was isolated in the course of a study to the prevalence of MA in Dutch pig herds and it was selected as a representative of one of the most frequently isolated serotypes in the Netherlands [START_REF] Komijn | Prevalence of Mycobacterium avium in slaughter pigs in The Netherlands and comparison of IS1245 restriction fragment length polymorphism patterns of porcine and human isolates[END_REF].

Experimental infection with MA

Thirty-two pigs, three weeks of age and crossbreeds of Yorkshire and Dutch landrace were obtained from a high health status herd of the Animal Sciences Group of Wageningen UR (Lelystad, The Netherlands).

Pigs were allotted in four groups of eight pigs each and housed in separate boxes at the animal facilities of Central Veterinary Institute of Wageningen UR (Lelystad, The Netherlands).

For preparation of the inoculum for the experimental infection, MAH strain 17404 was cultured in Middlebrook 7H9 medium enriched with OADC (Becton Dickinson, Breda, The Netherlands) at 35°C to an Optical Density (OD) of 2 at 600 nm. The cells were harvested by centrifugation at 3000 x g for 30 minutes and washed twice in isotonic saline. Until use, aliquots of one ml were stored in Tryptone Soya Broth medium (Oxoid B.V., Badhoevedorp, The Netherlands) in the presence of 20% glycerol at -70 °C.

Viability of the inoculum was determined by subculture on Coletsos Osein (Bio-Rad, Veenendaal, The Netherlands) and Dubos Tween albumin medium (Becton Dickinson, Breda, The Netherlands). Purity of the inoculum was determined from smear specimens stained by Ziehl-Neelsen. Prior to administration to the pigs the stored MAH bacteria were revived by culturing one ml of the stored inoculum in four ml Middlebrook 7H10 supplemented with OADC for two days at 37 °C.

A c c e p t e d M a n u s c r i p t

To study the influence of an early and late infection with MA on bacteriological, serological and pathological status we infected pigs at different ages. Three of the four groups were infected at 2½, 4½ and 18 weeks of age, respectively. To increase the probability of infection, pigs in the fourth group were inoculated with MAH at three time points (Table 1). A syringe was used to deposite the inoculum in the caudal area of the pharynx. To promote the penetration of the bacteria, the pharynx epithelial tissue was scarified with a cotton-wool swab before inoculation.

Until the end of the experiment at 24 weeks of age, pigs were monitored once a week for clinical signs of disease. Furthermore, blood serum samples were collected weekly to monitor the immune response.

White blood cells were counted, using a semi-cell bloodcounter (Sysmex, model F 800, Charles Goffin Medical Systems). The number of neutrophils was calculated after a differential count of Giemsa-stained blood smears. Three days before the end of the experiment, all pigs underwent an intradermal tuberculin test in the ear with 0.1 ml Avian Tuberculin PPD (25.000 I.U., ASG, Lelystad, The Netherlands). The presence at the injection site of erythema and induration was scored 24, 48 and 72 hours after injection.

After reading, pigs were euthanized. Organs were examined pathologically for deviations and lymph nodes were examined pathologically for granulomatous lesions and bacteriologically for MA. For bacteriological examinations, the surface of the lymph node specimens was decontaminated for 6 to 8 seconds in boiling water and cut aseptically into small pieces of 1 cm 3 . The specimens were sealed in polyethylene bags and squeezed in a Stomacher (Laméris Laboratorium B.V., Breukelen, The Netherlands). This material was treated for 10 min at room temperature with 3 volume parts of 6% H 2 SO 4 and subsequently centrifugated for 10 min at 1000 g. The supernatant was discarded and the sediment was washed twice with an excess of phosphate-buffered saline (PBS), 136.89 mM NaCl, 2.68 mM KCl, 8.1 mM Na 2 HPO 4 , 2.79 KH 2 PO 4 and resuspended in 0.5 ml PBS. This suspension was inoculated on Middlebrook 7H10 plates enriched with OADC, on Coletsos Osein and on Dubos Tween albumin medium, incubated for eight weeks at 35 °C and observed every week for growth. To identify colonies, Ziehl-Neelsen stain was performed for acid-fast bacilli and PCRs for the presence of IS1245 and IS901, which are characteristic for MA and MAA respectively [START_REF] Kunze | Biologically distinct subtypes of Mycobacterium avium differ in possession of insertion sequence IS901[END_REF][START_REF] Van Soolingen | IS1245 restriction fragment length polymorphism typing of Mycobacterium avium isolates: proposal for standardization[END_REF].

Collection of pig serum samples in the field

Field serum samples of pigs with a different MA health status were collected. Serum samples negative for infections with MA (n=153) were collected in the course of a previous study for the prevalence of MA infections in the Netherlands. The design and results of this study were described by [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF]. were farrow-to-finish farms. From farm A four batches of pigs were sampled in the slaughterhouse (n=184) and from farm B two batches (n=117). Blood serum samples and the sub-maxillary and mesenteric lymph nodes were collected at slaughter. In the laboratory, serum samples were stored at -20 °C and the lymph nodes were examined pathologically for granulomatous lesions and bacteriologically for MA as described above.

Isolation of lipid fractions from MAH

In order to harvest lipids as antigen for the serodiagnostic ELISA assay, MAH strain 17404 was inoculated in Middlebrook 7H9 supplemented with OADC (Becton Dickinson, Breda, The Netherlands).

The growth of MA was monitored by measuring weekly the OD at 600 nm in a spectrophotometer. The incubation was stopped at an OD of 1 and the MA cells were pelletted by centrifugation (15 min 5000g).

Lipids were extracted from the MA cells according to a protocol of [START_REF] Dobson | Systematic analysis of complex mycobacterial lipids[END_REF]. Briefly, the apolar lipids were extracted from MA cells by mixing these cells with methanol and petroleumether. The mixture was centrifuged, the upper layer with apolar lipids was harvested and stored. The lower layer was treated with petroleumether to extract remaining apolar lipids. After centrifugation, the upper layer containing a second yield of apolar lipids was harvested and combined with the already stored apolar fraction. The combined fractions of apolar lipids were dried under a gentle flow of nitrogen. The polar lipids were further extracted by adding a mixture of chloroform and methanol to the lower layer. The mixture was mixed during one hour and centrifuged. Supernatant was mixed with chloroform for 5 minutes and centrifuged. The lower layer containing the polar lipids was dried under a gentle flow of nitrogen.

Selection of lipid fraction for ELISA

Polar and apolar lipid fractions of MAH strain 17404 were tested in indirect ELISA assays for selection of the most promising fraction for use. Each well of polysorb microtiterplates (Nunc, Roskilde, Denmark) was coated for 16 hours at 37°C with 1 µg polar or apolar lipids suspended in 50mM NaHCO 3 , PH 9.6.

Endpoint serum samples of eight pigs, 21½ weeks after an experimental infection with MAH strain 17404 (see above and Table 1 group 1) were tested in a twofold serial dilutions from 1:40 to 1:81920 in PBS containing 0.5% Tween 80. As conjugate monoclonal antibody IgL 27.2.1 was used. This monoclonal A c c e p t e d M a n u s c r i p t 7 antibody recognizes the kappa chains of pig immunoglobulins [START_REF] Sinkora | Characterization of monoclonal antibodies recognizing immunoglobulin kappa and lambda chains in pigs by flow cytometry[END_REF]. As substrate TMB (3, 3', 5, 5'-tetramethylbenzidine) was used. Development of the reaction was stopped by adding 0.5 M H 2 SO 4 . The OD was determined at 450 nm in an ELISA reader. Titers were expressed as the reciprocal of the 2 log of the highest dilution showing an absorbance of more than 50% of the positive control.

Execution of the ELISA

For evaluation of the ELISA basically the test was performed as described above. As positive control, endpoint serum samples of a pig, 21½ weeks after an experimental infection with MAH strain 17404 was used (see above and in Table 1). As negative control, a serum sample was used from a pig negative in bacteriological examination for MA in its sub-maxillary and mesenteric lymph nodes [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF].

In each microtiterplate these positive and negative control serum samples were tested in twofold in a dilution of 1:200. Test results were calculated as percentage positivity (PP). To calculate the PP, the OD of the test serum samples was calculated as a percentage of the difference in OD of the negative and positive control serum samples. This results in a uniform and continuous scale from 0-100% calculated according to the following formula: PP = {OD (test sample) -OD (negative control)} / {OD (positive control) -OD (negative control)}.

