Trabajo de Grado

A study of optical properties of crocoite (PbCrO4) under compression

Julio de 2011

Alumno: Enrico Bandiello

Tutor (1): Domingo Martínez GarcíaTutor (2): Daniel Errandonea

To my parents.

i

Abstract

This thesis deals with the study of optical properties of the semiconductor crocoite (PbCrO4, bandgap energy Eg ' 2.2 eV) under high-pressure conditions, up to about 12 GPa. The experimentslead to the discovery of two phase transitions in the considered pressure range, both reversible.Also, the pressure dependence of the band gap has been studied. It seems that at pressures around11 GPa this semiconductor is likely to assume a metallic behavior.

The study has been performed on natural samples obtained from the Red Lead Mine (Aus-tralia); it has been carried out using optical absorption measurements, performed in a diamondanvil cell (DAC). X-ray diffraction (XRD) and Raman spectroscopy (RS) have been also performedto support the conclusions obtained in the optical studies.

This work has been carried out under the supervision of Prof. Domingo Martınez Garcıa andProf. Daniel Errandonea, from the “Department of Applied Physics and Electromagnetism” ofthe University of Valencia (Spain).

Resumen

El objeto de esta tesis es el estudio de las propiedades opticas del semiconductor crocoite (PbCrO4,energıa de la banda prohibida Eg ' 2.2 eV) bajo condiciones de alta presion, hasta 12 GPa. Losexperimentos muestran la presencia de dos transiciones de fase en nuestro rango de presiones,ambas reversibles. Ademas, ha sido analizado el comportamiento del band gap y se ha visto quea presiones alrededor de 11 GPa el semiconductor probablemente adquiere un comportamientometalico.

El estudio ha sido realizado sobre muestras naturales que provienen de las minas Red Lead(Australia) y se ha desarrollado por medio de experimentos de absorcion optica en celdas dediamantes (DAC). Tambien se han realizado experimentos de difraccion de rayos X (XRD) yespectroscopia Raman (RS) para apoyar las conclusiones obtenidas en las medidas opticas.

Este trabajo ha sido realizado bajo la supervision de los Profesores Domingo Martınez Garcıa yDaniel Errandonea, del “Departamento de Fısica Aplicada y Electromagnetismo” de la Universidadde Valencia (Espana).

ii

iii

Acknowledgements

First of all thanks to my tutors, Prof. Domingo Martınez Garcıa and Prof. Daniel Errandonea,for their help and their patience during the entire realization of this work, in particular in therealization of the experiments, the data analysis and interpretation and the various revisions ofthe manuscript. Above all, the opportunity to work and learn from them in my first approach toa “real” scientific research has been a great privilege.

Thanks to Javier Ruız Fuertes for the picture of crocoite structure in §2.2 and for the hints inthe normalization of the spectra; what’s more important, I’m grateful to him for the encouragementand for the serious answers to my frequent naive questions.

Thanks to Dr. David Santamarıa Perez for the assistance in X-ray diffraction experiments.Dulcis in fundo, thanks to my fantastic wife Karina for supporting me every day, putting up

with my moods, patiently listening to my complaints about almost everything in the World and,above all, for often believing in me more than I did myself.

iv

Contents

1 Methodology and experimental setup 11.1 Diamond anvil cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ruby fluorescence as a pressure gauge . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Experimental setup, sample and measurements . . . . . . . . . . . . . . . . . . . . 2

2 Properties of PbCrO4 at ambient conditions 52.1 General description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Lattice properties and constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Experimental results, data analysis and conclusions 73.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Dependence of Eg and σ on P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.4 Physical interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4.1 Phase I - Monazite (100 kPa ∼ 3.5 GPa) . . . . . . . . . . . . . . . . . . . . 123.4.2 Phase I - Phase II transition (3.5 GPa ∼ 7.5 GPa) . . . . . . . . . . . . . . 123.4.3 Phase II - Phase III transition (7.5 GPa ∼ 12.0 GPa) . . . . . . . . . . . . . 12

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.6 Conclusiones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Appendices 14

A XRD and Raman experiments 15A.1 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15A.2 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

B Software tools 17B.1 Free Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Bibliography 19

