Combined analysis: general principles and

theoryLuca Lutterotti

Needs

SOLSA project (EU H2020):

• mining/raw materials • mineralogy and composition of drill cores (phases +

elements) • automatic scanner (hyperspectra + XRD + XRF + Raman) • automatic analysis, no operator • clouds operating

evidences in the perspective of further systematic investigations of themany artefacts found in the site in view of a reliable archaeological in-terpretation and contextualisation.

In Table 1 the results of the XRD and XRF are summarised. All testswere conducted in a fully non-destructive way, just mounting each ar-tefact in the experimental apparatus.

Fig. 3. The investigated archaeological samples. Macrographs of the archaeological artefacts considered in the present study (see Table 1 for sample description). All archaeometricinvestigations have been conducted on the face/side of the specimen appearing in the relevant picture. a) ID 1122; b) ID 1123; c) ID 1124; d) ID 1125; e) ID 1083; f) RR29.

426 L. Lutterotti et al. / Microchemical Journal 126 (2016) 423–430

Needs

Cultural heritage objects:

• non destructive analysis • phases and chemical

compositions • fabrication processes,

history

1102 S. Gialanella et al.

tween the second half of the fifth and the first half of thesixth century AD.

In the nearby area also, animal bones have been found. Asto these latters, no conclusive hypotheses have been made ontheir origins, for the lack of a reliable archaeological contextconsequent to the already mentioned, uncontrolled disrup-tions of the site.

In association with the undamaged tombs, several objectsfrom funeral ornaments have been found. The interest of thepresent study is concentrated on two of them, featuring as acommon aspect, the use of gilding to decorate part of theirsurfaces with a gold layer. These items turned out to be madeof a copper and silver alloy, respectively. Of the differentgilding procedures [3], fire gilding [4] seems to be the oneused for the selected items. A common aspect of such ap-proach is the usage of a gold amalgam, a paste made of Auand Hg, whose consistency can be varied by suitable addi-tions or subtractions of mercury. In all cases, the final step ofthe manufacturing is a thermal treatment of a few minutes,conducted at an estimated temperature of 250–300 °C, thusbelow the boiling point of mercury, equal to 357 °C.

The main reason why these finds have been selected isthat, from an archaeological point of view, they belong towell established types, both having a broad distribution inItalian and European contexts [5], as concerns the respec-tive relevant periods. The investigation presented herewith,regarding technological and materials aspects, is thus meantto set the basis for the application of a similar approach to abroader number of specimens available in several Europeancollections that have not been analyzed from this point ofview as yet.

2 Sample description

One of the finds that has been investigated is a buckle, code-named n. 86, dating to the late Medieval time (second half ofthe fourteenth century) and diplayed in Figs. 1a and 1b. Themain body of the n. 86 artefact is made of a metal sheet, bentonto itself to hold the shaft of the tongue that is missing. Twoholes, with a diameter of 3 mm approximately, are visibleand can be interpreted as the sites of two small studs, whichwere there to join the belt, possibly made of tissue or leather,to the buckle, squeezed between the two edges of the bentsheet. For its shape and aestethical features, the item can beassociated to the class of the so-called lyre-buckle, with awidespread diffusion not only in Italian but also North Eu-ropean contexts of the period [5].

The other item considered in the present study (Figs. 1cand 1d) is a buckle, also completely different from the pre-vious one, even because much older. This buckle has beendated to the end of the sixth—beginning of the seventh cen-tury and codenamed as n. 85. Similar items, that were prob-

Fig. 1 (a) Micrographs of the two samples that have been investigatedin the present study (side of the squares = 10 mm): Copper buckleof the fourteenth century: front-gilded side. Codename: find n. 86.(b) back side. (c) Silver buckle of the seventh century: front side. Code-name: find n. 85. (d) Back side from which comes the analyzed sampledisplaying residual traces of gilding. Arrowed the ring-piece similar tothe detached one that analyzed and that is shown by Fig. 10 (see below)

ably used as footware accessories, have been found in sev-eral coeval sites of the Longobard Italy [5]. In this case, thetongue is still present and held in place by the bent sheet ofmetal. The two studs, as in the case of n. 86, are probablythere for connecting the buckle to the shoe string or belt. Onthe back side (Fig. 1d), ring-shaped pieces are present. Ac-tually, just one of the two is complete, being the other onepartially broken. However, this latter too was recovered dur-