Statistical analysis

The cut-off value of the MA-ELISA was determined as the mean plus three-fold standard deviation of the results on a set of serum samples (n=153) negative in bacteriological examination for MA [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF]. Sensitivity and specificity with 95% confidence intervals (CI) from the MA-ELISA and from the pathological examination of the sub-maxillary lymph nodes were calculated considering the results of bacteriological examination of lymph nodes for MA as a gold standard. McNemar's test was used as a significance test for differences in sensitivity and specificity of both tests. P values below 0.05 were considered statistically significant.

Results

Development of MA-ELISA

We started the development of the MA-ELISA by selection of the most promising lipid fraction for use in an ELISA. For this purpose we used serum samples of eight pigs, collected 21½ weeks after an Checkerboard titrations using a concentration range of the same set of serum samples and of the polar lipid fraction from MAH strain 17404 resulted in the selection of an optimal concentration of 2.4 µg/well of polar lipid and a dilution of 1:200 of pig serum samples for the MA-ELISA.

The development of the MA-ELISA was finalized with the determination of a cut-off value for negative and positive test results. For this purpose we tested serum samples of pigs (n=153) free of an MA infection [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF] in the MA-ELISA. The PP in 80 (52.3%) of these serum samples, was lower than 0% (Table 2). The highest titer detected in these 153 serum samples was 16 PP. The mean and standard deviation of the ELISA for these serum samples was 0.26 PP and 3.45 PP, respectively. The mean plus three standard deviations for the assay: 10.6 PP, was used as the cut-off value for the MA-ELISA.

Experimental infection with MAH

To evaluate the serodiagnostic ELISA test as an alternative for an inspection of lymph nodes by eye at slaughter we infected pigs experimentally with MAH strain 17404 and examined the correlation between the presence of MAH bacteria, the formation of lesions in lymph nodes of pigs and the antibody response.

Four groups of eight pigs were infected, one group at 2½ weeks of age, one group at 4½ weeks of age, one at 18 weeks of age, and one group at all three time points (2½, 4½ and 18 weeks of age). The experiment was terminated when all pigs were 24 weeks old. During the experimental phase the pigs showed no clinical disease symptoms and their leucocyte counts were normal (results not shown). In tuberculin skin tests three days before necropsy 31 out of 32 pigs reacted positive; the skin of the ear at the site of injection showed redness and focal swelling. Size of reactions 72 hours after injection varied between 10 and 20 mm. Pigs were subsequently euthanized and from the results of the bacteriological examination all 32 pigs appeared to be infected with MAH. Irrespective of the age at which pigs were infected, MAH bacteria were detected in one or more of the lymph nodes, most frequently in the submaxillary and mesenteric lymph nodes (Table 3). Corresponding to the results of the bacteriological examination of the lymph nodes, pathological examination showed that most frequently the sub-maxillary and mesenteric lymph nodes were affected. However, bacteriological examination gave more positive results as compared to pathological examination. Sixteen (50%) pigs had granulomatous lesions in one or more of the lymph nodes and 10 (31%) of the pigs in the sub-maxillary lymph nodes (Table 3). Results of A c c e p t e d M a n u s c r i p t the MA-ELISA on longitudinally serum samples obtained during the experimental phase showed that titers (in PP) were low at the time of infection and started to increase 6 to 8 weeks after infection. At 10-12 weeks after infection the mean PP of groups of pigs infected at an age of 2½ and 4½ weeks was maximal. In serum samples of pigs infected at three time points (2½ , 4½ and 18 weeks of age) titers increased further and at necropsy, 21½ weeks after infection these titers were at a maximum (Figure 1).

At that timepoint 69% of the pigs (22/32) were serologically positive (Table 4). Taken together, the sensitivity of the pathological examination as performed at slaughter was 31% and of the serological examination 69%. According to McNemar's test this difference in sensitivity was significant (p = 0.01).

We determined whether the length of the infection period influenced the formation of granulomatous lesions and the anti MA antibody response. In groups of pigs infected at 2½ and 4½ weeks of age, 7 out of 8 pigs showed granulomatous lesions in their lymph nodes at necropsy when pigs were 24 weeks of age. No lesions were detected in lymph nodes of pigs infected at 18 weeks of age when they were slaughtered 6 weeks later (Table 3). The results of the MA-ELISA showed that most (20/24) of the pigs infected at 2½ and 4½ weeks of age had detectable anti-MA antibody responses at an age of 24 weeks whereas 2 out of 8 pigs infected at 18 weeks of age had a positive antibody titer (Table 4). In conclusion, these results indicated that lesions and antibody responses can generally be detected 19½ weeks after experimental infection, but are relatively inconsistent after 6 weeks of infection.

Natural infections with MA

In order to evaluate the serodiagnostic ELISA test for use under field conditions we collected a considerable number of serum samples from pigs from two farms (A and B) with a recent history of MAH infections and performed bacteriological, serological and pathological examinations of particular lymph nodes. Results of bacteriological examination of the sub-maxillary and mesenteric lymph nodes showed that 56% (103/184) of the pigs on farm A were infected with MAH and 35% (41/117) of the pigs on farm B (Table 5). Granulomatous lesions in the sub-maxillary lymph nodes were detected by pathological examination in 31% (57/184) of the pigs originating from farm A and in 8% (9/117) of the pigs from farm B. Using the MA-ELISA, on farm A, 16% (29/184) of the pigs tested serologically positive and on farm B, 17% (15/117) of the pigs. These results indicate that, compared to the results of the pathological and serological examination, the bacteriological examination for MA is the most sensitive diagnostic method for detection of MA infections in these two herds. Furthermore, that on farm A the pathological Sensitivity and specificity of the pathological and serological examination were calculated on the samples of pigs from these two farms using the results of the bacteriological examination as a reference. For the MA-ELISA, sensitivity was 14% (9% -21% CI) and the specificity 83% (77% -89% CI). For the pathological examination of the sub-maxillary lymph nodes, sensitivity was 31% (23% -39% CI) and the specificity 86% (79% -91% CI). According to McNemar's test pathological examination of the submaxillary lymph nodes for granulomatous lesions had a significantly (p = 0.005) higher sensitivity than the serological examination by the MA-ELISA whereas statistically no difference was found in specificity of both tests.

Discussion

Diagnosis of MA infection in pigs is traditionally based on the detection of granulomatous lesions in lymph nodes seen by eye at slaughter. Since sensitivity and specificity of this approach is questioned [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF][START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF][START_REF] Offermann | The prevalence of Salmonella, Yersinia and Mycobacteria in slaughtered pigs in Switzerland[END_REF] we developed as an alternative a serodiagnostic ELISA assay on the basis of a polar lipid fraction from MA. We evaluated the MA-ELISA and found in samples from experimentally infected pigs a significantly higher sensitivity for the MA-ELISA (69%) as compared to pathological examination (31%). The MA-ELISA seemed also more specific since on a selected set of sera from MA negative pigs [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF] only one out of 153 pigs was positive in the MA-ELISA whereas 99 (65%) pigs had granulomatous lesions. This shows that the MA-ELISA was highly specific even when a high number of serum samples originated from pigs with lesions.

Results of the evalution of the MA-ELISA test on serum samples from pigs originating from two MA infected herds showed a variable picture. On samples of these pigs the sensitivity of the pathological examination (31%) was significantly higher than the MA-ELISA (14%). However, more positive results were obtained with the MA-ELISA on the first farm whereas on the second farm more pigs showed lesions in the sub-maxillary lymph nodes. A possible reason for the variation in results on the two MA infected farms may be related to antigenic variation between the MAH strain used for the preparation of polar lipid fraction for the MA-ELISA and the MAH strains circulating on both farms. Study in a wider range on MA infected farms will be needed to provide a more comprehensive view of the quality of both tests for detection of MA in infected farms. At the same time further optimization of MA-ELISA with use of Currently, diagnosis of MA infections in pigs is based on detection of granulomatous lesions in lymph nodes of pigs by incision and visual inspection at slaughter [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF][START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF]. In accordance with results of others we frequently detected MA bacteria whereas lesions were absent [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF][START_REF] Offermann | The prevalence of Salmonella, Yersinia and Mycobacteria in slaughtered pigs in Switzerland[END_REF]. Although the sensitivity we calculated on naturally and experimentally infected pigs was low (31%), it cannot be excluded that this sensitivity is still overestimated as we performed pathological examinations of the lymph nodes by multiple incisions and under optimal conditions in the facilities of the Central Veterinary Institute of Wageningen UR. Lesions in lymph nodes vary in size from pinpoint to pea size and especially mild lesions can easily be missed at slaughter due to the rapid line speed.