List of Figures

1.1 A typical DAC (scheme and photo). . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Photo of the sample in the DAC at ambient pressure (L) and at P = 3.5 GPa (R). 3

v

2.1 XFR analysis of PbCrO4 natural samples (L) and surface of the original crystalmagnified at 650x (R). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Crocoite lattice structure, (011) plane. . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Absorption spectra of PbCrO4 in the range 1.2 eV < E < 1.9 eV (L) and 1.5 eV <E < 2.4 eV (R) (increasing pressure). . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Absorption spectra of PbCrO4 (decreasing pressure). . . . . . . . . . . . . . . . . . 83.3 Semi-logarithmic plot of the curves in Figure 3.1 (same ranges). . . . . . . . . . . . 93.4 Fit of the absorption curve for PbCrO4 at ambient pressure. . . . . . . . . . . . . . 93.5 Eg(P ) for increasing pressure (L) and decreasing pressure (R). . . . . . . . . . . . 103.6 Eg(P ) for both increasing (circles) and decreasing pressure (boxes). The dashed

line is the data fitting for decreasing pressure. . . . . . . . . . . . . . . . . . . . . . 103.7 Variation of σ with P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.8 Schematic band structure of PbCrO4. . . . . . . . . . . . . . . . . . . . . . . . . . 12

A.1 X-ray diffraction patterns (L), Raman spectra (R). . . . . . . . . . . . . . . . . . . 15

List of Tables

2.1 Lattice parameters and atomic position for PbCrO4 at ambient pressure. . . . . . . 6

vi

Chapter 1

Methodology and experimentalsetup

Objectives

Our main goal is the study of the optical behavior of PbCrO4 crystal under compression andits relation with the structural changes of the mineral. For this, in Chapters 1 and 2 we give abrief description of our instruments and methods and a summary description of the mineral thatwe have been investigating, while in Chapter 3 our results and their physical interpretation arepresented. Finally, Appendix A shows additional experimental results supporting some of ourconclusions.

1.1 Diamond anvil cells

Diamond Anvil Cells (DACs) are the most commonly used instruments in the study of physicalbehavior of crystal samples upon high-pressure conditions (up to 300 GPa). A DAC basicallyconsists in a pair of diamonds that are cut leaving on each a small culet. A metal gasket acts asa separator between the facing culets, forming a sealed “chamber” where the sample is placed.This assembly is then inserted into a metal cylinder where a metallic membrane, being slowlyinflated with compressed helium, exerts a force (F ) on the diamonds. The pressure (P ) on theculets of the diamonds thus rises according to equation P = F/A, where A is the area of the culet.The uniaxial pressure supplied by the diamonds on the inner chamber is then transformed intohydrostatic pressure using a fluid pressure medium (a gas or a liquid; in our case the medium wasa 16:3:1 mixture of methanol, ethanol, water [1]). Figure 1.1 gives a schematic representation of aDAC along with a photo of the cell used in our experiment.

1.2 Ruby fluorescence as a pressure gauge

To measure pressure inside the DAC the ruby (Al2O3:Cr) fluorescence technique is used. Smallruby chips are loaded together with the sample inside the pressure chamber. Ruby fluorescenceis excited with a laser (λ = 523 nm in our case) producing a doublet R1, R2 whose wavelengthsat ambient conditions are λR1

(100 kPa) = 694.3 nm and λR2(100 kPa) = 692.7 nm [2]; these lines

regularly redshifts with increasing pressure1.Being the result of a data fit, there are many expressions of λR1

(P ), λR2(P ), according to

different authors; this notwithstanding, in our pressure range (100 kPa - 12 GPa) the differencesdue to the different expression of λR1(P ) are < 1%. In our analysis the following expression has

1100 kPa=10−4 GPa ' 1 atm (ambient pressure).

1

2 CHAPTER 1. METHODOLOGY AND EXPERIMENTAL SETUP

Figure 1.1: A typical DAC (scheme and photo).

been used [2]:

P (λR1) [GPa] =

1904 [GPa]

7.665

[(λR1

[nm]

694.38 [nm]

)7.665

− 1

](1.1)

1.3 Experimental setup, sample and measurements

Our experimental setup for the optical absorption experiments is depicted in Figure 1.2. There,“O1” and “O2” are two Cassegrain objectives, each mounted on micrometric slide with two axis(XY). Objective O1 is needed to concentrate the light from the halogen lamp (resp. the laser) ina small spot and to focus it on the sample (resp. the ruby) under examination, while O2 servesto focus the light from the sample on the detector.