Author's personal copy

general principles and theory

Pattern fitting: the Rietveld method• Least squares minimization of:

Combined techniques analysis

SUBSTRATE

BUFFER

CAP

XRF/EDSXRD

Reflectivity

15 nm

25 n

m

Combining XRD/XRF/XRR

• Goal: one structural model to fit XRD/XRF/XRR

• Composition, properties (refraction index, absorption etc.) are computed from the phases crystallography and layer structure

• Main advantages:

• In XRF: correct absorption calculation (matrix), intensities from XRD or XRR (for GIXRF)

• In XRD: more sensitivity to composition, mixed site occupations

• In XRR: unique solution

Theory• For GIXRF we start from De Boer formulation:

Au/Si multilayer

SiKα

AuLα

Multilayer example (Leti, Grenoble)

Si wafer

401.95 Å In2O3

401.87 Å In2O358.85 Å Ag

GIXRF

XRDXRR

Stress

In

Ag Si

Fluorescence spectra calculation

Cement: XRD-XRF combined analysis (and experiment)

• Combined Rw(%): 4.8 (3.9 for XRD, 6.9 for XRF)

• Wt(%): C3S=43.5±1.4, C2S=27.2±1.4, C3A=11.0±1, C4AF=8.8±0.3, Calcite=2.5±0.5, Rutile=0.4±0.02, Al2MgO4=6.6±0.4

• Chemical analysis: Ca/K=0.9836(8)/0.0164, Mn(C4AF)=0.0354(5), Cr(C4AF)=0.0101(3)

+

INEL Equinox + Si drift XRF detector, Cu radiation

Si

Ca

FeK

Ti CrMnAr

Equinox 3500 in Trentoθ/θ INEL goniometer Mo microfocus tube

ImXPAD detector Si drift X123 detector

Alpes coin

Ag L linesFe K lines

Cu K lines

Pb L lines

Dolomite rock

Kaolinite: modulated disorder

28

The reality:

C*

a*

b*

k = 0

k = 1

k = 2

k = 3

h = 0

h = 1

h = 2l = 0

l = 1

l = 2

l = 3

Kogure & Inoue, 2005

Kleeberg, Ufer, Bergmann, CMS 05

Kaolinite XRD (Mo X-ray)

Kaolinite XRF (Mo X-ray)

Depth profiling

θ/2θ

data

fit

New instrument configuration

Added: INEL CPS 120

Monochromator 1D

• XRD: channel-2theta calibration

• XRF: filters and air path absorption

Calibration

Dair~2.5 cm

Detector absorption/efficiency

Ar absorption

Energy (KeV)

Old calibration: Si-PbTiO3

XRD with Cu radiation

Mo with no monochromator

75%Si-25%PbTiO3 milled 14h

Si

hybrid (custom+xraylib)

Ti

Al sample holder

Fe,Cu W

16.6(2)wt%PbTiO3

Dair=2.395 cm

• Bad news: XRF is affected by absorption contrast too • Good news: quantitatively is the same as XRD

• The largest source of residual error in QPA by XRD is due to microabsorption

• Occurs when sample contains a mix of low & highly absorbing phases and grains in one of the phases are bigger than a critical value (~1 micron)

• High absorbers:

• Beam absorbed in surface of grain• Only a fraction of the grain diffracting

• Intensity under-overestimated – low QPA• Low absorbers:

• Beam penetrates further into grain• Greater likelihood of ‘volume diffraction’ occurring

• Intensity over-estimated – high QPA

Absorption contrast

The Brindley correction

7

• Apply a model to correct the absorption contrast in the analysis (this re-quires the knowledge of the grain sizes of the phases).