The specificity of the pathological examination of sub-maxillary lymph nodes on the two MA infected farms in this study was calculated to be 86%. Results of an earlier study of us on selected lymph node samples from nine pig herds in the Netherlands had given evidence about a low specificity since we found that granulomatous lesions in lymph nodes of slaughter pigs were not associated with the presence of MA bacteria but with R. equi [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF]. The MA infection level of the two for this study selected herds was high but low in the nine herds in our earlier study. Therefore it is most likely that in highly MA infected herds the pathological examination of lymph nodes is better correlated with the presence of MA bacteria than in populations where MA infections are absent or low. In the Netherlands the prevalence of MA infections is low [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF], for this reason the specificity as calculated in this study is probably lower in the real field situation. [START_REF] Brown | Lesions of swine lymph nodes as a diagnostic test to determine mycobacterial infection[END_REF] calculated a specificity of 53%, which confirms the idea that specificity could be lower than the 86% we found on the two MA infected herds.

We developed the MA-ELISA with the aim to detect MA infected pigs at slaughter when they are 26 weeks of age. Results of the experimental infection with MA showed that titers started to increase 6-8 weeks after infection and stayed detectable till the end of the experiment, 21½ weeks after infection.

There is no clear evidence at which age pigs are most at risk for an infection with MA. Infections in herds are reported when peat or compost are provided as a source of iron and minerals to piglets soon after birth [START_REF] Engel | Pig-compost" as a source of Mycobacterium avium infection in swine[END_REF][START_REF] Matlova | Distribution of Mycobacterium avium complex isolates in tissue samples of pigs fed peat naturally contaminated with mycobacteria as a supplement[END_REF] but infections later in on lifetime cannot be excluded. MA bacteria are present in bedding materials, sawdust and drinking water in the stables [START_REF] Matlova | Mycobacteria isolated from the environment of pig farms in the Czech Republic during the years 1996 to 2002[END_REF][START_REF] Thoen | Tuberculosis[END_REF], to this materials are pigs constantly exposed during their whole lifetime. Taking the results It was unexpected that in the experimental infection pigs repeatedly infected with MAH had a lower number of lesions compared to pigs once infected (Table 3). No differences were seen between groups regarding tuberculin reactions and isolation of MAH bacteria, but the development of immune response differed between the group of repeatedly infected pigs and fthe groups of once infected pigs. Whereas from the other groups the mean anti MA antibody titer was maximal at 10-12 weeks after infection, in the repeatedly infected group the mean anti MA antibody titer still further increased. Apparently, the repeated MA infection leads to this diffrent immune response associated with a lack of lesion formation.

For immunediagnosis of human MA infections lipid antigens derived from MA are successfully used [START_REF] Enomoto | Rapid serodiagnosis of Mycobacterium avium-intracellulare complex infection by ELISA with cord factor (trehalose 6, 6'-dimycolate), and serotyping using the glycopeptidolipid antigen[END_REF][START_REF] Kitada | Serodiagnosis of Mycobacterium avium-complex pulmonary disease using an enzyme immunoassay kit[END_REF][START_REF] Kitada | Serodiagnosis of pulmonary disease due to Mycobacterium avium complex with an enzyme immunoassay that uses a mixture of glycopeptidolipid antigens[END_REF][START_REF] Kitada | Use of glycopeptidolipid core antigen for serodiagnosis of Mycobacterium avium complex pulmonary disease in immunocompetent patients[END_REF], here we show that lipid fractions are also suitable for immunodiagnosis of MA infections in pigs. The polar lipid fraction showed a higher reactivity with sera from experimentally infected pigs than the apolar lipid fraction, for this reason the polar lipid fraction was chosen as antigen in the MA-ELISA. For detection of MA infections in humans, purified glycopeptidolipids (GPL) are used as antigen in ELISA tests with sufficient sensitivity and specificity [START_REF] Kitada | Serodiagnosis of Mycobacterium avium-complex pulmonary disease using an enzyme immunoassay kit[END_REF].

GPLs are immunodominant antigens from MAC and are well-characterized polar lipids [START_REF] Brennan | Structure of the specific oligosaccharides from the glycopeptidolipid antigens of serovars in the Mycobacterium avium-Mycobacterium intracellulare-Mycobacterium scrofulaceum complex[END_REF][START_REF] Inderlied | The Mycobacterium avium complex[END_REF]. In preliminary experiments we found that GPLs are indeed present in the polar lipid fraction we used for the MA-ELISA assay (results not shown). Although there are no reports on the immunogenicity of GPLs in MA infections in pigs it can be speculated that in our ELISA test, GPLs contribute to the difference between reactivity of the polar and apolar lipid fraction of MAH.

It can be concluded that sensitivity and specificity of the use of granulomatous lesions in lymph nodes as read out criterion for a potential MA infection performs poorly. A more sensitive and objective test for routine diagnosis of MA infections in slaughter pigs is needed. The MA serodiagnostic test could meet these requirements and may be a valuable tool for screening herds to prevent and control MA infections in pigs. Total 153 (100) a Serum samples were collected in the course of a study for the prevalence of MA infections in the Netherlands. The design and the outcome of the study was previously described by [START_REF] Komijn | Granulomatous lesions in lymph nodes of slaughter pigs bacteriologically negative for Mycobacterium avium subsp. avium and positive for Rhodococcus equi[END_REF].

  obtain positive field serum samples in the period October 2006 till June 2008 two herds (A and B) were selected where recently cases of MAH infections were detected in slaughter pigs. Both farms

  MAH. All these serum samples displayed a higher titer against the polar lipid fraction (range 290-1577) as compared to the apolar lipid fraction (range 20-250). Therefore the polar lipid fraction was selected for further use in an MA-ELISA.

  positive results than the serological examination, whereas on farm B the serological examination showed more positive results.

  s c r i p t lipid antigens from a broader range of serotypes may improve its performance in the face of infections with different MA serotypes.

  -ELISA into account, serodiagnosis offers possibilities to detect MA infections during the whole lifetime of the pig, except when pigs are infected in the latest weeks before slaughtering.

  Figure legendThree groups of eight pigs each were experimentally infected with M. avium subsp. hominissuis strain 17404 at 2½ (), 4½ ()and 18 ( ) weeks of age, the fourth group was infected three times at 2½, 4½ and 18 (X) weeks of age. All pigs were necropsied at 24 weeks of age. Longitudinal antibody responses were determined in ELISA tests against the polar lipid fraction of MAH strain 17404. Mean Percentage Positivity and Standard Deviation was calculated for each group and for each timepoint.

Table 1

 1 Design experimental infection of pigs with Mycobacterium avium subsp. hominissuis

	1

Table 2

 2 Distribution of PP obtained in the MA-ELISA assay on serum samples from pigs (n=153) negative for infections with Mycobacterium avium (MA)

	Percentage Positivity	Number (%)
	< 0%	80 (52.3)
	0 -5%	60 (39.2)
	5 -10%	10 (6.5)
	10 -15%	2 (1.3)
	15 -20%	1 (0.7)
	> 25%	0 (0)

a .

Table 3

 3 Post-mortem results recorded in pigs after experimental infection with Mycobacterium avium subsp. hominissuis

	Group	a

b Mes c Ing d Trach-br (le) e Trach-br (ri) f Retro-phar a Experimental design is described in Table 1A

b Lnn mandibularis c Lnn mesenterialis d Lnn inguinalis e Lnn trachea-bronchialis f Lnn retro-pharyngeal g Lnn retro-pharyngeal h Pathological lesions i Isolation of M. avium subsp. hominissuis at necropsy

Table 4

 4 Results of the MA-ELISA assay on endpoint serum samples of pigs experimentally infected with Mycobacterium avium subsp. hominissuis.