Schematically, each measurement involves the following steps:

1. choose a suitable value for the pressure on the sample

2. focus the laser beam on a ruby, with the aid of the ocular and the screen

3. pump helium slowly in the DAC, until the chosen pressure is achieved. Meanwhile, pressurevalue is checked in real-time using the laser and the spectrophotometer (§1.2)

4. replace laser with the helium lamp and focus the light spot (about 20µm in diameter) outsidethe sample. Take a reference spectrum of the direct beam.

5. focus the light on the sample and take another spectrum

6. the ratio between the first spectrum and the second one is then the transmittance of thesample at the chosen pressure

7. the transmittance spectrum is transformed into an absorption spectrum (the absorptioncoefficient as a function of energy), considering the thickness of the sample and its refractionindex [3].

In this experiment, two different samples of PbCrO4 have been used, with a thickness of ∼20µm. We recorded transmission spectra for both samples increasing and, subsequently, decreasingpressure.

1.3. EXPERIMENTAL SETUP, SAMPLE AND MEASUREMENTS 3

Laser diodeMirror

Mirror

Lens

Halogen

lamp

Optical

fiberOptical

fiberO1 O2

Prism

Screen

Spectrophotometer

Lens

Diaphragm Detector

with

diaphragm

Ocular

PC

DAC

(with sample, ruby

and pressure medium)

Figure 1.2: Experimental setup.

In this experiment at pressures around 10 GPa the sample becomes strongly opaque, so it isdifficult to obtain good transmittance spectra in the optical range. Because of this, the maximumpressure we reached was ∼ 12 GPa.

Figure 1.3 shows photos of one of the samples at ambient pressure and at P = 3.5 GPa. There’san evident change in color associated to a phase transition. A detailed explication will be givenin the text. The little sphere right under the sample is the ruby used for the determination of thepressure.

Figure 1.3: Photo of the sample in the DAC at ambient pressure (L) and at P = 3.5 GPa (R).

4 CHAPTER 1. METHODOLOGY AND EXPERIMENTAL SETUP

Chapter 2

Properties of PbCrO4 at ambientconditions

2.1 General description

Lead chromate (PbCrO4, “crocoite”) is a mineral that crystallizes at ambient conditions in amonoclinic structure belonging to P21/n space group (monazite structure) [4]. It is commonlyused in some pyrotechnic compositions and as a pigment in some paints, because it is practicallyinsoluble in water. It can also be used as a photocatalyst and has been proposed as a potentiallaser-host material. PbCrO4 is a very toxic substance. It’s quite rare in nature but it can becreated in laboratory.

Our samples were obtained from natural crystals, originated from the Red Lead Mine (Aus-tralia). Because of this, we performed an elemental microanalysis in a scanning electron microscope(SEM), to check for the presence and nature of impurities. Figure 2.1 (right) shows some crys-tals of PbCrO4 at 650x, while Figure 2.1 (left), is an X-ray fluorescence spectrum of our sample,that confirms its purity. Only a small amount of Fe is present in some regions, probably due toferrous oxides in the soil where the crystal growth took place). For our experiments, we selectedmicrocrystals of PbCrO4 with undetectable amount of impurities.

Figure 2.1: XFR analysis of PbCrO4 natural samples (L) and surface of the original crystalmagnified at 650x (R).

2.2 Lattice properties and constants

We performed X-ray diffraction on crocoite powder with Mo Kα radiation (λ = 0.7093 A). Theobtained lattice parameters are listed in Table 2.1 [5] together with the values given in the liter-ature [6]. Our measurements are in good agreement with the literature data. Table 2.1 also lists

5

6 CHAPTER 2. PROPERTIES OF PBCRO4 AT AMBIENT CONDITIONS

Figure 2.2: Crocoite lattice structure, (011) plane.