Most of the time only the third option is feasible and the most used correction is the so-called Brindley microabsorption model [9-10]. Applying it to the formula for quantitative analysis by the Rietveld method [10, 14-15] we get for a mixture of N phases:

where I is the scale factor from the Rietveld fitting, wi is the weight fraction for phase i, !i the density and "i the absorption contrast effect. Brindley has reported some tables for the absorption contrast effect from which we can extrapolate a function of a form similar to the absorption characteristic [11]. For spherical parti-cles the Brindley table can be fitted well by [11]:

where µi is the linear absorption coefficient for phase i, the mean linear ab-sorption coefficient of the mixture and Ri the mean particles radius. Similar formu-las can be obtained also for other shapes correction.

Amorphous and polymer crystallinity determination

Le Bail in 1995 [12] published how by diffraction it is impossible to distinguish between a real amorphous and a nanocrystalline structure without any long range order. So there is always the possibility to reproduce an amorphous diffraction pattern using a so-called pseudo-amorphous model in which the short range order is simulated by a particular crystal structure and the long range order is loosed by small crystallite sizes and/or high value of r.m.s. microstrain. The advantage of the description is that the short range order can be refined much better in the Rietveld framework instead of relying uniquely on Monte Carlo techniques. In 1998 Lut-terotti et al. [13] demonstrated how this pseudo-amorphous model can be used in the Rietveld to accurately measure the amorphous content without any internal or external standard. The classical formula developed for Rietveld phase analysis [13-14] works perfectly to give the amorphous content as a normal phase if the model is sufficiently accurate in describing the short range order. The benefits of this method are that no calibration, internal or external standard are needed and it can be applied also to bulk samples. Limitations are that it requires a model for the

7

• Apply a model to correct the absorption contrast in the analysis (this re-quires the knowledge of the grain sizes of the phases).

Most of the time only the third option is feasible and the most used correction is the so-called Brindley microabsorption model [9-10]. Applying it to the formula for quantitative analysis by the Rietveld method [10, 14-15] we get for a mixture of N phases:

where I is the scale factor from the Rietveld fitting, wi is the weight fraction for phase i, !i the density and "i the absorption contrast effect. Brindley has reported some tables for the absorption contrast effect from which we can extrapolate a function of a form similar to the absorption characteristic [11]. For spherical parti-cles the Brindley table can be fitted well by [11]:

where µi is the linear absorption coefficient for phase i, the mean linear ab-sorption coefficient of the mixture and Ri the mean particles radius. Similar formu-las can be obtained also for other shapes correction.

Amorphous and polymer crystallinity determination

Le Bail in 1995 [12] published how by diffraction it is impossible to distinguish between a real amorphous and a nanocrystalline structure without any long range order. So there is always the possibility to reproduce an amorphous diffraction pattern using a so-called pseudo-amorphous model in which the short range order is simulated by a particular crystal structure and the long range order is loosed by small crystallite sizes and/or high value of r.m.s. microstrain. The advantage of the description is that the short range order can be refined much better in the Rietveld framework instead of relying uniquely on Monte Carlo techniques. In 1998 Lut-terotti et al. [13] demonstrated how this pseudo-amorphous model can be used in the Rietveld to accurately measure the amorphous content without any internal or external standard. The classical formula developed for Rietveld phase analysis [13-14] works perfectly to give the amorphous content as a normal phase if the model is sufficiently accurate in describing the short range order. The benefits of this method are that no calibration, internal or external standard are needed and it can be applied also to bulk samples. Limitations are that it requires a model for the

Brindley G. W.: A theory of X-ray absorption in mixed powders. Philos. Mag. 36, 347-369 (1945)

The correction equation:

where τi is given by Brindley in a table and the following formula is fitting it well (spherical particles):

In Maud

• For each phase: • Edit and under microstructure:

• Select the Brindley microabsorption model • In Options select the proper Brindley model • Set the Grain Size for micro absorption correction to your estimated

grain size (not the crystallite value), don’t refine it • Run again the refinement for quantitative phase analysis and check if

the volume fractions have changed