	Group	No. of pigs	Weeks after	Number of pigs
			infection		Negative	Positive
	1	8	21.5		0	8
	2	8	19.5		3	5
	3	8	6		6	2
	4	8	21.5, 19.5, 6	a	1	7
	Total	32			10	22

a Pigs were three times infected.


Davide Ruffoni

John William

Chapman Dunlop

Peter Fratzl

Richard Weinkamer
email: richard.weinkamer@mpikg.mpg.de

Keywords: cellular structures, defects user supplied): strain energy density, trabecular bone cellular structures, defects, strain energy density, trabecular bone mc.manuscriptcentral.com/pm-pml

Introduction

The nature of interactions between physical entities results very often in their periodic arrangement. Examples exist over very different length scales from atomic crystal lattices [1] to mesoscopic materials created by self-assembly [2] up to macroscopic periodic structures [START_REF] Gibson | Cellular Solids : Structure and Properties[END_REF]. Despite their periodicity, these arrangements are never free of defects. The interest in these defects originates from their crucial influence on the macroscopic properties of the material. For instance, the physics of defects in crystalline solids, in particular also point defects in the form of impurities, has been studied intensively to understand their influence on strength and plastic behaviour [START_REF] Haasen | Physical metallurgy[END_REF].

On a much larger length scale periodic cellular solids have recently become a popular research topic (e.g. [START_REF] Gibson | Cellular Solids : Structure and Properties[END_REF][START_REF] Evans | [END_REF][6][7][8]). Cellular solids, in particular 2D honeycombs and 3D foams, are widely used technologically in light weight constructions. In addition cellular solids, both regular and random, are abundant in nature [9] with the sponge-like trabecular bone [10,11], the anisotropic cellular structure found in wood [12,13] and cork [14,15], and the glass sponge Euplectella [16] being only some of many examples studied. Their application both in nature and technology is based on the idea to use a minimal amount of material to create strong reinforcing structures. Again the impossibility of defect free periodic cellular solids raises the question about the influence of defects on the macroscopic mechanical performance. Intensive finite element analysis has been performed to understand the influence of non periodic microstructures [17,18] and of different types of morphological imperfections like missing cell walls, cell-wall waviness, misalignment and thickness on the elastic modulus, strength [19][20][21][22][23][24] and toughness [25].

Here we present work that focuses on the influence of a defect on its local environment within the cellular solid. In particular we investigate how a defect in the form of a structural perturbation can result in concentrations of the elastic strain energy, when a cellular solid is deformed. Concentrations of the strain energy indicate regions in the cellular architecture where brittle failure could initiate. Our research is motivated by the question whether these sites of high values of the strain energy can be predicted based on a geometrical analysis of the cellular structure. Considering trabecular bone this question has high priority to assess the quality of the bone architecture in osteoporotic patients [26]. Recent experimental advances in imaging trabecular bone using µ -CT [27] raise hopes that based on a structural analysis "weak points" in the bone structure can be identified, which could then act as initiators of (non-traumatic) bone fractures. Finite element studies investigating the distribution of forces in cellular solids demonstrated that the width of the force distribution depends critically on the degree of randomness of the structure, with increasing randomness resulting in a broader distribution [28]. In Voronoi honeycombs the axial strains in the cell walls have been found to be approximately normally distributed [19]. studied how the energy is distributed in different struts of a 3D open cell structure when loaded uniaxially by looking at frequency distributions of the energy. In cases of a small irregularity of the structure the distribution was sharply peaked indicating a concentration of the strain energy in few sites of the cellular solid [29].

To investigate the effect of a structural defect on its environment, our strategy is to study a model system of reduced complexity. A single defect is introduced in a twodimensional regular honeycomb structure. A regular honeycomb is a well-studied system [START_REF] Gibson | Cellular Solids : Structure and Properties[END_REF]30,31], which is mechanically isotropic and has relevance both in biology [12,32] and engineering . In this regular honeycomb a minimal structural defect is introduced. For a defect to carry geometrical information it has to comprise of at least several struts, which meet in a junction point. For honeycombs, joints have a coordination number of three (Fig. 1). For this work the point of view is therefore to consider the cellular structure as a periodic assembly of joints the same way a crystalline lattice is build up periodically by atoms. The single defect plays then the role of an impurity in an otherwise regular honeycomb. The aim is to classify defects in terms of their ability to concentrate the strain energy density. As a tool for the classification, we mechanically characterize the periodic irregular lattice honeycomb, which can be constructed in a unique way of identical copies of the defect joint. It is shown that a mechanically disadvantageous geometry of the defect does not necessarily lead to a concentration of the strain energy density in the defect, but to a concentration in its neighbouring environment.

Methods

The influence of different joint defects on their environment in an otherwise regular hexagonal honeycomb is investigated using a three-step approach. First, appropriate joints are selected, using the restriction that the joint should fit as a defect into a regular honeycomb lattice which strongly decreases the parameter space of possible joints. Second, the joint is mechanically characterized by constructing a periodic lattice in a unique way with the joint as a basic building block using analytical results from [33]. In the last step, the joint is introduced as a defect in the regular honeycomb lattice, and its performance and the influence on its environment under mechanical loading is studied using finite element modelling. The steps of this procedure are shown in Fig. 1 and are explained in more detail below.

Selection of joint

For general two-dimensional honeycombs, which have a coordination number 3 = Z , a joint consists of three beams, which meet each other at a junction point (Fig. 1b). Assuming cylindrical beams of circular cross section, a joint is geometrically characterized by 8 parameters: 3 beam lengths, 3 cross-sectional radii, and 2 angles. In the following the radii of the three struts forming the joint are assumed to be identical. The number of independent parameters is further reduced when the selection of joints is restricted to joints that can be inserted in a regular honeycomb to act as a defect. In this case the joint is fully characterized by the coordinates of the junction point, ) , ( , where the origin of the coordinate

system ) , ( 2 1 X X
, is conveniently chosen to be the junction point of a regular joint (Fig. 1a).

Selection of the junction point, P , within a T-shaped area defined in Fig. 1a excludes only extreme joint geometries of minor interest.

Classification of the joint (periodic irregular honeycomb)

In order to assess the mechanical performance of a joint, the joint is used to construct in a unique way a periodic irregular honeycomb lattice (Fig. 1c). , and applying a stress, i σ , mechanical quantities like the strain of the joint inside the periodic lattice, i ε , or the joint strain energy density (SED),

joint 2 / V C U j i ij ε ε = can be calculated. joint V
denotes the material volume corresponding to the joint with junction point ) , ( 21 x x P = , given by:

( )                       + +         + +       + +         - + - + = 2 2 2 1 2 2 2 1 2 2 2 1 2 joint 2 1 2 3 2 1 2 3 2 a x a x a x a x a x x r V π , ( 1
)
where a denotes the beam length of a regular joint (Fig. 1a).

Constructed in this way the different periodic honeycombs have, in addition to different geometries, also different relative densities, i.e. material volume per total volume. To exclude the influence of the relative density, the beam lengths of the joints are uniformly rescaled to result in the same relative density defined by the relative density of the regular hexagonal honeycomb. The different periodic lattices are characterized according to three loading conditions: compressive load along the horizontal 1 X direction, compressive load along the vertical 2 X direction and hydrostatic compression.

Effect of joint acting as a defect in a regular honeycomb

In the final step the joint, defined and characterized in the previous section, is implanted as a defect in a regular hexagonal honeycomb (Fig. 1d). The linear elastic mechanical problem under different loading conditions (hydrostatic compression, uniaxial compression) is solved numerically using the finite element method (FEM) (ABAQUS version 6.6; Rising Sun Mills, Providence, RI). Each half-beam of the joint is modelled as a Timoshenko beam [34,35] with a lattice size of

E

GPa and Poisson ratio 3 . 0 = ν

. The high slenderness ratio of the beams were chosen to reduce the influence of transverse shear, which was neglected in the analytical solutions which used Euler-Bernoulli beams to characterize the joints. Periodic boundary conditions for the displacement field were used [21] for a system of honeycombs with a linear system size of 105a , which corresponds to 8608 joints overall. The system size was large enough to avoid interactions of the defect with itself due to the periodic boundary conditions as tested with lattices of different size. Nevertheless, for the calculation of the total strain energy density of the lattice, only the inner half of the lattice was considered for the evaluation, since the periodic boundary conditions lead to distortions of the strain and stress fields at the boundaries [21]. Results shown here are restricted to the case that the joint has left-right symmetry, i.e., the junction point of the joint is defined as

) , 0 ( 2 1 x x P = .
In addition to the implantation of geometrical defects as described above, the effect of a second kind of defect was tested. Here the geometry of the regular honeycomb remained untouched, but the cross-sectional radius r of the beams of one joint (and its connection to the rest of the lattice) was changed. Such a "mass defect" is characterized by the parameter 0 / r r k = .