Lattice parameters

a [A] b [A] c [A] β [◦]

Exp. 7.098(1) 7.410(1) 6.778(8) 102.42(0)Lit. 7.127(2) 7.438(2) 6.799(2) 102.43(2)

Atomic positionsx/a y/b z/c

Pb .2218 .1450 .3974Cr .2010 .1651 .8800

O(1) .0354 .0989 .6944O(2) .1247 .3461 .9869O(3) .2534 .4982 .4540O(4) .3887 .2173 .7810

Table 2.1: Lattice parameters and atomic position for PbCrO4 at ambient pressure.

the atomic positions inside of the unit cell, in fraction of the lattice parameters [4]. In monazitestructure Cr is coordinated with 4 oxygens forming regular tetrahedra and Pb is coordinated with9 oxygens forming irregular polihedra, as shown in Figure 2.2.

2.3 Optical properties

Chromates with the monazite structure are translucent materials with a band gap between 2 and2.8 eV [7]. Their crystals are biaxial, having two optic axes. The birefringence of these materials isusually of the order of 0.05 and the average index of refraction is approximately 2.4. Among thisfamily, PbCrO4 is one of the less studied compounds and its band gap and other properties havenot been accurately determined yet.

Chapter 3

Experimental results, dataanalysis and conclusions

3.1 Experimental results

Optical measurements have been performed on two independent samples. Figures 3.1 and 3.2show the absorption spectra for one of the samples as a function of energy at selected pressures(pressure increases).

Graphs in Figure 3.1 show that PbCrO4 at ambient pressure presents an absorption tail startingaround E ' 2.2 eV. This likely accounts for the orange color of the samples at ambient conditions.When pressure increases between ambient pressure and 3 GPa the absorption front edge slowlyshifts towards smaller energies . The value of Eg then abruptly decreases at a pressure of 3.5 GPa(spectrum 8 in Figure 3.1) and correspondingly, as we already anticipated at the end of §1.3, thecolor of the sample shift from orange to reddish (it undergoes a phase transition). If the pressurecontinues to rise, Eg gradually decreases and the sample becomes more and more opaque, untilreaching P ' 12 GPa, when the quality of the transmittance spectra becomes very poor. This isthe reason for the high noise in the spectra taken at pressures & 10 GPa1.

α (a

rbitr

ary

uni

ts)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Energy (eV)

1.20 1.40 1.60 1.80

123

45

6

7

8

10

4.79

Gpa

9

1112

9.5

0 G

Pa

10

.15

GP

a1

0.8

4 G

Pa

11

.15

GP

a1

1.8

1 G

Pa

16

17

13

14

15 8 - 3.50 GPa 9 - 4.79 GPa10 - 4.96 GPa11 - 5,83 GPa12 - 6.50 GPa13 - 8.39 GPa14 - 9.50 GPa15 - 10.15 GPa16 - 10.84 GPa17 - 11.84 GPa

α(a

rbitra

ryu

nits)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Energy (eV)

1.60 1.80 2.00 2.20 2.40

123

45

6

7

8

109

1112

16

17

13

14

151 - 0.26 GPa2 - 0.46 GPa3 - 0.97 GPa4 - 1.56 GPa5 - 1.98 GPa6 - 2.58 GPa7 - 2.93 GPa

8 - 3.50 GPa9 - 4.79 GPa10 - 4.96 GPa11 - 5,83 GPa12 - 6.50 GPa13 - 8.39 GPa14 - 9.50 GPa15 - 10.15 GPa16 - 10.84 GPa17 - 11.84 GPa

Figure 3.1: Absorption spectra of PbCrO4 in the range 1.2 eV < E < 1.9 eV (L) and 1.5 eV <E < 2.4 eV (R) (increasing pressure).

110GPa ' 105 atm.

7

8 CHAPTER 3. EXPERIMENTAL RESULTS, DATA ANALYSIS AND CONCLUSIONS

The absorption spectra exhibit a steep absorption, characteristic of a direct band gap, plusa low energy absorption band, which envelops partially with the fundamental absorption. Thislow-energy absorption tail has been observed in related compounds and seems to be due to thepresence of defects. On the other hand, the steep absorption has an exponential dependence on thephotons energy, following Urbach’s law (see §3.2). This dependence is typical of direct absorptionedges with excitonic effects [8].

When releasing pressure Eg grows and suddenly, at about 1.8 GPa, the sample returns to itsoriginal orange color but becomes fragmented. This causes very high diffusion of the light beamthat in turn is the reason of the degradation of the absorption spectra, as can be seen in Figure3.2. Looking at graph in Figure 3.2 it is evident that the sample seems to recover its originalphase. Anyway, the poor quality of the spectra didn’t allow a quantitative confirmation.