Values of k in the range from 0.01 to 100 were studied.

Results

Classification of the joint (periodic irregular honeycomb)

Fig. 2 shows the strain energy density (SED) of periodic irregular honeycombs, which were generated starting from a joint with the procedure explained above (Fig. 1). According to this procedure, each coloured point in the contour plots of By compressing a periodic honeycomb lattice along the horizontal 1 X direction, the minimum SED is obtained when the 2 x coordinate of the junction point of the joint equals - 0.5 a (Fig. 2a). In this case, where the honeycomb resembles a brick wall (Fig. 2, bottom), beams of the joint align along the loading direction and the corresponding SED is three orders of magnitude less than the one stored in the regular lattice (SED 0 ). Already small deviations from this particular "brick wall" geometry result in significant drops in the SED. For a compressive load in the vertical 2 X direction, the stiffest honeycomb is not the regular isotropic one, but a lattice which is obtained when the junction point is moved along the vertical direction of about -0.2 a (Fig. 2b). The shallow colour gradient within the plot indicates that under this loading condition honeycombs are rather insensitive to the specific geometry of the honeycomb. In contrast, hydrostatic compression results in the strongest variations of the SED to over five orders of magnitude (Fig. 2c). The stiffest geometry is realized by a regular joint, )

= x x P 0 , 0 ( ) , ( 2 1 =
, resulting in an isotropic regular honeycomb.

Effect of joint acting as a defect in a regular honeycomb

The exchange of one joint in a regular honeycomb with a joint of different geometry leads to a redistribution of the SED, which is naturally homogeneous for the regular honeycomb. Firstly we investigate the problem, whether a joint, which was classified as soft or stiff (in the previous section), results in a softening or stiffening of the global lattice. The total strain energy density of the global lattice for the three loading cases as a function of the joint geometry is plotted (Fig. 3a) and compared with the strain energy density of the periodic irregular lattice (Fig. 3b). Since only symmetrical joints are considered, the 2 x -coordinate of the junction point suffices to identify different joints and is plotted on the x-axis. For hydrostatic compression (full grey line) there is a qualitative agreement between the two cases: a locally soft joint (Fig. 3b) weakens the lattice also at the global level (Fig. 3a). For uniaxial horizontal compression (full black line) the minimum in both lattices is shifted at -0.5 a and around that position the behaviour is also similar. For uniaxial vertical compression (dashed line), however, joints classified as soft do not soften the overall lattice for positive values of the junction point position (Fig. 3a, right part of the plot).

A plot of the spatial distribution of the SED allows studying the redistribution of the SED due to the inclusion of a defect. A representative case of an arrow-shaped geometrical defect, which is characterized by a junction point

) 75 . 0 , 0 ( a P - =
, is shown in Figure 4. The SED has its peak value in the defect when the honeycomb is compressed hydrostatically (Fig. 4a). The energy is strongly concentrated in the defect with a SED value more than 7 orders of magnitude larger than the far field value. Although not well presented by the logarithmic scaling of Fig. 4a, the SED returns very rapidly to its far field value, when moving away from the defect. The breaking of the up-down symmetry by the defect is clearly reflected in the asymmetric SED pattern. Under uniaxial vertical compression (Fig. 4b), the resulting SED pattern shows pronounced long-ranged anisotropy. The SED is concentrated in the joints, which form the horizontal extension of the defect. Values increased more than 10% in comparison with the far field value are found up to the 9 th nearest neighbour. Stripes of reduced SED are found in the remaining four directions of the six-fold symmetry. The largest SED values of about 1.6 SED 0 are found in the second nearest neighbour joints of the defect.

In the defect itself the SED is reduced to approximately 0.5 SED 0 .

While Fig. 4 shows the detail of the SED pattern for a specific case, Fig. 5 summarizes the results for all symmetric joints and compares the outcome with the SED obtained from the joint classification (full line) (see beginning of the results section, Fig. 2). Two pieces of information are given in Fig. 5: the SED of the defect joint (circles, and short dashed line) and joint classification predicts at least qualitatively their behaviour as a defect (Fig. 5a). The softer the joint was classified (full line), the higher were the values of the SED calculated from FE in the defect joint. Since for defects with junction points in the range Under uniaxial vertical compression the situation is reversed (Fig. 5b). Joints that have been classified as soft, display the lowest value of the SED when acting as a defect. The corresponding SED peak values show the opposite behaviour to the SED of the defect, being high when the SED in the defect is low.

When a mass defect is introduced, i.e. the beams in one joint have reduced or increased cross-sectional radii without perturbing the regular geometry of the honeycomb, the resulting SED pattern is even qualitatively very different depending on the amount of joint mass reduction (Fig. 6). In particular the maximum value of the SED is found in different positions with respect to the position of the defect. For very low mass of the defect

(approximately 07 . 0 ≤ k
) the maximum of the SED occurs at the location of the defect itself (Fig. 6a). For less severe reductions (

1 07 . 0 < < k
), the highest strain energy is observed at the third nearest neighbour joints of the defect located on the inclined symmetry directions of the honeycomb (Fig. 6b). When the defect presents beams which are thicker than the regular joint (

1 > k
), the maximum value of the SED is found in the fourth neighbours situated on a horizontal line passing thorough the defect (Fig. 6c). In all cases the six-fold symmetry of the honeycomb is reflected in an anisotropic long-ranged SED pattern.

Discussion

In this paper we combined analytical and numerical results to understand how the individual building blocks of a 2D cellular structure behave as defects. As elementary building blocks we introduced joints, which are the smallest entities in a cellular solid which carry geometrical information. They can be interpreted as the analogue of atoms in crystalline lattices. The individual mechanical behaviour of a joint, in terms of a classification in stiff and soft, was determined by constructing in a unique way an irregular periodic honeycomb using only identical copies of the joint. To test then the joint behaviour as a defect, we chose the simplest possible situation, i.e. to implement the joint as a defect in an isotropic regular honeycomb. For quantification of the local mechanical performance, the strain energy density (SED) as a simple scalar quantity was reported here, but qualitatively identical results were obtained by looking at the maximal strain or stress.

The classification of joints in Fig. 2 based on analytical solutions of the mechanical problem present known results in a new compact form. The stiffest joints for a given loading situation are the ones which minimize bending so that most of the deformation occurs by axial compression of the beams. For hydrostatic compression (Fig. 2c) the regular lattice is characterized by pure axial deformations with the result that the elastic properties scale linearly with the relative density [START_REF] Gibson | Cellular Solids : Structure and Properties[END_REF]. Even small deviations from the regular geometry introduce bending and therefore a significant increase in the amount of energy absorbed.

Under uniaxial horizontal compression (Fig. 2a) a brick-wall like architecture corresponding to a junction point of ) 5 . 0 , 0 ( a P -= also avoids bending in the small deformation limit. And also the minimum of SED around

) 2 . 0 , 0 ( a P - =
for uniaxial vertical compression (Fig. 2b) can be understood in terms of simple beam bending. Since the bending moment acting on one of the lower beams, 2 L or equivalently 3 L , is proportional to The insertion of a joint with given geometry as a defect in an otherwise regular honeycomb leads to intricate spatial distributions of the SED (Fig. 4 and6). Under vertical uniaxial loading the SED pattern displayed a hexagonal symmetry of long range. Joints of high values of the SED are either on the horizontal extension of the defect position or on lines at 60 and 120 degrees relative to the horizontal line. The answer to the question whether the "individual" joint behaviour is reflected in its behaviour as a defect depends crucially on the loading conditions. For hydrostatic compression, joints which were classified as soft, behaved also as a weak defect in the regular honeycomb by concentrating the SED in themselves.

Under uniaxial compression, however, the situation was reversed so that soft joints were so effective in shielding the loading from themselves, that SED values were very low in the defect itself, but highly increased in the neighbourhood of the defect. In the context of failure of a cellular solid like trabecular bone, this implies that not necessarily sites with a mechanically unfavourable geometry break first, but initiation of failure can be shifted to their nearer neighbourhood. Even in the situation where the geometry of the regular hexagonal honeycomb is unchanged, and only one joint is thinned or thickened, the question of where the SED is concentrated cannot be stated simply. For very thin defects, the concentration of the SED within the defect results from the low volume of the defect, which decreases faster than the strain energy in the defect. For moderately thin defects the strain energy density is not concentrated in the defect itself.

In conclusion, this paper has investigated the effect of defect geometry on the spatial distribution of the strain energy density around the defect within a regular two-dimensional cellular solid. This work of course is only a first step, being focused on simple defects within a 2D hexagonal honeycomb. Further investigations have to show whether our results are only specific to honeycombs or apply also to other lattices in two and three dimensions. Materials of course do not just contain single defects and it is likely that a more complex mechanical response would come from the interaction between defects, something that remains to be investigated. Such work could also have interesting implications for the understanding of the mechanics of bone remodeling. In this renewal process, small bone packets are resorbed and deposited on the bone surface. Bone remodelling is thought to be mechanically controlled allowing the trabecular bone architecture to adapt to a changing mechanical environment [36,37]. The basic control of this process is thought that removal of material increases the local loading and leads to repair. Our results questions whether such a feedback is a general property of cellular solids or depends on the specific architecture.

F

  Effect of minimal defects in periodic cellular solidsDavide Ruffoni a, b , John William Chapman Dunlop a , Peter Fratzl a , and Richard Weinkamer a* . a Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany. b Present Address: Institute for Biomechanics, ETH Zurich, Zurich, Switzerland.

Figure 2 ,

 2 top, represents the SED of a periodic honeycomb with different geometry, but the same relative density. The SED is normalized by the corresponding energy density of a regular honeycomb, SED 0 , under the same external loading conditions. For symmetry reasons only half of the T-shaped area of Fig.

  shown. For a given loading condition, joints are classified as "soft" or "stiff", where soft (stiff) joints are the sites of high (low) SED values. Note the very different lattice geometries, which are obtained by choosing the junction point P along the right-left axis of symmetry, i.e.

  of the SED (squares, and long dashed line), which can occur in the defect itself or in one of the surrounding joints of the regular honeycomb. Under hydrostatic load

  the SED occur in the defect, circles and squares superimpose for this case.

  of it under the condition that the relative density of the resulting honeycomb is equal to the regular one, leads to a minimum at around )

Figure. 1 :

 1 Figure CaptionsFigure.1: Procedure to generate different joint defects and to investigate their mechanical behaviour under two different scenarios. (a) Three cells of a regular hexagonal honeycomb where a single joint in their centre is perturbed by shifting the position of its junction point, P , inside a given T-shaped region (gray area). The size of this region is given in terms of the lattice dimension, a . The rectangular shape of this region is chosen for convenience. (b) The geometry of a joint characterized generally by 8 geometrical parameters. (c) Periodic irregular honeycomb lattice build up in a unique way by identical copies of the joint of Fig.1b. (d) The joint is introduced as a defect in an otherwise regular hexagonal honeycomb.

Figure. 2 :

 2 Figure. 2: Contour plots of the strain energy density (SED) for different irregular periodic honeycombs, renormalized to have the same relative density, under uniaxial horizontal (a), vertical (b), and hydrostatic (c) compression. Each coloured pixel in the plot represents a honeycomb of different geometry as defined in the text and Fig. 1. The SED is normalized by the energy density of the regular hexagonal honeycomb, SED 0 .

Figure. 3 :

 3 Figure. 3: Total strain energy density of the regular honeycomb with defect (a) and the irregular periodic honeycomb (b) constructed with the defect joint following the procedure of Fig. 1. The x 2 coordinate of the junction point of the joint suffices to characterize the defect (plotted on the x-axis), since only joints with left-right-symmetry are considered. The three different loading cases of uniaxial horizontal, uniaxial vertical and hydrostatic compression are shown with full, dashed and full grey lines, respectively.

Figure. 4 :

 4 Figure.[START_REF] Haasen | Physical metallurgy[END_REF]: Spatial pattern of the strain energy density around a central defect in a regular hexagonal honeycomb under hydrostatic (a) and uniaxial vertical (b) compression. The arrowshaped joint creating the defect is sketched between the two plots. The colour of each rectangular patch corresponds to the SED absorbed in that particular joint. Only a sub-region of the simulated lattice around the defect is shown. Again, the SED is normalized by the value for the regular honeycomb, SED 0 , which corresponds approximately to the energy density of joints far away from the defect.

Figure. 5 :

 5 Figure. 5: Strain energy density (SED) of the defect joint (circles) within a regular honeycomb under hydrostatic (a) and uniaxial (b) compression. The x 2 coordinate of the junction point of the joint suffices to characterize the defect (plotted on the x-axis), since only joints with left-right-symmetry are considered. The SED of the defect joint is compared with the maximum value of the SED within the lattice (squares) and the analytical result of the SED for the irregular periodic honeycomb constructed with the defect joint (full line).

Figure. 6 :

 6 Figure. 6: Spatial pattern of the strain energy density (SED) around a central defect in a regular hexagonal honeycomb under uniaxial vertical compression. The defect joint has unchanged geometry with respect to the regular honeycomb, but its beams have a crosssectional radius changed by a factor k. Three different such mass defects are plotted corresponding to a very thin (a), a thin (b) and a thick defect joint (c) compared to the dimensions of the other beams. White arrows indicate the sites of maximum SED.

  Procedure to generate different joint defects and to investigate their mechanical behaviour under two different scenarios. (a) Three cells of a regular hexagonal honeycomb where a single joint in their centre is perturbed by shifting the position of its junction point, P, inside a given T-shaped region (gray area). The size of this region is given in terms of the lattice dimension, a. The rectangular shape of this region is chosen for convenience. (b) The geometry of a joint characterized generally by 8 geometrical parameters. (c) Periodic irregular honeycomb lattice build up in a unique way by identical copies of the joint of Fig. 1b. (d) The joint is introduced as a defect in an otherwise regular hexagonal honeycomb. 254x190mm (300 x 300 DPI) Contour plots of the strain energy density (SED) for different irregular periodic honeycombs, renormalized to have the same relative density, under uniaxial horizontal (a), vertical (b), and hydrostatic (c) compression. Each coloured pixel in the plot represents a honeycomb of different geometry as defined in the text and Fig. 1. The SED is normalized by the energy density of the regular hexagonal honeycomb, SED0. 254x190mm (300 x 300 DPI) Total strain energy density of the regular honeycomb with defect (a) and the irregular periodic honeycomb (b) constructed with the defect joint following the procedure of Fig. 1. The x2 coordinate of the junction point of the joint suffices to characterize the defect (plotted on the x-axis), since only joints with left-right-symmetry are considered. The three different loading cases of uniaxial horizontal, uniaxial vertical and hydrostatic compression are shown with full, dashed and full grey lines, respectively. 254x190mm (300 x 300 DPI) Spatial pattern of the strain energy density around a central defect in a regular hexagonal honeycomb under hydrostatic (a) and uniaxial vertical (b) compression. The arrow-shaped joint creating the defect is sketched between the two plots. The colour of each rectangular patch corresponds to the SED absorbed in that particular joint. Only a sub-region of the simulated lattice around the defect is shown. Again, the SED is normalized by the value for the regular honeycomb, SED0, which corresponds approximately to the energy density of joints far away from the defect. 254x190mm (300 x 300 DPI) Strain energy density (SED) of the defect joint (circles) within a regular honeycomb under hydrostatic (a) and uniaxial (b) compression. The x2 coordinate of the junction point of the joint suffices to characterize the defect (plotted on the x-axis), since only joints with left-right-symmetry are considered. The SED of the defect joint is compared with the maximum value of the SED within the lattice (squares) and the analytical result of the SED for the irregular periodic honeycomb constructed with the defect joint (full line). 254x190mm (300 x 300 DPI) Spatial pattern of the strain energy density (SED) around a central defect in a regular hexagonal honeycomb under uniaxial vertical compression. The defect joint has unchanged geometry with respect to the regular honeycomb, but its beams have a cross-sectional radius changed by a factor k. Three different such mass defects are plotted corresponding to a very thin (a), a thin (b) and a thick defect joint (c) compared to the dimensions of the other beams. White arrows indicate the sites of maximum SED. 254x190mm (300 x 300 DPI) Page 22 of 22 http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