α (a

rbitr

ary

uni

ts)

0

500

1,000

1,500

2,000

2,500

3,000

3,500

Energy (eV)

1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

1 - 10.15 GPa 2 - 8.96 GPa 3 - 7.66 GPa 4 - 6.13 GPa 5 - 4.98 GPa 6 - 3.74 GPa 7 - 2.64 GPa 8 - 1.83 GPa 9 - 0.87 GPa10 - 0.46 GPa

1

2

3

4

5

6

7

8

910

Figure 3.2: Absorption spectra of PbCrO4 (decreasing pressure).

3.2 Data analysis

To analyze the absorption data we used Urbach’s rule, i.e. the spectra can be described by theequation:

α(E) = α0 exp

[σ

kBT(E − Eg)

](3.1)

where T is the absolute temperature, kB is the Boltzmann constant, α0 and σ are dimensionlesstemperature depending parameters and finally Eg is the energy gap. The three parameters arecharacteristic of each material, being α0 usually assumed as pressure independent [9]. On the otherhand, σ determines the shape of the absorption tail and indirectly gives indications on the presenceof defects in the crystal structure [9].

In our case, the experiment was realized at ambient temperature, so T ' 298 ◦K and kBT '0.0256 eV.

Equation (3.1) implies that the curves in Figures 3.1 and 3.2, when plotted in a semilogarithmicgraph, should be nearly parallel lines2 whose relative distances are due to the variation of Eg withthe pressure. Such a semi-logarithmic plot, confirming the validity of (3.1), is depicted in Figure3.3 (for the curves in Figure 3.1).

In Equation (3.1) α0 and Eg are clearly correlated. Therefore, we determined α0 at ambientpressure (α0 = 130 ± 1) considering Eg = 2.2 eV [7] and assumed that α0 is not modified under

2At least in the region where E > Eg.

3.3. DEPENDENCE OF Eg AND σ ON P 9

ln(α

) (ar

bitr

ary

uni

ts)

4

5

6

7

8

9

10

Energy (eV)

1.20 1.40 1.60 1.80

8 - 3.50 GPa 9 - 4.79 GPa10 - 4.96 Gpa11 - 5.83 GPa12 - 6.50 GPa13 - 8.39 GPa14 - 9.50 GPa15 - 10.15 GPa16 - 10.84 GPa17 - 11.81 GPa

1245

8910 7

1112

13

1415

1617

16

ln(α

) (ar

bitr

ary

uni

ts)

4

5

6

7

8

9

10

Energy (eV)

1.60 1.80 2.00 2.20 2.40

8 - 3.50 GPa 9 - 4.79 GPa10 - 4.96 Gpa11 - 5.83 GPa12 - 6.50 GPa13 - 8.39 GPa14 - 9.50 GPa15 - 10.15 GPa16 - 10.84 GPa17 - 11.81 GPa

1245

8910 7

1112

13

1415

1617

36

Figure 3.3: Semi-logarithmic plot of the curves in Figure 3.1 (same ranges).

α (a

rbitr

ary

uni

ts)

0

500

1,000

1,500

2,000

2,500

3,000

Energy (eV)

1.20 1.40 1.60 1.80 2.00 2.20 2.40

Figure 3.4: Fit of the absorption curve for PbCrO4 at ambient pressure.

compression. This method can lead to small uncertainties on the absolute value of Eg, but it isvery accurate to determine its pressure evolution. The fit of Urbach’s rule to our experimentaldata is quite good, as can be seen in Figure 3.4.

3.3 Dependence of Eg and σ on P

We studied separately Eg(P ) for increasing and decreasing pressure. The results are shown inFigure 3.5, where the different symbols denote the two samples, while Figure 3.6 shows both graphsin the same plot (now the circles and the boxes denote respectively increasing and decreasingpressure).