  Luxner et al. [29]

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http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

Acknowledgements

DR was supported by the EU Marie Curie EST Program on Biomimetic Systems, MEST-CT-2004-504465


Damir R Tadjiev

Russell J Hand
email: r.hand@shef.ac.uk

Simon A Hayes

Calibrating a nanoindenter for very shallow depth indentation using equivalent contact radius

Keywords: nanoindentation, mechanical properties user supplied): tip area function, calibration, shallow depths tip area function, calibration, nanoindentation, shallow depths

Calibrating a nanoindenter for very shallow depth indentation using equivalent contact radius

Damir R Tadjiev, Russell J Hand,

Introduction

Nanoindentation differs from conventional indentation in that the results are based not on imaging of the residual indent (which would be very challenging, and largely impracticable, for very low load indents), but rather on a calibrated tip area function (TAF) which describes the variation of the contact area (A c ) of the tip as a function of contact depth (h c ). In the ideal case the indenter has a simple axisymmetric shape and, hence, the TAF can be described by a simple mathematical function. Thus even the commonly used Berkovich indenter, which is actually a triangular pyramid, is usually modelled by an equivalent axisymmetric cone, as assumed in the conventional Oliver and Pharr (O&P) approach.

In actuality any real tip shape will deviate from its ideal geometry to some greater or lesser extent, even when new, and this will become more marked as the tip becomes worn over time due to its use in indentation [START_REF] Mencik | Determination of mechanical properties by instrumented indentation[END_REF] and, commonly, secondary use in imaging the residual indent [START_REF] Hysitron | User's Manual for Tribiscope Nanomechanical Test System NRL-M-015[END_REF]. Thus an equivalent cone model of a Berkovich tip will break down at some point [START_REF] Doerner | A method for interpreting the data from depth-sensing indentation instruments[END_REF][START_REF] Pethica | Hardness measurement at penetration depths as small as 20-nm[END_REF] and one approach to this problem is to treat the very near tip region using a Hertzian analysis (see, for example, [START_REF] Gerberich | Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations[END_REF]); clearly this still treats the tip as an axisymmetric object.

In the commonly adopted Oliver and Pharr approach TAF calibration is carried out by indenting a material of known modulus, which is assumed to have i) an elastic modulus that is unvarying with depth and ii) a low E/H value which means that there will be minimum pile-up and sink-in [START_REF] Oliver | Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology[END_REF]. The stiffness, S, of the combined indenter/ indented materials system is then assessed from the initial (elastic) part of the unloading curve and the area of the indentation is then obtained using where β is a geometric correction factor (in this work taken to be equal to 1.05) [START_REF] Oliver | Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology[END_REF] and E r is the reduced modulus, which accounts for the fact that the measured displacement includes contributions from the sample and the indenter. E r is given by

i i r E E E 2 2 1 1 1 ν ν - + - = (2)
where E, E i and ν, ν i are the elastic moduli and Poisson's ratios of sample and the indenter respectively. For the diamond Berkovich indenter E i = 1141 GPa and ν i = 0.07, and for fused silica (which largely obeys the two assumptions mentioned above) used as a standard in this work E = 72 GPa and ν = 0.17, respectively; hence E r is equal to 69.6 GPa. The TAF is then obtained by fitting A as a function of the contact depth, h c .

The work described here forms part of a larger project to examine the mechanical properties of the surface hydration layers formed on silicate glasses [START_REF] Hand | Nano-indentation and surface hydration of silicate glasses[END_REF][START_REF] Tadjiev | Inter-relationships between composition and near surface mechanical properties of silicate glasses[END_REF].

This requires reliable calibration of TAFs for shallow (we have been focusing on less than 80 nm indentation) depths. Calibration of the TAF for shallow depths is a particular problem for a number of reasons: imaging is most difficult in this region (and at the lowest loads impossible due to the occurrence of purely elastic behaviour);

and although the data are more sensitive to random errors in this region (i.e. they are noisier) the data obtained at larger depths tend to have larger absolute (as distinct from relative) residuals. The latter point means that any large depth data tend to dominate the curve fitting thereby reducing the accuracy of any fit at shallow depth.

Conventionally this issue is addressed by providing different fits over different depth ranges but an alternative method is to select an appropriate data transform [9]. Here it has been therefore decided to fit

π / A r c = (3)
as a function of h c , where r c is the contact radius of the equivalent axisymmetric body.

This has the advantage of giving an equal distribution of residuals due to the approximately linear scaling between r c and h c that can be reasonably expected for all tip geometries. Also combining equations ( 1) and (3) gives

r c E S r β 2 = (4) i.e. 1/ r c E r ∝
meaning that the calibration is based entirely on a linear relationship rather than a quadratic one.

Experimental procedure

Instrumentation and reference material

A commercial Prior to the measurements, the compliance of the indenter column (machine compliance) was measured by making at least 25 high-load indentations (5000 to 10000 µN) on fused silica and then plotting compliance (inverse stiffness) versus 1/P (where P is applied load) for the obtained data. Reliability of the determined compliance value was checked by plotting load over stiffness squared (P/S 2 ) versus contact depth and making sure that the slope of the curve is 0. This approach was originally proposed by Oliver and Pharr [START_REF] Oliver | Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology[END_REF] for the measurements at high-load indentations, but it has been found in this work that it also works well at low-load indentations.

Prior to each test the fused silica samples were cleaned by rinsing in pure ethanol and drying using a warm air blower. The surface region to be indented was then imaged using the instrument in the scanning probe microscope (SPM) mode to ensure that the surface was free of dirt and contamination.

Data analysis and TAF fitting

Following the standard O&P method [START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF] the initial unloading contact stiffness, S, was obtained from the slope of a power law fit to the initial part of the unloading curves using the installed Hysitron software. The power law used was

( ) m f h h P - = α (5)
where P is load, h is the measured indention depth, h f is the residual indentation depth after removal of the indenter and α and m are fitting constants. The unloading stiffness

( h P S d d =
) was then obtained by differentiation and equations (1) were used to obtain the equivalent axisymmetric contact radius.

Contact depth h c was calculated by the Hysitron indenter software using

max max 75 . 0 P S h h c - = (6)
where h max and P max are, respectively, the maximum depth and load during the indentation [START_REF] Tadjiev | Inter-relationships between composition and near surface mechanical properties of silicate glasses[END_REF].

Results and discussion

Figure 1 shows a plot of r c versus h c for the tip when new. In this case a linear fit was found to be applicable and a linear regression fit to the data shown gave

5 . 23 899 . 2 + = c c h r ( 7
)
with an r 2 value of 0.990. It is interesting to note that Thurn and Cook [START_REF] Thurn | Simplified area function for sharp indenter tips in depthsensing indentation[END_REF] proposed a three term area function, which actually involves only two independent parameters, to calibrate the TAF. They took a harmonic average of a spherical tip profile (with radius R) and a perfect conical shape (with included angle 2α) and obtained

α π π α π 2 2 2 2 cot 4 4 cot R h R h A c c + + = (8)
Combining equations ( 3) and [START_REF] Tadjiev | Inter-relationships between composition and near surface mechanical properties of silicate glasses[END_REF] gives

F o r P e e r R e v i e w O n l y α α cot 2 cot R h r c c + = (9)
i.e. a straight line as seen in figure (1a). The original derivation of equation [START_REF] Tadjiev | Inter-relationships between composition and near surface mechanical properties of silicate glasses[END_REF] involved use of the binomial expansion which requires that the contact radius

α cot 2R a >
, and implies that there is a flat end, the radius of which corresponds to the constant term in equation ( 8), even though the original harmonic average does not assume this. Using equation ( 9) for the data shown in figure 1 gives an included for example, [START_REF] Hay | Instrumented Indentation Testing[END_REF]). However, as noted above, equation ( 9) in fact indicates that there is a flat right at the tip. In the current case the radius of this flat is nm 9 . 0 5 .

± =

c r .
For comparative purposes a 9 term Oliver and Pharr TAF fit was also undertaken (see figure 1b). This gave

c c c c c c c c c h h h h h h h h h A + + × + + + × + + + = - - (10)
with an r 2 value of 0.988.

Figure 2a shows a later calibration on the same tip carried out after it had received significant usage. The fact that the regression line from the first calibration can be displaced upwards to overlay the data from the second calibration shows that although the very near tip region has indeed become blunter away from this region the tip is essentially unmodified. This fact cannot be simply inferred from a conventional TAF plot (figure 2b). It would also appear that although the tip shape has been modified that the effective radius of the flat right at the tip has remained essentially unchanged as dataset 2 intercepts the y-axis at essentially the same point as dataset 1. The exact displacement between the two curves was evaluated by ensuring that the residuals in the straight line portion were equally scattered about zero by examining the moving average. The moving average was also used to identify an appropriate break point below which an alternative curve fit was required. Empirically it was found that using a function based on that proposed by Oliver and Pharr for the tip area fit was most effective for this regime (see figure 3). The fitting was carried out using the non-linear regression routines supplied in SigmaPlot 10 (Systat). Thus for the particular dataset shown in figures 2 and

≥ + = < + + = c c c c c c c h h r h h h r ( 11
)
In this case the overall r 2 value for the fit was 0.999. The improved r 2 value for this fit compared to the original fit is due to a smaller spread in the initial data, which is due to the use of a calibration piece of silica with lower surface roughness. Although a split function approach could also be used for the TAF fit it is much less obvious as to where to split the fitting function. Thus the equivalent radius approach potentially offers some benefit in determining an appropriate fit.

Similar features were found with a third calibration carried out at a later date (see figure 4). Again at the greater depths the calibration data appeared to be simply displaced with respect to the original calibration but in the very near tip region the detailed shape had further changed and once again an empirical fit was used in this

≥ + = < + + = c c c c c c c h h r h h h r ( 12
)
It can be seen that the fit is slightly less good right at the increasingly blunt indenter tip but additional terms gave no benefit in terms of quality of fit. The overall r 2 value for the fit is 0.998. As well as showing how the tip geometry is being blunted over As a further check equations ( 7), [START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF] and [START_REF] Thurn | Simplified area function for sharp indenter tips in depthsensing indentation[END_REF] were substituted in equation ( 4 (5a) shows that the residuals are essentially equally distributed across the entire data range there is no evidence of any cleaning of contamination during successive indents. Hydration is more of a problem. Hydration layer depths of 5 nm to 10 nm [START_REF] Hand | Nano-indentation and surface hydration of silicate glasses[END_REF][START_REF] Hench | Physical chemistry of glass surfaces[END_REF] have previously been suggested for pure silica. Fundamentally this is an issue for any shallow depth calibration of a nanoindenter in that all calibration techniques assume that there is no variation of modulus with depth whereas a hydrated layer would be expected to result in a reduction in modulus as the surface is approached. In this case one would expect to see an apparent decrease in equivalent contact radius (i.e. an apparent sharpening of the tip) due to the over-estimation of the value of E r used in equation ( 4). The fact that we do not observe this behaviour, rather the opposite over time, suggests that for the silica sample examined here hydration is not a significant problem although its presence cannot be absolutely ruled out. The fact that the noise increases at the very shallowest of depths is, we believe, an inevitable consequence of the fact that the measured quantities are particularly small in this region and thus the signal to noise ratio is reduced.

For nanoindentation hardness is defined as as the tip becomes increasingly blunt. At depths greater than the minimum indentation depth for meaningful hardness measurements no indentation size effect is observed, which is in agreement with the results obtained by other researchers [START_REF] Doerner | A method for interpreting the data from depth-sensing indentation instruments[END_REF][START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF][START_REF] Gong | Analysis of the nanoindentation data measured with a Berkovich indenter for brittle materials: effect of the residual contact stress[END_REF][START_REF] Qian | Comparison of nano-indentation hardness to microhardness[END_REF].

The apparent decrease in hardness with decreasing depth very near the surface arises because in fact fully elastic deformation is occurring in this region and thus hardness is not actually a meaningful measurement in this region. The reduced elastic moduli (over the entire measured depth range) and hardness values (for indentation depths >15nm) obtained with the three different calibrations are compared in Table 1.

Reduced moduli and hardness values were also calculated using the results of 9 term Oliver and Pharr TAF type fits (see equation [START_REF] Oliver | An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments[END_REF] for the fit for calibration run 1) and the results are shown in figure 7. Although for calibration runs 2 and 3 the differences between the two fitting techniques are relatively small there is significant difference in the results from calibration run 1 where the Oliver and Pharr fit leads to a significant over-estimation of both reduced modulus and hardness at low depths (compare figures 6 & 7). One might argue that as a single 9 term Oliver and Pharr type fit has been used for all 3 calibration runs whereas for the equivalent contact radius technique for calibration runs 2 and 3 the data were split into 2 parts that we are biasing things against the Oliver and Pharr fit. However the Oliver and Pharr fit produced significant over-estimations of both reduced modulus and hardness at low depths with calibration run 1 where the data were not split for either fitting process.

Thus the Oliver and Pharr type fit seems not to capture the initial tip geometry (which is essentially ideal apart from a flat right at the tip) very well, even though once the tip shape is changed through use the Oliver and Pharr fit works well. Overall we suggest that the major advantage of the equivalent contact radius fitting over the Oliver and Pharr one is that it provides for a simple physical interpretation of the tip geometry and how it is changing with time.

Conclusions

3 detailed shallow depth calibrations at approximately yearly intervals have been carried out on the same tip. As one would expect there is clear evidence of blunting over time. When the tip was new the equivalent contact radius, which is related to the contact area via equation ( 3), was linearly related to the contact depth apart from a flat right at the tip thus demonstrating that the tip was geometrically good. The equivalent contact radius approach therefore gives a clear physical interpretation of the tip geometry and dealt with flat at the tip in a better fashion than a 9 term Oliver and Pharr type fit. The equivalent radius approach means that the shallow depth indentation data is automatically weighted equally in the fitting process. As the tip became blunter with use the relationship between equivalent radius and the contact depth starts to deviate from a linear relationship at very low depths but applies at larger depths and still provides a clear physical interpretation of the changes at the tip.

Thus, although as good calibrations can be obtained using an

  original tip conformed reasonably closely to the expected equivalent cone angle of 70.32° (see,

  figure[START_REF] Gerberich | Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations[END_REF] is wider (reflected in the poorer r 2 value for this fit) and there is an

  ) and the reduced modulus was recalculated for the three data sets and the results are shown in figure(6a). In all cases the data are essentially scattered around the expected value of 69.6 MPa. Figure (6a) also indicates that consistent measurements of very near surface elastic moduli can be made if the blunting of the tip over time is fully accounted for in the tip calibration.It is obvious that the surface contamination and hydration may compromise the accuracy of shallow depth indentations. As outlined above cleaning and SPM was used to ensure that the indented region was clean prior to indentation. Also as figure

  P max is the maximum load during the indentation. Hardnesses calculated in this fashion are shown in figure(6b). In all cases it can be seen that the measured hardness tends to decrease in the very near surface region. Unfortunately the greater amount of noise present in the original calibration 1 data makes it difficult to identify a clear trend in behaviour, although at very low depths there is an apparent decrease in hardness with decreasing indentation depth; a clearer decrease in hardness with decreasing indentation depth is apparent for the other two datasets and the minimum indentation depth required for meaningful hardness measurements appears to increase

Figure 2 .Figure 3 .Figure 4 Figure 5 .Figure 6 Figure 7

 234567 Figure 2. Original calibration data plus data from the second (later) calibration a) plotted as r c versus h c and b) plotted as A versus h c.

Table 1 .

 1 Summary of mechanical properties (quoted errors are 3 standard deviations). Figure1. Calibration data obtained when the tip was new.

	Oliver and Pharr type

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Acknowledgements

DT thanks the ORSAS, UK and the University of Sheffield for scholarships enabling him to undertake this work.