Looking at the graph it is clear that generally Eg(P ) is a linearly decreasing function of P .Starting with a value of Eg(100 kPa) ' 2.2 eV and up to 3.0 GPa we found that

dEg

dP= (−4.3± 0.2) · 10−2 eV GPa−1 (3.2)

10 CHAPTER 3. EXPERIMENTAL RESULTS, DATA ANALYSIS AND CONCLUSIONS

E g (e

V)

1.20

1.40

1.60

1.80

2.00

2.20

2.40

Pressu re (GPa)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

E g (e

V)

1.40

1.50

1.60

1.70

1.80

1.90

Pressure (GPa)0.00 2.00 4.00 6.00 8.00 10.00 12.00

Figure 3.5: Eg(P ) for increasing pressure (L) and decreasing pressure (R).

while past 3.0 GPa, as we already anticipated in §3.1, we can observe one phase transition: Eg

decreases abruptly with ∆Eg ' 0.35 eV and then it continues to decrease with a slope given by

dEg

dP= (−4.2± 0.1) · 10−2 eV GPa−1 (3.3)

The values in (3.2) and (3.3) can be considered the same within their error bars.

E g (e

V)

1.20

1.40

1.60

1.80

2.00

2.20

2.40

Pressure (GPa)

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Figure 3.6: Eg(P ) for both increasing (circles) and decreasing pressure (boxes). The dashed lineis the data fitting for decreasing pressure.

When pressure decreased and went back to ambient (100 kPa) we observed that

dEg

dP= (−3.99± 0.3) · 10−2 eV GPa−1 (3.4)

Again, the value in (3.4), within the error range, is the same value given in (3.2) and (3.3).This is an evidence that the pressure-induced changes in the mineral structure are reversibles,although we can observe an hysteresis phenomenon, given that Eg doesn’t go back to its original

3.4. PHYSICAL INTERPRETATION 11

σ (d

imen

sion

less

)

0.00

0.20

0.40

0.60

0.80

1.00

Pressure (GPa)0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Figure 3.7: Variation of σ with P .

value ' 2.2 eV when pressure decreases down to ambient (see Figure 3.6). The fragmentation ofthe sample that we mentioned in §3.1 made impossible for us to investigate further on this issue.

It is now interesting to observe the variation of σ with pressure. Looking at Figure 3.7 it isevident that σ somehow mimics the behavior of Eg. In the range 100 kPa - 3 GPa it grows withP with a slope given by

dσ

dP= (1.8± 0.6) · 10−2 GPa−1 (3.5)

while at pressure above 3.5 GPa the slope becomes negative and its value is

dσ

dP= (−1.7± 0.5) · 10−2 GPa−1 (3.6)

Again, when P goes back to ambient pressure3, we can observe for σ the same reversibilitythat manifested Eg, given that now the variation of σ with P is given by

dσ

dP= (−1.5± 0.7) · 10−2 GPa−1 (3.7)

and the values given in (3.7) and (3.6) are the same within the error bars.

3.4 Physical interpretation

The band gap collapse found beyond 3 GPa is possibly caused by a structural phase transformation.This hypothesis has been confirmed by XRD and Raman experiments (see Appendix A).

According with theoretical calculations [7], in PbCrO4 the main contribution of the bottom ofthe conduction band results from the antibonding interaction between the Cr(3d) orbitals and theO(2p) orbitals. The upper portion of the conduction band results primarily from the interactionbetween empty Pb(6p) orbitals and O(2p) orbitals. Since the space group symmetry permitsmixing of the Pb(6p) and Cr(3d) orbitals, a minimum contribution from the Pb(6p) orbitals isobserved at the bottom of the conduction band. On the other hand, the top of valence band ismainly compose of O(2p) non bonding orbitals with a small contribution of Pb(6s) orbitals. SeeFigure 3.8 for a visual representation of PbCrO4 band structure [7].

3The corresponding plot is not reported here, for brevity’s sake.

12 CHAPTER 3. EXPERIMENTAL RESULTS, DATA ANALYSIS AND CONCLUSIONS

En

erg

y (

eV

)

2.2 eV

-8.0

0.0

2.2

4.1

Pb(6s) - O(2p)

Cr(3d) - O(2p)

O(2p)

Pb(6s) - O(2p)

Cr(3d) - O(2p)

Pb(6p)

Figure 3.8: Schematic band structure of PbCrO4.

As we said before, we could observe up to three different phases in the mineral, in three differentranges of pressure. Let’s see in more detail what happens at different pressure ranges, trying tojustify our observations with some hypothesis on the changes occurring in PbCrO4 structure.

3.4.1 Phase I - Monazite (100 kPa ∼ 3.5 GPa)

In this first range we suppose that, as usually happens, the bond distances are reduced withincreasing pressure, while the lattice retains its monazite structure. For this, there’s an increaseof the crystal field acting on Cr(3d) and O(2p) states. As a result, there’s a reduction in Eg, sinceO(2p) states shift towards higher energies faster than Cr(3d) states. A similar behavior has beenobserved in lead wolframate, PbWO4

[10].

3.4.2 Phase I - Phase II transition (3.5 GPa ∼ 7.5 GPa)

In this range of pressures there’s an atomic reordering, as can be noted in diffraction peaks changingtheir height (see §A.1 in Appendix A). The point group symmetry of the crystal gets lower andproduces a band gap decrease. The mineral undergoes a transition to a different phase (unknown,at the present time). This fact is confirmed by XRD and Raman experiments (Appendix A).The behavior of Eg in phase II is similar to that of phase I, so electronic structure is probablystill determined by Cr(3d) and O(2p) states. Theoretical calculations are needed to confirm thishypothesis.

3.4.3 Phase II - Phase III transition (7.5 GPa ∼ 12.0 GPa)

In this pressure range Raman spectroscopy and X-ray diffraction experiments (§A.2 in AppendixA) show another phase transition around 10 GPa. However in our optical measurements this phasetransition is not evident due to the high opacity of the sample. This could be due to a metalliccharacter of phase III. This hypothesis is supported by the fact that others related compoundsend exhibiting metallic behavior beyond a certain pressure [11].

3.5. CONCLUSIONS 13

3.5 Conclusions

This work has to be considered an original first approach to a more complete study of PbCrO4

properties under pressure. This semiconductor has almost never been studied before, so the resultsobtained in this first phase are interesting per se.

First of all, we put in evidence that PbCrO4 undergoes up to two phase transitions in arelatively reduced pressure range. Also, these transformations appear to be completely reversible,showing a small hysteresis phenomenon. The first phase transition is clearly observable by meansof the optical measurements, while the second transition is evidenced clearly by powder diffractionand Raman spectroscopy.

Physical interpretations of the results have been attempted, partially supported by comparisonwith other related compounds, in particular PbWO4. However, further studies and experimentsare necessary. In particular, some of these would be:

• detailed Raman spectroscopy, to better localize transition pressures.

• another set of optical measurements, with better resolution in pressure, to obtain moredetailed data about Eg behavior near the transitions.

• exhaustive powder diffraction experiments, to obtain the structures of phases II and III,together with the evolution of lattice parameters with pressure.

• resistivity measurements under compression; in particular these experiments are needed toprove right or wrong the hypothesis about the metallic properties of phase III.

All these matters will eventually be the subject of a future Master thesis.This work has been done in the framework of a “Beca de Colaboracion” (collaboration grant)

with the High Pressure Research Group of the University of Valencia. The extension of this studywill be published in an international journal.

3.6 Conclusiones

Este trabajo se tiene que considerar un primer planteamiento para un estudio mas completo delas propiedades de PbCrO4 bajo presion. Este semiconductor practicamente no ha sido estudiadoanteriormente y por ello los resultados obtenidos en esta primera fase son interesantes de por si.

Primero de todo, hemos puesto en evidencia que el PbCrO4 esta sujeto a hasta dos transicionesde fase en un rango de presiones relativamente reducido. Ademas, estas transformaciones parecenser completamente reversibles, a parte un pequeno fenomeno de histeresis. La primera transicionde fase es observable de forma clara por medio de las medidas de absorcion optica, mientras quelas segunda es mas evidente en los experimentos de difraccion de rayos X y espectroscopia Raman.

Se han intentado interpretaciones a nivel fısico de los resultados, por comparacion con otroscristales afines, en particular PbWO4. Sin embargo, se necesitan ulteriores estudios y experimentos.En particular, algunos de estos serıan:

• espectroscopia Raman detallada, para localizar mejor las presiones de transicion.

• otro conjunto de medidas opticas, con mejor resolucion en presion, para obtener datos masdetallados sobre el comportamiento de Eg cerca de las presiones de transicion.

• experimentos exhaustivos de difraccion de rayos X, con el objeto de encontrar las estructurascristalinas de las fases II y III, junto con la evolucion de los parametros de celda en funcionde la presion.

• medidas de resistividad electricas bajo presion; en particular, estos experimentos se necesitanpara para confirmar o desmentir la hipotesis acerca de las propiedades metalicas de la faseIII.

14 CHAPTER 3. EXPERIMENTAL RESULTS, DATA ANALYSIS AND CONCLUSIONS

Todo esto sera eventualmente el objeto de una futura tesis de Master. Este trabajo ha sido realizadoen el marco de una Beca de Colaboracion con el Grupo de Altas Presiones de la Universidad deValencia. La extension de este estudio sera publicada en una revista internacional.

Appendix A

XRD and Raman experiments

A.1 X-ray diffraction

Figure A.1 (left) shows the evolution of X-ray diffraction patterns collected at different pressures.They have been obtained performing powder diffraction in DAC using Mo Kα wavelength (λ =0.7093 A) in an Xcalibur diffractometer (Agilent Technologies, former Oxford Diffraction Ltd.)with an Atlas charge coupled device (CCD).

Some hints of the first phase transition can be seen at a pressure between 3.25 and 4.43 GPa,when the peak at 2θ ∼ 11 ◦ begins to split in two separate peaks and the set of peaks at 2θ ∼ 15 ◦

fuse together. This is what we called phase II.

5 10 15

9.1 GPa phase III

8.1 GPa phase II + III

7.2 GPa phase II + III

6.1 GPa phase II + III

5.2 GPa phase II + III

4.43 GPa phase II

3.25 GPa monazite

1.5 GPa monazite

Inte

nsity

(ar

b. u

nits

)

2 tetha (degrees)

0.55 GPa monazite

PbCrO4

500 600 700 800 900 1000 1100

13 GPa - Phase III

11.6 GPa - Phase III

9.4 GPa - Phases II & III

7.5 GPa - Phase II

5.3 GPa - Phase II

3.5 GPa - Monazite

2.5 GPa - Monazite

1.5 GPa - Monazite

Inte

nsity

(ar

b. u

nits

)

Raman shift (cm-1)

0.95 GPa - Monazite

Figure A.1: X-ray diffraction patterns (L), Raman spectra (R).

The subsequent phase transitions, leading to phase III, begins to happen immediately after

15

16 APPENDIX A. XRD AND RAMAN EXPERIMENTS

4.43 GPa: some peaks begin to disappear (i.e. the one at 2θ ∼ 9 ◦), while others become visible(2θ ∼ 13 ◦). Phases II and III then coexist until ∼ 9.1 GPa, when the second transition appearsto be complete. This is consistent with the result of our experiments in optical absorption. Thechanges observablesin the XRD patterns suggest a symmetry increase in phase III.

A.2 Raman spectroscopy

Raman experiments were performed in the back scattering geometry using a 632.8 nm He-Nelaser and an Horiba Jobin-Yvon LabRAM high-resolution spectrometer, in combination with athermoelectrically cooled multichannel CCD with spectral resolution below 2 cm−1.

Results similar to those in §A.1 are found in our Raman experiments. Figure A.1 (right) showsthe Raman spectra at selected pressures. Phase I appears to be stable until at least 3.5 GPa.Phase II and III then coexist until about 9.4 GPa and finally, at a pressure of about 11.6 GPa,only phase III is observable.

For the moment, the only purpose of these results is to support the conclusions following the opticalmeasurements. An exhaustive analysis of these data is out of the scope of an undergraduate thesisbut, nevertheless, they can be a starting point for future investigations regarding PbCrO4.

Appendix B

Software tools

B.1 Free Software

But for Figures 2.1, 2.2, and A.1, exclusively Free Software has been used in this work:

→ Qtiplot for data plots and analysis (http://soft.proindependent.com/qtiplot.html).

→ Inkscape for SVG graphics (http://www.inkscape.org/).

→ The Gimp for photos and images editing (http://www.gimp.org).

→ LibreOffice for some data processing and text editing (http://www.libreoffice.org/).

→ Final document written using LATEX 2ε (http://www.latex-project.org/) in conjunctionwith Kile editor (http://kile.sourceforge.net/).

Operating system was “Sid” Debian GNU/Linux (http://www.debian.org) with KDE environ-ment (http://www.kde.org).

17

18 APPENDIX B. SOFTWARE TOOLS

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